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You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Green Brown Blue Brown Green Green Brown Brown Red Brown Blue Red Blue Gray Green Blue Purple Green Green Gray Green Red Green
Row 2: Red Gray Brown Blue Red Gray Blue Gray Blue Gray Green Brown Red Blue Blue Brown Blue Black Purple Red Red Gray Gray Purple Red
Row 3: Gray Brown Purple Brown Gray Gray Black Green Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green
Row 4: Black Black Gray Green Black Red Brown Purple Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Black
Row 5: Gray Black Blue Blue Blue Red Purple Black Blue Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Black Purple
Row 6: Black Black Brown Green Purple Black Gray Red Black Purple Green Green Green Green Green Green Green Green Green Yellow Green Green Green Red Gray
Row 7: Red Red Blue Black Red Black Blue Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Black Blue
Row 8: Purple Red Purple Black Brown Gray Brown Blue Gray Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Blue
Row 9: Red Red Blue Purple Gray Blue Gray Brown Purple Brown Black Blue Black Gray Blue Black Blue Black Purple Black Black Gray Red Red Red
Row 10: Brown Brown Red Green Gray Green Red Purple Black Gray Red Green Brown Brown Blue Black Black Green Red Brown Blue Gray Black Brown Blue
Row 11: Blue Purple Black Purple Gray Purple Red Red Brown Black Gray Gray Brown Brown Black Brown Brown Blue Purple Black Black Gray Brown Gray Purple
Row 12: Blue Black Blue Gray Black Purple Purple Brown Blue Red Purple Blue Green Brown Blue Blue Brown Gray Purple Blue Black Green Brown Red Blue
Row 13: Black Green Brown Gray Brown Red Gray Purple Black Gray Brown Brown Green Black Gray Blue Purple Gray Purple Black Gray Black Black Gray Red
Row 14: Gray Black Red Green Gray Black Green Black Green Gray Gray Green Blue Red Red Brown Red Brown Green Gray Green Black Green Black Purple
Row 15: Purple Red Gray Green Gray Purple Gray Green Green Purple Purple Brown Gray Red Green Red Red Blue Green Brown Green Gray Red Blue Green
Row 16: Blue Red Brown Red Black Blue Red Green Green Brown Red Red Green Purple Gray Black Gray Brown Purple Brown Green Red Black Green Red
Row 17: Purple Blue Green Gray Red Gray Green Brown Purple Purple Blue Black Blue Red Purple Brown Black Black Gray Green Gray Green Gray Purple Gray
Row 18: Red Brown Black Blue Green Brown Brown Brown Purple Black Gray Purple Purple Purple Black Gray Black Blue Black Blue Black Green Brown Green Gray
Row 19: Red Purple Blue Green Blue Gray Brown Red Green Blue Black Green Blue Green Purple Black Purple Green Blue Purple Green Purple Purple Blue Blue
Row 20: Gray Brown Black Blue Green Gray Green Purple Brown Red Green Brown Red Purple Gray Red Red Brown Brown Blue Gray Black Green Brown Red
Output:
Row 1: Green Yellow Green Green Green Green Green Green Green Yellow Green Green Green
Row 2: Green Yellow Green Green Green Green Green Green Green Yellow Green Green Green
Row 3: Green Yellow Green Green Green Green Green Green Green Yellow Green Green Green
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Green Yellow Green Green Green Green Green Green Green Yellow Green Green Green
Example 2
Input:
Row 1: Green Red Red Yellow Red Green Red Yellow Green Green Purple Purple Yellow Purple Yellow Purple Red Yellow Purple Purple Red Purple Green
Row 2: Purple Purple Purple Green Green Purple Purple Yellow Red Green Yellow Green Green Yellow Green Green Green Purple Red Yellow Yellow Green Red
Row 3: Green Green Green Green Purple Purple Green Purple Purple Yellow Green Green Yellow Purple Red Yellow Purple Green Red Purple Yellow Red Red
Row 4: Green Purple Yellow Yellow Purple Purple Purple Red Purple Yellow Red Purple Purple Purple Green Purple Yellow Red Purple Green Red Yellow Red
Row 5: Green Green Yellow Green Red Green Green Green Green Green Green Red Purple Red Yellow Purple Yellow Green Red Purple Purple Yellow Green
Row 6: Red Purple Red Purple Red Green Green Green Green Green Green Purple Red Yellow Red Purple Green Red Yellow Yellow Green Purple Purple
Row 7: Red Green Yellow Purple Red Green Green Green Green Green Green Green Yellow Yellow Green Purple Yellow Red Green Purple Green Red Red
Row 8: Red Yellow Purple Green Yellow Green Green Green Green Green Green Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Green Yellow Purple Green
Row 9: Green Red Yellow Yellow Red Green Green Green Green Brown Green Red Yellow Green Green Red Red Red Yellow Purple Yellow Yellow Purple
Row 10: Purple Purple Yellow Green Purple Green Green Green Green Green Green Purple Red Yellow Yellow Yellow Green Yellow Green Yellow Purple Purple Yellow
Row 11: Red Green Purple Green Yellow Green Green Brown Green Green Green Yellow Green Red Red Green Purple Yellow Yellow Green Red Yellow Purple
Row 12: Purple Purple Purple Red Purple Green Green Green Brown Green Green Green Purple Red Red Red Purple Green Purple Yellow Yellow Red Purple
Row 13: Green Green Purple Yellow Red Green Green Green Green Green Green Red Purple Purple Yellow Red Red Yellow Green Yellow Red Green Yellow
Row 14: Green Purple Red Red Purple Green Brown Green Green Green Green Yellow Green Red Yellow Yellow Purple Green Purple Green Green Green Purple
Row 15: Green Green Purple Purple Yellow Green Green Green Green Green Green Yellow Green Red Green Red Purple Green Red Yellow Yellow Purple Purple
Row 16: Yellow Purple Purple Yellow Green Green Green Green Green Green Green Red Purple Yellow Yellow Red Yellow Yellow Green Yellow Red Yellow Yellow
Row 17: Red Red Red Red Red Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Red Yellow Red Purple Red Purple Purple
Row 18: Green Red Green Yellow Purple Green Green Green Green Green Green Green Red Red Yellow Purple Purple Red Yellow Purple Red Red Red
Row 19: Red Green Purple Yellow Purple Red Yellow Green Red Purple Red Red Purple Yellow Green Red Purple Yellow Red Yellow Red Purple Yellow
Row 20: Purple Red Purple Yellow Yellow Red Yellow Yellow Green Yellow Green Yellow Red Red Green Green Yellow Yellow Red Yellow Red Purple Purple
Row 21: Yellow Green Red Yellow Red Red Red Purple Yellow Yellow Yellow Yellow Red Yellow Purple Red Green Red Yellow Red Green Red Green
Row 22: Purple Green Yellow Yellow Yellow Yellow Green Red Purple Green Red Red Green Yellow Yellow Purple Red Red Green Yellow Red Purple Green
Row 23: Red Green Yellow Green Yellow Green Yellow Purple Green Green Purple Red Purple Yellow Yellow Red Red Yellow Green Purple Green Yellow Yellow
Output:
Row 1: Green Brown Brown Brown Brown Green
Row 2: Green Brown Brown Brown Brown Green
Row 3: Green Brown Brown Brown Brown Green
Row 4: Green Brown Brown Brown Brown Green
Row 5: Brown Brown Brown Brown Brown Brown
Row 6: Green Brown Brown Brown Brown Green
Row 7: Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown
Row 9: Green Brown Brown Brown Brown Green
Row 10: Brown Brown Brown Brown Brown Brown
Row 11: Green Brown Brown Brown Brown Green
Row 12: Green Brown Brown Brown Brown Green
Row 13: Green Brown Brown Brown Brown Green
Row 14: Green Brown Brown Brown Brown Green
Example 3
Input:
Row 1: Black Blue Red Blue Blue Blue Black Blue Blue Red Green Brown Pink Red Green Pink Blue Brown Red Yellow Green Red Blue Green Purple Brown Purple Blue
Row 2: Yellow Brown Black Brown Pink Yellow Purple Black Pink Green Gray Pink Yellow Green Brown Purple Yellow Blue Blue Black Yellow Yellow Black Brown Green Blue Blue Pink
Row 3: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Brown Yellow Blue Brown Green Brown Blue
Row 4: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Red Black Gray Red Pink Black Purple Green
Row 5: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Pink Gray Blue Purple Pink Purple Brown
Row 6: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Pink Black Blue Red Brown Pink Purple Purple
Row 7: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Pink Yellow Green Black Green Black Black Gray
Row 8: Red Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Gray Gray Pink Purple Brown Brown Yellow Gray
Row 9: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Red Pink Brown Pink Blue Blue Green Black Black
Row 10: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Black Purple Brown Yellow Green Yellow Green Purple
Row 11: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Red Gray Red Yellow Black Red Blue
Row 12: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Red Yellow Black Pink Pink Yellow Yellow Black Blue
Row 13: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Yellow Green Gray Pink Yellow Red Yellow Pink
Row 14: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Brown Gray Yellow Red Black Yellow Pink Gray
Row 15: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Red Red Red Gray Pink Pink Pink Red
Row 16: Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Red Purple Gray Yellow Blue Pink Black Black Gray
Row 17: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Red Gray Blue Pink Blue Purple Pink
Row 18: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Gray Blue Black Blue Gray Pink Blue
Row 19: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Brown Green Blue Brown Pink Green Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Yellow Green Purple Black Pink Black Green Yellow Gray
Row 21: Black Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Yellow Gray Red Pink Yellow Black Red Red
Row 22: Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Gray Pink Yellow Red Yellow Red Red Purple
Row 23: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Brown Brown Black Pink Green Pink Pink Pink
Row 24: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Brown Yellow Brown Yellow Black Purple Gray Red
Row 25: Red Red Blue Pink Yellow Brown Blue Red Yellow Gray Yellow Yellow Yellow Purple Brown Black Blue Pink Blue Purple Black Red Pink Red Yellow Blue Purple Purple
Row 26: Purple Brown Brown Green Blue Yellow Yellow Purple Gray Purple Red Red Black Blue Gray Red Green Yellow Yellow Yellow Brown Black Brown Gray Gray Pink Yellow Red
Output:
Row 1: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 2: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 3: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 4: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 5: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 9: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 12: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 13: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 16: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 17: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 21: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Row 22: Blue Purple Purple Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Purple Blue Purple Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Green Yellow Pink Yellow Gray Green Red Red Red Yellow Yellow Pink Red Pink Gray Green
Row 2: Red Gray Blue Yellow Purple Blue Yellow Purple Red Blue Yellow Blue Blue Red Pink Yellow
Row 3: Yellow Yellow Red Blue Gray Pink Yellow Yellow Pink Red Yellow Blue Blue Blue Green Yellow
Row 4: Yellow Purple Yellow Purple Purple Blue Red Green Purple Gray Gray Purple Blue Gray Red Red
Row 5: Pink Gray Gray Pink Pink Yellow Purple Gray Pink Yellow Gray Blue Yellow Gray Gray Yellow
Row 6: Gray Yellow Blue Pink Green Blue Gray Red Pink Pink Pink Red Purple Gray Pink Purple
Row 7: Gray Blue Gray Blue Purple Gray Red Gray Red Green Purple Yellow Yellow Purple Green Red
Row 8: Yellow Green Purple Gray Pink Blue Pink Blue Green Pink Green Gray Blue Pink Purple Yellow
Row 9: Gray Yellow Pink Blue Gray Green Red Pink Green Purple Red Purple Purple Gray Purple Purple
Row 10: Green Blue Blue Red Green Orange Orange Orange Orange Orange Gray Green Pink Gray Pink Red
Row 11: Blue Red Green Purple Blue Orange Orange Orange Orange Orange Green Pink Yellow Purple Green Pink
Row 12: Yellow Pink Yellow Blue Purple Orange Orange Orange Orange Orange Gray Gray Green Blue Gray Yellow
Row 13: Blue Gray Red Purple Gray Orange Orange Orange Orange Orange Red Pink Blue Yellow Purple Green
Row 14: Green Green Gray Purple Blue Orange Orange Brown Orange Orange Green Red Red Gray Purple Blue
Row 15: Gray Yellow Red Blue Red Orange Orange Orange Brown Orange Gray Purple Yellow Purple Purple Purple
Row 16: Green Gray Purple Yellow Red Orange Orange Orange Orange Orange Red Pink Pink Blue Blue Blue
Row 17: Yellow Green Purple Red Gray Orange Brown Orange Orange Orange Blue Red Green Blue Gray Blue
Row 18: Red Purple Blue Purple Green Orange Orange Orange Orange Orange Purple Purple Pink Gray Gray Yellow
Row 19: Red Yellow Red Green Blue Orange Orange Orange Orange Orange Gray Gray Red Yellow Gray Blue
Row 20: Gray Gray Gray Pink Blue Orange Orange Orange Orange Orange Gray Yellow Gray Green Red Yellow
Row 21: Blue Gray Green Yellow Green Orange Orange Orange Orange Orange Yellow Pink Yellow Pink Blue Pink
Row 22: Purple Red Gray Pink Blue Orange Orange Orange Orange Orange Gray Purple Red Blue Red Pink
Row 23: Purple Green Pink Yellow Blue Orange Orange Orange Orange Orange Red Red Yellow Yellow Pink Blue
Row 24: Purple Green Blue Yellow Red Orange Orange Orange Orange Orange Purple Pink Red Red Purple Green
Row 25: Blue Red Gray Pink Yellow Orange Orange Orange Orange Orange Yellow Yellow Gray Red Gray Blue
Row 26: Yellow Blue Purple Purple Pink Orange Orange Orange Orange Orange Blue Yellow Green Gray Pink Yellow
Row 27: Yellow Pink Yellow Gray Red Pink Red Blue Pink Yellow Pink Yellow Purple Gray Green Red
Row 28: Yellow Pink Gray Purple Blue Gray Red Blue Blue Red Blue Yellow Red Red Purple Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown
Orange Brown Brown Brown Orange
Brown Brown Brown Brown Brown
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange
Orange Brown Brown Brown Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Black Blue Blue Blue Black Black Blue Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black
Row 2: Blue Blue Black Blue Black Black Black Blue Black Blue Blue Blue Black Blue Blue Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Blue Blue Blue Black Black Blue Black Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black
Row 5: Blue Blue Blue Blue Black Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black
Row 6: Blue Black Blue Blue Blue Black Black Blue Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black
Row 7: Blue Blue Black Blue Black Black Black Blue Black Blue Blue Blue Black Blue Blue Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Blue Blue Blue Black Black Blue Black Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black
Row 10: Blue Blue Blue Blue Black Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Red Black Red Red Red Black Black Red Black Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black
Row 2: Red Red Black Red Black Black Black Red Black Red Red Red Black Red Red Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Red Red Red Red Red Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Red Red Red Black Black Red Black Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black
Row 5: Red Red Red Red Black Red Black Black Black Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black
Row 6: Red Black Red Red Red Black Black Red Black Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black
Row 7: Red Red Black Red Black Black Black Red Black Red Red Red Black Red Red Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Red Red Red Red Red Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Red Red Red Black Black Red Black Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black
Row 10: Red Red Red Red Black Red Black Black Black Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black
Row 11: Red Black Red Red Red Black Black Red Black Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black
Row 12: Red Red Black Red Black Black Black Red Black Red Red Red Black Red Red Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Red Red Red Red Red Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Red Red Red Black Black Red Black Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black
Row 15: Red Red Red Red Black Red Black Black Black Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Black Black Black Brown Black Black Black
Row 2: Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black
Row 4: Black Black Black Brown Black Black Black
Row 5: Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black
Row 7: Black Black Black Brown Black Black Black
Row 8: Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Red Black Black Black
Row 2: Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black
Row 4: Black Black Black Red Black Black Black
Row 5: Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black
Row 7: Black Black Black Red Black Black Black
Row 8: Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black
Row 10: Black Black Black Red Black Black Black
Row 11: Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Black Black Orange Orange Orange Black Orange Black Black Orange Black Orange Orange Orange Black Black Black Black Black Black
Row 2: Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black
Row 3: Black Orange Orange Orange Orange Orange Orange Black Orange Black Black Black Black Orange Black Black Black Black Black Black
Row 4: Orange Orange Black Black Orange Orange Orange Orange Orange Black Orange Orange Black Orange Black Black Black Black Black Black
Row 5: Orange Black Orange Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black
Row 6: Black Black Orange Orange Orange Black Orange Black Black Orange Black Orange Orange Orange Black Black Black Black Black Black
Row 7: Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black
Row 8: Black Orange Orange Orange Orange Orange Orange Black Orange Black Black Black Black Orange Black Black Black Black Black Black
Row 9: Orange Orange Black Black Orange Orange Orange Orange Orange Black Orange Orange Black Orange Black Black Black Black Black Black
Row 10: Orange Black Orange Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black
Output:
Row 1: Black Black Red Red Red Black Red Black Black Red Black Red Red Red Black Black Black Black Black Black
Row 2: Red Red Red Red Black Black Black Red Red Red Red Red Red Red Black Black Black Black Black Black
Row 3: Black Red Red Red Red Red Red Black Red Black Black Black Black Red Black Black Black Black Black Black
Row 4: Red Red Black Black Red Red Red Red Red Black Red Red Black Red Black Black Black Black Black Black
Row 5: Red Black Red Red Black Red Black Red Red Red Red Red Red Red Black Black Black Black Black Black
Row 6: Black Black Red Red Red Black Red Black Black Red Black Red Red Red Black Black Black Black Black Black
Row 7: Red Red Red Red Black Black Black Red Red Red Red Red Red Red Black Black Black Black Black Black
Row 8: Black Red Red Red Red Red Red Black Red Black Black Black Black Red Black Black Black Black Black Black
Row 9: Red Red Black Black Red Red Red Red Red Black Red Red Black Red Black Black Black Black Black Black
Row 10: Red Black Red Red Black Red Black Red Red Red Red Red Red Red Black Black Black Black Black Black
Row 11: Black Black Red Red Red Black Red Black Black Red Black Red Red Red Black Black Black Black Black Black
Row 12: Red Red Red Red Black Black Black Red Red Red Red Red Red Red Black Black Black Black Black Black
Row 13: Black Red Red Red Red Red Red Black Red Black Black Black Black Red Black Black Black Black Black Black
Row 14: Red Red Black Black Red Red Red Red Red Black Red Red Black Red Black Black Black Black Black Black
Row 15: Red Black Red Red Black Red Black Red Red Red Red Red Red Red Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Black Black Black
Row 2: Black Black Black
Row 3: Black Black Black
Row 4: Black Pink Black
Row 5: Black Black Black
Row 6: Black Black Black
Row 7: Black Black Black
Row 8: Pink Black Black
Row 9: Black Black Black
Row 10: Black Black Black
Row 11: Black Black Black
Row 12: Black Pink Black
Row 13: Black Black Black
Row 14: Black Black Black
Row 15: Black Black Black
Row 16: Pink Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Black
Black Black Black
Black Black Black
Black Red Black
Black Black Black
Black Black Black
Black Black Black
Red Black Black
Black Black Black
Black Black Black
Black Black Black
Black Red Black
Black Black Black
Black Black Black
Black Black Black
Red Black Black
Black Black Black
Black Black Black
Black Black Black
Black Red Black
Black Black Black
Black Black Black
Black Black Black
Red Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Brown
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Gray Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Gray Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Gray Brown
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Gray Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Gray Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Row 7: Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green Green Green Pink Pink
Row 8: Pink Pink Pink Pink Yellow Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink
Row 9: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink
Row 10: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Yellow Pink
Row 11: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Green Green Green Green Green Pink Pink
Row 12: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink
Row 13: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink
Row 14: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Green Green Green Green Green Pink Pink
Row 15: Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green Green Green Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 29: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Red Red Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Gray Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Red Red Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 29: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Pink Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Purple Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Purple Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Purple Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Purple Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Purple Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink Pink Pink Purple Purple Pink Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Blue Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple
Row 2: Purple Green Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Orange Purple Green Purple Purple Purple Purple Purple Purple Brown Purple Brown Green Purple Purple Purple Purple
Row 4: Purple Purple Purple Green Purple Purple Purple Orange Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple
Row 6: Purple Blue Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Green Purple Purple Purple Purple Black Black Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Black Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Green Orange Purple Purple Purple Purple Orange Purple Purple
Row 11: Purple Brown Brown Orange Purple Purple Purple Purple Purple Black Purple Purple Brown Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple
Row 12: Orange Purple Purple Purple Purple Purple Blue Orange Purple Purple Purple Purple Purple Orange Black Orange Brown Purple Purple Purple Brown Purple Purple
Row 13: Purple Purple Black Purple Blue Purple Purple Purple Blue Purple Purple Blue Green Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Orange Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Gray Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple
Row 2: Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Gray Purple Gray Gray Purple Purple Purple Purple
Row 4: Purple Purple Purple Gray Purple Purple Purple Gray Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple
Row 6: Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Gray Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Gray Purple Purple
Row 11: Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple
Row 12: Gray Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Gray Purple Purple
Row 13: Purple Purple Gray Purple Gray Purple Purple Purple Gray Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Gray Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Pink Purple Pink Pink Purple
Row 2: Purple Purple Purple Pink Pink
Row 3: Purple Pink Pink Purple Pink
Output:
Row 1: Pink Gray Pink Pink Gray
Row 2: Gray Gray Gray Pink Pink
Row 3: Gray Pink Pink Gray Pink
Example 3
Input:
Row 1: Pink Red Orange Red Pink Brown Pink
Row 2: Brown Red Red Red Red Red Blue
Row 3: Brown Brown Pink Red Pink Pink Orange
Row 4: Orange Orange Red Orange Brown Red Orange
Row 5: Blue Orange Blue Red Red Pink Blue
Row 6: Red Red Brown Blue Blue Red Blue
Row 7: Blue Blue Red Red Pink Brown Red
Row 8: Red Red Red Red Red Blue Blue
Row 9: Brown Brown Pink Blue Red Brown Red
Row 10: Blue Blue Red Orange Red Red Pink
Row 11: Orange Red Orange Red Blue Brown Pink
Row 12: Orange Orange Red Red Red Red Orange
Row 13: Brown Brown Brown Blue Red Red Red
Row 14: Brown Red Red Red Pink Red Red
Row 15: Red Red Brown Red Orange Orange Orange
Row 16: Red Brown Orange Red Orange Orange Orange
Row 17: Red Blue Pink Red Red Red Brown
Row 18: Blue Red Red Red Blue Red Red
Row 19: Brown Blue Brown Brown Brown Brown Red
Row 20: Red Red Red Pink Brown Brown Orange
Row 21: Red Red Blue Red Orange Red Red
Row 22: Orange Brown Pink Brown Orange Brown Red
Row 23: Red Pink Pink Orange Orange Blue Brown
Row 24: Pink Red Orange Blue Red Red Blue
Row 25: Red Orange Blue Brown Brown Red Orange
Row 26: Red Orange Red Pink Brown Red Orange
Output:
Row 1: Gray Red Gray Red Gray Gray Gray
Row 2: Gray Red Red Red Red Red Gray
Row 3: Gray Gray Gray Red Gray Gray Gray
Row 4: Gray Gray Red Gray Gray Red Gray
Row 5: Gray Gray Gray Red Red Gray Gray
Row 6: Red Red Gray Gray Gray Red Gray
Row 7: Gray Gray Red Red Gray Gray Red
Row 8: Red Red Red Red Red Gray Gray
Row 9: Gray Gray Gray Gray Red Gray Red
Row 10: Gray Gray Red Gray Red Red Gray
Row 11: Gray Red Gray Red Gray Gray Gray
Row 12: Gray Gray Red Red Red Red Gray
Row 13: Gray Gray Gray Gray Red Red Red
Row 14: Gray Red Red Red Gray Red Red
Row 15: Red Red Gray Red Gray Gray Gray
Row 16: Red Gray Gray Red Gray Gray Gray
Row 17: Red Gray Gray Red Red Red Gray
Row 18: Gray Red Red Red Gray Red Red
Row 19: Gray Gray Gray Gray Gray Gray Red
Row 20: Red Red Red Gray Gray Gray Gray
Row 21: Red Red Gray Red Gray Red Red
Row 22: Gray Gray Gray Gray Gray Gray Red
Row 23: Red Gray Gray Gray Gray Gray Gray
Row 24: Gray Red Gray Gray Red Red Gray
Row 25: Red Gray Gray Gray Gray Red Gray
Row 26: Red Gray Red Gray Gray Red Gray
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Green Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Red Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Gray Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Orange Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Orange Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Orange Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Orange Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Orange Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Blue Brown Orange Orange Brown Orange Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Blue Brown Orange Orange Brown Brown Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Blue Brown Orange Orange Brown Brown Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Blue Brown Orange Brown Brown Orange Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Blue Brown Orange Orange Brown Brown Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Blue Brown Orange Orange Brown Orange Orange Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Blue Brown Orange Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Green Green Green Pink Pink Green Green
Row 2: Green Green Pink Pink Pink Pink Green
Row 3: Green Green Green Green Green Green Green
Row 4: Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Green Yellow Green Green Green Green Yellow
Row 6: Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green
Row 13: Green Yellow Green Green Green Green Yellow
Row 14: Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Green Green Green Green Green Green Green
Row 16: Green Green Pink Green Pink Pink Green
Row 17: Green Green Pink Pink Green Pink Green
Row 18: Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green
Row 4: Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Green Yellow Green Green Green Green Yellow
Row 6: Green Green Pink Pink Pink Pink Green
Row 7: Green Green Green Pink Pink Green Green
Row 8: Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green
Row 11: Green Green Pink Pink Green Pink Green
Row 12: Green Green Pink Green Pink Pink Green
Row 13: Green Yellow Green Green Green Green Yellow
Row 14: Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Brown Brown Brown Brown Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Brown Blue Blue Brown Blue Blue Blue
Row 4: Brown Brown Brown Brown Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Brown Brown Brown Brown Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Pink Blue Brown Brown Brown Brown Blue Blue Blue Brown Blue Blue Brown Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Pink Blue Brown Brown Brown Brown Blue Blue Blue Brown Brown Brown Brown Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Gray Gray Pink Pink
Row 2: Pink Pink Pink Red Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Red
Row 3: Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Red
Row 4: Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink
Row 5: Pink Pink Pink Red Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink
Row 6: Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink
Row 7: Pink Pink Pink Red Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink
Row 8: Pink Pink Pink Red Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Red
Row 9: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Gray Gray Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Gray Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Red Pink Pink Pink Red Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Red Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Red Pink Pink Pink Pink Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Red Pink Pink Pink Pink Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Pink Red Pink Pink Pink Red Pink Gray Pink Pink
Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Gray Gray Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Gray Green Yellow Green Yellow Brown Gray Green Yellow Green Yellow Brown Gray Green Yellow Green Yellow
Row 2: Orange Yellow Orange Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow
Row 3: Yellow Green Yellow Brown Orange Brown Yellow Green Yellow Brown Orange Brown Yellow Green Yellow Brown Orange Brown
Row 4: Brown Blue Green Yellow Yellow Yellow Brown Blue Green Yellow Yellow Yellow Brown Blue Green Yellow Yellow Yellow
Row 5: Purple Purple Yellow Green Orange Yellow Purple Purple Yellow Green Orange Yellow Purple Purple Yellow Green Orange Yellow
Row 6: Yellow Brown Blue Yellow Yellow Purple Yellow Brown Blue Yellow Yellow Purple Yellow Brown Blue Yellow Yellow Purple
Row 7: Yellow Brown Yellow Yellow Purple Orange Yellow Brown Yellow Yellow Purple Orange Yellow Brown Yellow Yellow Purple Orange
Row 8: Yellow Blue Yellow Yellow Green Yellow Yellow Blue Yellow Yellow Green Yellow Yellow Blue Yellow Yellow Green Yellow
Row 9: Brown Yellow Yellow Yellow Yellow Green Brown Yellow Yellow Yellow Yellow Green Brown Yellow Yellow Yellow Yellow Green
Row 10: Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow
Row 11: Brown Purple Purple Gray Purple Yellow Brown Purple Purple Gray Purple Yellow Brown Purple Purple Gray Purple Yellow
Row 12: Yellow Blue Yellow Yellow Brown Purple Yellow Blue Yellow Yellow Brown Purple Yellow Blue Yellow Yellow Brown Purple
Row 13: Yellow Yellow Yellow Brown Green Yellow Yellow Yellow Yellow Brown Green Yellow Yellow Yellow Yellow Brown Green Yellow
Row 14: Yellow Yellow Yellow Green Purple Yellow Yellow Yellow Yellow Green Purple Yellow Yellow Yellow Yellow Green Purple Yellow
Row 15: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow
Row 16: Yellow Yellow Blue Yellow Green Orange Yellow Yellow Blue Yellow Green Orange Yellow Yellow Blue Yellow Green Orange
Row 17: Orange Purple Purple Yellow Yellow Blue Orange Purple Purple Yellow Yellow Blue Orange Purple Purple Yellow Yellow Blue
Row 18: Yellow Purple Purple Yellow Green Blue Yellow Purple Purple Yellow Green Blue Yellow Purple Purple Yellow Green Blue
Row 19: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow
Row 20: Purple Yellow Yellow Yellow Blue Yellow Purple Yellow Yellow Yellow Blue Yellow Purple Yellow Yellow Yellow Blue Yellow
Row 21: Green Yellow Blue Blue Red Purple Green Yellow Blue Blue Red Purple Green Yellow Blue Blue Red Purple
Output:
Row 1: Brown Gray Green Yellow Green Yellow
Row 2: Orange Yellow Orange Yellow Yellow Yellow
Row 3: Yellow Green Yellow Brown Orange Brown
Row 4: Brown Blue Green Yellow Yellow Yellow
Row 5: Purple Purple Yellow Green Orange Yellow
Row 6: Yellow Brown Blue Yellow Yellow Purple
Row 7: Yellow Brown Yellow Yellow Purple Orange
Row 8: Yellow Blue Yellow Yellow Green Yellow
Row 9: Brown Yellow Yellow Yellow Yellow Green
Row 10: Yellow Yellow Blue Yellow Yellow Yellow
Row 11: Brown Purple Purple Gray Purple Yellow
Row 12: Yellow Blue Yellow Yellow Brown Purple
Row 13: Yellow Yellow Yellow Brown Green Yellow
Row 14: Yellow Yellow Yellow Green Purple Yellow
Row 15: Yellow Yellow Yellow Yellow Purple Yellow
Row 16: Yellow Yellow Blue Yellow Green Orange
Row 17: Orange Purple Purple Yellow Yellow Blue
Row 18: Yellow Purple Purple Yellow Green Blue
Row 19: Yellow Yellow Yellow Yellow Green Yellow
Row 20: Purple Yellow Yellow Yellow Blue Yellow
Row 21: Green Yellow Blue Blue Red Purple
Example 2
Input:
Row 1: Blue Gray Gray Gray Brown Gray Gray Red Black Blue Gray Gray Gray Brown Gray Gray Red Black Blue Gray Gray Gray Brown Gray Gray Red Black
Row 2: Gray Pink Yellow Gray Gray Gray Gray Red Gray Gray Pink Yellow Gray Gray Gray Gray Red Gray Gray Pink Yellow Gray Gray Gray Gray Red Gray
Row 3: Black Purple Gray Gray Purple Gray Gray Gray Gray Black Purple Gray Gray Purple Gray Gray Gray Gray Black Purple Gray Gray Purple Gray Gray Gray Gray
Row 4: Gray Blue Gray Blue Blue Gray Gray Gray Brown Gray Blue Gray Blue Blue Gray Gray Gray Brown Gray Blue Gray Blue Blue Gray Gray Gray Brown
Row 5: Gray Gray Gray Yellow Gray Gray Red Yellow Orange Gray Gray Gray Yellow Gray Gray Red Yellow Orange Gray Gray Gray Yellow Gray Gray Red Yellow Orange
Row 6: Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray
Row 7: Gray Pink Gray Gray Gray Gray Gray Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Blue Gray Pink Gray Gray Gray Gray Gray Gray Blue
Row 8: Gray Pink Gray Gray Pink Gray Gray Brown Pink Gray Pink Gray Gray Pink Gray Gray Brown Pink Gray Pink Gray Gray Pink Gray Gray Brown Pink
Row 9: Gray Blue Yellow Black Gray Pink Gray Purple Gray Gray Blue Yellow Black Gray Pink Gray Purple Gray Gray Blue Yellow Black Gray Pink Gray Purple Gray
Row 10: Red Red Blue Gray Gray Orange Gray Gray Gray Red Red Blue Gray Gray Orange Gray Gray Gray Red Red Blue Gray Gray Orange Gray Gray Gray
Row 11: Gray Purple Pink Brown Gray Gray Red Purple Gray Gray Purple Pink Brown Gray Gray Red Purple Gray Gray Purple Pink Brown Gray Gray Red Purple Gray
Row 12: Blue Gray Gray Pink Gray Pink Gray Gray Gray Blue Gray Gray Pink Gray Pink Gray Gray Gray Blue Gray Gray Pink Gray Pink Gray Gray Gray
Row 13: Gray Gray Purple Gray Gray Gray Black Gray Gray Gray Gray Purple Gray Gray Gray Black Gray Gray Gray Gray Purple Gray Gray Gray Black Gray Gray
Row 14: Gray Gray Gray Pink Yellow Gray Gray Gray Brown Gray Gray Gray Pink Yellow Gray Gray Gray Brown Gray Gray Gray Pink Yellow Gray Gray Gray Brown
Row 15: Gray Gray Gray Red Gray Gray Blue Gray Yellow Gray Gray Gray Red Gray Gray Blue Gray Yellow Gray Gray Gray Red Gray Gray Blue Gray Yellow
Row 16: Purple Purple Pink Black Red Pink Gray Gray Blue Purple Purple Pink Black Red Pink Gray Gray Blue Purple Purple Pink Black Red Pink Gray Gray Blue
Row 17: Pink Gray Red Gray Gray Gray Gray Red Yellow Pink Gray Red Gray Gray Gray Gray Red Yellow Pink Gray Red Gray Gray Gray Gray Red Yellow
Row 18: Gray Gray Gray Red Brown Gray Gray Blue Gray Gray Gray Gray Red Brown Gray Gray Blue Gray Gray Gray Gray Red Brown Gray Gray Blue Gray
Row 19: Brown Gray Gray Gray Gray Yellow Gray Pink Purple Brown Gray Gray Gray Gray Yellow Gray Pink Purple Brown Gray Gray Gray Gray Yellow Gray Pink Purple
Row 20: Gray Gray Gray Gray Gray Yellow Yellow Blue Pink Gray Gray Gray Gray Gray Yellow Yellow Blue Pink Gray Gray Gray Gray Gray Yellow Yellow Blue Pink
Row 21: Yellow Gray Red Gray Pink Gray Red Green Gray Yellow Gray Red Gray Pink Gray Red Green Gray Yellow Gray Red Gray Pink Gray Red Green Gray
Row 22: Gray Gray Gray Brown Gray Gray Red Green Gray Gray Gray Gray Brown Gray Gray Red Green Gray Gray Gray Gray Brown Gray Gray Red Green Gray
Output:
Row 1: Blue Gray Gray Gray Brown Gray Gray Red Black
Row 2: Gray Pink Yellow Gray Gray Gray Gray Red Gray
Row 3: Black Purple Gray Gray Purple Gray Gray Gray Gray
Row 4: Gray Blue Gray Blue Blue Gray Gray Gray Brown
Row 5: Gray Gray Gray Yellow Gray Gray Red Yellow Orange
Row 6: Gray Gray Gray Blue Gray Gray Gray Gray Gray
Row 7: Gray Pink Gray Gray Gray Gray Gray Gray Blue
Row 8: Gray Pink Gray Gray Pink Gray Gray Brown Pink
Row 9: Gray Blue Yellow Black Gray Pink Gray Purple Gray
Row 10: Red Red Blue Gray Gray Orange Gray Gray Gray
Row 11: Gray Purple Pink Brown Gray Gray Red Purple Gray
Row 12: Blue Gray Gray Pink Gray Pink Gray Gray Gray
Row 13: Gray Gray Purple Gray Gray Gray Black Gray Gray
Row 14: Gray Gray Gray Pink Yellow Gray Gray Gray Brown
Row 15: Gray Gray Gray Red Gray Gray Blue Gray Yellow
Row 16: Purple Purple Pink Black Red Pink Gray Gray Blue
Row 17: Pink Gray Red Gray Gray Gray Gray Red Yellow
Row 18: Gray Gray Gray Red Brown Gray Gray Blue Gray
Row 19: Brown Gray Gray Gray Gray Yellow Gray Pink Purple
Row 20: Gray Gray Gray Gray Gray Yellow Yellow Blue Pink
Row 21: Yellow Gray Red Gray Pink Gray Red Green Gray
Row 22: Gray Gray Gray Brown Gray Gray Red Green Gray
Example 3
Input:
Row 1: Gray Orange Yellow Purple Gray Orange Yellow Purple Gray Orange Yellow Purple
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Red Gray Gray Gray Red Gray Gray Gray Red Gray
Row 4: Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Pink Gray
Row 5: Yellow Pink Gray Gray Yellow Pink Gray Gray Yellow Pink Gray Gray
Row 6: Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Pink Gray
Row 7: Pink Gray Yellow Gray Pink Gray Yellow Gray Pink Gray Yellow Gray
Row 8: Gray Gray Orange Yellow Gray Gray Orange Yellow Gray Gray Orange Yellow
Row 9: Gray Red Purple Orange Gray Red Purple Orange Gray Red Purple Orange
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Yellow Pink Gray Gray Yellow Pink Gray Gray Yellow Pink
Row 12: Gray Yellow Purple Gray Gray Yellow Purple Gray Gray Yellow Purple Gray
Row 13: Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Gray
Row 14: Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray
Row 15: Yellow Orange Gray Gray Yellow Orange Gray Gray Yellow Orange Gray Gray
Row 16: Gray Orange Pink Red Gray Orange Pink Red Gray Orange Pink Red
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Purple Gray Orange Orange Purple Gray Orange Orange Purple Gray Orange Orange
Row 19: Gray Pink Gray Red Gray Pink Gray Red Gray Pink Gray Red
Row 20: Orange Gray Red Gray Orange Gray Red Gray Orange Gray Red Gray
Row 21: Yellow Pink Gray Gray Yellow Pink Gray Gray Yellow Pink Gray Gray
Row 22: Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray
Row 23: Gray Red Gray Yellow Gray Red Gray Yellow Gray Red Gray Yellow
Row 24: Orange Gray Yellow Orange Orange Gray Yellow Orange Orange Gray Yellow Orange
Row 25: Gray Red Gray Gray Gray Red Gray Gray Gray Red Gray Gray
Row 26: Pink Orange Gray Gray Pink Orange Gray Gray Pink Orange Gray Gray
Row 27: Yellow Yellow Purple Purple Yellow Yellow Purple Purple Yellow Yellow Purple Purple
Output:
Row 1: Gray Orange Yellow Purple
Row 2: Gray Gray Gray Gray
Row 3: Gray Gray Red Gray
Row 4: Gray Gray Pink Gray
Row 5: Yellow Pink Gray Gray
Row 6: Gray Gray Pink Gray
Row 7: Pink Gray Yellow Gray
Row 8: Gray Gray Orange Yellow
Row 9: Gray Red Purple Orange
Row 10: Gray Gray Gray Gray
Row 11: Gray Gray Yellow Pink
Row 12: Gray Yellow Purple Gray
Row 13: Pink Pink Pink Gray
Row 14: Yellow Red Gray Gray
Row 15: Yellow Orange Gray Gray
Row 16: Gray Orange Pink Red
Row 17: Yellow Yellow Yellow Yellow
Row 18: Purple Gray Orange Orange
Row 19: Gray Pink Gray Red
Row 20: Orange Gray Red Gray
Row 21: Yellow Pink Gray Gray
Row 22: Yellow Red Gray Gray
Row 23: Gray Red Gray Yellow
Row 24: Orange Gray Yellow Orange
Row 25: Gray Red Gray Gray
Row 26: Pink Orange Gray Gray
Row 27: Yellow Yellow Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray
Row 2: Red Red Red
Row 3: Red Red Red
Row 4: Red Red Red
Row 5: Yellow Yellow Yellow
Row 6: Gray Gray Gray
Row 7: Red Red Red
Row 8: Red Red Red
Row 9: Red Red Red
Row 10: Red Red Red
Row 11: Yellow Yellow Yellow
Row 12: Gray Gray Gray
Row 13: Red Red Red
Row 14: Red Red Red
Row 15: Brown Brown Brown
Row 16: Red Red Red
Row 17: Yellow Yellow Yellow
Row 18: Red Red Red
Row 19: Gray Gray Gray
Row 20: Brown Brown Brown
Row 21: Red Red Red
Row 22: Brown Brown Brown
Row 23: Red Red Red
Row 24: Red Red Red
Row 25: Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray
Red
Red
Red
Yellow
Gray
Red
Red
Red
Red
Yellow
Gray
Red
Red
Brown
Red
Yellow
Red
Gray
Brown
Red
Brown
Red
Red
Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Pink Red Red Red Red Red Red Pink Pink Pink Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Red Red
Row 3: Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Pink Pink Pink Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red Pink Red Red Pink Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Pink
Row 11: Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Red
Row 12: Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red
Row 15: Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red Gray Gray Pink Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Pink Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Red Red Red Red Red Pink
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red Red Red Red
Row 25: Red Red Red Red Pink Red Red Red Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Gray Gray Pink Red Red Red Gray Gray Pink Gray Gray Gray Gray Gray Gray Pink Pink Pink Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Pink Pink Pink Red Red
Row 3: Red Gray Gray Pink Red Red Red Red Red Red Red Red Red Gray Gray Pink Red Gray Gray Gray Gray Gray Gray Pink Pink Pink Red Red
Row 4: Red Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Gray Gray Pink Gray Gray Pink Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red
Row 7: Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Red Red Red Gray Gray Gray Gray Pink Pink Red Red
Row 8: Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Red Red Red Red Red Red Red Red Gray Gray Pink
Row 11: Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Pink Red Red Red Red Red Red
Row 12: Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Gray Gray Pink Red Red Red Red Red Red Gray Gray Pink Red Red Red Red Red Red Red Red
Row 14: Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Pink Red Red Red
Row 15: Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red Gray Gray Pink Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Gray Gray Pink Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red Red Gray Gray Pink Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Pink Red Red Red Red Red
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Red Gray Gray Gray Gray Pink Pink Red Red Red Gray Gray Pink
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red Red Red
Row 25: Red Red Gray Gray Pink Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red
Row 26: Red Red Red Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red Red Red Gray Gray Gray Gray Pink Pink Red Red Red
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Green Pink Blue Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Green Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Green Pink Blue Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Blue Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Row 12: Blue Blue Pink Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink
Row 13: Green Pink Blue Pink Pink Pink Pink Pink Pink Green Pink Blue Pink Pink
Row 14: Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Green Green Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Green Green Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Brown Brown Blue Pink Pink Pink Pink Pink Blue Blue Pink
Row 9: Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Blue Blue Pink
Row 10: Pink Pink Pink Blue Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink
Row 13: Pink Pink Blue Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink Pink
Row 22: Pink Pink Blue Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink Pink
Row 24: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink
Row 29: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Blue Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Blue Brown Brown Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Blue
Row 5: Pink Pink Pink Pink Pink Pink Pink Brown Brown Blue Pink Brown Brown Brown
Row 6: Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Blue Brown Brown
Row 7: Pink Pink Pink Pink Pink Pink Pink Blue Brown Brown Pink Pink Pink Pink
Row 8: Pink Pink Pink Brown Brown Blue Pink Brown Brown Brown Brown Blue Blue Pink
Row 9: Pink Pink Pink Brown Brown Brown Pink Brown Brown Brown Brown Blue Blue Pink
Row 10: Pink Pink Pink Blue Brown Brown Pink Brown Brown Brown Brown Brown Brown Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Blue Blue Brown Brown Brown Brown Pink
Row 13: Brown Brown Blue Pink Pink Pink Pink Blue Blue Brown Brown Brown Brown Pink
Row 14: Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Blue Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Blue Brown Brown Pink Pink Pink Brown Brown Blue Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Brown Brown Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Brown Brown Brown Brown Brown Brown Blue Blue Blue Pink Pink
Row 22: Brown Brown Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Pink Pink
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Pink Pink
Row 24: Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink
Row 25: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink
Row 26: Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink
Row 27: Pink Pink Pink Blue Blue Blue Brown Brown Brown Brown Brown Brown Pink Pink
Row 28: Pink Pink Pink Blue Blue Blue Brown Brown Brown Brown Brown Brown Pink Pink
Row 29: Pink Pink Pink Blue Blue Blue Brown Brown Brown Brown Brown Brown Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown
Row 2: Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown
Row 3: Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Blue Blue Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Blue Blue Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Blue Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Blue Blue Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Blue Blue Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Blue Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Purple Blue Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown
Row 13: Brown Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Blue Blue Brown Brown Brown
Brown Purple Purple Brown Blue Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Blue Blue Brown Brown Brown
Brown Brown Blue Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Purple Purple Blue Blue Brown Brown Brown
Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Purple Purple Blue Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Blue Brown
Brown Brown Brown Purple Purple Purple Purple Brown Brown Blue Blue Brown Brown Brown Brown Purple Purple Brown Blue Purple Blue Brown
Brown Brown Brown Purple Purple Purple Purple Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown
Brown Brown Brown Brown Brown Blue Blue Purple Purple Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Blue Blue Purple Purple Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Purple Purple Brown Blue Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Purple Blue Brown Brown Brown
Brown Brown Purple Purple Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown
Brown Brown Brown Blue Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Purple Purple Brown Blue Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Brown Blue Purple Blue Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Black Pink Pink Pink Pink Yellow Pink Pink Pink Pink Brown Pink Pink Orange Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 2: Pink Black Pink Pink Pink Pink Yellow Pink Pink Pink Pink Brown Pink Pink Orange Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 3: Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow
Row 4: Pink Black Pink Pink Pink Pink Yellow Pink Pink Pink Pink Brown Pink Pink Orange Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 5: Pink Black Pink Pink Pink Pink Yellow Pink Pink Pink Pink Brown Pink Pink Orange Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 6: Pink Black Pink Pink Pink Pink Yellow Pink Pink Pink Pink Brown Pink Pink Orange Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Brown Black Black Black
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Brown Pink Pink Pink
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Brown Red Red Red
Output:
Row 1: Red Red Red
Row 2: Red Red Red
Row 3: Red Red Red
Row 4: Red Red Red
Row 5: Red Red Red
Example 3
Input:
Row 1: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 2: Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 3: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 4: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 5: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 6: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 7: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 8: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 9: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 10: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 11: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 12: Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue
Row 13: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 14: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 15: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 16: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 17: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 18: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 19: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 20: Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 22: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple
Row 2: Purple Purple Purple
Row 3: Purple Purple Purple
Row 4: Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green Green Green Green Green Green
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray
Gray Gray
Gray Gray
Gray Gray
Gray Gray
Gray Gray
Gray Gray
Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Yellow Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Green Purple Yellow Purple Yellow Purple Purple Purple Purple
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Yellow Brown Brown Brown Brown
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Yellow Yellow Purple Yellow Purple
Row 4: Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Yellow Green Yellow Purple Yellow Yellow Purple Purple Yellow Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Yellow Purple Yellow Yellow Purple Purple Purple
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Purple Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Purple Purple Green Yellow Purple Purple Yellow Yellow Purple Purple Purple
Row 8: Yellow Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Yellow Yellow Purple Purple Yellow
Output:
Row 1: Green Brown Brown Brown Yellow
Row 2: Green Purple Purple Purple Yellow
Row 3: Green Yellow Yellow Yellow Yellow
Row 4: Green Purple Yellow Yellow Yellow
Row 5: Green Orange Orange Orange Orange
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Black Green Purple Yellow Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 10: Green Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Green Black Purple Purple Yellow Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 22: Purple Green Purple Purple Purple Green Purple Purple Black Purple Purple Yellow Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Green
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Output:
Row 1: Brown Brown Brown Brown
Row 2: Black Purple Purple Yellow
Row 3: Black Purple Purple Yellow
Row 4: Black Green Purple Yellow
Row 5: Black Green Purple Yellow
Row 6: Black Green Purple Yellow
Row 7: Black Green Purple Yellow
Row 8: Black Green Purple Yellow
Row 9: Black Green Purple Yellow
Row 10: Black Green Purple Yellow
Row 11: Black Green Purple Yellow
Row 12: Black Green Purple Yellow
Row 13: Black Green Purple Yellow
Row 14: Black Green Purple Yellow
Row 15: Black Green Purple Yellow
Row 16: Green Green Green Green
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Purple Pink Pink
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 8: Pink Orange Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Purple Pink Pink
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 2: Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Purple
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Red Gray Gray Gray Gray Gray Gray Red Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Row 5: Gray Gray Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Black Gray Gray Gray Gray
Row 6: Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black
Red Red Red Red Red Red Red Red Gray Gray Gray Black
Red Green Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink
Row 2: Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray
Row 3: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 4: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 5: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 12: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 13: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 17: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 18: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Red Gray Red Gray Red Gray Red Gray Red Gray Red Gray
Row 25: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 26: Gray Red Gray Red Gray Red Gray Red Gray Red Gray Red
Row 27: Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink
Row 28: Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray Pink Gray
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Brown Gray Brown Gray Brown Gray Brown Gray Brown Gray Brown
Row 2: Gray Brown Gray Brown Gray Brown Gray Brown Gray Brown Gray
Row 3: Brown Gray Brown Gray Brown Gray Brown Gray Brown Gray Brown
Row 4: Gray Brown Gray Brown Gray Brown Gray Brown Gray Brown Gray
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Red Red Red Red Red Red Red Red Red
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Red Red Red Red Red Red Red Red Red
Row 7: Green Green Green Green Green Green Green Green Green
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Red Red Red Red Red Red Red Red Red
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Green Green Green Green Green Green Green Green Green
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Green Green Green Green Green Green Green Green Green
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Green Green Green Green Green Green Green Green Green
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Green Green Green Green Green Green Green Green Green
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Red Red Red Red Red Red Red Red Red
Row 26: Green Green Green Green Green Green Green Green Green
Output:
Row 1: Red Green Red Green Red Green Red Green Red
Row 2: Purple Red Purple Red Purple Red Purple Red Purple
Row 3: Red Blue Red Blue Red Blue Red Blue Red
Row 4: Pink Green Pink Green Pink Green Pink Green Pink
Row 5: Orange Purple Orange Purple Orange Purple Orange Purple Orange
Row 6: Red Purple Red Purple Red Purple Red Purple Red
Row 7: Green Pink Green Pink Green Pink Green Pink Green
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Red Green Red Green Red Green Red Green Red
Row 10: Orange Blue Orange Blue Orange Blue Orange Blue Orange
Row 11: Red Green Red Green Red Green Red Green Red
Row 12: Red Orange Red Orange Red Orange Red Orange Red
Row 13: Blue Green Blue Green Blue Green Blue Green Blue
Row 14: Green Blue Green Blue Green Blue Green Blue Green
Row 15: Orange Red Orange Red Orange Red Orange Red Orange
Row 16: Green Red Green Red Green Red Green Red Green
Row 17: Blue Orange Blue Orange Blue Orange Blue Orange Blue
Row 18: Green Red Green Red Green Red Green Red Green
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Pink Green Pink Green Pink Green Pink Green Pink
Row 21: Purple Red Purple Red Purple Red Purple Red Purple
Row 22: Purple Orange Purple Orange Purple Orange Purple Orange Purple
Row 23: Green Pink Green Pink Green Pink Green Pink Green
Row 24: Blue Red Blue Red Blue Red Blue Red Blue
Row 25: Red Purple Red Purple Red Purple Red Purple Red
Row 26: Green Red Green Red Green Red Green Red Green
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow
Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue Yellow Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 6: Blue Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Blue Blue Pink Blue Blue Blue Pink Blue
Row 7: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 12: Blue Blue Blue Blue Blue Pink Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue Pink
Row 13: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Pink Blue Blue Pink Blue Pink Blue Blue Pink Blue
Row 19: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Output:
Row 1: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 6: Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Yellow Blue
Row 7: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 8: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 9: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 10: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 11: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 12: Blue Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Yellow
Row 13: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 14: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 15: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 16: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 17: Green Green Green Green Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Yellow Blue Yellow Blue Blue Yellow Blue
Row 19: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 2: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 3: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 4: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 5: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 8: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 9: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 10: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 11: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 12: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown
Row 13: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 14: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 15: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 16: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 17: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 20: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 21: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 22: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 23: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 26: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 27: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 28: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Row 29: Gray Gray Gray Brown Gray Gray Gray Brown Gray Gray Gray
Output:
Row 1: Green Green Green Brown Green Green Green Brown Green Green Green
Row 2: Green Green Green Brown Green Green Green Brown Green Green Green
Row 3: Green Green Green Brown Green Green Green Brown Green Green Green
Row 4: Green Green Green Brown Green Green Green Brown Green Green Green
Row 5: Green Green Green Brown Green Green Green Brown Green Green Green
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Green Green Green Brown Green Green Green Brown Green Green Green
Row 8: Green Green Green Brown Green Green Green Brown Green Green Green
Row 9: Green Green Green Brown Green Green Green Brown Green Green Green
Row 10: Green Green Green Brown Green Green Green Brown Green Green Green
Row 11: Green Green Green Brown Green Green Green Brown Green Green Green
Row 12: Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown
Row 13: Green Green Green Brown Green Green Green Brown Green Green Green
Row 14: Green Green Green Brown Green Green Green Brown Green Green Green
Row 15: Green Green Green Brown Green Green Green Brown Green Green Green
Row 16: Green Green Green Brown Green Green Green Brown Green Green Green
Row 17: Green Green Green Brown Green Green Green Brown Green Green Green
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Green Green Green Brown Green Green Green Brown Green Green Green
Row 20: Green Green Green Brown Green Green Green Brown Green Green Green
Row 21: Green Green Green Brown Green Green Green Brown Green Green Green
Row 22: Green Green Green Brown Green Green Green Brown Green Green Green
Row 23: Green Green Green Brown Green Green Green Brown Green Green Green
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Green Green Green
Row 26: Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green
Row 27: Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green
Row 28: Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green
Row 29: Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green
Example 3
Input:
Row 1: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 2: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 3: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 4: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 5: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 6: Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Row 7: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 8: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 9: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 10: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 11: Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 14: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 15: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 16: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 17: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 20: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 21: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 22: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 23: Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Output:
Row 1: Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green Brown Green Green Green
Row 2: Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green Brown Green Green Green
Row 3: Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green Brown Green Green Green
Row 4: Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green Brown Green Green Green
Row 5: Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green Brown Green Green Green
Row 6: Brown Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown
Row 7: Green Green Green Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 8: Green Green Green Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 9: Green Green Green Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 10: Green Green Green Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 11: Green Green Green Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 14: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 15: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 16: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 17: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 20: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 21: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 22: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Row 23: Green Green Green Brown Green Green Green Brown Yellow Yellow Yellow Brown Green Green Green Brown Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 12: Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green
Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Green Red Red Red Red Red Red Red Red Blue
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Blue Red Red Red Red Red Red Red Red Green
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Blue Green Blue Gray Red Gray Gray Red Gray Green Blue
Row 2: Red Red Blue Blue Blue Red Red Red Red Red Red Green Green
Row 3: Red Red Red Gray Red Red Red Red Red Red Red Red Gray
Row 4: Red Red Green Green Green Red Red Red Red Red Red Blue Blue
Row 5: Red Red Green Blue Green Gray Red Gray Gray Red Gray Blue Green
Row 6: Red Red Green Green Green Red Red Red Red Red Red Blue Blue
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red
Row 4: Red Red Orange Red Red Red Blue
Row 5: Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red
Row 18: Red Red Blue Red Red Red Orange
Row 19: Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red
Row 29: Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red
Row 3: Red Blue Blue Blue Red Orange Orange
Row 4: Red Blue Orange Blue Gray Orange Blue
Row 5: Red Blue Blue Blue Red Orange Orange
Row 6: Red Red Gray Red Red Red Gray
Row 7: Red Red Red Red Red Red Red
Row 8: Red Red Gray Red Red Red Gray
Row 9: Red Red Red Red Red Red Red
Row 10: Red Red Gray Red Red Red Gray
Row 11: Red Red Red Red Red Red Red
Row 12: Red Red Gray Red Red Red Gray
Row 13: Red Red Red Red Red Red Red
Row 14: Red Red Gray Red Red Red Gray
Row 15: Red Red Red Red Red Red Red
Row 16: Red Red Gray Red Red Red Gray
Row 17: Red Orange Orange Orange Red Blue Blue
Row 18: Red Orange Blue Orange Gray Blue Orange
Row 19: Red Orange Orange Orange Red Blue Blue
Row 20: Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red
Row 29: Red Red Red Red Red Red Red
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Brown Brown Brown Green Green Green Green Green Green Green Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Brown Orange Brown Gray Green Gray Green Green Gray Green Gray Orange Brown Orange Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Brown Brown Brown Green Green Green Green Green Green Green Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Orange Orange Orange Green Green Green Green Green Green Green Green Brown Brown Brown Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Orange Brown Orange Gray Green Gray Green Green Gray Green Gray Brown Orange Brown Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Orange Orange Orange Green Green Green Green Green Green Green Green Brown Brown Brown Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Brown Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Black Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Brown Brown Brown Blue Blue Blue Blue Black Black Black Blue
Blue Blue Blue Brown Black Brown Gray Blue Blue Gray Black Brown Black Blue
Blue Blue Blue Brown Brown Brown Blue Blue Blue Blue Black Black Black Blue
Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Gray Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Gray Blue Blue
Blue Blue Blue Black Black Black Blue Blue Blue Blue Brown Brown Brown Blue
Blue Blue Blue Black Brown Black Gray Blue Blue Gray Brown Black Brown Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Blue Brown Brown Blue Purple Gray Brown Yellow Orange Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Purple Blue Brown Brown Blue Blue Gray Brown Yellow Purple Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Output:
Row 1: Purple Blue Brown Brown Blue Purple Gray Brown Yellow Orange Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 2: Purple Blue Brown Brown Blue Brown Gray Brown Yellow Brown Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 3: Purple Blue Brown Brown Blue Brown Gray Brown Yellow Brown Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 4: Purple Blue Brown Brown Blue Brown Gray Brown Yellow Brown Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 5: Purple Blue Brown Brown Blue Brown Gray Brown Yellow Brown Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 6: Purple Blue Brown Brown Blue Brown Gray Brown Yellow Brown Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 7: Purple Blue Brown Brown Blue Brown Gray Brown Yellow Brown Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Row 8: Purple Blue Brown Brown Blue Blue Gray Brown Yellow Purple Yellow Brown Blue Black Black Blue Green Pink Blue Brown Purple Green Pink Green Brown Gray Purple Black Green
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red
Row 4: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 7: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black
Row 10: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red
Row 4: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black
Row 10: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Gray Gray Blue Orange Black Brown Gray Red Yellow Orange Orange Green Orange
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Pink Red Blue Orange Gray Brown Green Pink Yellow Pink Pink Black Pink
Output:
Row 1: Gray Gray Blue Orange Black Brown Gray Red Yellow Orange Orange Green Orange
Row 2: Blue Blue Blue Orange Blue Brown Blue Blue Yellow Blue Blue Blue Blue
Row 3: Blue Blue Blue Orange Blue Brown Blue Blue Yellow Blue Blue Blue Blue
Row 4: Blue Blue Blue Orange Blue Brown Blue Blue Yellow Blue Blue Blue Blue
Row 5: Blue Blue Blue Orange Blue Brown Blue Blue Yellow Blue Blue Blue Blue
Row 6: Blue Blue Blue Orange Blue Brown Blue Blue Yellow Blue Blue Blue Blue
Row 7: Blue Blue Blue Orange Blue Brown Blue Blue Yellow Blue Blue Blue Blue
Row 8: Pink Red Blue Orange Gray Brown Green Pink Yellow Pink Pink Black Pink
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Brown Purple Orange Black Black Orange
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Purple Red Pink Yellow Purple Black Black Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Brown Purple Orange Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Gray Gray Gray Gray Gray Black Black Orange
Purple Red Pink Yellow Purple Black Black Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black
Row 8: Black Black Black Black Black Green
Row 9: Black Gray Gray Gray Green Black
Row 10: Black Gray Gray Green Red Black
Row 11: Black Gray Green Red Red Black
Row 12: Black Green Red Red Red Black
Row 13: Green Black Black Black Black Black
Row 14: Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black
Row 3: Black Black Black Black Black Green
Row 4: Black Black Black Black Green Black
Row 5: Black Black Black Green Black Black
Row 6: Black Black Green Black Black Black
Row 7: Black Green Black Black Black Black
Row 8: Green Black Black Black Black Green
Row 9: Black Black Black Black Green Black
Row 10: Black Black Black Green Black Black
Row 11: Black Black Green Black Black Black
Row 12: Black Green Black Black Black Black
Row 13: Green Black Black Black Black Green
Row 14: Black Black Black Black Green Black
Row 15: Black Black Black Green Black Black
Row 16: Black Black Green Black Black Black
Row 17: Black Green Black Black Black Black
Row 18: Green Black Black Black Black Black
Row 19: Black Black Black Black Black Black
Example 2
Input:
Row 1: Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Brown Purple Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Brown Brown Purple Brown Brown Pink Pink Pink Pink
Row 5: Pink Pink Pink Brown Brown Brown Purple Brown Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink
Row 4: Purple Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink
Row 5: Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink
Row 6: Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Purple
Row 7: Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink
Row 8: Pink Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink
Row 9: Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink
Row 10: Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Purple
Row 11: Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Gray Brown Brown Purple Purple Purple Purple Purple
Row 16: Purple Blue Gray Brown Purple Purple Purple Purple Purple
Row 17: Purple Blue Blue Gray Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Gray Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Gray Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Gray Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Gray Purple Purple Purple Purple Purple
Row 14: Gray Purple Purple Purple Gray Purple Purple Purple Purple
Row 15: Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 16: Purple Purple Gray Purple Purple Purple Gray Purple Purple
Row 17: Purple Purple Purple Gray Purple Purple Purple Gray Purple
Row 18: Gray Purple Purple Purple Gray Purple Purple Purple Gray
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Gray Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Gray Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Gray Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Gray Blue Blue Blue Red Red Red Red Red
Row 6: Red Red Red Red Gray Blue Blue Red Red Red Red Red
Row 7: Red Red Red Red Red Gray Blue Red Red Red Red Red
Row 8: Red Red Red Red Red Red Gray Red Red Red Red Red
Row 9: Red Red Red Red Red Red Brown Gray Red Red Red Red
Row 10: Red Red Red Red Red Red Brown Brown Gray Red Red Red
Row 11: Red Red Red Red Red Red Brown Brown Brown Gray Red Red
Row 12: Red Red Red Red Red Red Brown Brown Brown Brown Gray Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Gray Red Red Red Red Red Red Red
Gray Red Red Red Red Gray Red Red Red Red Red Red
Red Gray Red Red Red Red Gray Red Red Red Red Red
Red Red Gray Red Red Red Red Gray Red Red Red Red
Red Red Red Gray Red Red Red Red Gray Red Red Red
Red Red Red Red Gray Red Red Red Red Gray Red Red
Red Red Red Red Red Gray Red Red Red Red Gray Red
Gray Red Red Red Red Red Gray Red Red Red Red Gray
Red Gray Red Red Red Red Red Gray Red Red Red Red
Red Red Gray Red Red Red Red Red Gray Red Red Red
Red Red Red Gray Red Red Red Red Red Gray Red Red
Red Red Red Red Gray Red Red Red Red Red Gray Red
Red Red Red Red Red Gray Red Red Red Red Red Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Red Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Yellow Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Red Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Yellow Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Blue Brown Brown Red Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Green Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Black Black Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple
Row 7: Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Black Black Purple Purple Black Black Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Black Black Purple Purple Black Black Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Black Black Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Black Black Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Black Black Purple Purple Black Black Purple Purple Black Black Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Black Black Purple Purple Black Black Purple Purple Purple Purple Purple Purple Black Black Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Blue Purple Purple Red Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Black Black Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Black Black Purple Purple Purple Green Purple Purple Yellow Purple Purple Purple Blue Purple Purple Red Purple Purple
Row 5: Purple Green Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple
Row 6: Blue Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple
Row 7: Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple Purple
Row 8: Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Green Purple Purple Yellow Purple Purple Purple Blue Purple Purple Red Purple Blue Purple Purple Red Blue Purple Purple Red
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Black Black Purple Purple Black Black Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Black Black Purple Purple Black Black Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple Green Purple Purple Yellow Green Purple Purple Yellow
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Blue Purple Purple Red Purple Purple Purple Blue Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Black Black Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Black Black Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Blue Purple Purple Red Purple
Row 17: Green Purple Purple Yellow Purple Purple Purple Green Purple Purple Yellow Purple Purple Purple Purple Purple Black Black Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Red Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Blue Purple Purple Red Blue Purple Purple Red Purple Black Black Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Black Black Purple Purple Black Black Purple Purple Black Black Purple Blue Purple Purple Red Purple
Row 23: Purple Purple Purple Purple Black Black Purple Purple Black Black Purple Green Purple Purple Yellow Purple Black Black Purple Purple
Row 24: Purple Purple Purple Green Purple Purple Yellow Green Purple Purple Yellow Purple Purple Purple Purple Purple Black Black Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 4: Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Red Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 3: Blue Pink Pink Red Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 4: Pink Gray Gray Pink Pink Pink Pink Pink Pink Green Pink Pink Yellow Pink Pink Pink
Row 5: Pink Gray Gray Pink Blue Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Green Pink Pink Yellow Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Green Pink Pink Yellow Pink Pink Pink Pink Blue Pink Pink Red
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Yellow
Row 12: Pink Pink Pink Pink Pink Pink Blue Pink Pink Red Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Blue Pink Pink Red Pink
Row 15: Pink Pink Pink Pink Pink Pink Green Pink Pink Yellow Pink Pink Gray Gray Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Yellow Pink
Row 18: Pink Pink Pink Pink Blue Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Green Pink Pink Yellow Pink Blue Pink Pink Red Pink Pink Pink
Row 22: Pink Pink Pink Blue Pink Pink Red Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Gray Gray Pink Pink Pink Green Pink Pink Yellow Pink Pink Pink
Row 25: Pink Pink Pink Green Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange
Row 3: Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange
Row 7: Orange Orange Pink Pink Orange Orange Pink Pink Orange Orange
Row 8: Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Pink Pink Orange Orange Pink Pink Orange
Row 14: Orange Orange Orange Pink Pink Orange Orange Pink Pink Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Pink Pink Orange Orange Pink Pink Orange Orange
Row 28: Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Orange Orange Red Orange Blue Orange Orange Red Orange
Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange
Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange
Green Orange Orange Yellow Orange Green Orange Orange Yellow Orange
Orange Orange Orange Orange Orange Blue Orange Orange Red Orange
Orange Blue Orange Orange Red Orange Pink Pink Orange Orange
Orange Orange Pink Pink Orange Orange Pink Pink Orange Orange
Orange Orange Pink Pink Orange Green Orange Orange Yellow Orange
Orange Green Orange Orange Yellow Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Blue Orange Orange Red Blue Orange Orange Red
Orange Orange Orange Pink Pink Orange Orange Pink Pink Orange
Orange Orange Orange Pink Pink Orange Orange Pink Pink Orange
Orange Orange Green Orange Orange Yellow Green Orange Orange Yellow
Orange Orange Blue Orange Orange Red Orange Orange Orange Orange
Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange
Orange Orange Orange Pink Pink Orange Blue Orange Orange Red
Orange Orange Green Orange Orange Yellow Orange Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange
Orange Blue Orange Orange Red Orange Green Orange Orange Yellow
Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange
Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange
Orange Green Orange Orange Yellow Orange Orange Orange Orange Orange
Orange Blue Orange Orange Red Orange Orange Orange Orange Orange
Orange Orange Pink Pink Orange Blue Orange Orange Red Orange
Orange Orange Pink Pink Orange Orange Pink Pink Orange Orange
Orange Green Orange Orange Yellow Orange Pink Pink Orange Orange
Orange Orange Orange Orange Orange Green Orange Orange Yellow Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Green Gray Gray Gray Green Gray Brown Gray Gray Brown Gray Green Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Blue Gray Gray Gray Brown
Row 4: Gray Gray Gray Gray Gray Gray Green Green Pink Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray
Row 5: Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Orange Purple Green Purple
Row 6: Gray Gray Gray Pink Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray
Row 8: Brown Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Green Gray Pink Gray Blue Gray Gray Gray
Row 9: Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Green Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Brown Gray Green Gray
Row 13: Gray Gray Pink Pink Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Orange Gray Purple Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Orange Brown Orange Green Orange Orange Brown Orange Red Orange Red Orange Orange Brown Green Gray Purple
Row 2: Orange Purple Orange Orange Orange Green Brown Orange Orange Gray Orange Orange Green Brown Red Orange Orange
Row 3: Orange Orange Green Orange Brown Purple Gray Purple Orange Brown Orange Gray Orange Orange Green Purple Orange
Row 4: Orange Orange Brown Gray Gray Orange Orange Gray Brown Orange Orange Orange Orange Green Purple Orange Orange
Row 5: Orange Green Orange Orange Gray Orange Gray Orange Gray Brown Gray Orange Orange Orange Green Brown Orange
Row 6: Orange Orange Red Orange Green Purple Orange Gray Orange Orange Orange Orange Orange Orange Purple Orange Gray
Row 7: Orange Brown Brown Orange Purple Gray Gray Orange Orange Green Gray Orange Orange Purple Red Orange Brown
Row 8: Orange Orange Red Red Gray Gray Orange Purple Red Gray Purple Orange Green Purple Orange Orange Orange
Row 9: Brown Orange Green Green Brown Orange Orange Orange Orange Purple Orange Gray Purple Orange Orange Orange Gray
Row 10: Orange Red Gray Red Orange Orange Orange Orange Orange Orange Green Green Orange Orange Brown Green Orange
Row 11: Orange Purple Orange Green Red Red Orange Orange Orange Orange Red Red Orange Orange Orange Brown Red
Row 12: Orange Gray Red Gray Gray Red Purple Red Orange Brown Brown Orange Gray Purple Orange Purple Orange
Row 13: Purple Orange Orange Orange Red Brown Orange Orange Red Orange Purple Orange Gray Purple Orange Brown Gray
Row 14: Orange Orange Orange Purple Gray Orange Brown Orange Orange Brown Orange Orange Gray Brown Orange Orange Purple
Row 15: Purple Purple Orange Orange Purple Orange Orange Orange Orange Gray Orange Orange Red Red Green Orange Purple
Row 16: Gray Brown Orange Red Orange Gray Green Brown Orange Green Orange Orange Gray Purple Orange Red Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Red Purple Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Black Red Green
Row 3: Red Red Brown Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Green Red Red Red Red
Row 6: Red Pink Red Red Green Red Red Red Red Red Red
Row 7: Red Gray Red Red Red Red Red Red Red Red Yellow
Row 8: Red Red Red Purple Red Green Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Gray Red Orange
Row 10: Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Orange Red Red Red Red Pink Red
Row 13: Red Red Red Red Yellow Red Red Red Red Red Red
Row 14: Red Red Purple Brown Red Red Red Red Red Red Red
Row 15: Red Red Gray Red Green Green Yellow Orange Yellow Red Gray
Row 16: Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Black Red Red Red Red Black
Row 18: Red Red Red Red Gray Black Red Red Gray Red Red
Row 19: Red Red Red Red Red Red Yellow Red Red Red Red
Row 20: Red Red Red Green Red Gray Red Red Red Red Red
Row 21: Red Red Red Red Red Red Yellow Red Red Red Brown
Row 22: Blue Red Red Purple Red Blue Pink Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Purple
Row 24: Red Red Red Red Red Red Red Red Blue Red Yellow
Row 25: Yellow Pink Red Red Red Red Black Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Green Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Green Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Black Red Red Red Red Red
Row 18: Red Red Red Red Red Black Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Gray Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Blue Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Pink Brown Brown Brown Gray Brown Pink Brown
Row 2: Brown Brown Brown Brown Gray Brown Gray Brown Gray Brown Brown
Row 3: Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Gray Brown Brown Brown Brown Gray Gray Brown Brown Brown Pink
Row 5: Brown Pink Gray Gray Brown Gray Brown Brown Brown Brown Brown
Row 6: Gray Brown Gray Gray Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Gray Brown Brown Brown Brown Brown Pink Pink Gray Gray
Row 8: Brown Gray Pink Gray Brown Pink Brown Brown Brown Brown Brown
Row 9: Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Pink
Row 10: Pink Brown Brown Brown Brown Gray Gray Brown Gray Pink Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 13: Purple Purple Green Green Blue Green Blue Green Blue Blue Green Blue Green Green Green Green Purple Purple Purple Purple
Row 14: Purple Purple Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 15: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 16: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 17: Purple Purple Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Purple Purple Purple Purple
Row 18: Purple Purple Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 19: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Purple Purple Purple Purple
Row 20: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 21: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 22: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 23: Purple Purple Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Purple Purple Purple Purple
Row 24: Purple Purple Green Green Blue Green Green Blue Blue Green Blue Green Green Green Green Green Purple Purple Purple Purple
Row 25: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 13: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 14: Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue
Row 15: Purple Purple Green Green Green Blue Green Green Green Green Green Green Blue Blue Green Green Purple Purple Purple Purple
Row 16: Purple Purple Green Green Green Blue Green Green Green Green Green Green Blue Blue Green Green Purple Purple Purple Purple
Row 17: Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue
Row 18: Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue
Row 19: Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue
Row 20: Purple Purple Green Green Green Blue Green Green Green Green Green Green Blue Blue Green Green Purple Purple Purple Purple
Row 21: Purple Purple Green Green Green Blue Green Green Green Green Green Green Blue Blue Green Green Purple Purple Purple Purple
Row 22: Purple Purple Green Green Green Blue Green Green Green Green Green Green Blue Blue Green Green Purple Purple Purple Purple
Row 23: Purple Purple Green Green Green Blue Green Green Green Green Green Green Blue Blue Green Green Purple Purple Purple Purple
Row 24: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 25: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Row 5: Yellow Yellow Pink Pink Pink Pink Yellow Gray Gray Gray
Row 6: Yellow Yellow Pink Pink Pink Yellow Yellow Gray Gray Gray
Row 7: Yellow Yellow Pink Yellow Yellow Yellow Yellow Gray Gray Gray
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Output:
Row 1: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink
Row 6: Yellow Yellow Yellow Pink Pink Yellow Yellow Gray Gray Gray
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Purple Purple Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green
Row 4: Red Red Red Red Red Red Red Red Green
Row 5: Red Red Red Red Red Red Red Red Green
Row 6: Red Red Black Black Black Black Red Red Green
Row 7: Red Black Black Black Black Black Red Red Green
Row 8: Red Red Black Black Black Black Black Red Green
Row 9: Red Red Black Black Black Black Red Red Green
Row 10: Red Red Black Black Black Black Red Red Green
Row 11: Red Black Black Black Black Black Black Red Green
Row 12: Red Red Black Black Black Black Red Red Green
Row 13: Red Red Black Black Black Black Red Red Green
Row 14: Red Red Black Black Black Black Red Red Green
Row 15: Red Red Red Red Red Black Red Red Green
Row 16: Red Red Red Red Red Red Red Red Green
Row 17: Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Black Green Green Green
Green Green Green Green Green Black Green Green Green
Green Green Green Green Green Black Green Green Green
Red Red Red Red Red Red Red Red Green
Red Red Red Red Red Red Red Red Green
Red Red Black Black Black Red Red Red Green
Red Red Red Red Red Red Red Red Black
Red Red Red Red Red Red Red Red Black
Red Red Black Black Black Red Red Red Green
Red Red Black Black Black Red Red Red Green
Red Red Red Red Red Red Red Red Black
Red Red Black Black Black Red Red Red Green
Red Red Black Black Black Red Red Red Green
Red Red Black Black Black Red Red Red Green
Red Red Red Red Red Red Red Red Green
Red Red Red Red Red Red Red Red Green
Green Green Green Green Green Black Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green
Row 7: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 8: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 9: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 10: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 11: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 12: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 13: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 14: Green Green Pink Pink Pink Pink Green Green Green Green Green
Row 15: Green Green Pink Pink Pink Pink Green Green Green Green Green
Row 16: Green Green Pink Pink Pink Pink Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green
Row 22: Gray Gray Gray Green Green Green Green Green Green Green Green
Row 23: Gray Gray Gray Green Green Green Green Green Green Green Green
Row 24: Gray Gray Gray Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green Green Green Green Green
Row 28: Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green
Row 7: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 8: Yellow Purple Purple Purple Yellow Green Green Green Green Green Green
Row 9: Yellow Purple Purple Purple Yellow Green Green Green Green Green Green
Row 10: Yellow Purple Purple Purple Yellow Green Green Green Green Green Green
Row 11: Yellow Purple Purple Purple Yellow Green Green Green Green Green Green
Row 12: Yellow Purple Purple Purple Yellow Green Green Green Green Green Green
Row 13: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green
Row 14: Green Green Pink Pink Pink Pink Green Green Green Green Green
Row 15: Green Green Pink Purple Purple Pink Green Green Green Green Green
Row 16: Green Green Pink Pink Pink Pink Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green
Row 22: Gray Gray Gray Green Green Green Green Green Green Green Green
Row 23: Gray Purple Gray Green Green Green Green Green Green Green Green
Row 24: Gray Gray Gray Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green Green Green Green Green
Row 28: Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Gray Purple Purple Purple Gray Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Black Purple Purple Purple Black Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Red Red Red Red Red Green
Row 3: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Red Red Red Red Red Green
Row 4: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Red Red Red Red Red Green
Row 5: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Red Red Red Red Red Green
Row 6: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Gray Gray Gray Green Black Black Black Black Green Green Green Green Green Green
Row 8: Green Green Brown Brown Brown Green Gray Gray Gray Green Black Black Black Black Green Green Green Green Green Green
Row 9: Green Green Brown Brown Brown Green Gray Gray Gray Green Black Black Black Black Green Green Green Green Green Green
Row 10: Green Green Brown Brown Brown Green Green Green Green Green Black Black Black Black Green Green Green Green Green Green
Row 11: Green Orange Orange Orange Orange Orange Green Green Green Green Black Black Black Black Green Green Green Green Green Green
Row 12: Green Orange Orange Orange Orange Orange Green Green Green Green Black Black Black Black Green Green Green Green Green Green
Row 13: Green Orange Orange Orange Orange Orange Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Yellow Purple Yellow Green Green Green Green Red Red Red Red Red Green
Row 3: Green Green Green Green Green Green Green Yellow Purple Yellow Green Green Green Green Red Purple Purple Purple Red Green
Row 4: Green Green Green Green Green Green Green Yellow Purple Yellow Green Green Green Green Red Purple Purple Purple Red Green
Row 5: Green Green Green Green Green Green Green Yellow Purple Yellow Green Green Green Green Red Red Red Red Red Green
Row 6: Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Gray Gray Gray Green Black Black Black Black Green Green Green Green Green Green
Row 8: Green Green Brown Brown Brown Green Gray Purple Gray Green Black Purple Purple Black Green Green Green Green Green Green
Row 9: Green Green Brown Purple Brown Green Gray Gray Gray Green Black Purple Purple Black Green Green Green Green Green Green
Row 10: Green Green Brown Brown Brown Green Green Green Green Green Black Purple Purple Black Green Green Green Green Green Green
Row 11: Green Orange Orange Orange Orange Orange Green Green Green Green Black Purple Purple Black Green Green Green Green Green Green
Row 12: Green Orange Purple Purple Purple Orange Green Green Green Green Black Black Black Black Green Green Green Green Green Green
Row 13: Green Orange Orange Orange Orange Orange Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Pink Purple Purple Purple Purple Purple Pink Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Pink Purple Purple Purple Purple Purple Pink Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Pink Purple Purple Purple Purple Purple Pink Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Blue Blue Blue Red Red Red Red
Row 5: Pink Pink Pink Pink Blue Blue Blue Red Red Red Red
Row 6: Pink Pink Pink Pink Blue Blue Blue Red Red Red Red
Row 7: Pink Pink Pink Pink Red Red Gray Gray Gray Red Red
Row 8: Pink Pink Pink Pink Red Red Gray Gray Gray Red Red
Row 9: Pink Pink Pink Pink Red Red Gray Gray Gray Red Red
Row 10: Red Red Red Red Red Red Gray Gray Gray Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Black Black Black Red Red Red Red Red
Row 13: Red Red Red Black Black Black Red Red Red Red Red
Row 14: Red Red Red Black Black Black Red Red Red Red Red
Row 15: Red Red Red Black Black Black Red Red Red Red Red
Row 16: Red Red Red Black Black Black Red Red Red Red Red
Row 17: Red Red Red Black Black Black Yellow Yellow Yellow Red Red
Row 18: Red Red Red Red Red Red Yellow Yellow Yellow Red Red
Row 19: Red Red Red Red Red Red Yellow Yellow Yellow Red Red
Row 20: Orange Orange Orange Orange Orange Red Yellow Yellow Yellow Red Red
Row 21: Orange Orange Orange Orange Orange Red Yellow Yellow Yellow Red Red
Row 22: Orange Orange Orange Orange Orange Red Yellow Yellow Yellow Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Blue Blue Blue Red Red Red Red
Pink Pink Pink Pink Blue Purple Blue Red Red Red Red
Pink Purple Purple Pink Blue Blue Blue Red Red Red Red
Pink Purple Purple Pink Red Red Gray Gray Gray Red Red
Pink Purple Purple Pink Red Red Gray Purple Gray Red Red
Pink Pink Pink Pink Red Red Gray Purple Gray Red Red
Red Red Red Red Red Red Gray Gray Gray Red Red
Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Black Black Black Red Red Red Red Red
Red Red Red Black Purple Black Red Red Red Red Red
Red Red Red Black Purple Black Red Red Red Red Red
Red Red Red Black Purple Black Red Red Red Red Red
Red Red Red Black Purple Black Red Red Red Red Red
Red Red Red Black Black Black Yellow Yellow Yellow Red Red
Red Red Red Red Red Red Yellow Purple Yellow Red Red
Red Red Red Red Red Red Yellow Purple Yellow Red Red
Orange Orange Orange Orange Orange Red Yellow Purple Yellow Red Red
Orange Purple Purple Purple Orange Red Yellow Purple Yellow Red Red
Orange Orange Orange Orange Orange Red Yellow Yellow Yellow Red Red
Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Black Orange Yellow Brown Yellow Black Orange Yellow Brown Yellow Black Orange Yellow Brown
Row 2: Green Yellow Yellow Yellow Red Green Yellow Yellow Yellow Red Green Yellow Yellow Yellow Red
Row 3: Blue Yellow Orange Yellow Yellow Blue Yellow Orange Yellow Yellow Blue Yellow Orange Yellow Yellow
Row 4: Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow
Row 5: Blue Yellow Blue Blue Red Blue Yellow Blue Blue Red Blue Yellow Blue Blue Red
Row 6: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Green
Row 7: Black Yellow Blue Black Black Black Yellow Blue Black Black Black Yellow Blue Black Black
Row 8: Yellow Blue Blue Yellow Orange Yellow Blue Blue Yellow Orange Yellow Blue Blue Yellow Orange
Row 9: Black Brown Yellow Yellow Yellow Black Brown Yellow Yellow Yellow Black Brown Yellow Yellow Yellow
Row 10: Green Blue Red Yellow Red Green Blue Red Yellow Red Green Blue Red Yellow Red
Row 11: Yellow Orange Yellow Red Yellow Yellow Orange Yellow Red Yellow Yellow Orange Yellow Red Yellow
Row 12: Blue Blue Yellow Blue Yellow Blue Blue Yellow Blue Yellow Blue Blue Yellow Blue Yellow
Row 13: Yellow Yellow Green Yellow Black Yellow Yellow Green Yellow Black Yellow Yellow Green Yellow Black
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Brown Yellow Yellow Yellow Black Brown Yellow Yellow Yellow Black Brown Yellow Yellow Yellow Black
Row 16: Brown Red Yellow Yellow Blue Brown Red Yellow Yellow Blue Brown Red Yellow Yellow Blue
Row 17: Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow
Row 18: Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow
Row 19: Black Green Brown Yellow Yellow Black Green Brown Yellow Yellow Black Green Brown Yellow Yellow
Row 20: Yellow Yellow Yellow Black Brown Yellow Yellow Yellow Black Brown Yellow Yellow Yellow Black Brown
Row 21: Blue Yellow Green Red Yellow Blue Yellow Green Red Yellow Blue Yellow Green Red Yellow
Output:
Row 1: Yellow Black Orange Yellow Brown
Row 2: Green Yellow Yellow Yellow Red
Row 3: Blue Yellow Orange Yellow Yellow
Row 4: Yellow Blue Yellow Yellow Yellow
Row 5: Blue Yellow Blue Blue Red
Row 6: Yellow Yellow Yellow Yellow Green
Row 7: Black Yellow Blue Black Black
Row 8: Yellow Blue Blue Yellow Orange
Row 9: Black Brown Yellow Yellow Yellow
Row 10: Green Blue Red Yellow Red
Row 11: Yellow Orange Yellow Red Yellow
Row 12: Blue Blue Yellow Blue Yellow
Row 13: Yellow Yellow Green Yellow Black
Row 14: Yellow Yellow Yellow Yellow Yellow
Row 15: Brown Yellow Yellow Yellow Black
Row 16: Brown Red Yellow Yellow Blue
Row 17: Yellow Yellow Yellow Black Yellow
Row 18: Yellow Black Yellow Yellow Yellow
Row 19: Black Green Brown Yellow Yellow
Row 20: Yellow Yellow Yellow Black Brown
Row 21: Blue Yellow Green Red Yellow
Example 2
Input:
Row 1: Green Brown Brown Blue Blue Green Green Green Brown Brown Blue Blue Green Green Green Brown Brown Blue Blue Green Green
Row 2: Blue Blue Blue Blue Brown Brown Green Blue Blue Blue Blue Brown Brown Green Blue Blue Blue Blue Brown Brown Green
Row 3: Brown Blue Brown Brown Brown Blue Brown Brown Blue Brown Brown Brown Blue Brown Brown Blue Brown Brown Brown Blue Brown
Row 4: Brown Blue Green Brown Blue Blue Blue Brown Blue Green Brown Blue Blue Blue Brown Blue Green Brown Blue Blue Blue
Row 5: Brown Green Brown Blue Brown Green Blue Brown Green Brown Blue Brown Green Blue Brown Green Brown Blue Brown Green Blue
Output:
Row 1: Green Brown Brown Blue Blue Green Green
Row 2: Blue Blue Blue Blue Brown Brown Green
Row 3: Brown Blue Brown Brown Brown Blue Brown
Row 4: Brown Blue Green Brown Blue Blue Blue
Row 5: Brown Green Brown Blue Brown Green Blue
Example 3
Input:
Row 1: Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue
Row 2: Blue Blue Blue Orange Red Blue Blue Blue Blue Blue Blue Orange Red Blue Blue Blue Blue Blue Blue Orange Red Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue
Row 4: Blue Red Blue Orange Blue Blue Blue Blue Blue Red Blue Orange Blue Blue Blue Blue Blue Red Blue Orange Blue Blue Blue Blue
Row 5: Blue Blue Orange Blue Blue Red Blue Blue Blue Blue Orange Blue Blue Red Blue Blue Blue Blue Orange Blue Blue Red Blue Blue
Row 6: Red Blue Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Red Blue Blue
Row 7: Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Orange Blue Blue Blue Blue Blue Red Blue Orange Blue Blue Blue Blue Blue Red Blue Orange Blue Blue Blue Blue Blue Red
Row 12: Orange Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Red Blue Blue Blue Blue
Row 2: Blue Blue Blue Orange Red Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Red Blue
Row 4: Blue Red Blue Orange Blue Blue Blue Blue
Row 5: Blue Blue Orange Blue Blue Red Blue Blue
Row 6: Red Blue Blue Blue Blue Red Blue Blue
Row 7: Blue Blue Blue Blue Blue Red Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Red Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Orange Blue Blue Blue Blue Blue Red
Row 12: Orange Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Red
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Red Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Orange Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Gray Green Blue Black Green Blue Green Green Gray Green Blue Black Green Blue Green Green Gray Green Blue Black Green Blue Green Green
Row 2: Green Green Green Green Black Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green Black Green Green Green
Row 3: Gray Blue Orange Brown Gray Black Blue Black Gray Blue Orange Brown Gray Black Blue Black Gray Blue Orange Brown Gray Black Blue Black
Row 4: Green Green Red Green Green Green Green Green Green Green Red Green Green Green Green Green Green Green Red Green Green Green Green Green
Row 5: Blue Brown Green Green Green Green Orange Green Blue Brown Green Green Green Green Orange Green Blue Brown Green Green Green Green Orange Green
Row 6: Green Blue Green Green Yellow Red Green Brown Green Blue Green Green Yellow Red Green Brown Green Blue Green Green Yellow Red Green Brown
Row 7: Brown Green Green Green Green Green Green Red Brown Green Green Green Green Green Green Red Brown Green Green Green Green Green Green Red
Row 8: Black Green Green Green Green Green Black Green Black Green Green Green Green Green Black Green Black Green Green Green Green Green Black Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Green Blue Black Green Blue Green Green
Green Green Green Green Black Green Green Green
Gray Blue Orange Brown Gray Black Blue Black
Green Green Red Green Green Green Green Green
Blue Brown Green Green Green Green Orange Green
Green Blue Green Green Yellow Red Green Brown
Brown Green Green Green Green Green Green Red
Black Green Green Green Green Green Black Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Orange Green Red Green Green Green Green Red Green Green Green Green Red Green Orange Pink Green
Row 2: Green Pink Green Green Red Green Pink Orange Green Red Green Pink Green Orange Red Green Green Green Green
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Green Green Green Green Red Pink Orange Green Green Red Green Green Orange Green Red Green Pink Green Green
Row 5: Green Green Orange Pink Red Green Green Green Green Red Green Green Green Green Red Orange Green Green Green
Output:
Row 1: Green Green Green Green Red Green Green Green Green Red Orange Orange Orange Orange Red Green Green Green Green
Row 2: Green Green Green Green Red Green Green Green Green Red Orange Orange Orange Orange Red Green Green Green Green
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Green Green Green Green Red Green Green Green Green Red Green Green Green Green Red Green Green Green Green
Row 5: Green Green Green Green Red Green Green Green Green Red Green Green Green Green Red Green Green Green Green
Example 2
Input:
Row 1: Brown Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Brown Gray Gray Gray
Row 2: Gray Gray Gray Gray Orange Gray Gray Gray Green Orange Green Gray Gray Brown Orange Gray Green Gray Gray
Row 3: Green Gray Gray Gray Orange Gray Gray Gray Brown Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Gray Green Gray Gray Orange Gray Gray Gray Gray Orange Green Gray Gray Gray Orange Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Orange Gray Gray Brown Gray Orange Gray Gray Brown Gray Orange Gray Brown Gray Gray
Row 7: Gray Gray Gray Brown Orange Gray Green Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Green Gray
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Gray Gray Gray Orange Brown Green Gray Gray Orange Gray Gray Green Brown Orange Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Green Gray
Row 11: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Brown Gray Gray Gray
Output:
Row 1: Brown Brown Brown Brown Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 2: Brown Brown Brown Brown Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 3: Brown Brown Brown Brown Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray Gray Gray Gray
Example 3
Input:
Row 1: Pink Pink Black Pink Green Purple Pink Pink Red Black Pink Purple Red Pink Pink Pink Pink Purple Black Pink Pink Green Red Purple Red Pink Pink Pink Pink
Row 2: Pink Red Pink Pink Pink Purple Pink Pink Pink Pink Green Purple Pink Pink Green Pink Pink Purple Pink Pink Pink Pink Pink Purple Black Pink Green Pink Pink
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Pink Red Black Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Green Pink Pink Pink Purple Pink Black Pink Pink Pink Purple Red Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Green Purple Pink Red Green Pink Black Purple Pink Pink Black Red Pink Purple Pink Pink Green Pink Red Purple Pink Black Green Pink Pink
Output:
Row 1: Red Red Red Red Red Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 2: Red Red Red Red Red Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Green Green Green Green Green Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Green Green Green Green Green Purple Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Blue Pink Blue Blue Orange Blue Red Pink Blue Orange Blue Blue Purple Red Orange Blue Blue Pink Black
Row 2: Red Purple Blue Blue Orange Black Blue Gray Blue Orange Black Gray Blue Pink Orange Purple Gray Red Blue
Row 3: Blue Gray Blue Black Orange Blue Blue Purple Blue Orange Blue Blue Blue Blue Orange Blue Blue Blue Blue
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Blue Blue Blue Black Orange Pink Blue Blue Blue Orange Blue Blue Blue Red Orange Gray Blue Red Blue
Row 6: Blue Blue Gray Purple Orange Blue Blue Red Purple Orange Purple Blue Gray Pink Orange Blue Purple Blue Pink
Row 7: Red Blue Pink Blue Orange Black Blue Blue Gray Orange Blue Blue Black Blue Orange Blue Black Blue Blue
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Blue Blue Blue Pink Orange Blue Red Black Blue Orange Purple Blue Blue Blue Orange Blue Red Blue Purple
Row 10: Blue Gray Purple Blue Orange Blue Blue Purple Blue Orange Blue Pink Blue Black Orange Blue Pink Gray Blue
Row 11: Blue Red Black Blue Orange Blue Gray Blue Blue Orange Blue Red Blue Gray Orange Blue Blue Black Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Orange Red Red Red Red Orange Black Black Black Black Orange Blue Blue Blue Blue
Blue Blue Blue Blue Orange Red Red Red Red Orange Black Black Black Black Orange Blue Blue Blue Blue
Blue Blue Blue Blue Orange Red Red Red Red Orange Black Black Black Black Orange Blue Blue Blue Blue
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Blue Blue Blue Blue Orange Blue Blue Blue Blue Orange Purple Purple Purple Purple Orange Blue Blue Blue Blue
Blue Blue Blue Blue Orange Blue Blue Blue Blue Orange Purple Purple Purple Purple Orange Blue Blue Blue Blue
Blue Blue Blue Blue Orange Blue Blue Blue Blue Orange Purple Purple Purple Purple Orange Blue Blue Blue Blue
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Blue Blue Blue Blue Orange Gray Gray Gray Gray Orange Blue Blue Blue Blue Orange Blue Blue Blue Blue
Blue Blue Blue Blue Orange Gray Gray Gray Gray Orange Blue Blue Blue Blue Orange Blue Blue Blue Blue
Blue Blue Blue Blue Orange Gray Gray Gray Gray Orange Blue Blue Blue Blue Orange Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 3: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 4: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 5: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 6: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 7: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 8: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 9: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 10: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 11: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 12: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 13: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Gray Gray Gray Red Red Red Red Red
Row 16: Red Red Gray Gray Gray Yellow Yellow Yellow Yellow Red
Row 17: Red Red Gray Gray Gray Yellow Yellow Yellow Yellow Red
Row 18: Red Red Gray Gray Gray Yellow Yellow Yellow Yellow Red
Row 19: Red Red Red Red Red Yellow Yellow Yellow Yellow Red
Row 20: Red Red Red Red Red Yellow Yellow Yellow Yellow Red
Row 21: Red Red Red Red Red Yellow Yellow Yellow Yellow Red
Row 22: Red Red Red Red Red Yellow Yellow Yellow Yellow Red
Row 23: Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 3: Red Red Orange Red Red Red Red Red Orange Red
Row 4: Red Red Orange Red Red Red Red Red Orange Red
Row 5: Red Red Orange Red Red Red Red Red Orange Red
Row 6: Red Red Orange Red Red Red Red Red Orange Red
Row 7: Red Red Orange Red Red Red Red Red Orange Red
Row 8: Red Red Orange Orange Orange Orange Orange Orange Orange Red
Row 9: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 10: Red Blue Red Red Red Red Red Blue Red Red
Row 11: Red Blue Red Red Red Red Red Blue Red Red
Row 12: Red Blue Red Red Red Red Red Blue Red Red
Row 13: Red Blue Blue Blue Blue Blue Blue Blue Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Gray Gray Gray Red Red Red Red Red
Row 16: Red Red Gray Red Gray Yellow Yellow Yellow Yellow Red
Row 17: Red Red Gray Red Gray Yellow Red Red Yellow Red
Row 18: Red Red Gray Gray Gray Yellow Red Red Yellow Red
Row 19: Red Red Red Red Red Yellow Red Red Yellow Red
Row 20: Red Red Red Red Red Yellow Red Red Yellow Red
Row 21: Red Red Red Red Red Yellow Red Red Yellow Red
Row 22: Red Red Red Red Red Yellow Yellow Yellow Yellow Red
Row 23: Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Red Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Black Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Black Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 4: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 5: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 6: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 8: Green Green Green Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 9: Green Green Green Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 10: Green Green Green Green Green Brown Brown Brown Brown Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Brown Brown Brown Brown Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Gray Green Green Gray Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 4: Green Green Green Green Green Green Gray Green Green Gray Green Green Green Green Green Green Green Green Green Black Green Green Black Green Green Green
Row 5: Green Green Green Green Green Green Gray Green Green Gray Green Green Green Green Green Green Green Green Green Black Green Green Black Green Green Green
Row 6: Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Black Green Green Black Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green Black Green Green Green
Row 8: Green Green Green Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Black Green Green Black Green Green Green
Row 9: Green Green Green Green Green Brown Green Green Brown Green Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green
Row 10: Green Green Green Green Green Brown Green Green Brown Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Brown Brown Brown Brown Green Green Yellow Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Black Black Black Blue Blue
Row 4: Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Black Black Black Blue Blue
Row 5: Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Black Black Black Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Row 10: Yellow Yellow Yellow Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Row 11: Yellow Yellow Yellow Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Row 12: Yellow Yellow Yellow Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Red Red Red Red Red Blue Orange Orange Orange Orange Orange Orange Blue
Row 15: Blue Blue Blue Red Red Red Red Red Blue Orange Orange Orange Orange Orange Orange Blue
Row 16: Blue Blue Blue Red Red Red Red Red Blue Orange Orange Orange Orange Orange Orange Blue
Row 17: Blue Blue Blue Red Red Red Red Red Blue Orange Orange Orange Orange Orange Orange Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue
Row 29: Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue
Row 30: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Black Black Black Blue Blue
Blue Blue Blue Blue Gray Blue Gray Blue Blue Blue Blue Black Blue Black Blue Blue
Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Black Black Black Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Blue
Yellow Yellow Yellow Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Blue
Yellow Blue Yellow Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Blue
Yellow Yellow Yellow Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Blue
Blue Blue Blue Red Red Red Red Red Blue Orange Orange Orange Orange Orange Orange Blue
Blue Blue Blue Red Blue Blue Blue Red Blue Orange Blue Blue Blue Blue Orange Blue
Blue Blue Blue Red Blue Blue Blue Red Blue Orange Blue Blue Blue Blue Orange Blue
Blue Blue Blue Red Red Red Red Red Blue Orange Blue Blue Blue Blue Orange Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Orange Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue
Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue
Blue Blue Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue
Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Purple Blue Blue
Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Purple Blue Blue
Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Yellow Black Black
Row 2: Black Black Yellow Black
Row 3: Black Black Black Black
Row 4: Black Black Black Black
Row 5: Black Black Black Black
Row 6: Black Black Black Black
Output:
Row 1: Black Yellow Black Yellow
Row 2: Yellow Black Yellow Black
Row 3: Black Yellow Black Yellow
Row 4: Yellow Black Black Black
Row 5: Black Black Black Black
Row 6: Black Black Black Black
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Brown Brown Brown Purple Brown Brown Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Brown Purple Brown
Row 2: Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Brown Purple
Row 3: Brown Purple Purple Purple Purple Brown Brown Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Brown
Row 4: Purple Brown Purple Purple Purple Brown Brown Brown Brown Purple Brown Purple Purple Purple Purple Purple Brown Purple Brown Purple Brown Purple
Row 5: Brown Purple Brown Purple Brown Purple Purple Brown Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Purple Brown Purple Brown
Row 6: Brown Brown Purple Brown Purple Purple Purple Purple Brown Brown Brown Purple Brown Purple Brown Purple Brown Purple Brown Purple Brown Brown
Row 7: Brown Brown Brown Purple Brown Purple Purple Purple Purple Brown Brown Brown Purple Brown Purple Brown Purple Brown Purple Brown Brown Brown
Row 8: Purple Brown Brown Brown Purple Brown Purple Purple Purple Purple Brown Brown Brown Purple Brown Purple Brown Purple Brown Brown Brown Brown
Row 9: Brown Purple Brown Brown Brown Purple Brown Purple Purple Purple Purple Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Purple
Row 10: Purple Brown Purple Brown Brown Brown Purple Brown Purple Purple Brown Purple Brown Brown Brown Purple Brown Brown Brown Brown Purple Purple
Row 11: Brown Purple Brown Purple Brown Brown Brown Purple Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 12: Purple Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Purple Purple Brown
Row 13: Purple Purple Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Purple Brown Brown Purple
Row 14: Purple Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 15: Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Purple Brown
Row 16: Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Purple
Row 17: Purple Purple Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Purple Purple Brown Brown Brown
Row 18: Brown Purple Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Purple Purple Purple Brown Brown
Row 19: Purple Brown Purple Brown Purple Brown Purple Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown Purple Purple Purple Brown Brown
Row 20: Brown Purple Brown Purple Brown Purple Brown Brown Brown Brown Purple Brown Purple Brown Brown Brown Purple Brown Purple Brown Brown Purple
Row 21: Purple Brown Purple Brown Purple Brown Brown Brown Brown Purple Brown Purple Brown Purple Brown Brown Brown Purple Brown Brown Purple Purple
Row 22: Brown Purple Brown Purple Brown Brown Brown Brown Purple Purple Purple Brown Purple Brown Purple Brown Brown Brown Brown Brown Purple Purple
Row 23: Purple Brown Purple Brown Brown Brown Brown Purple Purple Purple Brown Purple Brown Purple Brown Purple Brown Brown Brown Purple Brown Purple
Row 24: Brown Purple Brown Brown Brown Brown Brown Purple Purple Brown Purple Purple Purple Brown Purple Brown Brown Brown Brown Brown Purple Brown
Row 25: Purple Brown Brown Brown Brown Purple Purple Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown Purple Brown Brown Brown Purple
Example 3
Input:
Row 1: Green Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Purple Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green
Row 22: Green Purple Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Purple Green Purple Green Green Purple Green Green Green Purple Green Green Green Green Green Green Purple Green Purple Green
Row 2: Green Purple Green Purple Green Green Purple Green Purple Green Purple Green Green Green Green Purple Green Purple Green Green
Row 3: Purple Green Purple Green Purple Green Green Purple Green Green Green Purple Green Green Purple Green Purple Green Green Green
Row 4: Green Green Green Purple Green Purple Purple Green Purple Green Green Green Purple Purple Green Purple Green Green Green Purple
Row 5: Green Green Green Green Purple Purple Purple Green Green Purple Green Green Purple Purple Purple Green Green Green Purple Green
Row 6: Purple Green Green Green Purple Purple Green Purple Green Green Purple Purple Green Purple Purple Green Green Purple Green Purple
Row 7: Green Purple Green Purple Green Green Purple Green Purple Green Purple Purple Purple Green Green Purple Purple Green Purple Purple
Row 8: Green Green Purple Green Green Green Green Purple Green Purple Green Purple Purple Green Green Purple Purple Purple Purple Purple
Row 9: Green Purple Green Purple Green Green Green Green Purple Green Purple Green Green Purple Purple Green Purple Purple Purple Purple
Row 10: Purple Green Green Green Purple Green Green Purple Green Purple Green Purple Green Purple Purple Purple Purple Purple Purple Green
Row 11: Green Purple Green Green Green Purple Purple Green Purple Green Purple Green Purple Green Purple Purple Purple Purple Green Purple
Row 12: Green Green Purple Green Green Purple Purple Purple Green Green Green Purple Green Purple Purple Purple Purple Green Purple Green
Row 13: Green Green Green Purple Purple Green Purple Purple Green Green Purple Green Purple Purple Purple Purple Green Purple Green Green
Row 14: Green Green Green Purple Purple Purple Green Green Purple Purple Green Purple Purple Purple Purple Purple Purple Green Purple Green
Row 15: Purple Green Purple Green Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple
Row 16: Green Purple Green Purple Green Green Purple Purple Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green
Row 17: Purple Green Purple Green Green Green Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Green Purple Purple
Row 18: Green Purple Green Purple Green Purple Green Purple Purple Purple Purple Green Purple Green Green Green Green Purple Purple Purple
Row 19: Purple Green Green Green Purple Green Purple Purple Purple Purple Green Purple Green Purple Green Green Green Purple Purple Green
Row 20: Green Purple Green Purple Green Purple Purple Purple Purple Green Purple Green Green Green Purple Green Purple Green Green Purple
Row 21: Purple Green Purple Green Purple Purple Purple Purple Green Purple Green Purple Green Green Green Purple Green Green Green Green
Row 22: Green Purple Green Purple Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Green Purple Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Orange Green Green Green Orange Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Orange Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Orange Green Green Green Green Orange Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Orange Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Orange Orange Green Green Orange Green Green Green Green Green Green
Row 17: Green Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Green Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Green Orange
Orange Orange Orange Green Orange Green Green Green Orange Orange Orange Orange Orange Orange Green Orange Orange
Orange Orange Orange Orange Green Orange Green Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange Orange Green Orange Orange Orange Green
Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange Green Orange
Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Orange
Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange
Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green
Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green
Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green
Green Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Orange Green Orange Orange Orange Orange Orange Orange Green Orange Orange Green Orange Orange Green Orange Orange
Green Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Green Orange Orange Green Orange
Orange Orange Orange Green Orange Orange Green Orange Orange Orange Green Orange Orange Green Orange Orange Green
Orange Orange Green Orange Orange Green Orange Green Orange Orange Orange Green Orange Orange Green Orange Orange
Orange Green Orange Orange Orange Orange Green Green Green Orange Orange Orange Green Orange Orange Green Orange
Green Orange Orange Green Orange Orange Green Green Green Green Orange Orange Orange Green Orange Orange Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black
Row 9: Green Green Green Black Black Black Black Black Black Black Black
Row 10: Green Green Green Black Black Black Black Black Black Black Black
Row 11: Purple Green Green Black Black Black Black Black Black Black Black
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Purple
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Purple
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Purple Green Green Purple
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 14: Green Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 15: Green Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 17: Green Green Green Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 18: Green Green Green Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 19: Purple Purple Purple Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 20: Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 21: Green Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Row 22: Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple Green Green Purple
Example 2
Input:
Row 1: Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black
Row 4: Black Black Black Green Green Green Green
Row 5: Black Black Black Green Green Green Green
Row 6: Black Black Black Green Green Orange Orange
Row 7: Black Black Black Green Green Orange Green
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Orange Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Green Green Green Orange Green Green Green Green Green Green Green Green Green
Row 7: Orange Green Green Green Orange Green Green Green Green Green Green Green Green Green
Row 8: Orange Green Green Green Orange Green Green Green Green Green Green Green Green Green
Row 9: Orange Green Green Green Orange Green Green Green Orange Orange Orange Orange Orange Orange
Row 10: Orange Green Green Green Orange Green Green Green Orange Green Green Green Green Green
Row 11: Orange Green Green Green Orange Green Green Green Orange Green Green Green Green Green
Row 12: Orange Green Green Green Orange Green Green Green Orange Green Green Green Green Green
Row 13: Orange Green Green Green Orange Green Green Green Orange Green Green Green Orange Orange
Row 14: Orange Green Green Green Orange Green Green Green Orange Green Green Green Orange Green
Example 3
Input:
Row 1: Black Black Black Black Black Black
Row 2: Black Brown Brown Brown Brown Brown
Row 3: Black Brown Brown Brown Brown Brown
Row 4: Black Brown Brown Green Green Green
Row 5: Black Brown Brown Green Green Green
Row 6: Black Brown Brown Green Green Yellow
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Green Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Green Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Green Yellow Brown Brown Green Green Green Green Green Green Green Green
Row 6: Green Yellow Brown Brown Green Green Green Green Green Green Green Green
Row 7: Green Yellow Brown Brown Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Green Yellow Brown Brown Green Green Yellow Brown Brown Brown Brown Brown
Row 9: Green Yellow Brown Brown Green Green Yellow Brown Brown Brown Brown Brown
Row 10: Green Yellow Brown Brown Green Green Yellow Brown Brown Green Green Green
Row 11: Green Yellow Brown Brown Green Green Yellow Brown Brown Green Green Green
Row 12: Green Yellow Brown Brown Green Green Yellow Brown Brown Green Green Yellow
Here is the input grid for the test example:
Input:
Row 1: Pink Pink
Row 2: Pink Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink
Pink Yellow Yellow Yellow
Pink Yellow Pink Pink
Pink Yellow Pink Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Blue
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Gray
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Yellow Yellow
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Yellow
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 27: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Row 28: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Blue Blue
Example 3
Input:
Row 1: Pink Brown Pink Pink Pink
Row 2: Pink Brown Pink Pink Pink
Row 3: Pink Brown Pink Pink Pink
Row 4: Pink Brown Pink Pink Pink
Row 5: Pink Brown Pink Pink Pink
Row 6: Pink Brown Pink Pink Pink
Row 7: Pink Brown Pink Pink Pink
Row 8: Pink Brown Pink Pink Pink
Row 9: Pink Brown Pink Pink Pink
Row 10: Pink Brown Pink Pink Pink
Row 11: Pink Brown Pink Pink Pink
Row 12: Pink Brown Pink Pink Pink
Row 13: Pink Brown Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink
Output:
Row 1: Blue Brown Green Green Green
Row 2: Blue Brown Green Green Green
Row 3: Blue Brown Green Green Green
Row 4: Blue Brown Green Green Green
Row 5: Blue Brown Green Green Green
Row 6: Blue Brown Green Green Green
Row 7: Blue Brown Green Green Green
Row 8: Blue Brown Green Green Green
Row 9: Blue Brown Green Green Green
Row 10: Blue Brown Green Green Green
Row 11: Blue Brown Green Green Green
Row 12: Blue Brown Green Green Green
Row 13: Pink Brown Green Green Green
Row 14: Pink Pink Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Blue Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Blue Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Blue Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Blue Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Blue Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Purple Yellow Red Orange
Row 2: Yellow Yellow Yellow Yellow Red Purple Red Red Red Red Red Red
Row 3: Red Red Yellow Red Purple Red Red Red Red Red Yellow Red
Row 4: Red Red Red Red Orange Red Red Red Red Yellow Red Red
Row 5: Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Purple Purple Red Red
Row 7: Red Yellow Red Purple Red Yellow Yellow Red Red Red Red Red
Row 8: Orange Red Red Red Yellow Red Purple Red Red Red Red Red
Row 9: Purple Red Red Red Red Red Purple Red Yellow Red Red Red
Row 10: Red Red Purple Red Yellow Yellow Red Red Purple Red Red Yellow
Row 11: Red Red Red Yellow Red Purple Red Red Red Red Red Yellow
Row 12: Red Yellow Red Red Red Red Red Red Yellow Red Red Yellow
Output:
Row 1: Red Red Red Red Red Red Red Red Purple Yellow Red Orange
Row 2: Yellow Yellow Yellow Yellow Red Purple Red Red Red Red Red Red
Row 3: Red Red Yellow Red Purple Red Red Red Red Red Yellow Red
Row 4: Red Red Red Red Orange Red Red Red Red Yellow Red Red
Row 5: Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Purple Purple Red Red
Row 7: Red Yellow Red Purple Red Yellow Yellow Red Red Red Red Red
Row 8: Orange Red Red Red Yellow Red Purple Red Red Red Red Red
Row 9: Purple Red Red Red Red Red Purple Red Yellow Red Red Red
Row 10: Red Red Purple Red Yellow Yellow Red Red Purple Red Red Yellow
Row 11: Red Red Red Yellow Red Purple Red Red Red Red Red Yellow
Row 12: Red Yellow Red Red Red Red Red Red Yellow Red Red Yellow
Row 13: Red Yellow Red Red Red Red Red Red Yellow Red Red Yellow
Row 14: Red Red Red Yellow Red Purple Red Red Red Red Red Yellow
Row 15: Red Red Purple Red Yellow Yellow Red Red Purple Red Red Yellow
Row 16: Purple Red Red Red Red Red Purple Red Yellow Red Red Red
Row 17: Orange Red Red Red Yellow Red Purple Red Red Red Red Red
Row 18: Red Yellow Red Purple Red Yellow Yellow Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Purple Purple Red Red
Row 20: Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 21: Red Red Red Red Orange Red Red Red Red Yellow Red Red
Row 22: Red Red Yellow Red Purple Red Red Red Red Red Yellow Red
Row 23: Yellow Yellow Yellow Yellow Red Purple Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Purple Yellow Red Orange
Example 2
Input:
Row 1: Green Green Purple Green Purple Purple Green Purple Green Purple Purple Green Purple Purple Green Purple Purple Purple Green Purple Green Purple Purple Green Green Green Green Purple
Row 2: Purple Green Purple Green Purple Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Purple Green Purple Green Green Purple Green Purple Green
Row 3: Purple Green Green Purple Green Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green Purple Green Green Purple Purple Green Green Purple Purple Green Green
Row 4: Purple Purple Purple Green Purple Green Purple Green Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Green Green
Row 5: Purple Green Purple Purple Green Green Purple Green Green Green Purple Purple Green Green Purple Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green Green
Row 6: Purple Green Green Purple Green Green Green Green Green Green Purple Green Purple Green Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Green Purple Purple
Row 7: Purple Green Green Purple Purple Purple Green Green Green Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple Purple
Row 8: Purple Purple Purple Purple Purple Green Green Purple Green Purple Purple Purple Green Purple Green Purple Purple Purple Green Purple Purple Green Green Green Green Green Purple Green
Row 9: Purple Purple Purple Purple Green Green Green Purple Green Green Green Green Purple Purple Purple Green Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Green Green Green Green Purple Green Purple Purple Green Purple Purple Green Purple
Row 11: Green Purple Purple Green Green Green Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Green Purple Purple Purple Green Purple Green Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Purple Green Green
Row 13: Purple Purple Purple Green Purple Green Purple Green Purple Purple Purple Green Purple Purple Green Purple Green Purple Purple Purple Green Green Purple Purple Purple Green Purple Purple
Row 14: Purple Green Green Purple Green Green Purple Purple Purple Purple Green Green Purple Purple Green Purple Green Green Purple Green Green Purple Green Purple Green Purple Green Purple
Row 15: Green Green Purple Purple Purple Green Green Purple Green Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Green
Output:
Row 1: Green Green Purple Green Purple Purple Green Purple Green Purple Purple Green Purple Purple Green Purple Purple Purple Green Purple Green Purple Purple Green Green Green Green Purple
Row 2: Purple Green Purple Green Purple Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Purple Green Purple Green Green Purple Green Purple Green
Row 3: Purple Green Green Purple Green Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green Purple Green Green Purple Purple Green Green Purple Purple Green Green
Row 4: Purple Purple Purple Green Purple Green Purple Green Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Green Green
Row 5: Purple Green Purple Purple Green Green Purple Green Green Green Purple Purple Green Green Purple Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green Green
Row 6: Purple Green Green Purple Green Green Green Green Green Green Purple Green Purple Green Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Green Purple Purple
Row 7: Purple Green Green Purple Purple Purple Green Green Green Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple Purple
Row 8: Purple Purple Purple Purple Purple Green Green Purple Green Purple Purple Purple Green Purple Green Purple Purple Purple Green Purple Purple Green Green Green Green Green Purple Green
Row 9: Purple Purple Purple Purple Green Green Green Purple Green Green Green Green Purple Purple Purple Green Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Green Green Green Green Purple Green Purple Purple Green Purple Purple Green Purple
Row 11: Green Purple Purple Green Green Green Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Green Purple Purple Purple Green Purple Green Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Purple Green Green
Row 13: Purple Purple Purple Green Purple Green Purple Green Purple Purple Purple Green Purple Purple Green Purple Green Purple Purple Purple Green Green Purple Purple Purple Green Purple Purple
Row 14: Purple Green Green Purple Green Green Purple Purple Purple Purple Green Green Purple Purple Green Purple Green Green Purple Green Green Purple Green Purple Green Purple Green Purple
Row 15: Green Green Purple Purple Purple Green Green Purple Green Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Green
Row 16: Green Green Purple Purple Purple Green Green Purple Green Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Green
Row 17: Purple Green Green Purple Green Green Purple Purple Purple Purple Green Green Purple Purple Green Purple Green Green Purple Green Green Purple Green Purple Green Purple Green Purple
Row 18: Purple Purple Purple Green Purple Green Purple Green Purple Purple Purple Green Purple Purple Green Purple Green Purple Purple Purple Green Green Purple Purple Purple Green Purple Purple
Row 19: Purple Purple Purple Green Purple Purple Purple Green Purple Green Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Purple Green Green
Row 20: Green Purple Purple Green Green Green Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Purple Green Purple Green Green Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Green Green Green Green Purple Green Purple Purple Green Purple Purple Green Purple
Row 22: Purple Purple Purple Purple Green Green Green Purple Green Green Green Green Purple Purple Purple Green Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Purple
Row 23: Purple Purple Purple Purple Purple Green Green Purple Green Purple Purple Purple Green Purple Green Purple Purple Purple Green Purple Purple Green Green Green Green Green Purple Green
Row 24: Purple Green Green Purple Purple Purple Green Green Green Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple Purple
Row 25: Purple Green Green Purple Green Green Green Green Green Green Purple Green Purple Green Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Green Purple Purple
Row 26: Purple Green Purple Purple Green Green Purple Green Green Green Purple Purple Green Green Purple Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green Green
Row 27: Purple Purple Purple Green Purple Green Purple Green Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Green Green
Row 28: Purple Green Green Purple Green Green Purple Purple Purple Purple Green Purple Purple Green Purple Green Green Purple Green Green Purple Purple Green Green Purple Purple Green Green
Row 29: Purple Green Purple Green Purple Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Purple Green Purple Green Green Purple Green Purple Green
Row 30: Green Green Purple Green Purple Purple Green Purple Green Purple Purple Green Purple Purple Green Purple Purple Purple Green Purple Green Purple Purple Green Green Green Green Purple
Example 3
Input:
Row 1: Black Blue Gray Red Black
Row 2: Yellow Black Black Black Black
Row 3: Yellow Black Red Orange Green
Row 4: Black Purple Black Purple Brown
Row 5: Black Black Orange Black Black
Row 6: Pink Black Black Blue Orange
Row 7: Orange Black Black Black Black
Row 8: Black Black Black Purple Pink
Row 9: Black Red Black Gray Red
Row 10: Yellow Pink Gray Black Black
Row 11: Green Black Green Black Red
Output:
Row 1: Black Blue Gray Red Black
Row 2: Yellow Black Black Black Black
Row 3: Yellow Black Red Orange Green
Row 4: Black Purple Black Purple Brown
Row 5: Black Black Orange Black Black
Row 6: Pink Black Black Blue Orange
Row 7: Orange Black Black Black Black
Row 8: Black Black Black Purple Pink
Row 9: Black Red Black Gray Red
Row 10: Yellow Pink Gray Black Black
Row 11: Green Black Green Black Red
Row 12: Green Black Green Black Red
Row 13: Yellow Pink Gray Black Black
Row 14: Black Red Black Gray Red
Row 15: Black Black Black Purple Pink
Row 16: Orange Black Black Black Black
Row 17: Pink Black Black Blue Orange
Row 18: Black Black Orange Black Black
Row 19: Black Purple Black Purple Brown
Row 20: Yellow Black Red Orange Green
Row 21: Yellow Black Black Black Black
Row 22: Black Blue Gray Red Black
Here is the input grid for the test example:
Input:
Row 1: Brown Purple Purple Brown Purple Yellow Purple Purple Purple Purple Purple Orange Blue Blue Purple Gray Brown Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Purple Purple Brown Purple Yellow Purple Purple Purple Purple Purple Orange Blue Blue Purple Gray Brown Purple
Brown Purple Purple Brown Purple Yellow Purple Purple Purple Purple Purple Orange Blue Blue Purple Gray Brown Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray
Example 2
Input:
Row 1: Red Yellow Red Red Orange Red Red Red Red Yellow Red Red Yellow Red Yellow Yellow Red Orange Red Yellow Red Orange Red Orange Yellow Red Orange Red
Row 2: Red Red Red Red Orange Red Red Red Red Red Red Yellow Yellow Red Red Yellow Red Red Red Red Red Red Red Red Red Red Yellow Orange
Row 3: Orange Yellow Red Yellow Red Red Orange Red Red Red Red Red Yellow Yellow Red Red Red Red Yellow Red Red Red Red Red Red Yellow Yellow Orange
Row 4: Yellow Red Yellow Red Red Red Yellow Red Red Yellow Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Yellow Red Red
Row 5: Red Yellow Red Orange Red Red Red Red Red Orange Red Yellow Orange Red Orange Red Orange Yellow Red Red Red Red Yellow Yellow Red Red Yellow Red
Row 6: Red Yellow Red Red Red Orange Red Red Red Red Red Yellow Yellow Orange Red Red Orange Red Red Red Red Orange Red Red Red Red Yellow Orange
Row 7: Yellow Yellow Red Red Red Red Red Red Yellow Orange Yellow Yellow Red Red Red Yellow Red Red Red Red Yellow Red Red Yellow Red Yellow Red Red
Row 8: Red Red Yellow Yellow Yellow Red Orange Yellow Yellow Orange Red Red Yellow Yellow Yellow Red Red Red Red Yellow Red Yellow Yellow Red Yellow Red Red Orange
Row 9: Red Red Yellow Red Red Red Red Red Yellow Red Orange Red Red Red Red Yellow Red Red Orange Red Red Yellow Yellow Red Red Orange Yellow Orange
Row 10: Red Yellow Orange Yellow Orange Red Red Red Red Red Red Yellow Yellow Red Yellow Red Red Red Yellow Orange Yellow Orange Yellow Orange Yellow Red Red Orange
Row 11: Yellow Orange Yellow Red Orange Yellow Red Red Yellow Yellow Red Yellow Red Yellow Red Red Yellow Orange Red Yellow Red Red Red Yellow Red Red Red Red
Row 12: Yellow Red Red Yellow Yellow Red Red Yellow Yellow Red Red Red Red Red Red Yellow Red Red Red Orange Red Red Red Red Yellow Red Red Red
Row 13: Red Red Red Red Yellow Red Yellow Orange Red Red Red Red Red Red Red Red Yellow Red Red Red Red Yellow Red Red Red Red Yellow Red
Row 14: Red Yellow Red Red Yellow Red Orange Yellow Red Red Red Yellow Red Yellow Red Red Yellow Red Yellow Red Orange Orange Red Red Red Red Red Red
Row 15: Red Red Orange Yellow Yellow Yellow Red Red Yellow Yellow Red Red Red Yellow Yellow Red Red Red Yellow Orange Red Red Yellow Yellow Red Red Orange Red
Row 16: Red Red Yellow Red Red Red Yellow Orange Red Red Yellow Yellow Yellow Red Red Red Orange Yellow Red Red Red Red Red Red Red Yellow Red Orange
Row 17: Yellow Yellow Orange Red Red Yellow Red Yellow Yellow Orange Yellow Yellow Red Red Red Orange Red Red Red Red Red Red Red Orange Red Red Yellow Red
Row 18: Yellow Red Red Orange Red Red Red Red Yellow Red Yellow Red Orange Yellow Yellow Red Yellow Red Red Red Red Yellow Red Yellow Red Yellow Orange Yellow
Row 19: Red Orange Red Red Orange Red Red Red Yellow Orange Orange Red Red Red Yellow Red Orange Orange Red Red Yellow Red Orange Yellow Red Red Red Red
Row 20: Red Red Red Orange Red Yellow Yellow Red Red Red Red Red Red Red Red Yellow Red Red Red Yellow Yellow Red Red Red Red Red Red Yellow
Row 21: Yellow Red Red Red Red Red Red Red Red Red Red Yellow Red Yellow Orange Yellow Red Red Red Red Red Yellow Yellow Yellow Red Red Red Red
Row 22: Red Red Yellow Orange Red Red Red Red Red Red Yellow Yellow Red Red Red Red Red Red Red Red Yellow Red Yellow Yellow Red Red Red Yellow
Row 23: Yellow Red Orange Yellow Orange Orange Yellow Red Yellow Red Yellow Red Orange Yellow Red Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Yellow
Row 24: Red Red Red Red Yellow Red Yellow Yellow Red Yellow Red Red Red Red Yellow Red Red Red Red Red Red Yellow Red Yellow Yellow Yellow Yellow Red
Row 25: Red Yellow Red Red Yellow Red Red Yellow Orange Yellow Red Yellow Yellow Red Red Orange Red Red Yellow Red Yellow Orange Red Red Red Red Yellow Red
Row 26: Yellow Red Yellow Red Red Orange Yellow Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Red Yellow Red
Row 27: Red Red Red Red Yellow Red Red Red Red Red Yellow Red Yellow Red Yellow Red Red Red Yellow Yellow Orange Red Yellow Red Red Red Red Orange
Row 28: Red Red Red Yellow Red Red Yellow Red Red Red Red Yellow Red Red Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Red Yellow Red
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Green Pink Green Pink Pink Green Pink Green Green Green Green Green Green
Row 2: Green Green Pink Pink Green Green Pink Green Pink Green Pink Pink Green
Row 3: Pink Pink Pink Green Pink Pink Green Green Pink Green Green Green Pink
Row 4: Green Green Pink Pink Pink Green Pink Green Green Green Green Green Pink
Row 5: Pink Green Green Pink Pink Green Green Pink Pink Green Green Green Green
Row 6: Green Green Green Green Green Pink Green Green Green Green Pink Green Green
Row 7: Pink Green Green Pink Green Pink Pink Green Green Green Pink Pink Pink
Row 8: Pink Pink Pink Green Green Pink Green Green Green Pink Green Pink Pink
Row 9: Green Pink Green Green Pink Green Green Green Pink Pink Green Pink Green
Row 10: Pink Green Pink Pink Green Green Pink Pink Pink Green Pink Green Pink
Row 11: Pink Pink Green Pink Pink Pink Orange Green Orange Green Green Pink Green
Row 12: Green Pink Pink Green Pink Pink Pink Orange Pink Orange Orange Green Green
Row 13: Green Green Pink Green Green Pink Green Green Green Pink Pink Green Pink
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Gray
Row 2: Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 3: Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 4: Black Black Black Black Black Black Black Black Black Gray Black Black Black
Row 5: Black Black Black Black Black Black Black Black Gray Black Black Black Black
Row 6: Black Black Black Black Black Black Black Gray Black Black Black Black Black
Row 7: Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 8: Black Black Black Black Black Gray Black Black Black Black Black Black Black
Row 9: Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 10: Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 11: Black Black Gray Black Black Black Black Black Black Black Black Black Black
Row 12: Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 13: Gray Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Green Black Black Green Black Green Green Green Green Green Black Black Green Green Green Black Black Black Black Black Black
Row 2: Green Black Green Black Green Green Green Black Green Green Green Black Green Green Black Green Black Black Green Green Green
Row 3: Black Black Green Black Green Black Black Black Black Black Green Black Black Green Green Black Green Green Green Black Green
Row 4: Black Green Green Green Green Green Green Black Green Black Black Green Black Black Green Green Black Black Black Black Black
Row 5: Green Black Black Green Black Green Black Green Green Black Black Black Black Green Green Black Green Green Black Green Black
Row 6: Black Green Green Black Black Black Black Black Black Green Green Green Green Green Black Green Green Black Green Green Black
Row 7: Black Green Black Green Green Green Green Green Black Black Green Green Green Black Black Black Black Black Green Black Black
Row 8: Black Green Green Green Black Green Green Green Black Black Green Green Black Green Green Green Black Black Black Black Green
Row 9: Black Black Green Green Black Green Black Black Green Black Black Green Black Black Green Green Green Black Green Black Green
Row 10: Green Black Black Black Black Black Black Green Green Black Green Black Black Black Green Black Green Black Green Black Green
Row 11: Green Black Black Black Black Black Green Green Green Black Black Green Black Green Green Green Black Green Green Black Green
Row 12: Black Black Green Green Green Green Black Black Green Black Black Green Green Black Green Green Green Green Black Green Black
Row 13: Black Black Black Green Black Green Black Black Green Green Black Black Green Green Black Black Black Green Green Black Black
Row 14: Black Black Green Green Black Green Black Green Black Green Black Green Green Green Green Green Black Green Green Green Black
Row 15: Black Black Black Black Green Black Green Black Green Green Green Green Black Black Black Black Green Green Green Black Green
Row 16: Black Green Black Black Black Black Black Green Green Green Black Black Green Green Green Green Green Black Black Green Black
Row 17: Black Black Black Black Black Green Black Black Green Green Black Black Green Black Green Black Green Green Black Black Green
Row 18: Green Green Black Green Green Green Black Green Black Black Green Green Black Green Black Green Black Black Green Green Green
Row 19: Black Black Green Black Green Black Black Green Black Green Green Green Green Black Green Green Black Green Black Green Black
Row 20: Black Green Green Black Green Black Black Green Green Black Green Black Black Black Green Black Black Black Green Black Green
Row 21: Black Green Black Green Black Black Black Black Green Green Green Black Black Black Green Green Black Black Green Green Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Blue Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Blue Orange Blue Orange Orange Orange Orange Orange Blue Orange Blue Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Blue Orange Orange Orange Brown Orange Brown Orange Orange Orange Blue Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Blue Orange Orange Orange Brown Orange Brown Orange Orange Orange Blue Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Blue Orange Blue Orange Orange Orange Orange Orange Blue Orange Blue Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Blue Orange Blue Orange Blue Orange Blue Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Pink Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Black Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Pink Blue Black Blue Black Blue Black Blue Black Blue Black Blue Pink Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Black Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Black Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Black Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Black Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Pink Blue Black Blue Black Blue Black Blue Black Blue Black Blue Pink Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Orange Black Brown Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Brown Black Blue Black Gray Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Gray Black Gray Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Orange Black Brown Black Brown Black Brown Black Brown Black Orange Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Brown Black Blue Black Gray Black Gray Black Blue Black Brown Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Brown Black Gray Black Gray Black Gray Black Gray Black Brown Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Brown Black Gray Black Black Black Black Black Gray Black Brown Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Brown Black Gray Black Gray Black Gray Black Gray Black Brown Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Brown Black Blue Black Gray Black Gray Black Blue Black Brown Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Orange Black Brown Black Brown Black Brown Black Brown Black Orange Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Gray Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Brown Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Brown Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Brown Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Gray Purple Gray Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Yellow Purple Gray Purple Pink Purple Pink Purple Gray Purple Yellow Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Yellow Purple Gray Purple Pink Purple Pink Purple Gray Purple Yellow Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Gray Purple Gray Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Brown Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Brown Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow
Row 6: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow
Row 2: Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Purple
Row 3: Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Yellow
Row 4: Yellow Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 5: Yellow Yellow Yellow Purple Yellow Purple Yellow Purple Purple
Row 6: Yellow Yellow Purple Yellow Purple Yellow Purple Purple Purple
Row 7: Yellow Purple Yellow Purple Yellow Purple Purple Yellow Yellow
Row 8: Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple
Row 9: Purple Purple Yellow Purple Purple Yellow Yellow Purple Purple
Row 10: Purple Purple Purple Purple Yellow Yellow Purple Purple Purple
Row 11: Yellow Purple Purple Purple Yellow Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 13: Purple Yellow Yellow Purple Purple Purple Purple Yellow Yellow
Row 14: Purple Purple Purple Purple Purple Purple Purple Yellow Yellow
Row 15: Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 16: Purple Purple Purple Purple Yellow Yellow Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Yellow Yellow Purple Purple
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 5: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue
Row 10: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Black Blue Black Black Blue Blue Blue Blue Black Blue Blue Black Black Black Black Blue Blue Blue Black
Row 2: Black Blue Blue Black Black Black Blue Blue Black Blue Black Blue Black Black Black Black Blue Blue Black Black
Row 3: Blue Black Black Blue Blue Black Black Black Blue Blue Blue Black Black Black Black Black Black Black Black Blue
Row 4: Black Black Black Blue Blue Blue Black Black Blue Blue Black Black Black Blue Blue Black Black Black Blue Black
Row 5: Black Black Blue Black Blue Black Blue Black Black Black Black Black Blue Black Blue Black Black Black Black Blue
Row 6: Blue Black Black Blue Black Blue Blue Blue Black Black Black Blue Blue Blue Black Black Blue Black Black Black
Row 7: Blue Blue Black Black Blue Black Blue Black Black Black Black Blue Blue Black Black Black Black Blue Black Black
Row 8: Blue Blue Black Black Black Blue Black Black Black Blue Black Black Black Black Blue Black Black Blue Blue Black
Row 9: Blue Black Blue Blue Black Black Black Black Blue Blue Blue Black Black Blue Black Blue Blue Black Blue Blue
Row 10: Black Blue Blue Blue Black Black Black Blue Black Blue Black Black Black Black Blue Blue Blue Blue Black Blue
Row 11: Blue Black Blue Black Black Black Black Black Blue Black Black Blue Black Black Black Blue Blue Blue Blue Black
Row 12: Blue Blue Black Black Black Blue Blue Black Black Black Black Black Blue Blue Black Black Blue Blue Blue Blue
Example 3
Input:
Row 1: Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Yellow Yellow Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Row 2: Yellow Yellow Blue Yellow Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Blue
Row 3: Yellow Yellow Yellow Blue Yellow Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue
Row 4: Blue Yellow Yellow Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green
Row 16: Black Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Black Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Black Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Black
Green Green Green Green Green Green Green Black Green
Green Green Green Green Green Green Black Green Green
Green Green Green Green Green Black Green Green Green
Green Green Green Green Black Green Green Green Green
Black Green Green Black Green Green Green Green Black
Green Black Black Green Green Green Green Black Green
Green Black Black Green Green Green Black Green Green
Black Green Green Black Green Black Green Green Green
Black Black Green Green Black Green Green Green Green
Green Black Black Black Green Black Green Green Green
Green Green Black Black Green Green Black Green Black
Green Black Green Black Black Green Green Black Green
Black Green Green Green Black Black Black Green Black
Green Green Green Green Green Black Black Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Orange
Row 2: Red Red Red Red Red Red Red Red Red Red Red Orange
Row 3: Red Red Red Red Red Red Red Red Green Orange Orange Orange
Row 4: Red Red Red Red Red Red Red Red Red Red Red Orange
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Orange
Row 2: Red Red Red Red Red Red Red Red Red Red Red Orange
Row 3: Red Red Red Red Red Red Red Red Red Orange Orange Green
Row 4: Red Red Red Red Red Red Red Red Red Red Red Orange
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 8: Orange Orange Orange Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 11: Orange Orange Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 23: Orange Orange Orange Orange Orange Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 25: Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 8: Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 11: Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Black
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 23: Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 25: Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Brown Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Brown Red Brown Red
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Blue Blue Blue Blue Blue Blue
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 14: Yellow Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 20: Yellow Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 23: Yellow Yellow Yellow Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Brown
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Green Green Green
Row 2: Green Black Brown Black
Row 3: Brown Purple Black Gray
Output:
Row 1: Black Green Green Green
Row 2: Yellow Black Brown Black
Row 3: Yellow Yellow Black Gray
Example 2
Input:
Row 1: Brown Red Orange Orange Brown Orange Blue Orange Brown Orange Orange Purple Brown Black Green Orange Brown Green Orange Red Brown Orange Orange Blue Brown
Row 2: Green Brown Blue Brown Black Brown Orange Brown Red Brown Orange Brown Orange Brown Orange Brown Orange Brown Orange Brown Green Brown Orange Brown Purple
Row 3: Orange Orange Brown Blue Green Orange Brown Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Red Brown Red Black Green Brown Orange Orange
Output:
Row 1: Brown Red Orange Orange Brown Yellow Yellow Yellow Brown Orange Orange Purple Brown Black Green Orange Brown Yellow Yellow Yellow Brown Orange Orange Blue Brown
Row 2: Yellow Brown Blue Brown Black Brown Yellow Brown Red Brown Orange Brown Yellow Brown Orange Brown Orange Brown Yellow Brown Green Brown Orange Brown Yellow
Row 3: Yellow Yellow Brown Blue Green Orange Brown Orange Orange Orange Brown Yellow Yellow Yellow Brown Orange Orange Red Brown Red Black Green Brown Yellow Yellow
Example 3
Input:
Row 1: Orange Purple Green Green Orange Pink Gray Purple Orange Brown Purple Green Orange Gray Gray Gray Orange
Row 2: Black Orange Brown Orange Green Orange Green Orange Purple Orange Brown Orange Purple Orange Purple Orange Blue
Row 3: Purple Brown Orange Brown Black Purple Orange Blue Black Brown Orange Green Black Purple Orange Gray Pink
Output:
Row 1: Orange Purple Green Green Orange Yellow Yellow Yellow Orange Brown Purple Green Orange Gray Gray Gray Orange
Row 2: Yellow Orange Brown Orange Green Orange Yellow Orange Purple Orange Brown Orange Yellow Orange Purple Orange Blue
Row 3: Yellow Yellow Orange Brown Black Purple Orange Blue Black Brown Orange Yellow Yellow Yellow Orange Gray Pink
Here is the input grid for the test example:
Input:
Row 1: Red Gray Gray Gray Brown Gray Gray
Row 2: Green Red Gray Gray Orange Gray Gray
Row 3: Gray Gray Red Orange Blue Gray Red
Row 4: Blue Gray Blue Red Black Red Gray
Row 5: Green Black Gray Gray Red Gray Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Gray Gray Gray Brown Gray Gray
Yellow Red Gray Gray Orange Gray Gray
Yellow Yellow Red Orange Blue Gray Red
Yellow Yellow Yellow Red Black Red Gray
Yellow Yellow Yellow Yellow Red Gray Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Yellow Gray Green Green Green Green Green Black Green
Row 2: Green Green Purple Green Green Green Green Green Green Green Purple Purple Green Brown Green Green Green Green
Row 3: Green Green Orange Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Green Green Green Green
Row 5: Brown Green Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green
Row 6: Green Green Green Green Green Green Black Green Green Green Green Green Blue Green Green Orange Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green
Row 8: Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Gray Green Red Green
Row 9: Purple Green Green Green Green Green Green Green Green Brown Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Black Green Green
Row 11: Green Green Green Green Green Yellow Green Green Green Green Green Green Green Yellow Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Red Green Gray Green Green Green
Output:
Row 1: Blue Blue Blue
Row 2: Green Blue Blue
Row 3: Green Blue Green
Example 2
Input:
Row 1: Red Red Brown Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Black Red Red Red
Row 3: Red Red Gray Red Red Red Red Red Red Red Green Red Red Orange Red Brown Red Red Red Red Red Red Red Gray
Row 4: Red Red Red Red Red Orange Red Black Red Red Red Red Red Green Red Red Brown Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Red Green Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Brown Orange Red Green Red
Row 8: Red Red Red Red Red Red Brown Red Green Red Red Red Red Red Red Red Red Red Red Red Red Black Red Green
Row 9: Red Red Red Red Brown Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Pink Red Red Red
Row 10: Red Black Red Red Brown Red Red Red Red Red Red Red Red Brown Red Red Red Red Pink Pink Pink Red Red Red
Row 11: Red Red Red Red Brown Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Gray Red Red Red
Row 12: Gray Red Red Red Red Red Red Red Red Red Red Brown Red Red Brown Red Red Red Red Red Red Red Red Orange
Row 13: Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Gray Brown Red Red Red Gray Red Red
Row 14: Red Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Brown Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 16: Red Red Red Green Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Orange Red Red
Row 17: Red Red Brown Gray Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Orange Red Red Black Black
Row 18: Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red Green Red Brown Red Red
Row 19: Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Gray Red Red Red Green Red Red Red Red Red Red Gray Red Red Red
Output:
Row 1: Red Red Pink
Row 2: Pink Pink Pink
Example 3
Input:
Row 1: Blue Pink Purple Blue Orange Blue Green Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue
Row 3: Blue Purple Blue Blue Blue Blue Green Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Black Blue Blue Green Pink Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Gray Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 8: Gray Gray Gray Gray Blue Yellow Blue Blue Blue Blue
Row 9: Gray Gray Gray Blue Blue Pink Blue Blue Blue Blue
Row 10: Gray Blue Gray Blue Yellow Blue Blue Blue Purple Blue
Row 11: Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Green Red Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Purple Red Blue Green Blue Blue Red Blue Blue
Row 16: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue
Output:
Row 1: Gray Blue Gray Blue
Row 2: Gray Gray Gray Gray
Row 3: Gray Gray Gray Blue
Row 4: Gray Blue Gray Blue
Row 5: Blue Blue Gray Blue
Row 6: Blue Blue Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Pink Gray Orange Gray Orange Pink Gray
Row 2: Orange Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray
Row 3: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink
Row 4: Orange Gray Gray Gray Orange Gray Orange Orange Gray Gray Gray Gray
Row 5: Gray Gray Orange Gray Gray Pink Gray Gray Pink Gray Gray Gray
Row 6: Gray Orange Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray
Row 7: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Row 9: Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Orange
Row 10: Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray
Row 20: Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray
Row 21: Orange Gray Orange Gray Orange Orange Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray
Row 25: Gray Gray Orange Gray Pink Gray Gray Black Black Gray Gray Pink
Row 26: Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Gray
Black Black Black
Gray Black Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Blue Blue Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 9: Pink Blue Blue Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 10: Pink Blue Blue Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 11: Pink Blue Blue Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 12: Pink Blue Blue Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 13: Pink Blue Blue Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Blue Pink Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 9: Pink Blue Blue Blue Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink
Row 10: Pink Blue Pink Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 11: Pink Blue Blue Blue Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink
Row 12: Pink Blue Pink Blue Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 13: Pink Blue Blue Blue Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Orange Orange Orange Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 3: Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 4: Green Blue Blue Blue Green Purple Purple Purple Brown Brown Brown Green
Row 5: Green Blue Blue Blue Green Purple Purple Purple Brown Brown Brown Green
Row 6: Green Blue Blue Blue Green Purple Purple Purple Brown Brown Brown Green
Row 7: Green Green Green Green Green Purple Purple Purple Brown Brown Brown Green
Row 8: Green Green Green Green Green Purple Purple Purple Brown Brown Brown Green
Row 9: Black Black Black Green Green Purple Purple Purple Brown Brown Brown Green
Row 10: Black Black Black Green Green Purple Purple Purple Brown Brown Brown Green
Row 11: Black Black Black Green Green Purple Purple Purple Brown Brown Brown Green
Row 12: Green Green Green Green Green Purple Purple Purple Brown Brown Brown Green
Row 13: Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 14: Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 3: Green Green Green Green Green Purple Green Purple Green Green Green Green
Row 4: Green Blue Blue Blue Green Purple Purple Purple Brown Brown Brown Green
Row 5: Green Blue Green Blue Green Purple Green Purple Brown Green Brown Green
Row 6: Green Blue Blue Blue Green Purple Purple Purple Brown Brown Brown Green
Row 7: Green Green Green Green Green Purple Green Purple Brown Green Brown Green
Row 8: Green Green Green Green Green Purple Purple Purple Brown Brown Brown Green
Row 9: Black Black Black Green Green Purple Green Purple Brown Green Brown Green
Row 10: Black Green Black Green Green Purple Purple Purple Brown Brown Brown Green
Row 11: Black Black Black Green Green Purple Green Purple Brown Green Brown Green
Row 12: Green Green Green Green Green Purple Purple Purple Brown Brown Brown Green
Row 13: Green Green Green Green Green Purple Green Purple Green Green Green Green
Row 14: Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Brown Brown Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 12: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 13: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 14: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 15: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 16: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Brown Brown Brown Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Pink Brown Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Brown Brown Brown Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Brown Pink Brown Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Brown Brown Brown Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 12: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink
Row 13: Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 14: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink
Row 15: Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink
Row 16: Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 29: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Gray Pink Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Green Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Brown Blue Blue Black Blue Blue Blue Blue Blue
Row 3: Blue Blue Purple Purple Blue Brown Blue Blue Black Black Blue Blue Blue Brown Blue
Row 4: Blue Blue Purple Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue
Row 5: Blue Blue Brown Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Purple Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Black Black Blue Blue Blue Red Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Red Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Black Black Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Black Black Blue Blue Blue Blue Blue Purple Purple
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 15: Blue Blue Brown Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Purple
Row 16: Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Purple Purple Blue Blue Blue Blue Black Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Black Black Blue Blue
Row 21: Blue Black Blue Red Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 22: Black Black Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Purple Brown Blue Red Black Blue Blue Purple Purple Blue
Row 3: Blue Blue Purple Purple Blue Brown Purple Blue Black Black Blue Blue Purple Brown Blue
Row 4: Blue Blue Purple Brown Blue Purple Blue Blue Blue Blue Blue Blue Brown Purple Blue
Row 5: Blue Blue Brown Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue
Row 6: Blue Blue Purple Blue Blue Blue Red Black Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Black Black Blue Blue Blue Red Black Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Red Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Black Black Blue Blue Red Black Blue Blue Red Black Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Black Black Blue Blue Black Black Blue Purple Purple
Row 14: Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Brown
Row 15: Blue Purple Brown Blue Blue Red Black Blue Blue Red Black Blue Blue Brown Purple
Row 16: Blue Brown Purple Blue Blue Black Black Blue Blue Black Black Blue Blue Purple Blue
Row 17: Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Purple Purple Blue Blue Blue Red Black Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Purple Brown Blue Blue Blue Black Black Blue Blue
Row 21: Red Black Blue Red Black Blue Brown Purple Blue Blue Blue Blue Blue Blue Blue
Row 22: Black Black Blue Black Black Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Orange Orange Purple Orange Purple Purple Orange Orange Purple Orange Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Brown Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 7: Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple
Row 14: Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Brown Purple Purple Purple
Row 17: Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Purple
Row 20: Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Brown Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 3: Purple Purple Purple Orange Orange Purple Orange Purple Purple Orange Orange Purple Orange Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Brown Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Orange Orange Purple Orange
Row 5: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange
Row 6: Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple
Row 7: Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Brown Purple Purple Purple Purple Brown Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Orange Orange Purple Orange Purple Orange Orange Purple Orange
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Orange Orange Purple Purple Purple Orange Orange
Row 10: Purple Purple Purple Purple Orange Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Brown Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple
Row 13: Purple Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple
Row 14: Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Orange Orange Purple Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Orange Purple Purple Purple
Row 16: Purple Purple Purple Orange Orange Purple Purple Brown Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Brown Purple Purple Purple
Row 17: Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange
Row 18: Brown Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Purple Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange
Row 19: Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Orange Purple Orange Purple Brown Purple Purple Purple Purple Purple
Row 20: Purple Purple Orange Orange Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Orange Purple Orange Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 4: Purple Blue Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow
Row 11: Yellow Yellow Brown Black Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow
Row 12: Yellow Yellow Black Brown Yellow Yellow Purple Purple Yellow Yellow Black Yellow Yellow Black Yellow Yellow
Row 13: Yellow Yellow Black Yellow Yellow Purple Purple Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow
Row 17: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Purple Purple Yellow Yellow Pink Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Purple Purple Yellow Yellow Yellow Pink Pink Orange Yellow Yellow Yellow Yellow Green Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 25: Yellow Blue Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Yellow Yellow Yellow Yellow Brown Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Black Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Blue Yellow Yellow Black Brown Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Black Yellow Yellow Yellow Yellow
Row 4: Purple Blue Yellow Yellow Green Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Purple Purple Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Purple Purple Yellow Yellow Yellow Yellow Yellow Pink Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Orange Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Black Yellow
Row 11: Yellow Yellow Brown Black Yellow Purple Blue Yellow Yellow Yellow Yellow Yellow Yellow Black Brown Yellow
Row 12: Yellow Yellow Black Brown Yellow Yellow Purple Purple Yellow Brown Black Yellow Yellow Black Yellow Yellow
Row 13: Yellow Yellow Black Yellow Yellow Purple Purple Yellow Yellow Black Brown Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow
Row 17: Yellow Purple Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow
Row 18: Yellow Yellow Purple Purple Yellow Yellow Pink Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Purple Purple Yellow Yellow Yellow Pink Pink Orange Yellow Yellow Yellow Yellow Green Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Green Yellow Gray Yellow Yellow
Row 21: Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Black Yellow
Row 25: Purple Blue Yellow Yellow Gray Yellow Yellow Pink Orange Pink Yellow Yellow Yellow Black Brown Yellow
Row 26: Yellow Purple Purple Yellow Yellow Yellow Yellow Pink Pink Orange Yellow Yellow Yellow Black Yellow Yellow
Row 27: Purple Purple Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Yellow Black Blue Blue Blue Blue Purple Green Purple Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Yellow Black Blue Blue Blue Blue Purple Green Purple Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue
Blue Blue Yellow Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Yellow Yellow Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Yellow Black Black Black Black Black Black Black Black Black
Row 5: Yellow Black Black Black Black Black Black Black Black Black Black
Row 6: Black Yellow Black Black Black Black Yellow Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Yellow Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Yellow Black
Row 11: Yellow Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Yellow Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Yellow Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Yellow Black Black Yellow Black Black Black Black Black Black
Row 19: Black Yellow Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Yellow Black Black
Row 25: Yellow Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Green Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Green Black Black Black Black
Row 7: Black Black Black Green Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Green Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Green Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Green Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Green Black Black Black Black Black Black
Row 22: Black Black Green Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Green Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Green Black Black Black Black Black Black
Row 29: Black Black Black Black Black Black Black Green Black Black Black Black Black Black
Row 30: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Blue Pink Pink Pink Pink Blue Brown Brown Brown Brown Blue Orange Orange Orange Orange Blue Yellow Yellow Yellow Yellow Blue Pink Pink Pink Pink
Row 2: Red Red Red Red Blue Pink Blue Blue Pink Blue Brown Brown Brown Brown Blue Blue Orange Orange Blue Blue Blue Yellow Yellow Blue Blue Blue Pink Pink Blue
Row 3: Red Red Red Red Blue Pink Blue Blue Pink Blue Brown Brown Brown Brown Blue Blue Orange Orange Blue Blue Blue Yellow Yellow Blue Blue Blue Pink Pink Blue
Row 4: Red Red Red Red Blue Pink Pink Pink Pink Blue Brown Brown Brown Brown Blue Orange Orange Orange Orange Blue Yellow Yellow Yellow Yellow Blue Pink Pink Pink Pink
Output:
Row 1: Red Red Red Red Red Red
Row 2: Purple Purple Purple Purple Purple Purple
Row 3: Red Red Red Red Red Red
Row 4: Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green
Example 2
Input:
Row 1: Orange Orange Orange Orange Black Purple Purple Purple Purple
Row 2: Orange Orange Orange Orange Black Black Purple Purple Black
Row 3: Orange Orange Orange Orange Black Black Purple Purple Black
Row 4: Orange Orange Orange Orange Black Purple Purple Purple Purple
Output:
Row 1: Red Red
Row 2: Green Green
Example 3
Input:
Row 1: Green Green Green Green Orange Black Black Black Black Orange Green Green Green Green Orange Blue Blue Blue Blue Orange Red Red Red Red
Row 2: Green Orange Orange Green Orange Orange Black Black Orange Orange Green Green Green Green Orange Blue Blue Blue Blue Orange Red Red Red Red
Row 3: Green Orange Orange Green Orange Orange Black Black Orange Orange Green Green Green Green Orange Blue Blue Blue Blue Orange Red Red Red Red
Row 4: Green Green Green Green Orange Black Black Black Black Orange Green Green Green Green Orange Blue Blue Blue Blue Orange Red Red Red Red
Output:
Row 1: Purple Purple Purple Purple Purple
Row 2: Green Green Green Green Green
Row 3: Red Red Red Red Red
Row 4: Red Red Red Red Red
Row 5: Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Black Orange Orange Orange Orange
Row 2: Pink Pink Pink Pink Black Orange Orange Orange Orange
Row 3: Pink Pink Pink Pink Black Orange Orange Orange Orange
Row 4: Pink Pink Pink Pink Black Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red
Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Pink Pink Gray Gray Gray Pink Pink Pink Gray Gray Gray Gray Pink Pink Gray Pink Pink
Row 2: Gray Gray Pink Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Pink Pink Gray Gray Pink Pink Gray Gray Gray Pink Pink Gray Gray Pink Gray Pink Pink Gray
Row 4: Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Pink Gray Gray Pink Gray
Row 5: Pink Gray Pink Pink Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Pink Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Gray Pink Pink Pink Gray
Row 7: Pink Gray Pink Pink Gray Pink Gray Gray Gray Pink Pink Gray Pink Gray Pink Gray Gray Pink
Row 8: Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Pink
Row 9: Gray Gray Gray Pink Gray Gray Pink Pink Pink Gray Gray Pink Pink Gray Pink Pink Gray Gray
Row 10: Gray Gray Pink Pink Pink Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink
Row 11: Pink Pink Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Pink Gray Pink
Row 12: Pink Gray Pink Gray Pink Pink Gray Gray Pink Gray Gray Pink Pink Pink Gray Pink Gray Gray
Row 13: Gray Gray Pink Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Pink Pink Gray Gray
Row 14: Gray Gray Gray Pink Pink Gray Pink Gray Pink Pink Pink Pink Gray Gray Gray Gray Pink Pink
Output:
Row 1: Gray Red Red Gray Gray Gray Red Red Red Gray Gray Gray Gray Green Green Gray Green Green
Row 2: Gray Gray Red Gray Red Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Red Red Gray Gray Red Red Gray Gray Gray Red Red Gray Gray Red Gray Red Red Gray
Row 4: Gray Red Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Red Red Gray Gray Red Gray
Row 5: Blue Gray Green Green Gray Gray Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Blue Gray Gray Gray Gray Green Gray Gray Blue Gray Gray Gray Green Gray Blue Blue Blue Gray
Row 7: Blue Gray Green Green Gray Green Gray Gray Gray Red Red Gray Green Gray Blue Gray Gray Green
Row 8: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Green
Row 9: Gray Gray Gray Blue Gray Gray Red Red Red Gray Gray Red Red Gray Green Green Gray Gray
Row 10: Gray Gray Blue Blue Blue Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Green
Row 11: Red Red Gray Gray Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray Blue Gray Green
Row 12: Red Gray Green Gray Green Green Gray Gray Red Gray Gray Red Red Red Gray Blue Gray Gray
Row 13: Gray Gray Green Gray Gray Gray Red Red Gray Gray Gray Gray Gray Gray Blue Blue Gray Gray
Row 14: Gray Gray Gray Green Green Gray Red Gray Blue Blue Blue Blue Gray Gray Gray Gray Green Green
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Gray
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray
Row 6: Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Gray Yellow Gray Gray Gray Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Red
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red
Row 6: Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Red Yellow Red Red Red Yellow Yellow Yellow
Example 3
Input:
Row 1: Gray Gray Gray Gray Purple Purple Purple Gray Gray Purple Purple Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Gray Gray
Row 3: Purple Purple Gray Gray Purple Purple Purple Gray Gray Purple Gray Gray Gray Gray Gray
Row 4: Gray Gray Purple Purple Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray
Row 5: Gray Gray Purple Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Purple
Row 6: Gray Purple Gray Gray Purple Gray Gray Purple Gray Gray Purple Gray Gray Gray Gray
Row 7: Purple Purple Gray Gray Purple Purple Gray Purple Gray Gray Purple Purple Gray Purple Purple
Row 8: Gray Purple Gray Gray Purple Gray Purple Purple Gray Gray Purple Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray
Row 10: Purple Purple Gray Purple Gray Gray Gray Purple Purple Gray Gray Purple Gray Purple Gray
Row 11: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray
Row 12: Gray Gray Gray Purple Gray Gray Gray Gray Purple Purple Purple Gray Gray Purple Gray
Row 13: Purple Gray Gray Gray Gray Purple Purple Gray Purple Gray Gray Gray Gray Gray Gray
Row 14: Purple Purple Gray Gray Purple Gray Gray Gray Gray Gray Purple Purple Gray Gray Purple
Row 15: Gray Gray Purple Gray Purple Gray Purple Gray Purple Purple Gray Purple Gray Purple Purple
Row 16: Gray Gray Purple Gray Purple Gray Purple Gray Purple Gray Gray Purple Gray Purple Gray
Row 17: Purple Purple Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Red Red Red Gray Gray Green Green Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Gray Gray
Row 3: Green Green Gray Gray Red Red Red Gray Gray Blue Gray Gray Gray Gray Gray
Row 4: Gray Gray Red Red Gray Gray Gray Gray Gray Blue Blue Gray Gray Gray Gray
Row 5: Gray Gray Red Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Green Green
Row 6: Gray Blue Gray Gray Blue Gray Gray Blue Gray Gray Blue Gray Gray Gray Gray
Row 7: Blue Blue Gray Gray Blue Blue Gray Blue Gray Gray Blue Blue Gray Green Green
Row 8: Gray Blue Gray Gray Blue Gray Blue Blue Gray Gray Blue Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Green Gray Blue Gray
Row 10: Green Green Gray Red Gray Gray Gray Red Red Gray Gray Green Gray Blue Gray
Row 11: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 12: Gray Gray Gray Red Gray Gray Gray Gray Blue Blue Blue Gray Gray Blue Gray
Row 13: Red Gray Gray Gray Gray Green Green Gray Blue Gray Gray Gray Gray Gray Gray
Row 14: Red Red Gray Gray Red Gray Gray Gray Gray Gray Blue Blue Gray Gray Blue
Row 15: Gray Gray Green Gray Red Gray Red Gray Red Red Gray Blue Gray Blue Blue
Row 16: Gray Gray Green Gray Red Gray Red Gray Red Gray Gray Blue Gray Blue Gray
Row 17: Green Green Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Black Pink Pink Pink Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Pink Black Pink Pink Black
Row 3: Black Black Pink Pink Black Black Pink Black Black Pink Pink
Row 4: Black Black Black Black Black Black Black Black Pink Black Black
Row 5: Pink Pink Black Black Black Pink Black Black Pink Black Pink
Row 6: Black Black Black Black Black Pink Black Black Black Pink Pink
Row 7: Black Pink Black Black Pink Black Black Black Black Black Black
Row 8: Black Pink Pink Black Pink Black Black Black Black Black Black
Row 9: Black Black Black Pink Black Black Black Pink Pink Black Black
Row 10: Black Black Black Pink Pink Black Black Black Pink Pink Black
Row 11: Black Pink Pink Black Black Pink Black Black Black Black Black
Row 12: Black Black Black Black Black Pink Pink Black Pink Black Black
Row 13: Black Pink Pink Black Pink Black Black Black Pink Black Black
Row 14: Black Black Black Black Pink Pink Black Black Black Pink Pink
Row 15: Black Pink Black Black Black Black Pink Black Black Black Black
Row 16: Black Pink Black Black Black Black Pink Black Pink Black Black
Row 17: Pink Black Black Black Black Black Pink Black Pink Black Black
Row 18: Pink Pink Black Black Pink Pink Black Black Black Black Black
Row 19: Black Black Black Black Black Black Pink Pink Black Pink Black
Row 20: Black Black Black Pink Pink Black Pink Black Black Pink Black
Row 21: Pink Black Black Black Pink Black Black Black Pink Pink Black
Row 22: Pink Pink Black Black Black Black Black Black Black Black Black
Row 23: Black Pink Black Pink Pink Pink Black Black Pink Pink Black
Row 24: Black Black Black Pink Black Black Black Pink Black Black Pink
Row 25: Black Black Black Black Pink Black Pink Pink Black Black Pink
Row 26: Pink Black Black Black Pink Black Black Black Pink Black Black
Row 27: Pink Pink Pink Black Black Black Black Black Pink Black Black
Row 28: Black Black Black Black Black Black Pink Pink Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Red Red Red Black Black Black Black Black Black Black
Black Black Black Black Black Black Green Black Blue Blue Black
Black Black Green Green Black Black Green Black Black Blue Blue
Black Black Black Black Black Black Black Black Green Black Black
Green Green Black Black Black Green Black Black Green Black Red
Black Black Black Black Black Green Black Black Black Red Red
Black Red Black Black Green Black Black Black Black Black Black
Black Red Red Black Green Black Black Black Black Black Black
Black Black Black Red Black Black Black Blue Blue Black Black
Black Black Black Red Red Black Black Black Blue Blue Black
Black Green Green Black Black Red Black Black Black Black Black
Black Black Black Black Black Red Red Black Green Black Black
Black Green Green Black Red Black Black Black Green Black Black
Black Black Black Black Red Red Black Black Black Green Green
Black Green Black Black Black Black Red Black Black Black Black
Black Green Black Black Black Black Red Black Green Black Black
Red Black Black Black Black Black Red Black Green Black Black
Red Red Black Black Green Green Black Black Black Black Black
Black Black Black Black Black Black Red Red Black Blue Black
Black Black Black Red Red Black Red Black Black Blue Black
Blue Black Black Black Red Black Black Black Blue Blue Black
Blue Blue Black Black Black Black Black Black Black Black Black
Black Blue Black Blue Blue Blue Black Black Green Green Black
Black Black Black Blue Black Black Black Red Black Black Green
Black Black Black Black Green Black Red Red Black Black Green
Blue Black Black Black Green Black Black Black Green Black Black
Blue Blue Blue Black Black Black Black Black Green Black Black
Black Black Black Black Black Black Green Green Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Purple Purple Purple Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Brown Brown Brown Brown Brown
Row 17: Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Black Black Black Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Black Yellow Yellow Black Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow
Row 22: Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow
Row 23: Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow
Row 24: Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 30: Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Purple Purple Purple Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Brown Brown Brown Brown Brown
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Black Black Black Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow
Row 22: Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow
Row 23: Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow
Row 24: Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 30: Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Green Green Green Green Green Black Black Black Black Black
Row 7: Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black
Row 8: Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black
Row 9: Yellow Yellow Yellow Black Black Black Black Black Green Black Black Black Black Green Black Black
Row 10: Yellow Black Black Yellow Black Black Black Black Black Green Green Green Green Green Black Black
Row 11: Black Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Blue Blue Blue Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Blue Black Black Blue Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Blue Blue Blue Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Brown Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Green Green Green Green Green Black Black Black Black
Row 7: Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black
Row 8: Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black
Row 9: Black Yellow Yellow Yellow Black Black Black Black Black Green Black Black Black Green Black Black
Row 10: Black Yellow Black Yellow Black Black Black Black Black Green Green Green Green Green Black Black
Row 11: Black Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Blue Blue Blue Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Blue Black Blue Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Blue Blue Blue Black Black Black Black
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue
Row 3: Red Red Red Red Red Blue Blue
Row 4: Red Blue Blue Blue Blue Red Blue
Row 5: Blue Red Red Red Red Red Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Black Black Black Black Blue Blue
Row 10: Blue Black Blue Blue Blue Black Blue
Row 11: Blue Blue Black Black Black Black Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Gray Gray Gray Gray Blue Blue
Row 15: Blue Gray Blue Blue Blue Gray Blue
Row 16: Blue Blue Gray Gray Gray Gray Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue
Row 18: Gray Gray Gray Blue Blue Blue Blue
Row 19: Gray Blue Blue Gray Blue Blue Blue
Row 20: Blue Gray Gray Gray Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Red Red Red Red Red Blue
Row 4: Blue Red Blue Blue Blue Red Blue
Row 5: Blue Red Red Red Red Red Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Black Black Black Black Blue
Row 10: Blue Blue Black Blue Blue Black Blue
Row 11: Blue Blue Black Black Black Black Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Gray Gray Gray Gray Blue
Row 15: Blue Blue Gray Blue Blue Gray Blue
Row 16: Blue Blue Gray Gray Gray Gray Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Gray Gray Gray Blue Blue Blue
Row 19: Blue Gray Blue Gray Blue Blue Blue
Row 20: Blue Gray Gray Gray Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray
Row 16: Gray Blue Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray
Row 17: Gray Gray Blue Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray
Row 18: Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray
Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray
Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray
Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Gray Gray Gray Gray Gray Blue Gray Gray Blue Gray Gray Gray Gray
Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray
Gray Gray Blue Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray
Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray
Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green
Row 2: Yellow Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 2: Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow
Row 3: Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Blue Blue Green Blue Blue Orange Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Green Blue Blue Orange Blue Blue Blue
Row 2: Blue Green Blue Green Orange Blue Orange Blue Blue
Row 3: Blue Blue Green Blue Blue Orange Blue Blue Blue
Row 4: Blue Green Blue Green Orange Blue Orange Blue Blue
Row 5: Blue Blue Green Blue Blue Orange Blue Blue Blue
Row 6: Blue Green Blue Green Orange Blue Orange Blue Blue
Row 7: Blue Blue Green Blue Blue Orange Blue Blue Blue
Row 8: Blue Green Blue Green Orange Blue Orange Blue Blue
Row 9: Blue Blue Green Blue Blue Orange Blue Blue Blue
Row 10: Blue Green Blue Green Orange Blue Orange Blue Blue
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue
Row 5: Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple
Row 6: Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue
Row 10: Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown
Row 11: Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue Brown Blue
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Purple Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Red Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Purple Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Red Brown Brown
Brown Brown Brown Brown Purple Brown Purple Brown Black Brown Black Brown Brown Brown Brown Pink Brown Pink Brown Brown Red Brown Red Brown
Brown Brown Brown Brown Brown Purple Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Red Brown Brown
Brown Brown Brown Brown Purple Brown Purple Brown Black Brown Black Brown Brown Brown Brown Pink Brown Pink Brown Brown Red Brown Red Brown
Brown Brown Brown Brown Brown Purple Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Red Brown Brown
Brown Brown Brown Brown Purple Brown Purple Brown Black Brown Black Brown Brown Brown Brown Pink Brown Pink Brown Brown Red Brown Red Brown
Brown Brown Brown Brown Brown Purple Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Red Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Purple Green Purple Green Green Green Green Green Purple Green Purple Green
Row 2: Purple Green Green Green Purple Green Purple Green Green Green Green Green Purple Green Purple
Row 3: Green Purple Green Green Green Purple Green Purple Green Green Green Green Green Purple Green
Row 4: Green Green Purple Green Green Green Purple Green Purple Green Green Green Green Green Purple
Row 5: Purple Green Green Purple Green Green Green Purple Green Purple Green Green Green Green Green
Row 6: Green Purple Green Green Purple Green Green Green Purple Green Purple Green Green Green Green
Row 7: Green Green Purple Green Green Purple Green Green Green Purple Green Purple Green Green Green
Row 8: Purple Green Green Purple Green Green Purple Green Green Green Purple Green Purple Green Green
Row 9: Green Purple Green Green Purple Green Green Purple Green Green Green Purple Green Purple Green
Output:
Row 1: Green Green Green Purple Green Purple Green Green Green Green Green Purple Green Purple Green
Row 2: Purple Green Green Green Yellow Green Yellow Green Green Green Green Green Yellow Green Yellow
Row 3: Green Yellow Green Green Green Purple Green Purple Green Green Green Green Green Purple Green
Row 4: Green Green Purple Green Green Green Yellow Green Yellow Green Green Green Green Green Yellow
Row 5: Purple Green Green Yellow Green Green Green Purple Green Purple Green Green Green Green Green
Row 6: Green Yellow Green Green Purple Green Green Green Yellow Green Yellow Green Green Green Green
Row 7: Green Green Purple Green Green Yellow Green Green Green Purple Green Purple Green Green Green
Row 8: Purple Green Green Yellow Green Green Purple Green Green Green Yellow Green Yellow Green Green
Row 9: Green Yellow Green Green Purple Green Green Yellow Green Green Green Purple Green Purple Green
Example 2
Input:
Row 1: Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Row 3: Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 4: Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink
Row 5: Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink
Row 6: Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 7: Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 8: Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 9: Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 17: Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink
Row 18: Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink
Row 19: Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink
Row 20: Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink
Row 21: Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple
Row 22: Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink
Row 23: Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink
Row 24: Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink
Row 25: Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink
Row 26: Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple
Row 27: Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink
Row 28: Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink Purple
Row 29: Purple Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink Pink
Row 30: Pink Purple Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Purple Pink Purple Pink Pink
Output:
Row 1: Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink
Row 3: Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 4: Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink
Row 5: Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink
Row 6: Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Row 7: Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 8: Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 9: Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink
Row 17: Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink
Row 18: Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink
Row 19: Pink Pink Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple Pink Pink
Row 20: Pink Pink Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink
Row 21: Pink Pink Pink Pink Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Purple
Row 22: Pink Pink Pink Pink Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink
Row 23: Purple Pink Pink Pink Pink Pink Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink Pink Pink
Row 24: Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink
Row 25: Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink Purple Pink
Row 26: Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow
Row 27: Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink Purple Pink
Row 28: Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow
Row 29: Purple Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Yellow Pink Pink Purple Pink Purple Pink Pink Pink
Row 30: Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Purple Pink Pink Yellow Pink Yellow Pink Pink
Example 3
Input:
Row 1: Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange
Row 2: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 3: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 12: Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Blue Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange
Row 19: Blue Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange
Output:
Row 1: Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange
Row 2: Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Yellow
Row 3: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 12: Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Blue Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Yellow Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Blue Orange Orange Yellow Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Yellow Orange Orange Blue Orange Orange Orange Orange
Row 19: Blue Orange Orange Orange Blue Orange Orange Yellow Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Row 2: Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 3: Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 4: Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Row 7: Purple Pink Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Row 8: Pink Purple Pink Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink
Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Purple Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Pink Yellow Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Pink Pink Purple Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink
Purple Pink Pink Yellow Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Pink Yellow Pink Pink Purple Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Green Red Green
Row 2: Gray Green Green Purple
Output:
Row 1: Gray Green Green Purple
Row 2: Blue Green Red Green
Example 2
Input:
Row 1: Pink Brown Brown Yellow
Row 2: Brown Pink Brown Blue
Row 3: Yellow Brown Yellow Brown
Row 4: Pink Brown Pink Brown
Row 5: Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown
Row 2: Pink Brown Pink Brown
Row 3: Yellow Brown Yellow Brown
Row 4: Brown Pink Brown Blue
Row 5: Pink Brown Brown Yellow
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Brown Gray Yellow
Row 2: Gray Gray Gray Gray Gray Gray Gray Red Gray
Row 3: Gray Gray Gray Gray Gray Pink Gray Brown Gray
Row 4: Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Brown Purple
Row 6: Brown Gray Gray Gray Gray Gray Gray Blue Brown
Row 7: Brown Gray Gray Gray Red Gray Pink Gray Gray
Row 8: Gray Gray Gray Gray Pink Gray Gray Yellow Gray
Row 9: Red Gray Gray Gray Gray Brown Gray Gray Yellow
Row 10: Brown Gray Purple Purple Gray Gray Gray Red Gray
Row 11: Brown Brown Brown Gray Gray Brown Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Purple Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Brown Gray Brown Gray Gray Purple Gray
Row 16: Yellow Gray Gray Gray Gray Gray Gray Gray Purple
Row 17: Gray Gray Gray Gray Gray Gray Gray Purple Gray
Row 18: Purple Gray Gray Brown Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Brown Gray Gray Purple Gray
Row 20: Gray Purple Gray Red Purple Red Red Gray Brown
Row 21: Gray Gray Gray Gray Gray Red Brown Brown Gray
Row 22: Blue Gray Gray Red Brown Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Brown
Row 24: Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 25: Red Gray Gray Gray Pink Gray Gray Gray Purple
Row 26: Gray Yellow Red Gray Gray Gray Purple Gray Brown
Row 27: Orange Brown Gray Gray Gray Gray Purple Brown Gray
Row 28: Gray Gray Brown Gray Gray Gray Brown Yellow Gray
Row 29: Brown Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Brown Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Brown Gray Gray Gray Brown Yellow Gray
Row 3: Orange Brown Gray Gray Gray Gray Purple Brown Gray
Row 4: Gray Yellow Red Gray Gray Gray Purple Gray Brown
Row 5: Red Gray Gray Gray Pink Gray Gray Gray Purple
Row 6: Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Brown
Row 8: Blue Gray Gray Red Brown Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Red Brown Brown Gray
Row 10: Gray Purple Gray Red Purple Red Red Gray Brown
Row 11: Gray Gray Gray Gray Brown Gray Gray Purple Gray
Row 12: Purple Gray Gray Brown Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Purple Gray
Row 14: Yellow Gray Gray Gray Gray Gray Gray Gray Purple
Row 15: Gray Gray Brown Gray Brown Gray Gray Purple Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Purple Gray Gray Gray
Row 19: Brown Brown Brown Gray Gray Brown Gray Gray Gray
Row 20: Brown Gray Purple Purple Gray Gray Gray Red Gray
Row 21: Red Gray Gray Gray Gray Brown Gray Gray Yellow
Row 22: Gray Gray Gray Gray Pink Gray Gray Yellow Gray
Row 23: Brown Gray Gray Gray Red Gray Pink Gray Gray
Row 24: Brown Gray Gray Gray Gray Gray Gray Blue Brown
Row 25: Gray Gray Gray Gray Gray Gray Gray Brown Purple
Row 26: Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Pink Gray Brown Gray
Row 28: Gray Gray Gray Gray Gray Gray Gray Red Gray
Row 29: Gray Gray Gray Gray Gray Gray Brown Gray Yellow
Here is the input grid for the test example:
Input:
Row 1: Orange Yellow Purple Green Blue Yellow Yellow Yellow Orange Yellow Yellow Purple Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Green Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Blue Yellow Yellow Orange Blue Yellow Yellow Purple Yellow Blue
Row 3: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Orange Yellow Yellow Brown Green Purple Purple Yellow Yellow Yellow Blue Blue Purple Yellow Purple Yellow Yellow Yellow Blue
Row 5: Yellow Purple Purple Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange
Row 6: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Orange Yellow Yellow Orange Yellow Yellow Yellow Orange Blue Yellow
Row 7: Red Yellow Purple Yellow Yellow Yellow Blue Blue Yellow Yellow Orange Yellow Yellow Yellow Purple Yellow Purple Yellow Green Orange Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Green Purple
Row 9: Brown Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow
Row 10: Yellow Orange Yellow Yellow Yellow Green Purple Yellow Yellow Purple Blue Yellow Yellow Yellow Yellow Blue Red Purple Purple Yellow Orange
Row 11: Blue Orange Yellow Yellow Yellow Orange Blue Yellow Yellow Yellow Yellow Orange Purple Purple Yellow Yellow Yellow Blue Orange Yellow Yellow
Row 12: Purple Purple Yellow Yellow Yellow Green Yellow Red Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Yellow Yellow Yellow Green Yellow Red Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Blue Orange Yellow Yellow Yellow Orange Blue Yellow Yellow Yellow Yellow Orange Purple Purple Yellow Yellow Yellow Blue Orange Yellow Yellow
Yellow Orange Yellow Yellow Yellow Green Purple Yellow Yellow Purple Blue Yellow Yellow Yellow Yellow Blue Red Purple Purple Yellow Orange
Brown Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Green Purple
Red Yellow Purple Yellow Yellow Yellow Blue Blue Yellow Yellow Orange Yellow Yellow Yellow Purple Yellow Purple Yellow Green Orange Yellow
Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Orange Yellow Yellow Orange Yellow Yellow Yellow Orange Blue Yellow
Yellow Purple Purple Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange
Yellow Yellow Orange Yellow Yellow Brown Green Purple Purple Yellow Yellow Yellow Blue Blue Purple Yellow Purple Yellow Yellow Yellow Blue
Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Green Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Blue Yellow Yellow Orange Blue Yellow Yellow Purple Yellow Blue
Orange Yellow Purple Green Blue Yellow Yellow Yellow Orange Yellow Yellow Purple Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 2: Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 3: Yellow Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 4: Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Yellow Green Green Green Green Green Green Green
Row 7: Green Green Green Green Yellow Green Green Green Green Yellow Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Yellow Green Green Green Green
Row 11: Yellow Green Yellow Green Yellow Green Green Yellow Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Yellow
Output:
Row 1: Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 2: Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 3: Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Green Green Green
Row 4: Green Green Green Green Green Orange Orange Orange Orange Orange Green Green Green
Row 5: Green Green Green Green Green Yellow Green Yellow Yellow Yellow Green Green Green
Row 6: Green Green Green Green Green Yellow Green Yellow Yellow Yellow Green Green Green
Row 7: Green Green Green Green Yellow Green Green Yellow Yellow Yellow Green Green Green
Row 8: Green Green Green Green Green Green Green Yellow Yellow Green Green Green Green
Row 9: Green Green Green Green Green Green Green Yellow Yellow Green Green Green Green
Row 10: Green Green Green Green Green Green Green Yellow Yellow Green Green Green Green
Row 11: Yellow Green Yellow Green Yellow Green Green Yellow Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Yellow
Example 2
Input:
Row 1: Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Pink Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Gray Gray Pink
Row 4: Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray
Row 6: Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray
Row 8: Gray Gray Gray Gray Gray Pink Gray Gray Pink Pink Gray Pink Gray Pink Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Pink
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray
Row 14: Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink
Row 15: Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Gray Pink Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Pink Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Gray Gray Pink
Row 4: Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Pink Gray Pink Gray Pink Gray Gray Pink
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Pink Pink Pink Gray Gray Pink
Row 6: Gray Gray Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Pink Pink Gray Gray Pink
Row 7: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Gray Pink Pink Pink Pink Gray Pink
Row 8: Gray Gray Gray Gray Gray Pink Gray Gray Pink Pink Gray Pink Gray Pink Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Gray Pink
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Pink Pink Pink Pink Pink Pink Gray Pink
Row 10: Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Gray Pink
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Orange Brown
Row 3: Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown
Row 9: Orange Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange
Row 10: Brown Brown Orange Brown Brown Orange Brown Orange Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown
Row 12: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown
Row 13: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Orange
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Orange Brown Brown Orange Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange
Row 19: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Orange
Row 20: Brown Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Orange Brown
Row 3: Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange
Row 4: Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 8: Brown Orange Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown
Row 9: Orange Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange
Row 10: Orange Orange Orange Orange Brown Orange Brown Orange Brown Brown Brown Brown
Row 11: Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Brown Brown
Row 12: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown
Row 13: Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange
Row 14: Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Orange Brown Orange Orange Brown Brown Orange Brown Brown Brown
Row 16: Brown Brown Orange Brown Orange Brown Brown Brown Brown Orange Brown Brown
Row 17: Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Orange
Row 19: Brown Brown Orange Brown Orange Orange Brown Brown Brown Brown Brown Orange
Row 20: Brown Brown Orange Brown Orange Brown Orange Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Brown Pink Pink
Row 2: Pink Brown Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown
Row 4: Pink Pink Pink Pink Pink Brown Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Brown Pink Brown Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Brown
Row 6: Pink Pink Pink Pink Brown Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink
Row 7: Pink Brown Pink Brown Brown Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Brown Pink Brown Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Brown Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Brown Pink Pink Pink
Row 13: Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Brown Pink Pink
Pink Brown Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown
Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink
Pink Pink Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown
Pink Pink Pink Pink Brown Brown Brown Brown Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink
Pink Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink
Pink Pink Brown Pink Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Brown Pink Pink Pink
Pink Pink Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink
Pink Pink Pink Brown Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Brown Pink Pink Pink
Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange Yellow
Row 3: Orange Yellow Yellow Yellow Yellow Orange Orange Yellow Yellow
Row 4: Orange Yellow Orange Yellow Orange Red Red Yellow Orange
Row 5: Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Orange Yellow Black Yellow Yellow Yellow Orange Yellow Yellow
Row 10: Yellow Yellow Yellow Orange Yellow Orange Orange Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow Yellow Yellow
Row 3: Orange Yellow Yellow Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow Orange
Row 4: Orange Yellow Orange Yellow Orange Red Red Yellow Orange Orange Yellow Red Red Orange Yellow Orange Yellow Orange
Row 5: Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow
Row 6: Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Orange Yellow Black Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Black Yellow Orange
Row 10: Yellow Yellow Yellow Orange Yellow Orange Orange Yellow Yellow Yellow Yellow Orange Orange Yellow Orange Yellow Yellow Yellow
Example 2
Input:
Row 1: Red Red Blue Blue Brown Orange
Row 2: Brown Brown Blue Orange Orange Blue
Row 3: Red Red Red Red Red Yellow
Row 4: Red Red Orange Black Blue Red
Row 5: Blue Yellow Black Red Red Orange
Row 6: Blue Brown Red Red Blue Black
Row 7: Red Red Red Red Black Red
Row 8: Blue Red Red Red Red Orange
Row 9: Red Red Red Red Orange Red
Row 10: Red Blue Red Red Red Red
Row 11: Orange Red Black Blue Red Red
Row 12: Red Orange Red Blue Blue Red
Row 13: Red Brown Red Red Red Red
Output:
Row 1: Red Red Blue Blue Brown Orange Orange Brown Blue Blue Red Red
Row 2: Brown Brown Blue Orange Orange Blue Blue Orange Orange Blue Brown Brown
Row 3: Red Red Red Red Red Yellow Yellow Red Red Red Red Red
Row 4: Red Red Orange Black Blue Red Red Blue Black Orange Red Red
Row 5: Blue Yellow Black Red Red Orange Orange Red Red Black Yellow Blue
Row 6: Blue Brown Red Red Blue Black Black Blue Red Red Brown Blue
Row 7: Red Red Red Red Black Red Red Black Red Red Red Red
Row 8: Blue Red Red Red Red Orange Orange Red Red Red Red Blue
Row 9: Red Red Red Red Orange Red Red Orange Red Red Red Red
Row 10: Red Blue Red Red Red Red Red Red Red Red Blue Red
Row 11: Orange Red Black Blue Red Red Red Red Blue Black Red Orange
Row 12: Red Orange Red Blue Blue Red Red Blue Blue Red Orange Red
Row 13: Red Brown Red Red Red Red Red Red Red Red Brown Red
Example 3
Input:
Row 1: Orange Orange Orange Pink Orange Orange Orange Orange Orange Brown Orange Blue Green
Row 2: Green Orange Green Green Yellow Purple Pink Pink Orange Purple Yellow Orange Orange
Row 3: Brown Orange Orange Green Purple Orange Pink Orange Blue Blue Pink Orange Orange
Row 4: Orange Pink Orange Pink Yellow Orange Blue Brown Blue Yellow Green Green Orange
Row 5: Blue Orange Orange Purple Orange Blue Orange Orange Orange Red Orange Yellow Orange
Row 6: Orange Pink Green Purple Orange Orange Orange Orange Brown Orange Orange Blue Orange
Row 7: Orange Orange Pink Orange Orange Green Orange Orange Pink Orange Pink Red Orange
Output:
Row 1: Orange Orange Orange Pink Orange Orange Orange Orange Orange Brown Orange Blue Green Green Blue Orange Brown Orange Orange Orange Orange Orange Pink Orange Orange Orange
Row 2: Green Orange Green Green Yellow Purple Pink Pink Orange Purple Yellow Orange Orange Orange Orange Yellow Purple Orange Pink Pink Purple Yellow Green Green Orange Green
Row 3: Brown Orange Orange Green Purple Orange Pink Orange Blue Blue Pink Orange Orange Orange Orange Pink Blue Blue Orange Pink Orange Purple Green Orange Orange Brown
Row 4: Orange Pink Orange Pink Yellow Orange Blue Brown Blue Yellow Green Green Orange Orange Green Green Yellow Blue Brown Blue Orange Yellow Pink Orange Pink Orange
Row 5: Blue Orange Orange Purple Orange Blue Orange Orange Orange Red Orange Yellow Orange Orange Yellow Orange Red Orange Orange Orange Blue Orange Purple Orange Orange Blue
Row 6: Orange Pink Green Purple Orange Orange Orange Orange Brown Orange Orange Blue Orange Orange Blue Orange Orange Brown Orange Orange Orange Orange Purple Green Pink Orange
Row 7: Orange Orange Pink Orange Orange Green Orange Orange Pink Orange Pink Red Orange Orange Red Pink Orange Pink Orange Orange Green Orange Orange Pink Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Green Gray Gray Green Yellow Gray Gray Gray
Row 2: Gray Gray Yellow Gray Green Yellow Yellow Blue Gray Gray Green
Row 3: Yellow Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray
Row 4: Yellow Gray Green Green Gray Yellow Gray Gray Gray Gray Green
Row 5: Blue Blue Green Green Gray Gray Yellow Gray Gray Gray Gray
Row 6: Gray Gray Green Blue Gray Green Gray Yellow Gray Gray Gray
Row 7: Gray Yellow Gray Blue Gray Yellow Blue Gray Gray Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Green Gray Gray Green Yellow Gray Gray Gray Gray Gray Gray Yellow Green Gray Gray Green Gray Gray Gray
Gray Gray Yellow Gray Green Yellow Yellow Blue Gray Gray Green Green Gray Gray Blue Yellow Yellow Green Gray Yellow Gray Gray
Yellow Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Yellow
Yellow Gray Green Green Gray Yellow Gray Gray Gray Gray Green Green Gray Gray Gray Gray Yellow Gray Green Green Gray Yellow
Blue Blue Green Green Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Green Green Blue Blue
Gray Gray Green Blue Gray Green Gray Yellow Gray Gray Gray Gray Gray Gray Yellow Gray Green Gray Blue Green Gray Gray
Gray Yellow Gray Blue Gray Yellow Blue Gray Gray Green Green Green Green Gray Gray Blue Yellow Gray Blue Gray Yellow Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Pink Pink Pink
Row 2: Orange Pink Orange Pink Pink Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Pink Pink Pink Pink Orange Pink Orange Pink Orange Pink Pink Pink Orange Orange
Row 3: Pink Pink Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Orange Pink Orange Pink Pink Orange Pink Orange Pink Orange Orange Orange Pink Orange Pink Pink
Row 4: Pink Orange Pink Pink Orange Pink Pink Orange Orange Pink Pink Pink Orange Pink Pink Orange Pink Yellow Yellow Pink Pink Pink Yellow Pink Orange Orange Orange Orange Pink
Row 5: Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Orange Pink Orange Pink Orange Yellow Pink Yellow Yellow Yellow Pink Yellow Orange Pink Pink Pink Pink
Row 6: Pink Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Pink Yellow Yellow Yellow Yellow Yellow Orange Pink Orange Pink Pink
Row 7: Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Orange Orange Pink Pink Pink Orange Pink Yellow Yellow Yellow Yellow Pink Pink Yellow Orange Pink Orange Pink Orange
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Pink Orange Pink Pink Pink Pink Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Row 9: Orange Orange Pink Orange Orange Pink Pink Orange Pink Orange Orange Pink Orange Orange Pink Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Pink Pink Pink Orange
Row 10: Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Orange Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange
Row 11: Pink Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Orange Pink Orange Orange Pink Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Pink
Row 12: Orange Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Orange Pink Orange Pink Orange Orange Orange Pink Pink Orange Orange Pink Pink Pink Orange Pink Orange Orange
Row 13: Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Pink Pink Orange Orange Orange Pink
Row 14: Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange
Output:
Row 1: Pink Pink Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Pink Pink Pink
Row 2: Orange Pink Orange Pink Pink Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Pink Pink Pink Pink Orange Pink Orange Pink Orange Pink Pink Pink Orange Orange
Row 3: Pink Pink Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Orange Pink Orange Pink Pink Orange Pink Orange Pink Orange Orange Orange Pink Orange Pink Pink
Row 4: Pink Orange Pink Pink Orange Pink Pink Orange Orange Pink Pink Pink Orange Pink Pink Orange Pink Yellow Yellow Green Green Green Yellow Green Orange Orange Orange Orange Pink
Row 5: Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Orange Pink Orange Pink Orange Yellow Green Yellow Yellow Yellow Green Yellow Orange Pink Pink Pink Pink
Row 6: Pink Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Pink Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Orange Pink Orange Pink Pink
Row 7: Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Orange Orange Pink Pink Pink Orange Pink Yellow Yellow Yellow Yellow Green Green Yellow Orange Pink Orange Pink Orange
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Pink Orange Pink Pink Pink Pink Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Row 9: Orange Orange Pink Orange Orange Pink Pink Orange Pink Orange Orange Pink Orange Orange Pink Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Pink Pink Pink Orange
Row 10: Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Orange Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange
Row 11: Pink Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Orange Pink Orange Orange Pink Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Pink
Row 12: Orange Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Orange Pink Orange Pink Orange Orange Orange Pink Pink Orange Orange Pink Pink Pink Orange Pink Orange Orange
Row 13: Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Pink Pink Orange Orange Orange Pink
Row 14: Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange
Example 2
Input:
Row 1: Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Purple
Row 2: Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple
Row 3: Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Yellow Purple Purple
Row 4: Yellow Purple Yellow Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 5: Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Purple Yellow Yellow
Row 7: Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Yellow
Row 9: Yellow Purple Yellow Yellow Purple Purple Purple Yellow Yellow Purple Purple Yellow Yellow Purple
Row 10: Purple Purple Yellow Purple Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 11: Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Purple Purple Yellow Purple
Row 13: Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple
Row 14: Brown Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Purple Purple Purple Yellow
Row 15: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 17: Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple
Row 18: Yellow Brown Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow
Row 19: Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Purple
Row 20: Brown Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Purple
Row 21: Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow
Row 22: Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Purple Purple Purple Purple
Row 23: Yellow Purple Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Yellow Yellow
Row 24: Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Yellow
Row 25: Purple Purple Purple Purple Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Purple
Row 26: Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 27: Purple Purple Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Purple
Output:
Row 1: Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Purple
Row 2: Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple
Row 3: Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Yellow Purple Purple
Row 4: Yellow Purple Yellow Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 5: Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Purple Yellow Yellow
Row 7: Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Yellow
Row 9: Yellow Purple Yellow Yellow Purple Purple Purple Yellow Yellow Purple Purple Yellow Yellow Purple
Row 10: Purple Purple Yellow Purple Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 11: Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow
Row 12: Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Purple Purple Yellow Purple
Row 13: Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple
Row 14: Brown Green Yellow Purple Yellow Purple Purple Yellow Purple Yellow Purple Purple Purple Yellow
Row 15: Brown Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Green Green Yellow Purple Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 17: Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple
Row 18: Green Brown Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow
Row 19: Green Green Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Purple
Row 20: Brown Green Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Purple
Row 21: Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow
Row 22: Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Purple Purple Purple Purple
Row 23: Yellow Purple Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Yellow Yellow
Row 24: Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple Yellow Yellow Yellow
Row 25: Purple Purple Purple Purple Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Purple
Row 26: Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 27: Purple Purple Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Purple
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Brown Pink Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 30: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Brown Green Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 30: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Orange Gray
Row 3: Gray Orange Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray
Row 4: Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Orange Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Purple
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Gray
Row 9: Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Orange Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Orange Orange Gray
Gray Orange Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray
Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Green Green Green Green
Gray Gray Gray Gray Gray Gray Orange Gray Gray Orange Gray Gray Gray Green Green Green Green Purple
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Gray
Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Orange Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Blue Purple Orange Blue Yellow Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange
Output:
Row 1: Pink Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Pink Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Blue Purple Pink Blue Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Blue Purple Pink Blue Yellow Orange Pink Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Blue Purple Pink Blue Yellow Orange Pink Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Blue Purple Pink Blue Yellow Orange Pink Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Blue Purple Pink Blue Yellow Orange Pink Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Blue Purple Pink Blue Yellow Orange Pink Orange Orange Orange Black Orange Orange Orange Orange
Example 2
Input:
Row 1: Blue Brown Brown Brown
Row 2: Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown
Row 4: Black Brown Brown Brown
Row 5: Blue Brown Brown Brown
Row 6: Brown Brown Brown Brown
Output:
Row 1: Blue Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Blue Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Blue Brown Brown Brown Brown Brown
Row 4: Black Brown Brown Blue Brown Brown Brown Brown
Row 5: Blue Black Brown Brown Blue Brown Brown Brown
Row 6: Brown Blue Black Brown Brown Blue Brown Brown
Row 7: Brown Brown Blue Black Brown Brown Blue Brown
Row 8: Brown Brown Brown Blue Black Brown Brown Blue
Row 9: Brown Brown Brown Brown Blue Black Brown Brown
Row 10: Brown Brown Brown Brown Brown Blue Black Brown
Row 11: Brown Brown Brown Brown Brown Brown Blue Black
Row 12: Brown Brown Brown Brown Brown Brown Brown Blue
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Brown Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Brown Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Blue Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Pink Purple Gray Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Yellow Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Yellow Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Red Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Black Purple Purple Purple Purple Purple Yellow Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Pink Purple Gray Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Pink Purple Gray Yellow Purple Purple Blue Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Pink Purple Gray Yellow Purple Purple Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Pink Purple Gray Yellow Purple Purple Blue Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Pink Purple Gray Yellow Purple Purple Blue Purple Purple Purple
Yellow Purple Purple Purple Purple Purple Purple Pink Purple Gray Yellow Purple Purple Blue Purple Purple
Purple Yellow Purple Purple Purple Purple Red Purple Pink Purple Gray Yellow Purple Purple Blue Purple
Purple Purple Yellow Purple Purple Purple Purple Red Purple Pink Purple Gray Yellow Purple Purple Blue
Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple Pink Purple Gray Yellow Purple Purple
Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple Pink Purple Gray Yellow Purple
Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple Pink Purple Gray Yellow
Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple Pink Purple Gray
Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple Pink Purple
Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple Pink
Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red Purple
Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown Red
Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow Brown
Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Yellow Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Black Black Black Black Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Black Black Black Black Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown
Row 6: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown
Row 7: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown
Row 8: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown
Row 9: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown
Row 10: Brown Brown Brown Brown Black Black Black Black Black Black Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Orange Brown Purple Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Orange Brown
Row 2: Orange Orange Brown
Row 3: Orange Orange Orange
Row 4: Orange Orange Orange
Row 5: Orange Orange Orange
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Gray Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Black Black Black Black Black Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Pink Pink Black Black Pink Pink Black Black Black
Row 11: Black Black Black Black Black Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Pink Pink Black Black Pink Pink Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Purple Purple Purple Purple Purple
Row 2: Purple Black Purple Black Black
Row 3: Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Black Black Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 6: Black Black Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 7: Black Black Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Gray Gray Black Gray Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Gray Gray Gray Black Black Black Black Black Black
Row 12: Black Black Black Black Black Gray Gray Gray Gray Black Black Black Black Black Black
Row 13: Black Black Black Black Black Gray Gray Gray Gray Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Gray Gray Gray Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Pink Pink Pink Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Gray Gray Black Gray
Row 2: Black Gray Gray Gray
Row 3: Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray
Row 5: Black Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Purple Purple Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red
Row 5: Red Purple Red Purple Purple Red Red Blue Blue Blue Red Red Red Red Red Red Red Red
Row 6: Red Purple Purple Purple Purple Red Red Red Red Blue Red Red Red Red Red Red Red Red
Row 7: Red Purple Purple Purple Purple Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Black Black Red Red Black Black Black Black
Row 14: Red Red Red Red Red Red Red Red Red Red Black Black Red Red Black Black Black Black
Row 15: Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black
Row 16: Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Purple Purple Red
Purple Red Purple Purple
Purple Purple Purple Purple
Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black
Row 2: Black Red Red Red Red Red Red Red Red
Row 3: Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black
Row 6: Black Black Yellow Yellow Yellow Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Green
Row 11: Black Black Black Black Black Black Black Black Black
Row 12: Black Gray Gray Gray Gray Gray Gray Black Black
Row 13: Black Black Black Pink Pink Pink Pink Pink Black
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Green
Row 10: Black Black Black Black Black Black Yellow Yellow Yellow
Row 11: Black Black Black Black Pink Pink Pink Pink Pink
Row 12: Black Black Black Gray Gray Gray Gray Gray Gray
Row 13: Black Red Red Red Red Red Red Red Red
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black
Row 9: Black Blue Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Blue
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 2: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Orange Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Gray Green Purple
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Green Purple
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Purple
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Purple
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple
Row 2: Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple
Row 3: Gray Gray Yellow Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple
Row 4: Gray Gray Yellow Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Brown Purple
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Brown Purple
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Purple
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Green Purple Purple Purple Orange Pink Orange Purple Purple Purple
Row 3: Purple Purple Purple Purple Brown Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Orange Purple Orange Purple Green Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Pink Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Blue Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Gray Purple Gray Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange
Row 13: Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Green Purple Purple Purple Orange Pink Orange Purple Purple Purple
Row 3: Purple Purple Purple Purple Brown Purple Purple Purple Green Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Pink Orange
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Orange Pink Orange Purple Green Purple Gray Purple Gray Purple Purple Purple Brown Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Orange Pink Orange Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Gray Gray Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Blue Gray Gray Purple Purple Brown Purple Purple Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Gray Purple Gray Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Pink Orange
Row 13: Purple Purple Purple Purple Purple Purple Purple Yellow Purple Blue Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Purple Purple
Row 4: Purple Purple Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Purple
Row 6: Brown Purple Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown
Row 9: Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Yellow Green Brown Brown Brown Brown Brown Brown Purple Brown Brown
Row 11: Brown Brown Green Yellow Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown
Row 14: Brown Brown Red Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 17: Brown Green Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown
Row 18: Green Brown Brown Red Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 21: Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 24: Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Brown Yellow
Row 25: Brown Brown Green Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown
Row 26: Brown Green Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Purple Purple
Row 4: Purple Purple Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Red Brown
Row 5: Red Brown Brown Brown Yellow Green Brown Brown Brown Brown Brown Brown Purple
Row 6: Brown Purple Brown Brown Green Yellow Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Brown Brown
Row 9: Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 10: Brown Brown Yellow Green Brown Brown Yellow Yellow Brown Brown Purple Brown Brown
Row 11: Brown Brown Green Yellow Brown Brown Yellow Green Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Green Yellow Brown Brown Brown Brown Brown
Row 13: Brown Brown Purple Purple Brown Brown Brown Brown Brown Yellow Yellow Brown Brown
Row 14: Brown Brown Red Brown Brown Brown Brown Brown Brown Yellow Green Brown Brown
Row 15: Brown Brown Brown Purple Brown Brown Purple Purple Brown Green Yellow Brown Brown
Row 16: Yellow Yellow Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 17: Yellow Green Brown Purple Purple Brown Brown Purple Brown Purple Purple Brown Brown
Row 18: Green Yellow Brown Red Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 19: Brown Brown Brown Brown Purple Brown Purple Purple Brown Brown Purple Brown Brown
Row 20: Brown Purple Purple Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 21: Brown Red Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown
Row 22: Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Green
Row 24: Brown Yellow Yellow Brown Brown Brown Yellow Yellow Brown Brown Brown Green Yellow
Row 25: Brown Yellow Green Brown Brown Brown Yellow Green Brown Brown Brown Brown Brown
Row 26: Brown Green Yellow Brown Brown Brown Green Yellow Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Gray Pink Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Orange Gray Pink Gray
Row 6: Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 7: Gray Gray Black Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 8: Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Blue Gray Gray Black Gray Gray Black Gray Gray Blue Gray Gray Gray Blue Gray
Row 12: Blue Gray Black Orange Gray Black Gray Gray Gray Blue Gray Gray Gray Blue Gray
Row 13: Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray
Output:
Row 1: Gray Pink Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Blue Gray Black Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Blue Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Blue Gray Gray Gray Pink Gray Blue Gray Gray Gray Black Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray Black Orange Gray Pink Gray
Row 6: Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray Gray Gray Gray Blue Gray
Row 7: Gray Gray Black Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 8: Gray Black Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray
Row 11: Blue Gray Gray Black Gray Gray Black Gray Gray Blue Gray Gray Gray Blue Gray
Row 12: Blue Gray Black Orange Gray Black Orange Gray Gray Blue Gray Gray Gray Blue Gray
Row 13: Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray
Here is the input grid for the test example:
Input:
Row 1: Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Black Red
Row 2: Red Red Red Red Pink Red Red Red Red Red Red Red Black Red Red Pink Red Red Red Red Red Red Red Red Gray Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Pink Red Red Yellow Red Red Red Red Red Red Red
Row 4: Pink Red Red Yellow Red Red Red Pink Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red
Row 5: Red Red Red Red Red Yellow Red Red Red Red Red Black Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink
Row 6: Red Black Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Pink Red Red Red Red Gray Red Red Pink Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Black Red Red Yellow Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Black Red Red
Row 9: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Red
Row 10: Red Red Pink Red Red Red Red Red Red Red Red Red Red Pink Red Pink Red Red Red Red Red Red Red Black Red Red Red Red Red Red
Row 11: Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Black Red Red Gray Red Red Black Red Red Yellow Red Red Red Red Black Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Gray Red Red Red Red Red Black Red Red Red Red Pink
Row 15: Red Pink Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Black Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red
Row 17: Red Yellow Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Yellow Red Black Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Pink Red Pink Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Black Red Red Yellow Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Black Red Red Yellow Red Black Red
Red Red Gray Red Pink Red Red Red Red Red Red Red Black Red Red Pink Red Yellow Red Yellow Red Red Red Red Gray Red Pink Red Red Gray
Yellow Red Red Red Red Red Red Yellow Red Yellow Red Red Red Gray Red Red Red Pink Red Pink Red Red Yellow Red Red Red Red Red Red Red
Pink Red Red Yellow Red Red Red Pink Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Yellow Red Yellow
Red Red Red Pink Red Yellow Red Red Red Red Red Black Red Red Yellow Red Yellow Red Red Red Black Red Red Red Yellow Red Red Pink Red Pink
Red Black Red Red Red Pink Red Red Red Red Red Red Gray Red Pink Red Pink Red Red Red Red Gray Red Red Pink Red Red Red Red Red
Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red
Yellow Red Red Red Red Black Red Red Yellow Red Yellow Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Yellow Red Black Red Red
Pink Red Yellow Red Red Red Gray Red Pink Red Pink Red Red Yellow Red Yellow Red Red Red Red Black Red Red Red Red Pink Red Red Gray Red
Red Red Pink Red Red Red Red Red Red Red Red Red Red Pink Red Pink Red Black Red Red Red Gray Red Black Red Red Red Red Red Red
Black Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Gray Red Red Red Red Red
Red Gray Red Black Red Red Black Red Red Gray Red Red Black Red Red Yellow Red Red Red Red Black Red Red Red Red Red Red Red Red Red
Red Red Red Red Gray Red Red Gray Red Red Red Red Red Gray Red Pink Red Black Red Red Red Gray Red Red Red Red Red Yellow Red Yellow
Red Yellow Red Red Red Red Red Red Red Yellow Red Yellow Red Red Red Red Red Red Gray Red Red Red Red Red Black Red Red Pink Red Pink
Red Pink Red Red Red Red Black Red Red Pink Red Pink Red Red Red Red Red Red Red Red Yellow Red Red Red Red Gray Red Red Red Red
Red Red Red Red Black Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Yellow Red Red Red Red Red Red
Red Yellow Red Red Red Gray Red Red Red Yellow Red Yellow Red Yellow Red Yellow Red Black Red Red Red Red Red Pink Red Red Yellow Red Black Red
Red Pink Red Red Red Red Red Red Red Pink Red Pink Red Pink Red Pink Red Red Gray Red Red Red Red Red Red Red Pink Red Red Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Red Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Red Purple Purple Purple Red Purple Purple Red
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 8: Purple Purple Purple Purple Red Purple Red Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Red Red Purple Red Red Purple Purple Purple
Row 2: Red Purple Red Red Red Red Purple Purple Red
Row 3: Red Red Red Red Red Purple Red Red Purple
Row 4: Red Red Red Purple Red Red Red Red Red
Row 5: Red Red Red Red Purple Red Red Red Red
Row 6: Red Purple Red Red Red Purple Red Red Red
Row 7: Purple Purple Purple Red Red Red Red Red Red
Row 8: Purple Purple Red Purple Red Red Red Red Red
Row 9: Purple Red Purple Red Red Red Red Red Purple
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 8: Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Output:
Row 1: Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue
Row 2: Yellow Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue
Row 3: Blue Yellow Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue
Row 4: Blue Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow
Row 5: Blue Blue Blue Yellow Blue Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 7: Blue Yellow Blue Yellow Yellow Yellow Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Blue Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Blue Yellow Yellow Yellow Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 10: Yellow Yellow Yellow Blue Yellow Yellow Blue Blue Yellow Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 11: Yellow Yellow Blue Blue Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Red Red Blue Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Blue
Row 4: Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Blue Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red
Row 9: Blue Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Blue Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Blue Red Red Red Red Red Blue Red Red
Row 2: Blue Blue Red Blue Red Red Red Blue Red Blue Blue
Row 3: Blue Blue Red Red Blue Red Blue Red Red Blue Blue
Row 4: Red Red Blue Red Red Blue Red Red Blue Blue Red
Row 5: Red Red Red Blue Blue Red Blue Blue Blue Red Blue
Row 6: Red Red Red Blue Blue Red Blue Blue Red Blue Red
Row 7: Red Red Blue Red Red Blue Blue Red Blue Red Red
Row 8: Red Blue Red Red Blue Blue Blue Blue Red Blue Red
Row 9: Blue Red Red Blue Blue Red Blue Blue Red Red Blue
Row 10: Red Blue Blue Blue Red Blue Red Red Blue Red Red
Row 11: Red Blue Blue Red Blue Red Red Red Red Blue Red
Row 12: Blue Blue Red Blue Red Red Red Red Red Red Blue
Row 13: Blue Red Blue Red Blue Red Red Red Red Red Red
Row 14: Red Blue Red Red Red Blue Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Gray Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green
Row 17: Green Gray Green Green Green Green Green Green Green
Row 18: Green Green Green Gray Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Gray
Green Green Green Green Green Green Green Gray Green
Gray Green Green Green Green Green Gray Green Green
Green Gray Green Green Green Gray Green Green Gray
Green Green Gray Green Gray Green Green Gray Green
Green Green Green Gray Green Green Gray Green Green
Green Green Gray Green Gray Gray Green Green Gray
Green Gray Green Green Gray Gray Green Gray Green
Gray Green Green Gray Green Green Gray Green Green
Gray Gray Gray Green Green Gray Green Gray Green
Green Gray Gray Green Gray Green Green Green Gray
Gray Green Gray Gray Green Green Green Green Green
Green Green Gray Gray Gray Green Green Green Green
Green Gray Green Green Gray Gray Green Green Green
Gray Green Green Green Green Gray Gray Green Green
Green Green Green Green Green Green Gray Gray Green
Green Green Green Green Green Green Green Gray Gray
Green Green Green Green Green Green Green Green Gray
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Blue Yellow Yellow Brown Blue Yellow Yellow
Row 2: Yellow Yellow Brown Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Purple Purple Blue Purple Purple Brown Blue Yellow Purple Yellow Yellow Purple Purple Blue Purple Purple Brown Blue Yellow Purple
Row 2: Yellow Yellow Brown Pink Purple Purple Purple Purple Purple Yellow Purple Yellow Yellow Brown Pink Purple Purple Purple Purple Purple Yellow Purple
Row 3: Yellow Yellow Gray Purple Purple Purple Purple Purple Purple Yellow Gray Yellow Yellow Gray Purple Purple Purple Purple Purple Purple Yellow Gray
Row 4: Yellow Yellow Purple Purple Purple Purple Pink Purple Purple Yellow Purple Yellow Yellow Purple Purple Purple Purple Pink Purple Purple Yellow Purple
Row 5: Yellow Yellow Purple Purple Purple Blue Purple Purple Purple Yellow Purple Yellow Yellow Purple Purple Purple Blue Purple Purple Purple Yellow Purple
Row 6: Yellow Yellow Purple Purple Blue Purple Purple Brown Blue Yellow Purple Yellow Yellow Purple Purple Blue Purple Purple Brown Blue Yellow Purple
Row 7: Yellow Yellow Brown Pink Purple Purple Purple Purple Purple Yellow Purple Yellow Yellow Brown Pink Purple Purple Purple Purple Purple Yellow Purple
Row 8: Yellow Yellow Gray Purple Purple Purple Purple Purple Purple Yellow Gray Yellow Yellow Gray Purple Purple Purple Purple Purple Purple Yellow Gray
Row 9: Yellow Yellow Purple Purple Purple Purple Pink Purple Purple Yellow Purple Yellow Yellow Purple Purple Purple Purple Pink Purple Purple Yellow Purple
Row 10: Yellow Yellow Purple Purple Purple Blue Purple Purple Purple Yellow Purple Yellow Yellow Purple Purple Purple Blue Purple Purple Purple Yellow Purple
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 2: Gray Brown Gray Gray Gray Gray Gray Yellow Orange Gray Gray Green
Row 3: Gray Gray Gray Gray Gray Gray Black Gray Gray Pink Gray Gray
Row 4: Gray Brown Gray Gray Gray Gray Yellow Gray Orange Gray Gray Gray
Row 5: Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Pink Gray Gray Red Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Black Green Gray Brown Gray Green
Output:
Row 1: Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Blue Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Blue
Row 2: Gray Brown Gray Purple Purple Gray Purple Yellow Orange Purple Gray Green Gray Brown Gray Purple Purple Gray Purple Yellow Orange Purple Gray Green
Row 3: Gray Purple Gray Purple Purple Gray Black Purple Purple Pink Gray Purple Gray Purple Gray Purple Purple Gray Black Purple Purple Pink Gray Purple
Row 4: Gray Brown Gray Purple Purple Gray Yellow Purple Orange Purple Gray Purple Gray Brown Gray Purple Purple Gray Yellow Purple Orange Purple Gray Purple
Row 5: Gray Purple Gray Orange Purple Gray Purple Purple Purple Purple Gray Purple Gray Purple Gray Orange Purple Gray Purple Purple Purple Purple Gray Purple
Row 6: Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple
Row 7: Gray Purple Gray Pink Purple Gray Red Purple Purple Purple Gray Purple Gray Purple Gray Pink Purple Gray Red Purple Purple Purple Gray Purple
Row 8: Gray Purple Gray Purple Blue Gray Purple Purple Purple Purple Gray Purple Gray Purple Gray Purple Blue Gray Purple Purple Purple Purple Gray Purple
Row 9: Gray Purple Gray Purple Purple Gray Black Green Purple Brown Gray Green Gray Purple Gray Purple Purple Gray Black Green Purple Brown Gray Green
Row 10: Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Blue Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Blue
Row 11: Gray Brown Gray Purple Purple Gray Purple Yellow Orange Purple Gray Green Gray Brown Gray Purple Purple Gray Purple Yellow Orange Purple Gray Green
Row 12: Gray Purple Gray Purple Purple Gray Black Purple Purple Pink Gray Purple Gray Purple Gray Purple Purple Gray Black Purple Purple Pink Gray Purple
Row 13: Gray Brown Gray Purple Purple Gray Yellow Purple Orange Purple Gray Purple Gray Brown Gray Purple Purple Gray Yellow Purple Orange Purple Gray Purple
Row 14: Gray Purple Gray Orange Purple Gray Purple Purple Purple Purple Gray Purple Gray Purple Gray Orange Purple Gray Purple Purple Purple Purple Gray Purple
Row 15: Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple Gray Purple Gray Purple Purple Gray Purple Purple Purple Purple Gray Purple
Row 16: Gray Purple Gray Pink Purple Gray Red Purple Purple Purple Gray Purple Gray Purple Gray Pink Purple Gray Red Purple Purple Purple Gray Purple
Row 17: Gray Purple Gray Purple Blue Gray Purple Purple Purple Purple Gray Purple Gray Purple Gray Purple Blue Gray Purple Purple Purple Purple Gray Purple
Row 18: Gray Purple Gray Purple Purple Gray Black Green Purple Brown Gray Green Gray Purple Gray Purple Purple Gray Black Green Purple Brown Gray Green
Example 3
Input:
Row 1: Pink Pink Black Pink Black Pink Orange Orange Pink Pink Pink
Row 2: Pink Pink Pink Pink Yellow Orange Yellow Pink Pink Pink Pink
Row 3: Pink Pink Pink Red Pink Black Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Orange Pink Pink Black Pink Pink
Output:
Row 1: Pink Pink Black Purple Black Purple Orange Orange Purple Pink Pink Pink Pink Black Purple Black Purple Orange Orange Purple Pink Pink
Row 2: Pink Pink Purple Purple Yellow Orange Yellow Purple Purple Pink Pink Pink Pink Purple Purple Yellow Orange Yellow Purple Purple Pink Pink
Row 3: Pink Pink Purple Red Purple Black Purple Purple Purple Pink Pink Pink Pink Purple Red Purple Black Purple Purple Purple Pink Pink
Row 4: Pink Pink Purple Purple Purple Orange Purple Purple Black Pink Pink Pink Pink Purple Purple Purple Orange Purple Purple Black Pink Pink
Row 5: Pink Pink Black Purple Black Purple Orange Orange Purple Pink Pink Pink Pink Black Purple Black Purple Orange Orange Purple Pink Pink
Row 6: Pink Pink Purple Purple Yellow Orange Yellow Purple Purple Pink Pink Pink Pink Purple Purple Yellow Orange Yellow Purple Purple Pink Pink
Row 7: Pink Pink Purple Red Purple Black Purple Purple Purple Pink Pink Pink Pink Purple Red Purple Black Purple Purple Purple Pink Pink
Row 8: Pink Pink Purple Purple Purple Orange Purple Purple Black Pink Pink Pink Pink Purple Purple Purple Orange Purple Purple Black Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Blue Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Gray Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Gray Yellow Yellow Blue Gray Blue Blue Yellow Yellow Yellow Yellow
Row 5: Gray Gray Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Blue Yellow Yellow Blue Gray Yellow Yellow Gray Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Blue Yellow Gray Blue Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Blue Blue Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Gray Yellow
Row 12: Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow
Row 13: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Blue Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow Purple Purple Blue Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow
Gray Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow Gray Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow
Purple Purple Purple Purple Blue Purple Purple Purple Blue Purple Purple Purple Yellow Purple Purple Purple Purple Blue Purple Purple Purple Blue Purple Purple Purple Yellow
Purple Purple Gray Purple Purple Blue Gray Blue Blue Purple Purple Purple Yellow Purple Purple Gray Purple Purple Blue Gray Blue Blue Purple Purple Purple Yellow
Gray Gray Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Yellow Gray Gray Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Yellow
Purple Purple Blue Purple Purple Blue Gray Purple Purple Gray Purple Purple Yellow Purple Purple Blue Purple Purple Blue Gray Purple Purple Gray Purple Purple Yellow
Purple Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Yellow Purple Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Yellow
Purple Purple Purple Purple Blue Purple Gray Blue Purple Purple Purple Purple Yellow Purple Purple Purple Purple Blue Purple Gray Blue Purple Purple Purple Purple Yellow
Purple Blue Blue Purple Purple Blue Purple Purple Blue Purple Purple Gray Yellow Purple Blue Blue Purple Purple Blue Purple Purple Blue Purple Purple Gray Yellow
Purple Purple Purple Blue Purple Purple Purple Purple Purple Gray Purple Gray Yellow Purple Purple Purple Blue Purple Purple Purple Purple Purple Gray Purple Gray Yellow
Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Purple Purple Blue Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow Purple Purple Blue Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow
Gray Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow Gray Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Yellow
Purple Purple Purple Purple Blue Purple Purple Purple Blue Purple Purple Purple Yellow Purple Purple Purple Purple Blue Purple Purple Purple Blue Purple Purple Purple Yellow
Purple Purple Gray Purple Purple Blue Gray Blue Blue Purple Purple Purple Yellow Purple Purple Gray Purple Purple Blue Gray Blue Blue Purple Purple Purple Yellow
Gray Gray Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Yellow Gray Gray Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Yellow
Purple Purple Blue Purple Purple Blue Gray Purple Purple Gray Purple Purple Yellow Purple Purple Blue Purple Purple Blue Gray Purple Purple Gray Purple Purple Yellow
Purple Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Yellow Purple Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Yellow
Purple Purple Purple Purple Blue Purple Gray Blue Purple Purple Purple Purple Yellow Purple Purple Purple Purple Blue Purple Gray Blue Purple Purple Purple Purple Yellow
Purple Blue Blue Purple Purple Blue Purple Purple Blue Purple Purple Gray Yellow Purple Blue Blue Purple Purple Blue Purple Purple Blue Purple Purple Gray Yellow
Purple Purple Purple Blue Purple Purple Purple Purple Purple Gray Purple Gray Yellow Purple Purple Purple Blue Purple Purple Purple Purple Purple Gray Purple Gray Yellow
Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Green Green Green Green Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Brown Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Yellow Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red Red Red Red Yellow
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Red Red Red Red Red Red
Row 8: Red Red Yellow Red Red Red Red Red Red Red Yellow Red Red Red Green Green Green Green Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Green Green Green Green Green Green Green Green Green Green
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Green Green
Row 12: Yellow Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Green Green
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Green Green
Row 14: Red Red Red Red Red Red Red Red Red Red Red Yellow Green Green Green Green Green Green Green Red Red Red Green Green
Row 15: Red Yellow Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Green Green
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Red Red
Row 18: Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Red Red
Row 19: Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Red Red
Row 20: Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Red Red
Row 21: Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Red Red
Row 22: Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green
Row 24: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green
Row 25: Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Green Green Green
Row 26: Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Red Red Red Red Red Brown Green Green
Output:
Row 1: Red Red Red Yellow Red Red Yellow Red Red Yellow Red Yellow Red Red Green Brown Brown Brown Yellow Red Yellow Yellow Red Red
Row 2: Red Red Red Red Yellow Yellow Red Yellow Yellow Red Yellow Red Red Red Brown Green Brown Brown Red Yellow Yellow Yellow Red Yellow
Row 3: Yellow Red Red Red Yellow Yellow Red Yellow Yellow Yellow Red Red Red Yellow Green Brown Brown Green Yellow Yellow Red Red Yellow Red
Row 4: Red Yellow Red Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Brown Brown Green Brown Yellow Yellow Red Yellow Red Yellow
Row 5: Yellow Red Yellow Red Red Yellow Red Yellow Red Red Yellow Yellow Red Yellow Brown Green Brown Brown Red Red Yellow Red Yellow Red
Row 6: Yellow Yellow Red Yellow Yellow Red Yellow Red Yellow Red Yellow Yellow Yellow Yellow Green Brown Brown Green Red Yellow Red Yellow Red Red
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Yellow Red Yellow Yellow Red Brown Brown Green Green Yellow Red Yellow Red Yellow Red
Row 8: Red Red Yellow Yellow Yellow Yellow Red Red Yellow Red Yellow Yellow Red Yellow Brown Green Green Brown Red Yellow Red Red Red Yellow
Row 9: Red Yellow Red Yellow Yellow Red Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Brown Green Brown Green Brown Green Green Green Brown Green
Row 10: Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Green Brown Green Brown Green Green Green Brown Green Green
Row 11: Red Yellow Red Red Red Yellow Yellow Yellow Yellow Red Yellow Yellow Green Brown Brown Green Brown Green Green Red Yellow Red Green Green
Row 12: Yellow Red Red Red Yellow Red Yellow Yellow Red Yellow Yellow Red Green Brown Brown Brown Green Brown Green Yellow Red Red Green Green
Row 13: Red Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Green Brown Brown Green Green Brown Red Red Red Green Green
Row 14: Yellow Red Yellow Red Yellow Yellow Red Yellow Yellow Yellow Red Yellow Green Brown Green Green Brown Brown Green Yellow Red Red Green Green
Row 15: Red Yellow Red Yellow Yellow Red Yellow Yellow Red Yellow Yellow Red Brown Green Green Green Brown Brown Green Red Yellow Red Green Green
Row 16: Yellow Red Yellow Yellow Yellow Yellow Yellow Red Red Yellow Yellow Yellow Red Yellow Red Yellow Red Red Yellow Green Green Brown Red Red
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Red Red Yellow Red Yellow Yellow Yellow Red Yellow Red Red Red Red Brown Green Green Yellow Red
Row 18: Brown Brown Green Brown Brown Green Brown Yellow Red Yellow Red Red Yellow Yellow Red Yellow Red Red Red Green Brown Green Red Yellow
Row 19: Brown Green Brown Brown Green Brown Brown Yellow Yellow Red Red Red Yellow Yellow Yellow Red Yellow Red Red Green Green Brown Red Red
Row 20: Green Brown Brown Brown Green Yellow Yellow Yellow Yellow Red Red Yellow Red Red Yellow Yellow Red Yellow Red Green Green Green Yellow Red
Row 21: Brown Brown Green Green Brown Red Yellow Yellow Red Yellow Yellow Red Red Red Red Yellow Yellow Red Yellow Green Green Green Red Yellow
Row 22: Brown Green Green Brown Green Yellow Red Red Yellow Yellow Yellow Red Red Red Red Red Brown Brown Green Brown Green Green Green Green
Row 23: Red Red Yellow Red Yellow Red Yellow Red Yellow Yellow Red Yellow Red Red Red Red Green Brown Brown Green Brown Green Green Green
Row 24: Red Yellow Red Yellow Red Red Red Yellow Red Red Yellow Red Yellow Red Red Red Green Green Brown Brown Green Brown Green Brown
Row 25: Yellow Red Yellow Red Red Red Yellow Red Yellow Green Green Brown Green Brown Green Green Red Red Red Yellow Yellow Green Brown Green
Row 26: Red Yellow Red Red Red Yellow Red Red Red Brown Green Green Brown Green Brown Green Red Red Red Red Yellow Brown Green Brown
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink
Row 4: Brown Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Gray Gray Orange Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Brown Brown Gray Orange Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray
Row 10: Orange Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Orange Gray Orange
Row 13: Gray Gray Gray Gray Orange Gray Orange Pink Brown Brown Brown Brown Brown Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Pink Brown Brown Gray Gray Orange Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray
Row 17: Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Gray Gray
Output:
Row 1: Gray Orange Gray Orange Orange Orange Orange Gray Gray Orange Orange Gray Orange Orange Orange Gray Orange
Row 2: Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray Orange Gray
Row 3: Pink Pink Brown Pink Brown Pink Pink Pink Pink Brown Brown Pink Pink Brown Pink Brown Pink
Row 4: Brown Pink Pink Brown Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink
Row 5: Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink
Row 6: Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Brown Pink
Row 7: Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Brown Pink Brown
Row 8: Gray Orange Orange Pink Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 9: Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 10: Orange Orange Gray Pink Pink Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink
Row 11: Orange Orange Orange Pink Pink Pink Pink Brown Pink Pink Brown Pink Brown Pink Pink Pink Pink
Row 12: Gray Gray Orange Orange Gray Orange Orange Pink Pink Pink Pink Brown Pink Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Gray Orange Pink Pink Pink Pink Pink Pink Orange Gray Orange Orange
Row 14: Orange Orange Gray Orange Orange Orange Orange Pink Pink Pink Brown Pink Pink Gray Orange Gray Orange
Row 15: Orange Orange Orange Gray Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Gray Orange Gray
Row 16: Gray Orange Orange Orange Orange Gray Orange Pink Brown Pink Pink Pink Pink Orange Orange Gray Orange
Row 17: Pink Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange
Row 18: Brown Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Brown Orange Orange
Row 19: Pink Pink Brown Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Gray Orange
Row 20: Pink Brown Pink Brown Brown Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Orange Gray
Row 21: Brown Pink Brown Brown Pink Pink Brown Pink Pink Pink Brown Pink Pink Brown Pink Orange Orange
Row 22: Pink Brown Brown Pink Pink Brown Pink Brown Pink Pink Brown Pink Pink Pink Brown Orange Orange
Row 23: Brown Brown Pink Pink Brown Pink Brown Pink Brown Pink Pink Brown Brown Pink Pink Gray Orange
Example 3
Input:
Row 1: Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Pink Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Pink Purple
Row 4: Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Pink Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Blue Yellow Purple Purple Purple Purple Purple Purple
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Pink Purple Pink Purple
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Purple Pink Purple Purple Purple
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Pink Purple
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Pink Purple Purple Purple
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow
Output:
Row 1: Purple Pink Purple Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple Yellow Yellow Blue Pink Purple Pink Purple Purple Pink
Row 2: Pink Purple Pink Purple Pink Purple Pink Purple Pink Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Pink Yellow Blue Yellow Purple Pink Purple Pink Pink Pink
Row 3: Purple Pink Purple Pink Purple Pink Purple Pink Purple Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Purple Blue Yellow Yellow Purple Purple Pink Pink Pink Purple
Row 4: Purple Purple Pink Purple Pink Purple Pink Purple Pink Pink Pink Purple Purple Pink Pink Pink Pink Pink Purple Pink Yellow Blue Yellow Purple Purple Pink Pink Purple Pink
Row 5: Purple Pink Purple Pink Purple Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple Blue Yellow Blue Purple Pink Pink Purple Pink Purple
Row 6: Pink Purple Purple Purple Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Yellow Blue Yellow Pink Pink Purple Pink Purple Pink
Row 7: Purple Purple Purple Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Purple Pink Pink Pink Pink Blue Yellow Blue Pink Pink Pink Purple Purple Pink
Row 8: Purple Purple Pink Purple Purple Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink Pink Purple Pink Pink Pink Blue Blue Blue Pink Pink Pink Purple Pink Pink
Row 9: Blue Blue Yellow Yellow Blue Yellow Yellow Blue Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Yellow Blue Blue Blue Blue Blue Pink Pink Purple Pink Pink Pink
Row 10: Blue Blue Yellow Blue Yellow Yellow Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Pink Purple Pink Pink Pink Pink
Row 11: Yellow Yellow Blue Yellow Yellow Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink
Row 12: Yellow Blue Yellow Blue Yellow Blue Blue Blue Yellow Yellow Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Pink Pink Pink Pink Pink Purple
Row 13: Blue Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Blue Blue Blue Yellow Blue Yellow Yellow Blue Pink Pink Pink Pink Purple Pink
Row 14: Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Pink Pink Pink Pink Pink Purple
Row 15: Yellow Yellow Blue Blue Blue Yellow Blue Yellow Blue Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink
Row 16: Yellow Blue Blue Blue Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue Purple Purple Pink Pink Pink Pink
Row 17: Blue Blue Blue Yellow Yellow Yellow Blue Yellow Blue Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue Yellow Pink Purple Purple Pink Pink Pink
Row 18: Blue Blue Yellow Yellow Yellow Blue Yellow Yellow Yellow Blue Yellow Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue Yellow Blue Purple Pink Purple Purple Pink Pink
Row 19: Blue Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Blue Yellow Pink Purple Pink Purple Purple Pink
Row 20: Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Purple Pink Purple Pink Purple Pink
Row 21: Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Yellow Blue Yellow Pink Purple Pink Purple Pink Purple
Row 22: Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Blue Yellow Blue Purple Pink Purple Pink Purple Pink
Row 23: Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Yellow Pink Purple Pink Purple Pink Purple
Row 24: Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Row 25: Yellow Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Blue Yellow
Row 26: Yellow Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow Blue Yellow Blue Yellow Blue
Row 27: Yellow Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Yellow Blue Yellow Blue Yellow
Row 28: Yellow Blue Blue Yellow Blue Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Yellow Blue
Here is the input grid for the test example:
Input:
Row 1: Orange Pink Black Black Black Black Black Black Black Black
Row 2: Pink Pink Black Black Black Black Black Black Black Black
Row 3: Pink Pink Black Black Black Black Black Black Black Black
Row 4: Pink Pink Black Black Black Black Black Black Black Black
Row 5: Orange Pink Black Black Black Black Black Black Black Black
Row 6: Pink Pink Black Black Black Black Black Black Black Black
Row 7: Pink Pink Black Black Black Black Black Black Black Black
Row 8: Pink Pink Black Black Black Black Black Black Black Black
Row 9: Pink Pink Black Black Black Black Black Black Black Black
Row 10: Orange Pink Black Black Black Black Black Black Black Black
Row 11: Pink Pink Black Black Black Black Black Black Red Black
Row 12: Pink Pink Black Black Black Black Black Black Black Black
Row 13: Pink Pink Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Pink Black Black Red Black Black Black Black Red
Pink Orange Black Red Black Black Black Black Red Black
Orange Pink Red Black Black Black Black Red Black Black
Pink Orange Black Red Black Black Red Black Black Black
Orange Pink Red Black Red Red Black Black Black Black
Pink Orange Black Red Red Red Black Black Black Black
Pink Pink Red Red Red Black Red Black Black Black
Pink Pink Red Red Black Red Black Red Black Black
Pink Orange Black Black Red Black Red Black Red Black
Orange Pink Black Black Black Red Black Red Black Red
Pink Orange Black Black Black Black Red Black Red Black
Pink Pink Red Black Black Black Black Red Black Red
Pink Pink Black Red Black Black Red Black Red Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Gray Gray Orange Green Brown Black Black Black Black Black Black
Row 4: Black Black Black Brown Black Orange Yellow Yellow Pink Green Black Black Black Black Black Black
Row 5: Black Black Black Red Orange Green Green Black Black Blue Black Black Black Black Black Black
Row 6: Black Black Black Blue Black Red Green Pink Orange Gray Black Black Black Black Black Black
Row 7: Black Black Black Black Black Gray Black Blue Brown Red Black Blue Black Black Black Black
Row 8: Black Black Black Brown Gray Black Brown Black Green Blue Green Brown Black Black Black Black
Row 9: Black Black Black Black Black Black Black Red Blue Green Blue Red Black Black Black Black
Row 10: Black Black Black Black Black Black Black Brown Green Blue Green Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Blue Black Red Brown Blue Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Gray Gray Orange Green Brown Brown Black Blue Red Brown Black
Row 4: Black Black Black Brown Black Orange Yellow Yellow Pink Green Gray Black Black Orange Black Black
Row 5: Black Black Black Red Orange Green Green Black Black Blue Black Gray Red Green Orange Gray
Row 6: Black Black Black Blue Black Red Green Pink Orange Gray Brown Black Green Green Yellow Gray
Row 7: Black Black Black Black Black Gray Black Blue Brown Red Black Blue Pink Black Yellow Orange
Row 8: Black Black Black Brown Gray Black Brown Black Green Blue Green Brown Orange Black Pink Green
Row 9: Black Black Black Brown Green Blue Gray Red Blue Green Blue Red Gray Blue Green Brown
Row 10: Black Black Black Green Pink Black Orange Brown Green Blue Green Black Brown Black Gray Brown
Row 11: Black Black Black Orange Yellow Black Pink Blue Black Red Brown Blue Black Gray Black Black
Row 12: Black Black Black Gray Yellow Green Green Black Brown Gray Orange Pink Green Red Black Blue
Row 13: Black Black Black Gray Orange Green Red Gray Black Blue Black Black Green Green Orange Red
Row 14: Black Black Black Black Black Orange Black Black Gray Green Pink Yellow Yellow Orange Black Brown
Row 15: Black Black Black Black Brown Red Blue Black Brown Brown Green Orange Gray Gray Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Purple Purple Pink Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Pink Purple Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Pink Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Purple Purple Purple Pink Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Pink Pink Purple Pink Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Brown Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Brown Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Brown Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Brown Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Brown Brown Brown Black Brown Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Brown Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Brown Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Brown Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Orange Purple Orange Purple Purple
Row 9: Purple Purple Orange Purple Orange Purple Purple Purple
Row 10: Purple Purple Purple Orange Purple Orange Orange Purple
Row 11: Purple Purple Orange Purple Purple Orange Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Orange Orange Orange Orange Orange Purple
Purple Purple Orange Orange Purple Orange Orange Purple
Purple Purple Orange Purple Orange Purple Orange Purple
Purple Purple Orange Orange Purple Orange Orange Purple
Purple Purple Orange Orange Orange Orange Orange Purple
Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Blue Green Green
Row 2: Black Gray Gray Gray Gray
Row 3: Blue Gray Pink Pink Gray
Row 4: Green Gray Pink Pink Gray
Output:
Row 1: Black Black Black Black Black Black Black Black Blue Blue Blue Blue Green Green Green Green Green Green Green Green
Row 2: Black Black Black Black Black Black Black Black Blue Blue Blue Blue Green Green Green Green Green Green Green Green
Row 3: Black Black Black Black Black Black Black Black Blue Blue Blue Blue Green Green Green Green Green Green Green Green
Row 4: Black Black Black Black Black Black Black Black Blue Blue Blue Blue Green Green Green Green Green Green Green Green
Row 5: Black Black Black Black Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red
Row 6: Black Black Black Black Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray
Row 7: Black Black Black Black Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray
Row 8: Black Black Black Black Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray
Row 9: Blue Blue Blue Blue Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 10: Blue Blue Blue Blue Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 11: Blue Blue Blue Blue Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 12: Blue Blue Blue Blue Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 13: Green Green Green Green Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 14: Green Green Green Green Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 15: Green Green Green Green Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 16: Green Green Green Green Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Example 2
Input:
Row 1: Blue Blue Gray Black
Row 2: Gray Gray Gray Black
Row 3: Black Black Black Purple
Output:
Row 1: Blue Blue Blue Blue Blue Blue Gray Gray Gray Black Black Black
Row 2: Blue Blue Blue Blue Blue Blue Gray Gray Gray Black Black Black
Row 3: Blue Blue Blue Blue Blue Blue Gray Gray Gray Black Black Black
Row 4: Gray Gray Gray Gray Gray Gray Red Gray Gray Black Black Black
Row 5: Gray Gray Gray Gray Gray Gray Gray Red Gray Black Black Black
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Red Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Purple Purple Purple
Row 8: Black Black Black Black Black Black Black Black Black Purple Purple Purple
Row 9: Black Black Black Black Black Black Black Black Black Purple Purple Purple
Example 3
Input:
Row 1: Green Pink Pink Orange
Row 2: Green Pink Pink Orange
Row 3: Green Pink Pink Orange
Row 4: Green Pink Pink Brown
Row 5: Pink Pink Pink Brown
Row 6: Orange Brown Brown Brown
Output:
Row 1: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 2: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 3: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 4: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 5: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 6: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 7: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 8: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 9: Green Green Green Pink Pink Pink Pink Pink Pink Orange Orange Orange
Row 10: Green Green Green Pink Pink Pink Pink Pink Pink Brown Brown Brown
Row 11: Green Green Green Pink Pink Pink Pink Pink Pink Brown Brown Brown
Row 12: Green Green Green Pink Pink Pink Pink Pink Pink Brown Brown Brown
Row 13: Pink Pink Pink Red Pink Pink Pink Pink Pink Brown Brown Brown
Row 14: Pink Pink Pink Pink Red Pink Pink Pink Pink Brown Brown Brown
Row 15: Pink Pink Pink Pink Pink Red Pink Pink Pink Brown Brown Brown
Row 16: Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Green Brown Yellow Black
Row 2: Purple Purple Purple Yellow
Row 3: Purple Purple Purple Brown
Row 4: Pink Purple Purple Green
Row 5: Pink Purple Purple Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black
Green Green Green Green Green Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black
Green Green Green Green Green Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black
Green Green Green Green Green Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black
Green Green Green Green Green Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown
Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown
Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown
Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown
Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Orange Purple Orange Gray Orange Orange Orange Brown Orange Orange Pink Orange Pink Orange Orange Brown
Row 2: Orange Brown Orange Orange Orange Purple Orange Brown Orange Brown Orange Orange Orange Orange Blue Brown Orange
Row 3: Gray Orange Brown Orange Orange Black Brown Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange
Row 4: Red Orange Purple Brown Orange Brown Orange Orange Orange Orange Orange Brown Orange Brown Orange Black Pink
Row 5: Blue Orange Orange Orange Brown Pink Orange Orange Orange Orange Pink Orange Brown Orange Orange Orange Orange
Output:
Row 1: Brown Orange Purple Orange Gray Orange Orange Orange Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 2: Yellow Brown Orange Orange Orange Purple Orange Brown Orange Brown Yellow Yellow Yellow Yellow Yellow Brown Orange
Row 3: Yellow Yellow Brown Orange Orange Black Brown Orange Orange Orange Brown Yellow Yellow Yellow Brown Orange Orange
Row 4: Yellow Yellow Yellow Brown Orange Brown Orange Orange Orange Orange Orange Brown Yellow Brown Orange Black Pink
Row 5: Yellow Yellow Yellow Yellow Brown Pink Orange Orange Orange Orange Pink Orange Brown Orange Orange Orange Orange
Example 2
Input:
Row 1: Black Red Red Red Red Red Red Red Black Red Red Red Red Red Red Green Black Red Red Purple Red Red Red Blue
Row 2: Red Black Red Red Red Red Purple Black Red Black Red Red Red Red Red Black Red Black Red Red Red Red Red Black
Row 3: Red Red Black Red Red Red Black Red Red Red Black Red Red Red Black Red Red Red Black Red Red Red Black Red
Row 4: Red Red Red Black Red Black Red Red Red Red Red Black Red Black Red Red Red Gray Red Black Red Black Red Red
Row 5: Red Red Red Red Black Red Red Red Red Red Red Red Black Red Red Red Red Gray Red Red Black Red Red Red
Output:
Row 1: Black Red Red Red Red Red Red Red Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Red Red Purple Red Red Red Blue
Row 2: Yellow Black Red Red Red Red Purple Black Red Black Yellow Yellow Yellow Yellow Yellow Black Red Black Red Red Red Red Red Black
Row 3: Yellow Yellow Black Red Red Red Black Red Red Red Black Yellow Yellow Yellow Black Red Red Red Black Red Red Red Black Yellow
Row 4: Yellow Yellow Yellow Black Red Black Red Red Red Red Red Black Yellow Black Red Red Red Gray Red Black Red Black Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Black Red Red Red Red Red Red Red Black Red Red Red Red Gray Red Red Black Yellow Yellow Yellow
Example 3
Input:
Row 1: Pink Green Gray Orange Green Gray Pink Red Gray Red
Row 2: Gray Pink Green Red Gray Pink Red Pink Red Orange
Row 3: Red Gray Pink Green Pink Gray Gray Gray Pink Gray
Row 4: Red Gray Red Pink Orange Gray Gray Green Gray Pink
Output:
Row 1: Pink Green Gray Orange Green Gray Pink Yellow Yellow Yellow
Row 2: Yellow Pink Green Red Gray Pink Red Pink Yellow Yellow
Row 3: Yellow Yellow Pink Green Pink Gray Gray Gray Pink Yellow
Row 4: Yellow Yellow Yellow Pink Orange Gray Gray Green Gray Pink
Here is the input grid for the test example:
Input:
Row 1: Gray Blue Green Blue Gray Green Blue Blue Gray Blue Red Red Gray Blue Brown Blue Gray Blue Brown Blue Gray Blue Blue Blue Gray Blue Green Blue
Row 2: Blue Gray Blue Gray Blue Gray Blue Gray Brown Gray Brown Gray Blue Gray Blue Gray Brown Gray Brown Gray Blue Gray Brown Gray Red Gray Green Gray
Row 3: Brown Red Gray Blue Red Blue Gray Blue Red Blue Gray Blue Blue Blue Gray Blue Blue Brown Gray Brown Blue Green Gray Blue Blue Brown Gray Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Blue Green Blue Gray Yellow Yellow Yellow Gray Blue Red Red Gray Blue Brown Blue Gray Yellow Yellow Yellow Gray Blue Blue Blue Gray Blue Green Blue
Yellow Gray Blue Gray Blue Gray Yellow Gray Brown Gray Brown Gray Yellow Gray Blue Gray Brown Gray Yellow Gray Blue Gray Brown Gray Yellow Gray Green Gray
Yellow Yellow Gray Blue Red Blue Gray Blue Red Blue Gray Yellow Yellow Yellow Gray Blue Blue Brown Gray Brown Blue Green Gray Yellow Yellow Yellow Gray Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Purple Purple Black Yellow Yellow Yellow Yellow
Row 2: Pink Pink Purple Purple Black Yellow Purple Purple Yellow
Row 3: Black Black Black Black Black Black Black Black Black
Row 4: Purple Purple Red Purple Black Purple Brown Brown Brown
Row 5: Purple Purple Purple Red Black Brown Brown Purple Brown
Output:
Row 1: Pink Pink Yellow Yellow
Row 2: Pink Pink Purple Yellow
Example 2
Input:
Row 1: Orange Red Orange Purple Red Yellow Yellow
Row 2: Orange Red Orange Purple Yellow Red Yellow
Row 3: Red Orange Red Purple Yellow Red Yellow
Row 4: Red Red Orange Purple Red Yellow Red
Row 5: Orange Orange Orange Purple Yellow Yellow Yellow
Row 6: Red Orange Orange Purple Red Yellow Red
Row 7: Orange Orange Orange Purple Red Yellow Red
Row 8: Purple Purple Purple Purple Purple Purple Purple
Row 9: Red Red Gray Purple Black Black Black
Row 10: Red Red Red Purple Black Red Red
Row 11: Red Red Red Purple Black Black Black
Row 12: Red Red Red Purple Black Red Black
Row 13: Red Red Red Purple Black Black Black
Row 14: Red Gray Red Purple Black Red Red
Row 15: Red Red Red Purple Black Red Black
Output:
Row 1: Orange Yellow Orange
Row 2: Orange Red Orange
Row 3: Yellow Orange Yellow
Row 4: Black Yellow Orange
Row 5: Orange Orange Orange
Row 6: Black Orange Orange
Row 7: Orange Orange Orange
Example 3
Input:
Row 1: Orange Orange Blue Blue Purple Blue Blue Blue Pink
Row 2: Blue Blue Blue Orange Purple Blue Pink Blue Pink
Row 3: Blue Blue Blue Orange Purple Pink Pink Blue Pink
Row 4: Blue Blue Orange Blue Purple Pink Blue Blue Pink
Row 5: Blue Blue Orange Blue Purple Pink Blue Blue Pink
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Blue Brown Blue Blue Purple Gray Blue Blue Blue
Row 8: Blue Brown Blue Brown Purple Gray Gray Gray Gray
Row 9: Blue Brown Brown Blue Purple Blue Gray Gray Gray
Row 10: Brown Blue Blue Brown Purple Gray Gray Gray Gray
Row 11: Blue Blue Brown Brown Purple Gray Gray Gray Gray
Output:
Row 1: Orange Orange Blue Pink
Row 2: Gray Pink Gray Orange
Row 3: Pink Pink Brown Orange
Row 4: Pink Gray Orange Pink
Row 5: Pink Gray Orange Pink
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Orange Green Black Orange Black
Row 2: Orange Brown Brown Green Black Black Black
Row 3: Brown Orange Brown Green Orange Orange Black
Row 4: Orange Orange Brown Green Orange Orange Black
Row 5: Orange Brown Orange Green Orange Orange Black
Row 6: Green Green Green Green Green Green Green
Row 7: Purple Orange Purple Green Orange Orange Orange
Row 8: Purple Purple Purple Green Pink Pink Orange
Row 9: Purple Purple Purple Green Orange Orange Orange
Row 10: Purple Purple Purple Green Orange Pink Orange
Row 11: Purple Purple Purple Green Pink Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Black
Black Brown Brown
Brown Purple Brown
Purple Purple Brown
Purple Brown Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Blue
Row 2: Brown Brown
Row 3: Blue Blue
Row 4: Yellow Pink
Row 5: Orange Gray
Row 6: Purple Blue
Row 7: Pink Brown
Row 8: Blue Brown
Row 9: Yellow Brown
Row 10: Yellow Gray
Row 11: Pink Blue
Row 12: Purple Blue
Row 13: Orange Brown
Row 14: Purple Brown
Row 15: Pink Yellow
Row 16: Pink Black
Row 17: Blue Blue
Row 18: Orange Brown
Row 19: Orange Orange
Row 20: Yellow Purple
Row 21: Gray Pink
Output:
Row 1: Black Brown Blue Black
Row 2: Brown Brown Blue Blue
Row 3: Brown Brown Brown Brown
Row 4: Blue Blue Blue Blue
Row 5: Yellow Yellow Pink Pink
Row 6: Orange Orange Gray Gray
Row 7: Purple Purple Blue Blue
Row 8: Pink Pink Brown Brown
Row 9: Blue Blue Brown Brown
Row 10: Yellow Yellow Brown Brown
Row 11: Yellow Yellow Gray Gray
Row 12: Pink Pink Blue Blue
Row 13: Purple Purple Blue Blue
Row 14: Orange Orange Brown Brown
Row 15: Purple Purple Brown Brown
Row 16: Pink Pink Yellow Yellow
Row 17: Pink Pink Black Black
Row 18: Blue Blue Blue Blue
Row 19: Orange Orange Brown Brown
Row 20: Orange Orange Orange Orange
Row 21: Yellow Yellow Purple Purple
Row 22: Gray Gray Pink Pink
Row 23: Black Gray Pink Black
Example 2
Input:
Row 1: Yellow Purple Brown Yellow Black Orange Red Yellow Black Orange Orange Yellow Purple Red Blue Black Brown Red
Row 2: Brown Red Pink Black Pink Brown Orange Brown Black Blue Yellow Yellow Black Blue Blue Black Red Black
Row 3: Yellow Brown Yellow Blue Purple Orange Red Red Pink Brown Black Red Yellow Black Red Pink Orange Black
Row 4: Brown Purple Pink Orange Purple Yellow Black Purple Purple Red Black Blue Yellow Black Orange Red Brown Orange
Row 5: Brown Purple Orange Yellow Brown Black Orange Red Red Black Pink Blue Black Brown Black Purple Yellow Black
Row 6: Blue Pink Black Pink Blue Purple Blue Black Orange Red Brown Yellow Orange Blue Pink Brown Yellow Yellow
Row 7: Brown Orange Blue Purple Yellow Red Orange Purple Brown Pink Brown Black Red Black Pink Black Orange Pink
Row 8: Orange Yellow Yellow Pink Purple Blue Red Blue Purple Blue Pink Brown Brown Black Brown Orange Pink Purple
Row 9: Pink Pink Pink Orange Pink Black Brown Black Purple Orange Brown Purple Orange Purple Black Brown Pink Brown
Row 10: Yellow Brown Pink Red Yellow Blue Pink Orange Red Black Purple Orange Orange Purple Purple Blue Purple Blue
Row 11: Blue Black Red Pink Blue Red Red Yellow Yellow Blue Purple Purple Blue Brown Brown Yellow Pink Yellow
Row 12: Yellow Blue Blue Orange Black Pink Black Black Orange Purple Brown Red Orange Red Black Pink Pink Red
Row 13: Brown Black Brown Red Brown Brown Purple Orange Blue Yellow Blue Yellow Pink Black Pink Red Red Blue
Row 14: Black Yellow Orange Black Black Pink Purple Orange Yellow Brown Blue Pink Black Yellow Brown Yellow Black Red
Row 15: Pink Red Pink Purple Black Blue Orange Blue Blue Blue Orange Red Yellow Black Yellow Blue Pink Purple
Row 16: Pink Yellow Orange Red Red Red Black Brown Blue Brown Black Black Purple Blue Blue Black Purple Yellow
Row 17: Pink Orange Blue Blue Purple Orange Pink Black Blue Yellow Pink Orange Orange Red Blue Purple Black Pink
Row 18: Blue Orange Black Brown Brown Orange Brown Black Orange Red Brown Yellow Brown Yellow Yellow Pink Pink Blue
Row 19: Red Purple Purple Brown Pink Brown Black Brown Orange Yellow Orange Yellow Pink Brown Orange Red Blue Orange
Row 20: Red Yellow Blue Black Black Red Blue Blue Purple Orange Purple Purple Blue Blue Purple Blue Black Red
Row 21: Blue Brown Brown Orange Pink Blue Brown Yellow Purple Pink Yellow Red Purple Pink Blue Brown Black Black
Row 22: Pink Yellow Pink Purple Black Blue Pink Black Brown Brown Brown Blue Blue Black Yellow Orange Black Pink
Output:
Row 1: Black Yellow Purple Brown Yellow Black Orange Red Yellow Black Orange Orange Yellow Purple Red Blue Black Brown Red Black
Row 2: Yellow Yellow Purple Brown Yellow Black Orange Red Yellow Black Orange Orange Yellow Purple Red Blue Black Brown Red Red
Row 3: Brown Brown Red Pink Black Pink Brown Orange Brown Black Blue Yellow Yellow Black Blue Blue Black Red Black Black
Row 4: Yellow Yellow Brown Yellow Blue Purple Orange Red Red Pink Brown Black Red Yellow Black Red Pink Orange Black Black
Row 5: Brown Brown Purple Pink Orange Purple Yellow Black Purple Purple Red Black Blue Yellow Black Orange Red Brown Orange Orange
Row 6: Brown Brown Purple Orange Yellow Brown Black Orange Red Red Black Pink Blue Black Brown Black Purple Yellow Black Black
Row 7: Blue Blue Pink Black Pink Blue Purple Blue Black Orange Red Brown Yellow Orange Blue Pink Brown Yellow Yellow Yellow
Row 8: Brown Brown Orange Blue Purple Yellow Red Orange Purple Brown Pink Brown Black Red Black Pink Black Orange Pink Pink
Row 9: Orange Orange Yellow Yellow Pink Purple Blue Red Blue Purple Blue Pink Brown Brown Black Brown Orange Pink Purple Purple
Row 10: Pink Pink Pink Pink Orange Pink Black Brown Black Purple Orange Brown Purple Orange Purple Black Brown Pink Brown Brown
Row 11: Yellow Yellow Brown Pink Red Yellow Blue Pink Orange Red Black Purple Orange Orange Purple Purple Blue Purple Blue Blue
Row 12: Blue Blue Black Red Pink Blue Red Red Yellow Yellow Blue Purple Purple Blue Brown Brown Yellow Pink Yellow Yellow
Row 13: Yellow Yellow Blue Blue Orange Black Pink Black Black Orange Purple Brown Red Orange Red Black Pink Pink Red Red
Row 14: Brown Brown Black Brown Red Brown Brown Purple Orange Blue Yellow Blue Yellow Pink Black Pink Red Red Blue Blue
Row 15: Black Black Yellow Orange Black Black Pink Purple Orange Yellow Brown Blue Pink Black Yellow Brown Yellow Black Red Red
Row 16: Pink Pink Red Pink Purple Black Blue Orange Blue Blue Blue Orange Red Yellow Black Yellow Blue Pink Purple Purple
Row 17: Pink Pink Yellow Orange Red Red Red Black Brown Blue Brown Black Black Purple Blue Blue Black Purple Yellow Yellow
Row 18: Pink Pink Orange Blue Blue Purple Orange Pink Black Blue Yellow Pink Orange Orange Red Blue Purple Black Pink Pink
Row 19: Blue Blue Orange Black Brown Brown Orange Brown Black Orange Red Brown Yellow Brown Yellow Yellow Pink Pink Blue Blue
Row 20: Red Red Purple Purple Brown Pink Brown Black Brown Orange Yellow Orange Yellow Pink Brown Orange Red Blue Orange Orange
Row 21: Red Red Yellow Blue Black Black Red Blue Blue Purple Orange Purple Purple Blue Blue Purple Blue Black Red Red
Row 22: Blue Blue Brown Brown Orange Pink Blue Brown Yellow Purple Pink Yellow Red Purple Pink Blue Brown Black Black Black
Row 23: Pink Pink Yellow Pink Purple Black Blue Pink Black Brown Brown Brown Blue Blue Black Yellow Orange Black Pink Pink
Row 24: Black Pink Yellow Pink Purple Black Blue Pink Black Brown Brown Brown Blue Blue Black Yellow Orange Black Pink Black
Example 3
Input:
Row 1: Black Black Black Black Black Black Gray Black Gray Gray Gray Black Gray Black Black Gray Gray
Row 2: Black Gray Black Gray Gray Black Black Black Black Black Black Gray Black Gray Gray Black Gray
Row 3: Black Gray Black Black Black Gray Black Black Black Black Gray Black Black Gray Black Black Gray
Row 4: Gray Gray Black Black Black Gray Black Black Gray Gray Gray Gray Black Black Black Black Gray
Row 5: Gray Gray Gray Gray Black Black Gray Black Gray Black Gray Gray Black Black Gray Gray Gray
Row 6: Black Black Black Gray Gray Gray Gray Black Black Gray Gray Black Gray Gray Gray Black Gray
Row 7: Gray Gray Black Black Black Gray Gray Gray Gray Gray Gray Black Black Gray Gray Gray Black
Row 8: Gray Black Black Gray Black Gray Gray Black Gray Gray Black Black Black Black Gray Black Black
Row 9: Gray Black Gray Gray Gray Black Black Gray Gray Gray Black Black Gray Black Black Black Black
Row 10: Gray Black Gray Gray Black Black Gray Gray Gray Gray Gray Black Gray Gray Black Gray Gray
Row 11: Gray Black Black Gray Gray Black Black Gray Gray Gray Gray Black Gray Black Black Black Black
Row 12: Black Gray Black Gray Black Black Black Black Gray Gray Black Black Black Black Black Gray Gray
Row 13: Black Gray Black Black Black Gray Gray Gray Gray Gray Black Gray Black Gray Black Black Gray
Row 14: Black Gray Black Gray Black Gray Black Black Gray Gray Gray Black Black Black Black Black Black
Row 15: Black Black Gray Black Black Gray Black Black Black Gray Gray Gray Gray Gray Gray Black Gray
Row 16: Gray Black Black Gray Black Gray Black Gray Black Gray Gray Black Black Black Black Gray Gray
Row 17: Black Black Black Black Gray Gray Black Black Gray Black Black Gray Gray Black Black Black Gray
Row 18: Black Gray Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray
Row 19: Gray Black Black Gray Gray Black Black Black Gray Black Black Gray Black Gray Black Gray Black
Row 20: Gray Gray Black Gray Gray Gray Gray Black Gray Black Gray Black Gray Black Black Black Black
Row 21: Gray Black Gray Black Black Gray Gray Black Gray Gray Black Black Black Black Gray Black Black
Output:
Row 1: Black Black Black Black Black Black Black Gray Black Gray Gray Gray Black Gray Black Black Gray Gray Black
Row 2: Black Black Black Black Black Black Black Gray Black Gray Gray Gray Black Gray Black Black Gray Gray Gray
Row 3: Black Black Gray Black Gray Gray Black Black Black Black Black Black Gray Black Gray Gray Black Gray Gray
Row 4: Black Black Gray Black Black Black Gray Black Black Black Black Gray Black Black Gray Black Black Gray Gray
Row 5: Gray Gray Gray Black Black Black Gray Black Black Gray Gray Gray Gray Black Black Black Black Gray Gray
Row 6: Gray Gray Gray Gray Gray Black Black Gray Black Gray Black Gray Gray Black Black Gray Gray Gray Gray
Row 7: Black Black Black Black Gray Gray Gray Gray Black Black Gray Gray Black Gray Gray Gray Black Gray Gray
Row 8: Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray Gray Black Black Gray Gray Gray Black Black
Row 9: Gray Gray Black Black Gray Black Gray Gray Black Gray Gray Black Black Black Black Gray Black Black Black
Row 10: Gray Gray Black Gray Gray Gray Black Black Gray Gray Gray Black Black Gray Black Black Black Black Black
Row 11: Gray Gray Black Gray Gray Black Black Gray Gray Gray Gray Gray Black Gray Gray Black Gray Gray Gray
Row 12: Gray Gray Black Black Gray Gray Black Black Gray Gray Gray Gray Black Gray Black Black Black Black Black
Row 13: Black Black Gray Black Gray Black Black Black Black Gray Gray Black Black Black Black Black Gray Gray Gray
Row 14: Black Black Gray Black Black Black Gray Gray Gray Gray Gray Black Gray Black Gray Black Black Gray Gray
Row 15: Black Black Gray Black Gray Black Gray Black Black Gray Gray Gray Black Black Black Black Black Black Black
Row 16: Black Black Black Gray Black Black Gray Black Black Black Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 17: Gray Gray Black Black Gray Black Gray Black Gray Black Gray Gray Black Black Black Black Gray Gray Gray
Row 18: Black Black Black Black Black Gray Gray Black Black Gray Black Black Gray Gray Black Black Black Gray Gray
Row 19: Black Black Gray Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 20: Gray Gray Black Black Gray Gray Black Black Black Gray Black Black Gray Black Gray Black Gray Black Black
Row 21: Gray Gray Gray Black Gray Gray Gray Gray Black Gray Black Gray Black Gray Black Black Black Black Black
Row 22: Gray Gray Black Gray Black Black Gray Gray Black Gray Gray Black Black Black Black Gray Black Black Black
Row 23: Black Gray Black Gray Black Black Gray Gray Black Gray Gray Black Black Black Black Gray Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Blue Black Black Brown Orange Green Brown Black Purple Black Red Pink Purple Black Pink Green Orange Black Pink Brown Brown
Row 2: Blue Red Orange Green Red Green Purple Red Red Green Orange Brown Purple Red Black Brown Brown Purple Green Blue Red
Row 3: Orange Blue Brown Green Orange Red Pink Purple Red Brown Pink Green Black Green Orange Brown Green Blue Purple Green Pink
Row 4: Orange Red Green Black Brown Green Purple Pink Orange Pink Orange Brown Purple Red Brown Blue Purple Orange Green Green Purple
Row 5: Blue Green Red Green Pink Green Orange Black Orange Purple Green Brown Blue Purple Orange Pink Blue Brown Orange Blue Red
Row 6: Red Pink Pink Red Blue Brown Blue Orange Blue Green Black Red Pink Green Red Brown Brown Black Pink Brown Black
Row 7: Blue Blue Purple Brown Brown Orange Red Black Pink Brown Pink Black Orange Purple Purple Red Purple Blue Pink Red Green
Row 8: Brown Black Green Brown Orange Blue Pink Orange Red Red Green Red Brown Black Pink Orange Red Pink Red Brown Red
Row 9: Pink Pink Red Pink Black Red Red Blue Blue Green Black Pink Pink Red Red Purple Red Green Green Purple Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Blue Black Black Brown Orange Green Brown Black Purple Black Red Pink Purple Black Pink Green Orange Black Pink Brown Brown Black
Blue Blue Black Black Brown Orange Green Brown Black Purple Black Red Pink Purple Black Pink Green Orange Black Pink Brown Brown Brown
Blue Blue Red Orange Green Red Green Purple Red Red Green Orange Brown Purple Red Black Brown Brown Purple Green Blue Red Red
Orange Orange Blue Brown Green Orange Red Pink Purple Red Brown Pink Green Black Green Orange Brown Green Blue Purple Green Pink Pink
Orange Orange Red Green Black Brown Green Purple Pink Orange Pink Orange Brown Purple Red Brown Blue Purple Orange Green Green Purple Purple
Blue Blue Green Red Green Pink Green Orange Black Orange Purple Green Brown Blue Purple Orange Pink Blue Brown Orange Blue Red Red
Red Red Pink Pink Red Blue Brown Blue Orange Blue Green Black Red Pink Green Red Brown Brown Black Pink Brown Black Black
Blue Blue Blue Purple Brown Brown Orange Red Black Pink Brown Pink Black Orange Purple Purple Red Purple Blue Pink Red Green Green
Brown Brown Black Green Brown Orange Blue Pink Orange Red Red Green Red Brown Black Pink Orange Red Pink Red Brown Red Red
Pink Pink Pink Red Pink Black Red Red Blue Blue Green Black Pink Pink Red Red Purple Red Green Green Purple Black Black
Black Pink Pink Red Pink Black Red Red Blue Blue Green Black Pink Pink Red Red Purple Red Green Green Purple Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Blue Pink Green Yellow
Row 2: Orange Orange Orange Orange Orange
Row 3: Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple
Output:
Row 1: Red Blue Pink Green Yellow
Row 2: Orange Orange Orange Orange Orange
Row 3: Red Red Red Red Red
Row 4: Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Gray Gray Brown Pink
Row 2: Gray Gray Brown Blue
Row 3: Gray Gray Brown Green
Row 4: Gray Gray Brown Orange
Output:
Row 1: Blue Pink Brown Pink
Row 2: Blue Pink Brown Blue
Row 3: Blue Pink Brown Green
Row 4: Blue Pink Brown Orange
Example 3
Input:
Row 1: Red Red Orange Brown
Row 2: Red Red Orange Gray
Row 3: Red Red Orange Green
Row 4: Red Red Orange Pink
Output:
Row 1: Gray Brown Orange Brown
Row 2: Gray Brown Orange Gray
Row 3: Gray Brown Orange Green
Row 4: Gray Brown Orange Pink
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Gray Gray Gray Gray Gray Gray
Row 14: Blue Orange Gray Pink Brown Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue
Orange Orange Orange Orange Orange Orange
Gray Gray Gray Gray Gray Gray
Pink Pink Pink Pink Pink Pink
Brown Brown Brown Brown Brown Brown
Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue
Orange Orange Orange Orange Orange Orange
Gray Gray Gray Gray Gray Gray
Pink Pink Pink Pink Pink Pink
Brown Brown Brown Brown Brown Brown
Green Green Green Green Green Green
Gray Gray Gray Gray Gray Gray
Blue Orange Gray Pink Brown Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Gray Gray Gray Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Black Gray Black Gray Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Black Black Black Gray Gray Gray Black Green Green Green Green Green Green Green Green Green Green Gray Black Black Black
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Black Black
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Black Black Black
Row 8: Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Black Yellow Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Purple
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Purple Purple Purple
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Purple Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Purple Purple Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Purple Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Black Black Black Green Green Purple Purple Purple Black Green Green Green Green Green Green Black Yellow Yellow Yellow
Row 24: Green Green Black Black Black Green Green Purple Black Black Black Green Green Green Green Green Green Black Black Black Yellow
Row 25: Green Green Black Black Black Green Green Black Black Black Black Green Green Green Green Green Green Black Black Black Black
Output:
Row 1: Purple Purple Purple Black Gray Gray Gray Black Yellow Yellow Yellow
Row 2: Purple Black Black Black Black Gray Black Black Black Black Yellow
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Gray Black Black Black Black Black Black Black Black Black Purple
Row 5: Gray Gray Black Black Black Black Black Black Black Purple Purple
Row 6: Gray Black Black Black Black Black Black Black Black Black Purple
Row 7: Black Black Black Black Black Black Black Black Black Black Black
Row 8: Gray Black Black Black Black Yellow Black Black Black Black Purple
Row 9: Gray Gray Gray Black Yellow Yellow Yellow Black Purple Purple Purple
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Yellow
Row 3: Gray Yellow Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Yellow
Row 4: Gray Yellow Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Gray Purple Purple Purple Yellow Yellow
Row 5: Gray Yellow Yellow Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Yellow
Row 6: Gray Yellow Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Yellow
Row 7: Gray Yellow Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray
Row 9: Gray Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray
Row 10: Gray Green Purple Purple Purple Purple Purple Gray Gray Purple Black Purple Purple Purple Purple Purple Purple Orange Gray
Row 11: Gray Green Purple Purple Purple Purple Purple Gray Gray Black Black Black Black Purple Purple Purple Purple Orange Gray
Row 12: Gray Green Green Green Green Green Purple Gray Gray Gray Gray Gray Gray Purple Orange Orange Orange Orange Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Orange Orange Orange Orange Orange Purple Gray Orange Orange Orange Orange Gray Purple Yellow Yellow Yellow Yellow Gray
Row 18: Gray Orange Purple Purple Purple Purple Purple Gray Purple Orange Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 19: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 20: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 21: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 22: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 23: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 24: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 25: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 26: Gray Orange Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Yellow Gray
Row 27: Gray Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Gray
Output:
Row 1: Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Purple Yellow Yellow Yellow Yellow
Row 2: Orange Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Yellow
Row 3: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 4: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 5: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 6: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 7: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 8: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 9: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 10: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 13: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 14: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow
Row 15: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 16: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange
Row 19: Green Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Orange
Row 20: Green Green Green Green Green Purple Black Black Black Black Purple Orange Orange Orange Orange
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Black Black Yellow Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Black
Row 3: Black Black Yellow Pink Black Black Black Gray Gray Gray Gray Black Black Black Black
Row 4: Black Black Yellow Pink Black Black Black Gray Gray Gray Gray Black Black Black Black
Row 5: Black Yellow Yellow Pink Black Black Black Gray Gray Gray Gray Black Black Black Black
Row 6: Black Black Yellow Pink Pink Black Black Gray Gray Gray Gray Black Black Black Black
Row 7: Black Black Yellow Pink Black Black Black Gray Gray Gray Gray Black Black Black Black
Row 8: Black Black Yellow Pink Black Black Black Gray Gray Gray Gray Black Black Black Black
Row 9: Black Black Yellow Pink Black Black Black Gray Gray Gray Gray Black Black Black Black
Row 10: Gray Gray Gray Pink Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Black Black Black Gray Black Black Black Black Gray Gray Gray Gray Gray Gray Gray
Row 12: Black Black Orange Gray Yellow Black Black Black Black Black Black Black Gray Gray Gray
Row 13: Black Orange Orange Gray Yellow Yellow Yellow Black Black Black Green Black Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Black Green Green Gray Gray Green Green Green Black Gray Yellow Yellow Yellow Yellow Gray
Row 21: Black Black Green Gray Gray Green Black Black Black Gray Black Black Yellow Black Gray
Row 22: Black Black Green Gray Gray Green Black Black Black Gray Black Black Black Black Gray
Row 23: Black Black Green Gray Gray Green Black Black Black Gray Black Black Black Black Gray
Row 24: Black Black Green Gray Gray Green Black Black Black Gray Black Black Black Black Gray
Row 25: Black Black Black Gray Gray Black Black Black Black Gray Black Black Black Black Gray
Output:
Row 1: Green Green Green Black Yellow Yellow Yellow Yellow Black Green Green
Row 2: Green Black Black Black Black Black Yellow Black Black Black Green
Row 3: Green Black Black Black Black Black Black Black Black Black Green
Row 4: Green Black Black Black Black Black Black Black Black Black Green
Row 5: Green Black Black Black Black Black Black Black Black Black Green
Row 6: Black Black Black Black Black Black Black Black Black Black Black
Row 7: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 8: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 9: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 10: Pink Pink Black Black Black Black Black Black Black Yellow Yellow
Row 11: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 12: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 13: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 14: Pink Black Black Black Black Black Black Black Black Black Yellow
Row 15: Black Black Black Black Black Black Black Black Black Black Black
Row 16: Yellow Black Black Black Black Black Green Black Black Black Orange
Row 17: Yellow Yellow Yellow Black Green Green Green Green Black Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Black Black Black Blue Blue Blue Brown Brown Brown Blue Blue Blue Black Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Black Black Black Blue Blue Blue Black Brown Black Blue Blue Blue Black Black Black Black Black Black Black Black Brown Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Black Black Black Blue Blue Blue Black Black Black Blue Blue Blue Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Purple Purple Black Blue Blue Blue Blue Purple Black Black Blue Black Black Black Black Black Black Black Black Brown Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Purple Black Black Blue Blue Blue Blue Purple Purple Black Blue Black Black Black Black Black Black Black Brown Brown Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Black Black Black Blue Blue Blue Blue Purple Black Black Blue Black Black Black Black Black Black Black Black Brown Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Black Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue
Row 12: Blue Blue Blue Purple Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue
Row 13: Blue Blue Blue Purple Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue
Row 14: Blue Blue Blue Purple Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue
Row 15: Blue Blue Blue Purple Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue
Row 16: Blue Blue Blue Purple Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue
Row 17: Blue Blue Blue Purple Black Black Blue Blue Black Brown Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue
Row 18: Blue Blue Blue Purple Purple Black Blue Blue Brown Brown Brown Blue Blue Blue Blue Blue Black Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Black Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown
Purple Black Black Black Brown Black Black Black Black Black Black Black Black Black Brown
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Brown
Purple Purple Black Black Black Black Black Black Black Black Black Black Black Brown Brown
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Brown
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Purple Black Black Black Brown Black Black Black Black Black Black Black Black Black Purple
Purple Purple Black Brown Brown Brown Black Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Red Orange Green Brown Brown Brown Green Brown Orange Brown Brown Green Red Red Red Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Green Orange Brown Brown Green Brown Brown Brown Orange Green Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Orange Brown Brown Brown Brown Brown Green Orange Orange Red Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Red Orange Orange Brown Red Brown Orange Orange Orange Orange Brown Red Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Red Green Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Green Brown Orange Brown Orange Brown Red Green Brown Brown Red Orange Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Green Brown Red Orange Brown Red Brown Brown Red Brown Brown Brown Red Red Green Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Red Brown Brown Brown Red Green Orange Green Brown Brown Green Brown Red Green Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Green Brown Red Orange Brown Red Brown Brown Red Brown Brown Brown Red Red Green Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Red Brown Brown Brown Red Green Orange Green Brown Brown Green Brown Red Green Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Red Orange Green Brown Brown Brown Green Brown Orange Brown Brown Green Red Red Red Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Green Orange Brown Brown Green Brown Brown Brown Orange Green Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Orange Brown Brown Brown Brown Brown Green Orange Orange Red Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Red Orange Orange Brown Red Brown Orange Orange Orange Orange Brown Red Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Red Green Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Green Brown Orange Brown Orange Brown Red Green Brown Brown Red Orange Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Green Brown Red Orange Brown Red Brown Brown Red Brown Brown Brown Red Red Green Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Red Brown Brown Brown Red Green Orange Green Brown Brown Green Brown Red Green Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Red Orange Green Brown Brown Brown Green Brown Orange Brown Brown Green Red Red Red Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Green Orange Brown Brown Green Brown Brown Brown Orange Green Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Orange Brown Brown Brown Brown Brown Green Orange Orange Red Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Red Orange Orange Brown Red Brown Orange Orange Orange Orange Brown Red Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Red Green Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Green Brown Orange Brown Orange Brown Red Green Brown Brown Red Orange Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Green Brown Red Orange Brown Red Brown Brown Red Brown Brown Brown Red Red Green Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Red Brown Brown Brown Red Green Orange Green Brown Brown Green Brown Red Green Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Red Orange Green Brown Brown Brown Green Brown Orange Brown Brown Green Red Red Red Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Green Orange Brown Brown Green Brown Brown Brown Orange Green Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Orange Brown Brown Brown Brown Brown Green Orange Orange Red Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Red Orange Orange Brown Red Brown Orange Orange Orange Orange Brown Red Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Red Green Green Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Green Brown Orange Brown Orange Brown Red Green Brown Brown Red Orange Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Green Brown Red Orange Brown Red Brown Brown Red Brown Brown Brown Red Red Green Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Red Brown Brown Brown Red Green Orange Green Brown Brown Green Brown Red Green Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Black Black
Row 9: Black Black Black Black Black Red Red Red Red Red Red Red Black Black Black Purple Purple Purple Black Black
Row 10: Black Black Black Black Black Red Red Red Red Red Red Red Black Black Black Purple Purple Purple Black Black
Row 11: Black Black Black Black Black Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black
Row 19: Gray Gray Gray Gray Gray Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black
Row 20: Gray Gray Gray Gray Gray Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black
Row 21: Gray Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Gray Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Gray Gray Gray Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Gray
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Black Orange Orange Orange Orange Orange Orange Black
Row 10: Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Black Orange Orange Orange Orange Orange Orange Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Black
Row 14: Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Black
Row 15: Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Gray Gray Gray Gray Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black
Row 20: Black Gray Black Gray Gray Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black
Row 21: Black Gray Black Gray Gray Black Black Black Black Brown Brown Brown Black Black Black Green Green Green Green Green Green Black
Row 22: Black Gray Gray Gray Gray Black Black Black Black Brown Brown Brown Black Black Black Green Green Green Green Green Green Black
Row 23: Black Black Black Black Black Black Black Black Black Brown Brown Brown Black Black Black Green Green Green Green Green Green Black
Row 24: Black Black Black Black Black Black Black Black Black Brown Brown Brown Black Black Black Green Green Green Green Green Green Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Gray
Example 3
Input:
Row 1: Brown Brown Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Pink Pink Pink Pink Green Green Green Green Brown Brown
Row 4: Brown Brown Pink Pink Pink Pink Green Green Green Green Brown Brown
Row 5: Brown Brown Pink Pink Pink Pink Green Green Green Green Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Green Green Green Green Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Red Red Red Red Red Red Brown Brown Brown
Row 9: Brown Brown Brown Red Brown Brown Red Red Red Brown Brown Brown
Row 10: Brown Brown Brown Red Red Red Red Red Red Brown Brown Brown
Row 11: Brown Brown Brown Red Red Red Red Red Red Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Red
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Orange Orange Orange Orange Gray Gray
Row 2: Gray Gray Gray Gray Orange Orange Orange Orange Gray Gray
Row 3: Pink Pink Pink Gray Orange Orange Orange Orange Gray Gray
Row 4: Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 5: Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 6: Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray
Row 7: Brown Brown Brown Gray Gray Blue Blue Blue Blue Gray
Row 8: Brown Brown Brown Gray Gray Blue Blue Blue Blue Gray
Row 9: Brown Brown Brown Gray Gray Blue Blue Blue Blue Gray
Row 10: Brown Brown Brown Green Green Green Green Green Gray Gray
Row 11: Brown Brown Brown Green Green Green Green Green Gray Gray
Row 12: Brown Brown Brown Green Green Green Green Green Gray Gray
Row 13: Brown Brown Brown Green Green Green Green Green Gray Gray
Row 14: Purple Purple Purple Yellow Yellow Yellow Gray Gray Gray Gray
Row 15: Purple Purple Purple Yellow Yellow Yellow Gray Gray Gray Gray
Row 16: Purple Purple Purple Yellow Yellow Yellow Gray Gray Gray Gray
Row 17: Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 18: Purple Purple Purple Gray Gray Gray Black Black Black Gray
Row 19: Purple Purple Purple Gray Gray Gray Black Black Black Gray
Row 20: Gray Gray Gray Gray Gray Gray Black Black Black Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray
Row 2: Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray
Row 3: Gray Purple Gray Gray Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Gray
Row 4: Gray Purple Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Purple Gray Purple Gray Gray Gray Purple Gray
Row 5: Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray
Row 9: Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray
Row 10: Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray
Row 11: Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray
Row 12: Gray Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Purple Purple Purple Purple Purple Pink Gray Gray Gray Pink Pink Gray Gray Pink Purple Purple Purple Purple Purple Gray
Row 2: Gray Purple Gray Pink Gray Purple Pink Gray Gray Gray Pink Pink Gray Gray Pink Purple Gray Pink Gray Purple Gray
Row 3: Pink Purple Pink Pink Pink Purple Pink Pink Pink Purple Purple Purple Purple Purple Pink Purple Pink Pink Pink Purple Pink
Row 4: Gray Purple Gray Pink Gray Purple Pink Gray Gray Purple Pink Pink Gray Purple Pink Purple Gray Pink Gray Purple Gray
Row 5: Pink Purple Purple Purple Purple Purple Pink Pink Pink Purple Pink Pink Pink Purple Pink Purple Purple Purple Purple Purple Pink
Row 6: Gray Gray Gray Pink Gray Gray Pink Gray Gray Purple Pink Pink Gray Purple Pink Gray Gray Pink Gray Gray Gray
Row 7: Gray Gray Gray Pink Gray Gray Pink Gray Gray Purple Purple Purple Purple Purple Pink Gray Gray Pink Gray Gray Gray
Row 8: Gray Purple Purple Purple Purple Purple Pink Gray Purple Purple Purple Purple Purple Gray Pink Purple Purple Purple Purple Purple Gray
Row 9: Gray Purple Gray Pink Gray Purple Pink Gray Purple Gray Pink Pink Purple Gray Pink Purple Gray Pink Gray Purple Gray
Row 10: Pink Purple Pink Pink Pink Purple Pink Pink Purple Pink Pink Pink Purple Pink Pink Purple Pink Pink Pink Purple Pink
Row 11: Gray Purple Gray Pink Gray Purple Pink Gray Purple Gray Pink Pink Purple Gray Pink Purple Gray Pink Gray Purple Gray
Row 12: Gray Purple Purple Purple Purple Purple Pink Gray Purple Purple Purple Purple Purple Gray Pink Purple Purple Purple Purple Purple Gray
Row 13: Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray
Row 14: Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Pink Purple Purple Purple Purple Purple Pink Gray Gray Gray
Row 15: Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Pink Purple Gray Pink Gray Purple Pink Gray Gray Gray
Row 16: Pink Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink
Row 17: Gray Gray Gray Pink Purple Gray Pink Gray Purple Gray Pink Pink Purple Gray Pink Gray Purple Pink Gray Gray Gray
Row 18: Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Pink
Row 19: Gray Gray Gray Pink Purple Gray Pink Gray Purple Gray Pink Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray
Row 20: Gray Gray Gray Pink Purple Purple Purple Purple Purple Gray Pink Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue
Row 5: Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 6: Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 7: Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 8: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue
Row 11: Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 12: Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 13: Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 14: Blue Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 4: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue
Row 5: Gray Blue Pink Pink Gray Blue Blue Blue Blue Blue Blue
Row 6: Gray Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink
Row 7: Gray Blue Pink Pink Gray Blue Blue Blue Blue Blue Blue
Row 8: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue
Row 11: Blue Gray Pink Pink Blue Gray Blue Blue Blue Blue Blue
Row 12: Pink Gray Pink Pink Pink Gray Pink Pink Pink Pink Pink
Row 13: Blue Gray Pink Pink Blue Gray Blue Blue Blue Blue Blue
Row 14: Blue Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue
Row 15: Blue Blue Pink Pink Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Blue Blue Blue
Row 6: Brown Brown Brown Brown Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 7: Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 8: Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 9: Brown Blue Blue Blue Brown Blue Brown Brown Brown Brown Brown Blue Blue Blue
Row 10: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Brown Blue Blue Blue Brown Blue Brown Brown Brown Brown Brown Blue Blue Blue
Row 17: Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 18: Brown Brown Brown Brown Brown Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Blue Blue Blue
Output:
Row 1: Brown Brown Brown Brown Brown Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 2: Brown Blue Pink Blue Brown Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 3: Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Brown Blue Pink Blue Brown Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 5: Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Blue Blue Blue
Row 6: Brown Brown Brown Brown Brown Blue Brown Blue Pink Blue Brown Blue Blue Blue
Row 7: Brown Pink Pink Pink Brown Pink Brown Pink Pink Pink Brown Pink Pink Pink
Row 8: Brown Pink Pink Pink Brown Pink Brown Pink Pink Pink Brown Pink Pink Pink
Row 9: Brown Blue Pink Blue Brown Blue Brown Brown Brown Brown Brown Blue Blue Blue
Row 10: Brown Brown Brown Brown Brown Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 11: Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 12: Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 13: Blue Blue Pink Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 14: Brown Brown Brown Brown Brown Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 15: Brown Blue Pink Blue Brown Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 16: Brown Pink Pink Pink Brown Pink Brown Brown Brown Brown Brown Pink Pink Pink
Row 17: Brown Blue Pink Blue Brown Blue Brown Blue Pink Blue Brown Blue Blue Blue
Row 18: Brown Brown Brown Brown Brown Pink Brown Pink Pink Pink Brown Pink Pink Pink
Row 19: Blue Blue Pink Blue Blue Blue Brown Blue Pink Blue Brown Blue Blue Blue
Row 20: Blue Blue Pink Blue Blue Blue Brown Brown Brown Brown Brown Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Green Green Green Green Green Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Green Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Green Green Green Green Yellow
Row 17: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Green Yellow
Row 18: Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green
Row 22: Yellow Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green
Row 23: Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Green Yellow Yellow Yellow Green
Row 24: Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Green
Row 25: Yellow Green Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Green Green Green Green Green
Row 26: Yellow Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Pink Yellow Yellow Pink Pink Yellow Yellow
Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Green Green Green Green Green Pink Pink Yellow Yellow
Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Green Yellow Pink Yellow Green Pink Pink Yellow Yellow
Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink
Yellow Yellow Yellow Pink Green Yellow Pink Yellow Green Green Yellow Pink Yellow Green Green Green Green Green Green Yellow Green Yellow Pink Yellow Green Pink Pink Yellow Yellow
Pink Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink Pink Green Green Pink Pink Pink Green Pink Green Green Green Green Green Pink Pink Pink Pink
Pink Pink Pink Pink Green Pink Pink Pink Green Green Pink Pink Pink Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Yellow Yellow Yellow Pink Green Green Green Green Green Green Green Green Green Green Green Pink Pink Yellow Green Yellow Pink Yellow Pink Green Green Green Green Green Yellow
Yellow Yellow Yellow Pink Yellow Yellow Pink Green Green Green Green Green Yellow Yellow Green Green Green Green Green Yellow Pink Yellow Pink Green Yellow Pink Pink Green Yellow
Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink
Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Green Green Green Green Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink
Yellow Yellow Yellow Pink Yellow Yellow Pink Green Pink Pink Yellow Green Yellow Green Yellow Pink Pink Green Yellow Yellow Pink Yellow Pink Green Green Green Green Green Yellow
Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Green Pink Pink Pink Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink
Yellow Yellow Yellow Pink Green Green Green Green Green Pink Yellow Pink Yellow Green Yellow Pink Pink Green Green Yellow Pink Yellow Green Yellow Yellow Pink Pink Yellow Yellow
Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Green Green Green Green Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Green Green Green Green Green Pink
Yellow Yellow Yellow Pink Green Yellow Pink Yellow Green Green Green Green Green Green Yellow Pink Pink Yellow Green Green Green Green Green Green Yellow Pink Pink Green Yellow
Pink Pink Pink Pink Green Green Green Green Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink
Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Pink Green Yellow Pink Yellow Green Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Pink Green Green Green Green Green Yellow
Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Pink Green Green Green Green Green Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Pink Yellow Green Green Green Green Green
Yellow Green Green Green Green Green Green Green Green Green Green Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Pink Yellow Green Pink Pink Yellow Green
Pink Green Pink Pink Pink Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Green Pink Pink Pink Green
Pink Green Pink Pink Pink Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Pink Pink Pink Green
Pink Green Pink Pink Pink Green Green Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Green Pink Green Green Green Green Green
Yellow Green Green Green Green Green Green Green Green Green Green Pink Yellow Yellow Yellow Pink Pink Yellow Green Yellow Pink Yellow Green Yellow Yellow Pink Pink Yellow Yellow
Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Pink Pink Yellow Pink Yellow Yellow Yellow Pink Pink Yellow Green Green Green Green Green Yellow Yellow Pink Pink Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Black Orange Gray Gray Gray Gray Black Gray Gray
Row 2: Gray Gray Orange Gray Gray Pink Gray Orange Gray Gray
Row 3: Gray Orange Gray Orange Black Pink Pink Black Gray Black
Row 4: Gray Orange Black Orange Orange Gray Black Gray Orange Black
Row 5: Pink Orange Black Pink Orange Gray Pink Black Gray Gray
Row 6: Pink Gray Orange Orange Gray Gray Orange Gray Gray Gray
Row 7: Gray Pink Orange Gray Orange Orange Gray Orange Gray Black
Row 8: Orange Orange Orange Black Gray Pink Black Gray Gray Pink
Row 9: Gray Gray Black Gray Gray Gray Orange Black Black Gray
Row 10: Orange Gray Black Gray Black Orange Pink Gray Pink Gray
Row 11: Orange Pink Gray Black Gray Gray Pink Gray Black Pink
Row 12: Gray Gray Pink Black Pink Gray Black Gray Orange Orange
Row 13: Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink
Row 14: Gray Gray Gray Pink Pink Gray Black Pink Gray Black
Row 15: Black Orange Gray Pink Black Gray Pink Gray Gray Orange
Row 16: Gray Orange Gray Gray Pink Gray Pink Gray Gray Pink
Output:
Row 1: Orange Black Orange Gray Gray Gray Gray Black Gray Gray Gray Gray Black Gray Gray Gray Gray Orange Black Orange
Row 2: Gray Gray Orange Gray Gray Pink Gray Orange Gray Gray Gray Gray Orange Gray Pink Gray Gray Orange Gray Gray
Row 3: Gray Orange Gray Orange Black Pink Pink Black Gray Black Black Gray Black Pink Pink Black Orange Gray Orange Gray
Row 4: Gray Orange Black Orange Orange Gray Black Gray Orange Black Black Orange Gray Black Gray Orange Orange Black Orange Gray
Row 5: Pink Orange Black Pink Orange Gray Pink Black Gray Gray Gray Gray Black Pink Gray Orange Pink Black Orange Pink
Row 6: Pink Gray Orange Orange Gray Gray Orange Gray Gray Gray Gray Gray Gray Orange Gray Gray Orange Orange Gray Pink
Row 7: Gray Pink Orange Gray Orange Orange Gray Orange Gray Black Black Gray Orange Gray Orange Orange Gray Orange Pink Gray
Row 8: Orange Orange Orange Black Gray Pink Black Gray Gray Pink Pink Gray Gray Black Pink Gray Black Orange Orange Orange
Row 9: Gray Gray Black Gray Gray Gray Orange Black Black Gray Gray Black Black Orange Gray Gray Gray Black Gray Gray
Row 10: Orange Gray Black Gray Black Orange Pink Gray Pink Gray Gray Pink Gray Pink Orange Black Gray Black Gray Orange
Row 11: Orange Pink Gray Black Gray Gray Pink Gray Black Pink Pink Black Gray Pink Gray Gray Black Gray Pink Orange
Row 12: Gray Gray Pink Black Pink Gray Black Gray Orange Orange Orange Orange Gray Black Gray Pink Black Pink Gray Gray
Row 13: Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Pink Gray Gray Gray
Row 14: Gray Gray Gray Pink Pink Gray Black Pink Gray Black Black Gray Pink Black Gray Pink Pink Gray Gray Gray
Row 15: Black Orange Gray Pink Black Gray Pink Gray Gray Orange Orange Gray Gray Pink Gray Black Pink Gray Orange Black
Row 16: Gray Orange Gray Gray Pink Gray Pink Gray Gray Pink Pink Gray Gray Pink Gray Pink Gray Gray Orange Gray
Example 2
Input:
Row 1: Pink Pink Pink Gray Gray Black Gray Pink Pink Gray Orange
Row 2: Pink Pink Pink Pink Green Brown Black Red Red Red Gray
Row 3: Green Gray Gray Red Pink Black Pink Pink Pink Black Pink
Row 4: Gray Pink Pink Gray Pink Gray Green Pink Black Pink Gray
Row 5: Pink Pink Black Pink Pink Gray Brown Pink Pink Pink Red
Row 6: Red Black Red Pink Green Pink Green Red Pink Gray Pink
Row 7: Pink Pink Gray Pink Black Pink Gray Pink Pink Pink Pink
Row 8: Pink Black Black Pink Pink Pink Pink Gray Gray Red Pink
Row 9: Pink Gray Pink Pink Pink Green Pink Black Green Gray Gray
Row 10: Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Red Pink Black Pink Pink Pink Pink Red Orange Pink
Row 12: Green Gray Green Orange Brown Pink Pink Pink Gray Brown Pink
Row 13: Pink Pink Pink Pink Pink Gray Pink Pink Black Orange Pink
Row 14: Pink Red Gray Gray Pink Pink Red Pink Pink Pink Pink
Row 15: Pink Pink Brown Orange Pink Pink Pink Pink Orange Pink Green
Row 16: Orange Pink Gray Pink Green Black Green Orange Pink Pink Gray
Row 17: Black Pink Pink Pink Pink Black Pink Black Pink Pink Pink
Row 18: Black Pink Black Gray Pink Pink Pink Pink Pink Brown Pink
Row 19: Black Black Pink Pink Red Gray Pink Gray Pink Pink Green
Row 20: Pink Black Pink Pink Green Black Black Gray Pink Gray Red
Row 21: Pink Orange Pink Pink Black Pink Orange Gray Brown Orange Gray
Row 22: Gray Black Pink Red Pink Red Red Pink Green Pink Pink
Row 23: Pink Pink Gray Pink Pink Black Pink Gray Pink Gray Pink
Row 24: Green Pink Black Pink Pink Gray Black Pink Pink Gray Pink
Output:
Row 1: Pink Pink Pink Gray Gray Black Gray Pink Pink Gray Orange Orange Gray Pink Pink Gray Black Gray Gray Pink Pink Pink
Row 2: Pink Pink Pink Pink Green Brown Black Red Red Red Gray Gray Red Red Red Black Brown Green Pink Pink Pink Pink
Row 3: Green Gray Gray Red Pink Black Pink Pink Pink Black Pink Pink Black Pink Pink Pink Black Pink Red Gray Gray Green
Row 4: Gray Pink Pink Gray Pink Gray Green Pink Black Pink Gray Gray Pink Black Pink Green Gray Pink Gray Pink Pink Gray
Row 5: Pink Pink Black Pink Pink Gray Brown Pink Pink Pink Red Red Pink Pink Pink Brown Gray Pink Pink Black Pink Pink
Row 6: Red Black Red Pink Green Pink Green Red Pink Gray Pink Pink Gray Pink Red Green Pink Green Pink Red Black Red
Row 7: Pink Pink Gray Pink Black Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Black Pink Gray Pink Pink
Row 8: Pink Black Black Pink Pink Pink Pink Gray Gray Red Pink Pink Red Gray Gray Pink Pink Pink Pink Black Black Pink
Row 9: Pink Gray Pink Pink Pink Green Pink Black Green Gray Gray Gray Gray Green Black Pink Green Pink Pink Pink Gray Pink
Row 10: Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Row 11: Pink Red Pink Black Pink Pink Pink Pink Red Orange Pink Pink Orange Red Pink Pink Pink Pink Black Pink Red Pink
Row 12: Green Gray Green Orange Brown Pink Pink Pink Gray Brown Pink Pink Brown Gray Pink Pink Pink Brown Orange Green Gray Green
Row 13: Pink Pink Pink Pink Pink Gray Pink Pink Black Orange Pink Pink Orange Black Pink Pink Gray Pink Pink Pink Pink Pink
Row 14: Pink Red Gray Gray Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Gray Gray Red Pink
Row 15: Pink Pink Brown Orange Pink Pink Pink Pink Orange Pink Green Green Pink Orange Pink Pink Pink Pink Orange Brown Pink Pink
Row 16: Orange Pink Gray Pink Green Black Green Orange Pink Pink Gray Gray Pink Pink Orange Green Black Green Pink Gray Pink Orange
Row 17: Black Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Pink Pink Black Pink Black Pink Pink Pink Pink Black
Row 18: Black Pink Black Gray Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Gray Black Pink Black
Row 19: Black Black Pink Pink Red Gray Pink Gray Pink Pink Green Green Pink Pink Gray Pink Gray Red Pink Pink Black Black
Row 20: Pink Black Pink Pink Green Black Black Gray Pink Gray Red Red Gray Pink Gray Black Black Green Pink Pink Black Pink
Row 21: Pink Orange Pink Pink Black Pink Orange Gray Brown Orange Gray Gray Orange Brown Gray Orange Pink Black Pink Pink Orange Pink
Row 22: Gray Black Pink Red Pink Red Red Pink Green Pink Pink Pink Pink Green Pink Red Red Pink Red Pink Black Gray
Row 23: Pink Pink Gray Pink Pink Black Pink Gray Pink Gray Pink Pink Gray Pink Gray Pink Black Pink Pink Gray Pink Pink
Row 24: Green Pink Black Pink Pink Gray Black Pink Pink Gray Pink Pink Gray Pink Pink Black Gray Pink Pink Black Pink Green
Example 3
Input:
Row 1: Blue Purple Blue Pink Pink Pink Blue Blue Purple Pink Blue
Row 2: Blue Blue Green Blue Blue Blue Blue Purple Pink Purple Orange
Row 3: Blue Blue Blue Orange Pink Pink Blue Blue Green Orange Blue
Row 4: Blue Pink Purple Blue Purple Pink Blue Purple Pink Green Orange
Row 5: Blue Pink Blue Green Blue Blue Purple Blue Green Orange Blue
Row 6: Purple Green Blue Purple Orange Orange Blue Pink Green Blue Orange
Row 7: Purple Blue Green Pink Blue Blue Blue Blue Green Orange Pink
Row 8: Blue Purple Blue Pink Blue Purple Blue Green Green Green Green
Row 9: Blue Purple Blue Blue Blue Blue Blue Blue Green Blue Orange
Row 10: Blue Pink Blue Orange Pink Pink Orange Blue Green Blue Pink
Row 11: Green Blue Green Green Green Orange Blue Green Green Purple Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Green
Row 13: Orange Blue Blue Blue Green Blue Blue Purple Green Pink Purple
Row 14: Pink Green Blue Blue Blue Orange Green Blue Orange Blue Orange
Row 15: Purple Green Orange Blue Blue Green Blue Blue Orange Green Blue
Row 16: Blue Blue Blue Pink Green Blue Blue Green Blue Orange Purple
Row 17: Blue Green Blue Green Blue Pink Blue Blue Blue Blue Pink
Row 18: Blue Green Green Blue Blue Green Blue Purple Green Pink Blue
Row 19: Green Green Green Blue Orange Blue Purple Blue Blue Blue Green
Row 20: Green Purple Blue Orange Blue Blue Blue Green Green Pink Blue
Row 21: Purple Blue Pink Blue Purple Blue Orange Blue Blue Pink Blue
Row 22: Orange Green Blue Pink Blue Green Blue Blue Green Purple Orange
Row 23: Green Blue Orange Green Blue Blue Orange Purple Purple Purple Blue
Row 24: Blue Blue Blue Purple Orange Blue Pink Blue Pink Green Blue
Row 25: Pink Pink Blue Purple Blue Blue Blue Purple Green Blue Blue
Row 26: Blue Green Blue Blue Blue Green Purple Blue Green Orange Blue
Row 27: Green Green Blue Blue Blue Blue Green Green Blue Green Blue
Row 28: Blue Blue Blue Blue Green Blue Blue Orange Blue Blue Green
Row 29: Orange Blue Green Blue Green Orange Pink Green Blue Blue Blue
Output:
Row 1: Blue Purple Blue Pink Pink Pink Blue Blue Purple Pink Blue Blue Pink Purple Blue Blue Pink Pink Pink Blue Purple Blue
Row 2: Blue Blue Green Blue Blue Blue Blue Purple Pink Purple Orange Orange Purple Pink Purple Blue Blue Blue Blue Green Blue Blue
Row 3: Blue Blue Blue Orange Pink Pink Blue Blue Green Orange Blue Blue Orange Green Blue Blue Pink Pink Orange Blue Blue Blue
Row 4: Blue Pink Purple Blue Purple Pink Blue Purple Pink Green Orange Orange Green Pink Purple Blue Pink Purple Blue Purple Pink Blue
Row 5: Blue Pink Blue Green Blue Blue Purple Blue Green Orange Blue Blue Orange Green Blue Purple Blue Blue Green Blue Pink Blue
Row 6: Purple Green Blue Purple Orange Orange Blue Pink Green Blue Orange Orange Blue Green Pink Blue Orange Orange Purple Blue Green Purple
Row 7: Purple Blue Green Pink Blue Blue Blue Blue Green Orange Pink Pink Orange Green Blue Blue Blue Blue Pink Green Blue Purple
Row 8: Blue Purple Blue Pink Blue Purple Blue Green Green Green Green Green Green Green Green Blue Purple Blue Pink Blue Purple Blue
Row 9: Blue Purple Blue Blue Blue Blue Blue Blue Green Blue Orange Orange Blue Green Blue Blue Blue Blue Blue Blue Purple Blue
Row 10: Blue Pink Blue Orange Pink Pink Orange Blue Green Blue Pink Pink Blue Green Blue Orange Pink Pink Orange Blue Pink Blue
Row 11: Green Blue Green Green Green Orange Blue Green Green Purple Blue Blue Purple Green Green Blue Orange Green Green Green Blue Green
Row 12: Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Green Green Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Row 13: Orange Blue Blue Blue Green Blue Blue Purple Green Pink Purple Purple Pink Green Purple Blue Blue Green Blue Blue Blue Orange
Row 14: Pink Green Blue Blue Blue Orange Green Blue Orange Blue Orange Orange Blue Orange Blue Green Orange Blue Blue Blue Green Pink
Row 15: Purple Green Orange Blue Blue Green Blue Blue Orange Green Blue Blue Green Orange Blue Blue Green Blue Blue Orange Green Purple
Row 16: Blue Blue Blue Pink Green Blue Blue Green Blue Orange Purple Purple Orange Blue Green Blue Blue Green Pink Blue Blue Blue
Row 17: Blue Green Blue Green Blue Pink Blue Blue Blue Blue Pink Pink Blue Blue Blue Blue Pink Blue Green Blue Green Blue
Row 18: Blue Green Green Blue Blue Green Blue Purple Green Pink Blue Blue Pink Green Purple Blue Green Blue Blue Green Green Blue
Row 19: Green Green Green Blue Orange Blue Purple Blue Blue Blue Green Green Blue Blue Blue Purple Blue Orange Blue Green Green Green
Row 20: Green Purple Blue Orange Blue Blue Blue Green Green Pink Blue Blue Pink Green Green Blue Blue Blue Orange Blue Purple Green
Row 21: Purple Blue Pink Blue Purple Blue Orange Blue Blue Pink Blue Blue Pink Blue Blue Orange Blue Purple Blue Pink Blue Purple
Row 22: Orange Green Blue Pink Blue Green Blue Blue Green Purple Orange Orange Purple Green Blue Blue Green Blue Pink Blue Green Orange
Row 23: Green Blue Orange Green Blue Blue Orange Purple Purple Purple Blue Blue Purple Purple Purple Orange Blue Blue Green Orange Blue Green
Row 24: Blue Blue Blue Purple Orange Blue Pink Blue Pink Green Blue Blue Green Pink Blue Pink Blue Orange Purple Blue Blue Blue
Row 25: Pink Pink Blue Purple Blue Blue Blue Purple Green Blue Blue Blue Blue Green Purple Blue Blue Blue Purple Blue Pink Pink
Row 26: Blue Green Blue Blue Blue Green Purple Blue Green Orange Blue Blue Orange Green Blue Purple Green Blue Blue Blue Green Blue
Row 27: Green Green Blue Blue Blue Blue Green Green Blue Green Blue Blue Green Blue Green Green Blue Blue Blue Blue Green Green
Row 28: Blue Blue Blue Blue Green Blue Blue Orange Blue Blue Green Green Blue Blue Orange Blue Blue Green Blue Blue Blue Blue
Row 29: Orange Blue Green Blue Green Orange Pink Green Blue Blue Blue Blue Blue Blue Green Pink Orange Green Blue Green Blue Orange
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Blue Gray
Row 3: Purple Gray Gray Gray Brown Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Row 4: Gray Pink Purple Gray Gray Black Gray Gray Gray Gray Gray Purple Gray Pink Gray
Row 5: Purple Gray Gray Gray Pink Black Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 6: Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Pink Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Pink Gray Gray Brown Gray Pink Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Purple Gray Gray Gray Brown Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Brown Gray Gray Gray Purple
Gray Pink Purple Gray Gray Black Gray Gray Gray Gray Gray Purple Gray Pink Gray Gray Pink Gray Purple Gray Gray Gray Gray Gray Black Gray Gray Purple Pink Gray
Purple Gray Gray Gray Pink Black Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Black Pink Gray Gray Gray Purple
Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Pink Gray
Gray Gray Pink Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Pink Gray Gray
Gray Gray Gray Gray Pink Gray Gray Brown Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Brown Gray Gray Pink Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 29: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Output:
Row 1: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 2: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 3: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 4: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 5: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 6: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 7: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 8: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 9: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 10: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 11: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 12: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 13: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 14: Black Black Black Purple Black Black Orange Black Black Black Black Black Black Blue Black Black Black Black
Row 15: Black Black Black Gray Black Black Gray Black Black Black Black Black Black Gray Black Black Black Black
Row 16: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 17: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 18: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 19: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 20: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 21: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 22: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 23: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 24: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 25: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 26: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 27: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 28: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Row 29: Black Black Black Green Black Black Purple Black Black Black Black Black Black Red Black Black Black Black
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 3: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 4: Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 5: Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 12: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Black Black Black Black Black Black Black Black Black
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Red Red Red Red Red Red Red Red Red
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black
Row 12: Red Red Red Red Red Red Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Orange Red Red Red Red Red Red Red Red Red Red Red Orange
Row 5: Green Red Red Red Red Red Red Red Red Red Red Red Black
Row 6: Pink Red Red Red Red Red Red Red Red Red Red Red Green
Row 7: Brown Red Red Red Red Red Red Red Red Red Red Red Purple
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange
Row 5: Green Green Green Green Green Green Gray Black Black Black Black Black Black
Row 6: Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green
Row 7: Brown Brown Brown Brown Brown Brown Gray Purple Purple Purple Purple Purple Purple
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Green Red Green Brown Green Blue Green Green Brown Green Black Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Brown Green Blue Green Brown Green Green Blue Green Red Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Red Green Brown Green Blue Green Green Brown Green Black Green Green
Green Red Green Brown Green Blue Green Green Brown Green Black Green Green
Green Red Green Brown Green Blue Green Green Brown Green Black Green Green
Green Red Green Brown Green Blue Green Green Brown Green Black Green Green
Green Gray Green Gray Green Gray Green Green Gray Green Gray Green Green
Green Brown Green Blue Green Brown Green Green Blue Green Red Green Green
Green Brown Green Blue Green Brown Green Green Blue Green Red Green Green
Green Brown Green Blue Green Brown Green Green Blue Green Red Green Green
Green Brown Green Blue Green Brown Green Green Blue Green Red Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Green Green Blue Yellow
Row 2: Purple Green Red Gray Green
Row 3: Green Purple Red Green Green
Row 4: Orange Green Green Green Brown
Row 5: Green Green Green Pink Green
Row 6: Gray Blue Green Black Black
Row 7: Brown Brown Green Green Yellow
Output:
Row 1: Yellow Blue Green Green Pink
Row 2: Green Gray Red Green Purple
Row 3: Green Green Red Purple Green
Row 4: Brown Green Green Green Orange
Row 5: Green Pink Green Green Green
Row 6: Black Black Green Blue Gray
Row 7: Yellow Green Green Brown Brown
Example 2
Input:
Row 1: Yellow Yellow Green Yellow Blue Yellow Blue Yellow
Row 2: Green Yellow Green Yellow Purple Yellow Yellow Yellow
Row 3: Orange Yellow Yellow Yellow Orange Yellow Yellow Blue
Row 4: Orange Yellow Yellow Pink Yellow Yellow Yellow Pink
Row 5: Brown Brown Green Black Black Yellow Yellow Orange
Row 6: Yellow Yellow Blue Yellow Yellow Blue Pink Pink
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 8: Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow
Output:
Row 1: Yellow Blue Yellow Blue Yellow Green Yellow Yellow
Row 2: Yellow Yellow Yellow Purple Yellow Green Yellow Green
Row 3: Blue Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 4: Pink Yellow Yellow Yellow Pink Yellow Yellow Orange
Row 5: Orange Yellow Yellow Black Black Green Brown Brown
Row 6: Pink Pink Blue Yellow Yellow Blue Yellow Yellow
Row 7: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Yellow Yellow Yellow Yellow
Row 2: Yellow Purple Yellow Purple Purple Yellow Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Yellow Purple Purple Yellow Yellow Purple
Row 3: Yellow Yellow Purple Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 4: Purple Yellow Purple Yellow Yellow Yellow Purple Purple Purple Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple
Row 5: Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Purple Yellow Yellow Purple Yellow Yellow Yellow
Row 6: Purple Yellow Purple Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow
Row 7: Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple Purple Yellow Yellow Purple Purple Yellow Yellow
Row 8: Purple Purple Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Purple Yellow Purple
Row 9: Purple Purple Purple Yellow Purple Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Purple
Row 10: Purple Purple Yellow Purple Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple
Row 11: Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Purple Purple Yellow Purple Purple
Row 12: Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Purple Purple
Output:
Row 1: Yellow Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow
Row 2: Purple Yellow Yellow Purple Purple Yellow Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Yellow Purple Purple Yellow Purple Yellow
Row 3: Purple Purple Purple Purple Purple Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow
Row 4: Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow Purple Yellow Purple Purple Purple Yellow Yellow Yellow Purple Yellow Purple
Row 5: Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Purple Yellow Yellow Purple Purple Purple Yellow Yellow Yellow
Row 6: Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Purple Yellow Purple Purple Yellow Yellow Purple Yellow Yellow Purple Yellow Purple
Row 7: Yellow Yellow Purple Purple Yellow Yellow Purple Purple Yellow Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple
Row 8: Purple Yellow Purple Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Purple Purple
Row 9: Purple Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Purple Yellow Purple Purple Purple
Row 10: Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Purple Purple
Row 11: Purple Purple Yellow Purple Purple Yellow Yellow Purple Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow
Row 12: Purple Purple Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Brown Green Brown Green Brown Yellow Purple Green Yellow Brown Brown Green Green Green Brown Yellow Brown Green Green Yellow Green Green Green Green
Row 2: Green Green Brown Green Brown Green Green Green Green Brown Yellow Brown Green Brown Green Green Green Green Brown Green Green Purple Green Brown
Row 3: Purple Green Green Green Green Green Green Green Purple Green Green Brown Green Green Yellow Green Yellow Green Brown Brown Purple Green Brown Yellow
Row 4: Green Brown Brown Green Purple Green Green Yellow Green Green Green Green Yellow Green Yellow Green Green Green Yellow Brown Green Brown Green Green
Row 5: Green Green Brown Yellow Yellow Brown Green Green Yellow Purple Brown Brown Green Green Green Green Green Yellow Purple Green Green Brown Green Green
Row 6: Green Brown Yellow Yellow Green Green Brown Purple Green Green Green Yellow Brown Purple Green Brown Green Green Green Purple Green Brown Yellow Purple
Row 7: Brown Yellow Green Brown Green Brown Green Brown Green Green Green Green Purple Brown Green Green Green Purple Green Brown Green Brown Green Green
Row 8: Yellow Yellow Purple Green Green Yellow Green Purple Green Yellow Brown Green Green Green Green Green Green Yellow Yellow Brown Green Purple Green Green
Row 9: Green Green Brown Brown Green Brown Green Brown Green Green Brown Green Green Yellow Yellow Green Brown Green Brown Brown Green Brown Brown Green
Row 10: Yellow Green Brown Brown Yellow Yellow Green Green Purple Brown Brown Yellow Brown Green Green Green Green Brown Green Yellow Green Yellow Green Purple
Row 11: Brown Green Green Green Brown Green Green Brown Brown Green Green Green Yellow Green Green Green Purple Green Green Green Green Green Brown Purple
Row 12: Green Green Green Brown Yellow Brown Green Yellow Green Yellow Yellow Yellow Brown Green Green Brown Green Yellow Brown Green Green Green Purple Green
Row 13: Green Green Green Purple Green Green Yellow Green Yellow Purple Green Green Green Green Green Purple Yellow Purple Yellow Green Purple Green Green Brown
Row 14: Green Green Green Yellow Green Brown Green Brown Green Brown Yellow Brown Green Green Green Brown Brown Green Green Purple Green Green Yellow Yellow
Row 15: Green Green Brown Green Yellow Yellow Purple Yellow Green Brown Brown Green Green Purple Purple Green Green Brown Yellow Green Green Green Green Purple
Row 16: Green Green Green Green Brown Yellow Green Brown Green Green Green Brown Green Brown Brown Green Yellow Green Purple Green Purple Green Yellow Green
Row 17: Green Green Brown Purple Brown Green Brown Green Green Brown Green Green Green Green Green Brown Purple Green Brown Green Brown Green Green Brown
Row 18: Green Purple Purple Yellow Brown Green Purple Green Green Brown Green Brown Green Green Yellow Yellow Yellow Green Brown Brown Green Green Green Yellow
Row 19: Purple Green Green Brown Green Brown Brown Green Green Green Brown Yellow Green Purple Brown Green Green Green Yellow Brown Brown Green Brown Green
Row 20: Brown Brown Green Green Green Brown Green Green Green Yellow Purple Yellow Green Yellow Green Brown Yellow Green Green Green Green Green Yellow Green
Row 21: Brown Purple Brown Yellow Green Yellow Green Brown Green Green Purple Green Green Green Green Brown Green Yellow Green Green Purple Yellow Purple Green
Row 22: Green Green Purple Green Yellow Green Yellow Green Brown Yellow Green Green Brown Green Green Brown Brown Purple Green Yellow Yellow Green Purple Brown
Row 23: Brown Green Yellow Green Brown Brown Green Brown Green Green Brown Purple Green Purple Green Brown Yellow Yellow Brown Green Green Brown Yellow Green
Row 24: Brown Green Brown Green Green Brown Green Green Brown Yellow Green Yellow Yellow Brown Green Green Brown Yellow Green Yellow Green Brown Green Yellow
Row 25: Brown Brown Brown Yellow Green Brown Green Purple Purple Yellow Green Purple Brown Yellow Yellow Yellow Brown Brown Green Green Green Green Brown Green
Row 26: Green Purple Green Green Brown Green Yellow Purple Yellow Purple Green Yellow Green Brown Green Brown Green Yellow Yellow Purple Yellow Brown Yellow Brown
Row 27: Green Green Brown Purple Purple Green Purple Purple Green Brown Brown Yellow Brown Purple Green Green Purple Brown Brown Brown Purple Green Brown Brown
Row 28: Green Brown Yellow Green Green Green Green Green Yellow Green Green Green Green Yellow Green Brown Green Yellow Green Green Green Brown Brown Yellow
Row 29: Brown Yellow Brown Brown Purple Yellow Green Purple Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Yellow Green Green Brown Yellow Brown Green Green Green Brown Brown Yellow Green Purple Yellow Brown Green Brown Green Brown
Brown Green Purple Green Green Brown Green Green Green Green Brown Green Brown Yellow Brown Green Green Green Green Brown Green Brown Green Green
Yellow Brown Green Purple Brown Brown Green Yellow Green Yellow Green Green Brown Green Green Purple Green Green Green Green Green Green Green Purple
Green Green Brown Green Brown Yellow Green Green Green Yellow Green Yellow Green Green Green Green Yellow Green Green Purple Green Brown Brown Green
Green Green Brown Green Green Purple Yellow Green Green Green Green Green Brown Brown Purple Yellow Green Green Brown Yellow Yellow Brown Green Green
Purple Yellow Brown Green Purple Green Green Green Brown Green Purple Brown Yellow Green Green Green Purple Brown Green Green Yellow Yellow Brown Green
Green Green Brown Green Brown Green Purple Green Green Green Brown Purple Green Green Green Green Brown Green Brown Green Brown Green Yellow Brown
Green Green Purple Green Brown Yellow Yellow Green Green Green Green Green Green Brown Yellow Green Purple Green Yellow Green Green Purple Yellow Yellow
Green Brown Brown Green Brown Brown Green Brown Green Yellow Yellow Green Green Brown Green Green Brown Green Brown Green Brown Brown Green Green
Purple Green Yellow Green Yellow Green Brown Green Green Green Green Brown Yellow Brown Brown Purple Green Green Yellow Yellow Brown Brown Green Yellow
Purple Brown Green Green Green Green Green Purple Green Green Green Yellow Green Green Green Brown Brown Green Green Brown Green Green Green Brown
Green Purple Green Green Green Brown Yellow Green Brown Green Green Brown Yellow Yellow Yellow Green Yellow Green Brown Yellow Brown Green Green Green
Brown Green Green Purple Green Yellow Purple Yellow Purple Green Green Green Green Green Purple Yellow Green Yellow Green Green Purple Green Green Green
Yellow Yellow Green Green Purple Green Green Brown Brown Green Green Green Brown Yellow Brown Green Brown Green Brown Green Yellow Green Green Green
Purple Green Green Green Green Yellow Brown Green Green Purple Purple Green Green Brown Brown Green Yellow Purple Yellow Yellow Green Brown Green Green
Green Yellow Green Purple Green Purple Green Yellow Green Brown Brown Green Brown Green Green Green Brown Green Yellow Brown Green Green Green Green
Brown Green Green Brown Green Brown Green Purple Brown Green Green Green Green Green Brown Green Green Brown Green Brown Purple Brown Green Green
Yellow Green Green Green Brown Brown Green Yellow Yellow Yellow Green Green Brown Green Brown Green Green Purple Green Brown Yellow Purple Purple Green
Green Brown Green Brown Brown Yellow Green Green Green Brown Purple Green Yellow Brown Green Green Green Brown Brown Green Brown Green Green Purple
Green Yellow Green Green Green Green Green Yellow Brown Green Yellow Green Yellow Purple Yellow Green Green Green Brown Green Green Green Brown Brown
Green Purple Yellow Purple Green Green Yellow Green Brown Green Green Green Green Purple Green Green Brown Green Yellow Green Yellow Brown Purple Brown
Brown Purple Green Yellow Yellow Green Purple Brown Brown Green Green Brown Green Green Yellow Brown Green Yellow Green Yellow Green Purple Green Green
Green Yellow Brown Green Green Brown Yellow Yellow Brown Green Purple Green Purple Brown Green Green Brown Green Brown Brown Green Yellow Green Brown
Yellow Green Brown Green Yellow Green Yellow Brown Green Green Brown Yellow Yellow Green Yellow Brown Green Green Brown Green Green Brown Green Brown
Green Brown Green Green Green Green Brown Brown Yellow Yellow Yellow Brown Purple Green Yellow Purple Purple Green Brown Green Yellow Brown Brown Brown
Brown Yellow Brown Yellow Purple Yellow Yellow Green Brown Green Brown Green Yellow Green Purple Yellow Purple Yellow Green Brown Green Green Purple Green
Brown Brown Green Purple Brown Brown Brown Purple Green Green Purple Brown Yellow Brown Brown Green Purple Purple Green Purple Purple Brown Green Green
Yellow Brown Brown Green Green Green Yellow Green Brown Green Yellow Green Green Green Green Yellow Green Green Green Green Green Yellow Brown Green
Purple Purple Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Purple Green Yellow Purple Brown Brown Yellow Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Green Green
Row 2: Yellow Green Green Green Green Green Green Green Yellow Green Green Yellow Yellow Yellow
Row 3: Yellow Green Green Green Green Green Green Green Yellow Green Green Yellow Green Yellow
Row 4: Yellow Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 6: Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Green
Row 7: Yellow Green Yellow Green Green Green Green Green Green Green Green Yellow Green Green
Row 8: Yellow Yellow Yellow Green Green Green Green Green Green Green Green Yellow Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Yellow Yellow Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Green
Row 12: Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Green
Row 13: Green Yellow Green Green Green Green Green Green Green Green Green Green Yellow Green
Row 14: Green Yellow Green Green Green Green Green Green Green Green Green Green Yellow Green
Row 15: Green Yellow Green Green Green Yellow Yellow Green Yellow Green Green Green Yellow Green
Row 16: Green Yellow Green Green Green Green Yellow Green Yellow Yellow Green Green Green Green
Row 17: Green Yellow Green Green Green Green Yellow Green Green Green Green Green Green Green
Output:
Row 1: Blue Blue Blue Blue Blue Green Green Green Green Green Green Red Green Green
Row 2: Blue Green Green Green Green Green Green Green Blue Green Green Red Red Red
Row 3: Blue Green Green Green Green Green Green Green Blue Green Green Red Green Red
Row 4: Blue Green Green Green Green Green Green Green Blue Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Blue Green Green Green Green Green
Row 6: Pink Green Green Blue Blue Blue Blue Blue Blue Green Pink Pink Green Green
Row 7: Pink Green Pink Green Green Green Green Green Green Green Green Pink Green Green
Row 8: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Pink Pink Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Green
Row 12: Green Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue Green
Row 13: Green Blue Green Green Green Green Green Green Green Green Green Green Blue Green
Row 14: Green Blue Green Green Green Green Green Green Green Green Green Green Blue Green
Row 15: Green Blue Green Green Green Blue Blue Green Blue Green Green Green Blue Green
Row 16: Green Blue Green Green Green Green Blue Green Blue Blue Green Green Green Green
Row 17: Green Blue Green Green Green Green Blue Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple
Row 17: Gray Gray Gray Gray Purple Purple Purple Purple Orange Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple
Row 18: Gray Purple Purple Gray Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple
Row 17: Pink Pink Pink Pink Purple Purple Purple Purple Red Purple Purple Red Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Row 18: Pink Purple Purple Pink Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Purple Purple Purple Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 2: Purple Orange Purple Orange Orange Purple Purple Purple Orange Orange Yellow Orange Orange Orange Orange Brown Brown Brown
Row 3: Purple Orange Purple Orange Orange Orange Orange Purple Orange Orange Yellow Orange Orange Orange Orange Brown Orange Brown
Row 4: Orange Orange Orange Orange Orange Orange Orange Purple Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Brown
Row 5: Orange Orange Orange Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 6: Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange
Row 7: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Black Black Black Orange
Row 8: Orange Orange Purple Orange Orange Orange Black Orange Brown Brown Orange Orange Yellow Orange Orange Orange Black Orange
Row 9: Orange Orange Purple Purple Orange Orange Black Orange Brown Orange Orange Orange Yellow Yellow Orange Orange Black Orange
Row 10: Orange Orange Orange Orange Orange Orange Black Orange Brown Brown Orange Orange Orange Orange Orange Orange Black Orange
Row 11: Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 12: Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange
Row 14: Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange
Row 15: Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange
Row 16: Orange Orange Black Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Orange Orange Orange Orange
Row 17: Orange Orange Black Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Black Orange Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Yellow Orange Orange Yellow Orange Orange Orange Brown Orange Purple Purple Purple Purple Purple
Row 20: Orange Orange Orange Orange Yellow Orange Orange Yellow Orange Orange Brown Brown Orange Orange Orange Purple Orange Orange
Row 21: Orange Brown Brown Orange Yellow Orange Orange Yellow Orange Orange Orange Orange Black Black Orange Purple Orange Orange
Row 22: Orange Brown Orange Orange Yellow Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Purple Orange Orange
Row 23: Orange Brown Orange Orange Orange Orange Orange Yellow Orange Orange Yellow Orange Orange Black Orange Purple Purple Purple
Row 24: Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Black Orange Orange Orange Orange
Row 25: Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Black Orange Orange Orange Orange
Row 26: Brown Brown Brown Orange Brown Brown Brown Brown Brown Orange Yellow Orange Black Black Black Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Brown Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Pink Pink Pink Orange Orange Orange Orange Orange Red Red Red Orange Orange Orange Orange Orange Orange Orange
Row 2: Pink Orange Pink Orange Orange Pink Pink Pink Orange Orange Red Orange Orange Orange Orange Pink Pink Pink
Row 3: Pink Orange Pink Orange Orange Orange Orange Pink Orange Orange Red Orange Orange Orange Orange Pink Orange Pink
Row 4: Orange Orange Orange Orange Orange Orange Orange Pink Orange Red Red Red Orange Orange Orange Orange Orange Pink
Row 5: Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 6: Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange
Row 7: Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Pink Pink Orange
Row 8: Orange Orange Pink Orange Orange Orange Blue Orange Pink Pink Orange Orange Pink Orange Orange Orange Pink Orange
Row 9: Orange Orange Pink Pink Orange Orange Blue Orange Pink Orange Orange Orange Pink Pink Orange Orange Pink Orange
Row 10: Orange Orange Orange Orange Orange Orange Blue Orange Pink Pink Orange Orange Orange Orange Orange Orange Pink Orange
Row 11: Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange
Row 12: Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Pink Pink Pink Pink Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange
Row 14: Orange Orange Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange
Row 15: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange
Row 16: Orange Orange Blue Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Orange Orange Orange Orange
Row 17: Orange Orange Blue Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Blue Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Red Orange Orange Red Orange Orange Orange Blue Orange Red Red Red Red Red
Row 20: Orange Orange Orange Orange Red Orange Orange Red Orange Orange Blue Blue Orange Orange Orange Red Orange Orange
Row 21: Orange Red Red Orange Red Orange Orange Red Orange Orange Orange Orange Red Red Orange Red Orange Orange
Row 22: Orange Red Orange Orange Red Orange Orange Red Orange Orange Orange Orange Orange Red Orange Red Orange Orange
Row 23: Orange Red Orange Orange Orange Orange Orange Red Orange Orange Blue Orange Orange Red Orange Red Red Red
Row 24: Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Red Orange Orange Orange Orange
Row 25: Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Red Orange Orange Orange Orange
Row 26: Red Red Red Orange Red Red Red Red Red Orange Blue Orange Red Red Red Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Red Orange Blue Blue Orange Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Green Green Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple
Row 15: Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple
Row 21: Green Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple
Row 22: Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple
Row 23: Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Pink Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Purple Purple
Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple
Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple
Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Brown Brown Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Green Green Green Green Black Black Black Red Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Orange Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Red Red Red Black Purple Black Purple Purple Orange Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Red Red Black Black Purple Purple Purple Purple Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Red Black Black Purple Purple Purple Purple Black Gray Gray Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Brown Brown Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Orange Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Red Red Red Black Purple Red Purple Purple Orange Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Red Red Black Black Purple Purple Purple Purple Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Red Black Black Purple Purple Purple Purple Black Gray Gray Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 4: Orange Orange Red Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 5: Black Orange Red Orange Orange Red Red Red Red Red Red Red Orange
Row 6: Black Orange Red Red Red Red Red Red Red Red Orange Red Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Red Red Orange Red Orange
Row 8: Orange Orange Orange Red Red Red Orange Orange Red Orange Orange Red Orange
Row 9: Orange Yellow Yellow Red Orange Red Orange Orange Red Red Red Red Orange
Row 10: Orange Yellow Yellow Red Red Red Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Blue Orange Brown Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Blue Orange Brown Orange Orange Orange Orange
Row 16: Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Yellow Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 22: Orange Purple Orange Yellow Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 23: Orange Purple Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange
Row 26: Orange Orange Orange Green Orange Orange Orange Orange Purple Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Purple Purple Orange Orange Orange Orange
Row 28: Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Red Red Red Red Red Red Orange Orange Orange Orange Orange
Row 4: Orange Orange Red Gray Gray Gray Gray Red Orange Orange Orange Orange Orange
Row 5: Black Orange Red Gray Gray Red Red Red Red Red Red Red Orange
Row 6: Black Orange Red Red Red Red Red Red Red Red Purple Red Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Red Red Purple Red Orange
Row 8: Orange Orange Orange Red Red Red Orange Orange Red Purple Purple Red Orange
Row 9: Orange Yellow Yellow Red Green Red Orange Orange Red Red Red Red Orange
Row 10: Orange Yellow Yellow Red Red Red Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Blue Orange Brown Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Blue Orange Brown Orange Orange Orange Orange
Row 16: Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Yellow Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 22: Orange Purple Orange Yellow Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 23: Orange Purple Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 28: Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Green Green Green Green Green
Row 2: Blue Green Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Red Green Green Blue Blue Blue Blue
Row 4: Green Green Green Green Green Green Green Green Green Orange Green Green Blue Blue Blue Blue Blue Green Green Green Red Red Green Green Blue Green Blue Blue
Row 5: Green Green Green Green Green Brown Green Green Green Orange Green Green Blue Green Green Green Blue Green Green Green Green Green Yellow Green Blue Green Blue Blue
Row 6: Green Green Green Green Green Brown Brown Green Green Green Green Green Blue Green Green Green Blue Green Green Green Green Green Yellow Green Blue Blue Blue Blue
Row 7: Green Green Green Green Gray Green Green Green Green Green Green Green Blue Green Green Green Blue Green Green Green Green Green Yellow Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Gray Green Green
Row 10: Green Green Green Green Green Black Black Black Green Green Green Green Green Green Green Purple Purple Green Green Blue Green Green Blue Blue Blue Gray Gray Green
Row 11: Green Green Green Green Green Black Black Black Green Green Green Green Green Green Green Purple Purple Purple Purple Blue Green Green Green Green Blue Gray Gray Green
Row 12: Green Green Green Green Green Black Black Black Green Blue Blue Blue Blue Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Green Green Green
Row 13: Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Blue Green Green Blue Green Green Green Green Green Blue Green Blue Blue Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green
Row 15: Blue Green Green Blue Green Green Green Green Green Blue Green Green Blue Green Green Orange Orange Green Blue Blue Blue Green Green Green Green Green Green Green
Row 16: Blue Blue Blue Blue Green Green Green Green Green Blue Green Green Blue Green Green Orange Orange Orange Blue Green Blue Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green Green Orange Orange Blue Blue Blue Green Green Green Green Green Green Green
Output:
Row 1: Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Blue Orange Orange Orange Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Blue Orange Blue Blue
Row 5: Green Green Green Green Green Brown Green Green Green Green Green Green Blue Black Black Black Blue Green Green Green Green Green Yellow Green Blue Orange Blue Blue
Row 6: Green Green Green Green Green Brown Brown Green Green Green Green Green Blue Black Black Black Blue Green Green Green Green Green Yellow Green Blue Blue Blue Blue
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Blue Black Black Black Blue Green Green Green Green Green Yellow Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Purple Purple Blue Blue Blue Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Purple Purple Purple Purple Blue Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Green Green Green
Row 13: Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Blue Red Red Blue Green Green Green Green Green Blue Gray Blue Blue Green Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green
Row 15: Blue Red Red Blue Green Green Green Green Green Blue Gray Gray Blue Green Green Orange Orange Green Blue Blue Blue Green Green Green Green Green Green Green
Row 16: Blue Blue Blue Blue Green Green Green Green Green Blue Gray Gray Blue Green Green Orange Orange Orange Blue Gray Blue Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green Green Orange Orange Blue Blue Blue Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Orange Green Green Purple Purple Purple Purple Green Green
Row 3: Purple Purple Purple Black Black Green Green Orange Orange Green Green Purple Purple Purple Purple Green Green
Row 4: Purple Green Purple Black Black Green Green Orange Orange Green Green Purple Purple Green Purple Green Green
Row 5: Purple Green Purple Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green
Row 6: Purple Green Purple Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green
Row 7: Purple Purple Purple Green Green Green Green Green Green Green Green Purple Purple Purple Purple Green Green
Row 8: Green Green Green Gray Green Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 9: Green Green Green Gray Gray Green Green Green Green Green Purple Green Purple Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Gray Gray Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green
Row 13: Green Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Row 14: Green Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Row 15: Green Green Green Purple Green Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Row 16: Green Green Green Purple Green Green Purple Purple Purple Green Green Green Green Purple Green Green Purple
Row 17: Green Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Row 19: Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Yellow Yellow Yellow Green Green Blue Green Green Green Green Green Green Green Green
Row 22: Green Green Green Yellow Yellow Yellow Yellow Green Blue Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Blue Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple Green Green
Purple Purple Purple Black Black Green Green Green Green Green Green Purple Purple Purple Purple Green Green
Purple Blue Purple Black Black Green Green Green Green Green Green Purple Purple Orange Purple Green Green
Purple Blue Purple Green Green Green Green Green Green Green Green Purple Orange Orange Purple Green Green
Purple Blue Purple Green Green Green Green Green Green Green Green Purple Orange Orange Purple Green Green
Purple Purple Purple Green Green Green Green Green Green Green Green Purple Purple Purple Purple Green Green
Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Purple Gray Purple Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Green Green Green Green
Green Green Green Green Green Green Green Green Gray Gray Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green
Green Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Green Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Green Green Green Purple Gray Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Green Green Green Purple Gray Gray Purple Purple Purple Green Green Green Green Purple Pink Pink Purple
Green Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple
Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Pink Purple Purple Purple Purple Purple Blue Blue Blue Blue
Row 6: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Pink Pink Purple Purple Purple Purple Purple Purple Purple Blue
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Pink Blue Blue Blue Blue Purple Purple Purple Purple Purple
Row 6: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Pink Pink Blue Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow
Row 2: Yellow Yellow Orange Yellow Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Yellow Yellow Orange Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 17: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 18: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 19: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 20: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 21: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 22: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 23: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 24: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 25: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 26: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 27: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 28: Yellow Purple Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 29: Yellow Purple Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Output:
Row 1: Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow
Row 2: Yellow Purple Orange Yellow Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Purple Orange Yellow Yellow
Row 3: Yellow Purple Yellow Yellow Yellow Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Yellow Orange Purple Orange Orange Orange Orange Orange Purple Orange Yellow Yellow
Row 4: Yellow Purple Yellow Yellow Yellow Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Yellow Purple Purple Orange Orange Orange Orange Yellow Purple Orange Yellow Yellow
Row 5: Yellow Purple Yellow Yellow Yellow Orange Purple Orange Purple Orange Orange Orange Orange Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Orange Yellow Purple Orange Yellow Yellow
Row 6: Yellow Purple Yellow Yellow Yellow Yellow Yellow Orange Purple Yellow Orange Orange Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Orange Yellow Purple Orange Yellow Yellow
Row 7: Yellow Purple Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Orange Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Orange Yellow Yellow
Row 8: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 9: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 10: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 11: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 12: Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 13: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow
Row 14: Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Green Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black
Row 10: Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Green Black Black Black Black
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Black Black Black Black Black Black Black Black
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green
Row 2: Green Green Green Pink Pink Pink Pink Green Green Pink Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Row 17: Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Green
Row 18: Green Green Green Yellow Yellow Green Green Green Yellow Yellow Green Green Green Green
Row 19: Green Green Green Yellow Yellow Green Green Green Yellow Yellow Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green
Green Green Green Pink Pink Pink Pink Green Yellow Pink Green Green Green Green
Green Green Green Yellow Yellow Green Green Green Yellow Yellow Green Green Green Green
Green Green Green Yellow Yellow Green Green Green Yellow Yellow Green Green Green Green
Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 2: Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue
Row 3: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 6: Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue
Row 7: Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue
Row 8: Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue
Row 9: Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue
Row 10: Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue
Row 14: Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue
Row 15: Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue
Row 16: Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow
Row 17: Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 18: Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue
Row 2: Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue Blue Blue
Row 3: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 6: Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue Blue
Row 7: Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue Blue
Row 8: Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue Blue
Row 9: Blue Blue Blue Blue Blue Yellow Blue Blue Blue Yellow Blue Blue
Row 10: Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue
Row 14: Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow Blue
Row 15: Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Yellow
Row 16: Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Yellow
Row 17: Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 18: Blue Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Yellow Blue Blue Yellow Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Brown Brown Brown Green Green Green Pink Pink Pink Pink Pink Green Green Green Red Red Red Red Red Red Green Green Green Green Green Green Green
Row 2: Brown Green Green Brown Green Green Pink Green Green Green Green Pink Green Green Red Green Green Green Green Green Red Green Green Green Green Green Green
Row 3: Green Brown Green Green Brown Green Green Pink Green Green Green Green Pink Green Green Red Green Green Green Green Green Red Green Green Green Green Green
Row 4: Green Green Brown Brown Brown Green Green Green Pink Pink Pink Pink Pink Green Green Green Red Red Red Red Red Red Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Pink Pink Pink Green Green Green Green Green Green Green Green Gray Green Green Gray Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Pink Green Green Pink Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green
Row 9: Green Green Yellow Yellow Yellow Yellow Yellow Green Green Green Pink Green Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Yellow Green Green Green Green Yellow Green Green Green Pink Pink Pink Green Green Pink Pink Pink Pink Pink Pink Green Green Green Green Green
Row 11: Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Green Green Green Pink Green Green Green Green Green Pink Green Green Green Green
Row 12: Green Green Green Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Gray Green Green Green Brown Brown Brown Brown Brown Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Gray Green Green Brown Green Green Green Green Brown Green Green
Row 17: Green Red Red Red Red Red Green Green Green Green Green Gray Green Green Green Green Green Gray Green Green Brown Green Green Green Green Brown Green
Row 18: Green Red Green Green Green Green Red Green Green Green Green Green Gray Gray Gray Gray Gray Gray Green Green Green Brown Green Green Green Green Brown
Row 19: Green Green Red Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown
Row 20: Green Green Green Red Green Green Green Green Red Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Red Red Red Red Red Green Green Green Yellow Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green
Output:
Row 1: Green Brown Brown Brown Green Green Green Pink Pink Pink Pink Pink Green Green Green Red Red Red Red Red Red Green Green Green Green Green Green
Row 2: Green Brown Green Green Brown Green Green Pink Green Green Green Green Pink Green Green Red Green Green Green Green Green Red Green Green Green Green Green
Row 3: Green Green Brown Green Brown Green Green Green Pink Green Green Green Pink Green Green Green Red Green Green Green Green Red Green Green Green Green Green
Row 4: Green Green Brown Brown Brown Green Green Green Pink Pink Pink Pink Pink Green Green Green Red Red Red Red Red Red Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Green Green Green Green Green Green Green Green Gray Green Gray Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Pink Green Green Pink Green Green Green Green Green Green Green Gray Gray Gray Green Green Green
Row 9: Green Green Green Yellow Yellow Yellow Yellow Yellow Green Green Green Pink Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Yellow Green Green Green Green Yellow Green Green Pink Pink Pink Green Green Green Pink Pink Pink Pink Pink Pink Green Green Green Green
Row 11: Green Green Green Green Yellow Green Green Green Yellow Green Green Green Green Green Green Green Green Pink Green Green Green Green Pink Green Green Green Green
Row 12: Green Green Green Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Gray Green Green Green Brown Brown Brown Brown Brown Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Green Gray Green Green Brown Green Green Green Green Brown Green
Row 17: Green Green Red Red Red Red Red Green Green Green Green Green Gray Green Green Green Green Gray Green Green Green Brown Green Green Green Green Brown
Row 18: Green Green Red Green Green Green Green Red Green Green Green Green Gray Gray Gray Gray Gray Gray Green Green Green Green Brown Green Green Green Brown
Row 19: Green Green Green Red Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown
Row 20: Green Green Green Green Red Green Green Green Red Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Red Red Red Red Red Green Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Brown Purple Purple Brown Purple Purple Purple Green Green Green Green Green Green Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Brown Purple Purple Brown Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Green Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Green Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Brown Purple Purple Brown Purple Purple Purple Green Green Green Green Green Green Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Brown Purple Brown Purple Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Green Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Green Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown
Row 3: Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Red
Row 4: Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Red Red Red Red Red
Row 5: Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Red Red Red Red Red
Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Red Brown Brown Brown Red
Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Brown Red Red Red Red Red
Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Black Purple Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple
Row 12: Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Orange Gray Brown Pink Orange Yellow Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Red Red Orange Gray Brown Pink Orange Yellow Red Red Orange Gray Brown Pink Orange Yellow Red Red
Row 14: Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Yellow Red Pink Orange Green Blue Purple Yellow Pink Red Red Red Red Red Red Red Red Red Red Red
Row 17: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Yellow Pink Pink Orange Green Blue Purple Yellow Pink Pink Orange Green Blue Purple Yellow Pink Pink Orange Green Blue
Row 17: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Orange Black Green Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red
Blue Orange Black Green Blue Orange Black Green Blue Orange Black Green Blue Orange Black Green Blue Orange Black Green Blue Orange
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Purple Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple
Row 3: Purple Purple Purple Yellow Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple
Row 5: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple
Row 7: Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Purple Purple Purple Yellow
Row 12: Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Row 14: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple
Output:
Row 1: Yellow Purple Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple
Row 3: Purple Purple Purple Yellow Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple
Row 5: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Row 6: Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple
Row 7: Purple Purple Yellow Purple Purple Green Yellow Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Yellow Purple Purple Purple Purple Green Yellow Green Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow
Row 9: Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Purple Purple Purple Yellow
Row 12: Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple
Row 14: Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple
Example 2
Input:
Row 1: Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 3: Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 6: Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple
Row 10: Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 12: Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Row 20: Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Blue Purple Purple Purple Blue Purple Purple Blue Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Blue Purple Purple Blue Purple Purple
Output:
Row 1: Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 3: Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Green Green Green Green Purple Purple Purple Blue Purple
Row 6: Purple Green Blue Blue Green Purple Purple Purple Purple Purple
Row 7: Purple Green Green Green Green Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple
Row 10: Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 12: Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple
Row 20: Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Blue Purple Purple Purple Blue Purple Purple Blue Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Blue Purple Purple Blue Purple Purple
Example 3
Input:
Row 1: Blue Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink
Row 2: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Blue Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 13: Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Blue Green Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Green Blue Green Pink Pink
Row 2: Blue Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Green Blue Green Pink Pink
Row 3: Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Green Green Green Pink Blue
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink
Row 9: Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Green Blue Blue Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Pink Pink
Row 11: Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Green Blue Blue Green Pink Pink
Row 12: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Pink Blue
Row 13: Pink Pink Pink Pink Green Blue Blue Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Blue Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Green Blue Blue Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Blue Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Blue Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black
Row 4: Blue Black Black Black Blue Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black
Row 5: Blue Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Blue Black Black Blue
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black
Row 7: Black Black Blue Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Blue Black Black Blue Black Black Black Black Black Black
Row 9: Black Blue Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Blue Blue Black Black
Row 12: Black Black Black Black Black Blue Black Black Black Black Black Black Blue Black Black Black Black Black Black Black
Row 13: Blue Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Blue Black Black Black
Row 15: Black Blue Black Black Black Blue Black Black Black Black Black Black Black Blue Black Black Black Black Black Black
Row 16: Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Blue Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Blue
Row 19: Black Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black Blue Black Black Blue
Row 20: Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black
Row 21: Black Black Black Black Black Blue Black Black Black Black Black Black Black Blue Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Blue Black Black Black
Row 24: Black Black Black Black Black Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue
Row 25: Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Black Black Blue Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Blue
Row 29: Blue Black Black Black Blue Black Black Black Black Black Black Blue Black Black Black Black Blue Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black
Black Black Black Blue Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Blue Black
Green Green Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black
Blue Green Black Black Blue Black Black Black Black Black Black Black Blue Black Black Green Green Green Black Black
Blue Green Black Black Black Black Black Black Blue Black Black Black Black Black Black Green Blue Green Black Blue
Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Green Blue Green Black Black
Black Black Blue Black Black Black Black Blue Black Black Black Black Black Black Black Green Green Green Black Black
Black Black Black Black Black Black Black Black Black Black Blue Black Black Blue Black Black Black Black Black Black
Black Blue Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Black
Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Green Blue Blue Green Black
Black Black Black Black Black Blue Black Black Black Black Black Black Blue Black Black Green Green Green Green Black
Blue Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Green Green Green Black Black Black Blue Black Black Black Black Black Blue Black Black Black
Black Blue Black Black Green Blue Green Black Black Black Black Black Black Blue Black Black Black Black Black Black
Black Black Black Black Green Blue Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Blue Black Black Black Green Green Green Black Black Blue Black Black Black Black Black Black Black Black Green Green
Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Green Green Green Green Blue
Green Green Green Black Blue Black Black Blue Black Black Black Black Black Black Black Green Blue Green Green Blue
Blue Blue Green Black Black Black Black Black Black Black Black Black Black Black Black Green Blue Green Green Green
Green Green Green Black Black Blue Black Black Green Green Green Black Black Blue Black Green Green Green Black Black
Black Black Black Black Black Black Black Black Green Blue Green Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Green Blue Green Black Black Black Black Black Blue Black Black Black
Black Black Black Black Black Black Blue Black Green Green Green Black Blue Black Black Black Black Black Black Blue
Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Blue Black Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Blue
Blue Black Black Black Blue Black Black Black Black Black Black Blue Black Black Black Black Blue Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Pink Pink Pink Pink Red Red Black Red
Row 3: Red Red Red Pink Pink Red Red Red Red Black Red
Row 4: Brown Brown Red Red Red Red Red Red Red Red Black
Row 5: Brown Brown Red Brown Brown Red Red Red Red Red Red
Row 6: Red Brown Brown Brown Brown Red Red Gray Red Red Red
Row 7: Brown Red Red Red Brown Red Red Red Gray Gray Red
Row 8: Red Red Red Red Red Red Red Red Gray Red Gray
Row 9: Yellow Yellow Yellow Yellow Red Red Gray Gray Red Red Red
Row 10: Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red
Row 11: Yellow Red Red Yellow Red Red Red Red Red Red Red
Row 12: Red Yellow Yellow Red Red Red Red Purple Red Red Red
Row 13: Yellow Red Red Yellow Red Red Red Red Purple Purple Red
Row 14: Red Red Red Red Red Red Red Red Purple Red Red
Row 15: Red Red Red Red Red Purple Red Red Purple Red Red
Row 16: Red Red Red Red Red Purple Red Purple Purple Red Red
Row 17: Red Red Red Gray Red Purple Purple Purple Red Red Red
Row 18: Red Red Gray Gray Red Red Purple Red Purple Red Red
Output:
Row 1: Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow
Row 3: Yellow Red Red Yellow
Row 4: Red Yellow Yellow Red
Row 5: Yellow Red Red Yellow
Example 2
Input:
Row 1: Red Orange Red Orange Red Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Red Red Orange Orange Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Red Red Red Red Red Red Orange Orange Orange Orange Brown Brown Orange Brown Brown Brown Brown Orange Pink Pink Pink Orange Pink Orange Orange Orange Orange Orange
Row 4: Red Red Orange Orange Red Red Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Brown Brown Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange
Row 5: Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange
Row 6: Orange Orange Orange Red Orange Red Orange Orange Yellow Orange Orange Orange Orange Brown Brown Orange Brown Brown Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange
Row 7: Orange Orange Orange Orange Red Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Brown Orange Brown Brown Orange Brown Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange
Row 8: Orange Yellow Yellow Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Brown Brown Orange Brown Brown Brown Orange Orange Orange Pink Orange Orange Orange Gray Orange Orange
Row 9: Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Brown Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray
Row 10: Orange Orange Yellow Orange Orange Yellow Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 11: Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange Gray Orange Orange
Row 12: Orange Orange Orange Orange Yellow Orange Orange Orange Black Black Black Black Black Orange Orange Orange Orange Green Green Orange Orange Green Green Orange Orange Gray Gray Gray Orange Orange
Row 13: Orange Orange Blue Orange Orange Orange Orange Orange Black Black Black Black Orange Black Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Gray Gray Orange Orange Orange
Row 14: Orange Orange Orange Blue Orange Black Orange Orange Orange Orange Black Orange Black Black Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Gray Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Black Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Black Orange Black Orange Orange Orange Gray Orange Gray Gray Gray Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Black Black Orange Black Black Orange Gray Gray Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Black Black Orange Black Black Orange Orange Gray Gray Orange Gray Orange Orange Orange Orange Orange Purple Orange Orange Purple Orange Purple Orange Orange Orange Pink Orange Orange
Row 21: Orange Orange Black Orange Black Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Purple Orange Orange Orange Orange Pink Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Gray Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Pink Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Gray Orange Gray Orange Orange Orange Purple Orange Purple Orange Orange Purple Orange Orange Orange Orange Pink Pink Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Purple Orange Purple Purple Orange Orange Purple Purple Orange Pink Orange Orange Orange
Output:
Row 1: Orange Green Orange Orange Green Orange
Row 2: Green Green Orange Orange Green Green
Row 3: Orange Green Green Green Green Orange
Row 4: Orange Green Green Green Green Orange
Row 5: Green Green Green Green Green Green
Row 6: Orange Orange Green Green Orange Orange
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Brown Brown
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Yellow Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Brown Yellow Brown
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Brown Brown
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Yellow Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow
Row 9: Yellow Yellow Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Pink Pink Yellow Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Pink Pink Pink Pink Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Green Green Green Green Green Yellow Yellow
Row 12: Yellow Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow Green Green Green Yellow Yellow
Row 13: Yellow Pink Pink Pink Pink Pink Pink Yellow Yellow Red Red Red Red Yellow Yellow Green Green Yellow Yellow Green Green Green Green Yellow Yellow
Row 14: Yellow Pink Pink Pink Pink Pink Pink Yellow Red Red Yellow Yellow Red Red Yellow Yellow Green Green Green Green Green Green Green Yellow Yellow
Row 15: Yellow Pink Pink Pink Pink Pink Pink Yellow Red Yellow Red Red Yellow Red Yellow Green Green Yellow Yellow Yellow Green Green Green Yellow Yellow
Row 16: Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Red Red Red Red Red Red Yellow Green Green Green Yellow Yellow Green Green Green Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Yellow Green Green Yellow Green Yellow Yellow Green Green Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Yellow Green Green Yellow Green Green Green Green Green Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Yellow Yellow Yellow Yellow Pink Pink Pink Pink Yellow Yellow Yellow Pink Yellow
Row 21: Yellow Red Yellow Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Pink Pink Yellow Yellow
Row 22: Yellow Yellow Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Pink Yellow Pink Yellow Yellow
Row 23: Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Yellow Pink Yellow
Row 24: Yellow Red Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Yellow
Row 25: Yellow Yellow Red Red Yellow Red Yellow Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Yellow
Row 26: Yellow Red Yellow Red Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow
Row 27: Yellow Red Red Yellow Yellow Yellow Yellow Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Pink Pink Pink Pink Yellow
Row 28: Yellow Red Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Red Red Red Red Yellow
Row 2: Red Red Yellow Yellow Red Red
Row 3: Red Yellow Red Red Yellow Red
Row 4: Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red
Row 8: Yellow Yellow Red Red Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange
Row 2: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange
Row 3: Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Blue Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Blue Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Green Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Green Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Green Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Green
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Green Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Green Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Green Red Red Red Red Red Red Red Red Red Red Green
Row 18: Red Red Green Red Red Red Red Red Red Green Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Green Red Red Red Red
Row 20: Red Red Red Red Red Red Red Green Green Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Green Red Green Green Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Green Red Green Red Red Red Green Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Output:
Row 1: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green
Row 3: Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red
Row 5: Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Red Green Red Red Red Red Red
Row 6: Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 9: Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Red Red Red Red Red Red Green Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Green Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Green Red
Example 2
Input:
Row 1: Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Purple Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple Pink Green Pink Pink Pink Green Green Pink Pink Pink Pink Green Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Green Green Pink Pink Pink Pink Pink Pink Pink Purple
Row 4: Purple Pink Pink Pink Green Green Pink Green Pink Green Pink Pink Pink Yellow Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Purple Pink
Row 2: Purple Pink Pink Pink
Row 3: Pink Green Pink Pink
Row 4: Green Pink Pink Pink
Row 5: Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink
Row 7: Pink Pink Pink Purple
Row 8: Pink Green Pink Pink
Row 9: Pink Green Green Pink
Row 10: Pink Pink Green Pink
Row 11: Pink Pink Pink Yellow
Row 12: Pink Pink Pink Pink
Row 13: Pink Green Pink Pink
Row 14: Pink Pink Pink Pink
Row 15: Pink Purple Pink Green
Row 16: Pink Purple Green Pink
Row 17: Pink Pink Pink Green
Row 18: Pink Pink Pink Pink
Row 19: Pink Pink Pink Green
Row 20: Pink Pink Pink Green
Row 21: Pink Pink Pink Pink
Row 22: Green Pink Pink Pink
Row 23: Pink Pink Pink Pink
Row 24: Pink Pink Pink Purple
Example 3
Input:
Row 1: Pink Orange Pink Pink Pink Green Pink Red Pink Pink Red Gray Pink Purple Pink Pink Gray Pink Pink Black Pink Purple Purple Orange Green Pink Pink Pink
Row 2: Orange Purple Pink Pink Black Black Pink Black Pink Pink Gray Pink Purple Red Pink Orange Orange Pink Gray Pink Gray Red Pink Pink Green Gray Pink Pink
Row 3: Blue Green Pink Green Pink Pink Gray Pink Pink Orange Orange Pink Pink Purple Green Pink Pink Pink Orange Pink Green Orange Pink Pink Pink Pink Pink Orange
Row 4: Pink Pink Pink Pink Orange Gray Pink Pink Pink Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Green Red Pink Orange Orange Gray Black Pink
Row 5: Purple Pink Pink Orange Pink Black Pink Orange Pink Pink Purple Pink Black Pink Green Gray Pink Pink Gray Green Gray Pink Orange Red Gray Pink Pink Gray
Row 6: Pink Pink Gray Blue Pink Orange Blue Pink Pink Orange Gray Orange Pink Pink Pink Green Pink Orange Pink Pink Green Orange Pink Green Pink Pink Pink Pink
Row 7: Pink Pink Pink Orange Gray Pink Pink Purple Green Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Green Pink Gray Blue Pink Purple Pink
Row 8: Black Gray Blue Pink Pink Pink Pink Pink Green Red Pink Pink Pink Purple Pink Pink Pink Pink Pink Orange Green Pink Black Pink Pink Green Pink Pink
Row 9: Pink Pink Pink Gray Pink Pink Gray Orange Pink Pink Pink Pink Gray Black Purple Pink Pink Pink Pink Purple Green Red Black Green Pink Pink Gray Pink
Row 10: Gray Pink Green Purple Pink Red Pink Pink Purple Pink Red Pink Pink Gray Pink Orange Orange Gray Green Black Orange Purple Pink Orange Green Green Red Gray
Row 11: Green Pink Green Gray Pink Purple Red Black Green Pink Pink Pink Pink Pink Pink Gray Orange Gray Pink Black Pink Orange Pink Pink Pink Black Gray Pink
Row 12: Pink Pink Pink Orange Pink Pink Pink Pink Green Pink Green Pink Pink Green Gray Pink Pink Blue Purple Pink Orange Pink Orange Pink Pink Pink Pink Black
Row 13: Pink Pink Pink Pink Green Pink Orange Purple Gray Pink Green Orange Green Gray Orange Pink Pink Pink Pink Gray Red Pink Pink Pink Black Pink Pink Red
Row 14: Pink Orange Pink Orange Pink Pink Pink Orange Pink Pink Orange Pink Gray Pink Green Red Green Pink Gray Pink Purple Pink Pink Pink Pink Pink Orange Orange
Row 15: Orange Pink Orange Green Pink Pink Pink Orange Gray Pink Pink Pink Gray Gray Purple Green Pink Pink Purple Gray Green Pink Pink Orange Pink Orange Pink Green
Row 16: Pink Pink Gray Pink Pink Pink Pink Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Purple Orange Pink Orange Pink Pink Black
Row 17: Pink Gray Pink Green Pink Black Gray Purple Orange Pink Gray Purple Pink Green Orange Pink Orange Pink Gray Pink Green Purple Orange Pink Pink Pink Pink Pink
Row 18: Gray Pink Pink Orange Green Pink Gray Orange Orange Pink Red Pink Purple Pink Pink Pink Pink Orange Pink Orange Pink Green Gray Orange Pink Pink Pink Pink
Row 19: Purple Orange Purple Pink Pink Pink Pink Pink Orange Orange Blue Pink Green Pink Pink Pink Purple Pink Gray Pink Pink Pink Pink Green Pink Gray Pink Green
Row 20: Pink Pink Purple Black Pink Pink Orange Purple Pink Pink Orange Black Gray Pink Black Pink Orange Gray Orange Black Black Orange Pink Pink Green Pink Pink Pink
Row 21: Pink Orange Orange Pink Purple Pink Pink Purple Gray Pink Pink Orange Green Orange Gray Pink Pink Pink Pink Gray Green Red Pink Pink Pink Pink Orange Pink
Row 22: Red Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Orange Gray Pink Red Pink Green Pink Pink Pink Purple Gray Orange Pink Orange Pink Pink Pink
Row 23: Gray Gray Orange Pink Pink Green Pink Pink Pink Orange Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Black Purple Pink Pink Pink Green Pink Pink
Row 24: Green Pink Purple Black Purple Green Pink Green Red Orange Pink Pink Pink Purple Pink Pink Pink Pink Pink Gray Pink Pink Green Pink Black Pink Pink Pink
Output:
Row 1: Pink Pink Orange Pink Gray Pink Pink Pink Pink Gray Pink Black Red Orange Green Black Pink Pink Green Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Black Pink Pink Purple Pink Gray Red Gray Pink Pink Orange Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink
Row 3: Pink Gray Pink Gray Pink Pink Pink Green Pink Green Black Pink Pink Pink Orange Pink Pink Pink Gray Pink Pink Pink Green Pink
Row 4: Green Green Pink Orange Gray Pink Blue Pink Pink Green Pink Pink Black Pink Pink Orange Pink Pink Pink Green Pink Orange Pink Black
Row 5: Orange Pink Pink Orange Red Green Gray Pink Green Orange Pink Pink Pink Pink Orange Pink Pink Orange Green Pink Pink Pink Pink Pink
Row 6: Purple Pink Pink Pink Orange Pink Pink Black Black Pink Pink Orange Pink Pink Pink Orange Orange Gray Pink Pink Pink Orange Pink Green
Row 7: Purple Red Orange Red Pink Orange Green Pink Red Purple Orange Pink Pink Pink Pink Purple Purple Green Pink Orange Red Gray Purple Pink
Row 8: Pink Gray Green Green Gray Green Pink Green Green Orange Pink Orange Red Purple Green Orange Green Pink Pink Black Green Purple Black Pink
Row 9: Black Pink Pink Pink Green Pink Pink Orange Purple Black Black Pink Gray Pink Gray Pink Pink Orange Pink Black Gray Pink Pink Gray
Row 10: Pink Gray Orange Pink Gray Pink Pink Pink Pink Green Pink Purple Pink Gray Purple Pink Gray Pink Gray Orange Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Orange Pink Pink Pink Gray Gray Blue Pink Pink Pink Pink Pink Orange Pink Gray Pink Pink Pink Pink
Row 12: Gray Orange Pink Pink Pink Pink Pink Pink Pink Orange Orange Pink Pink Green Pink Pink Orange Pink Purple Orange Pink Green Pink Pink
Row 13: Pink Orange Pink Pink Gray Green Pink Pink Pink Orange Gray Pink Pink Red Green Pink Pink Pink Pink Pink Pink Pink Purple Pink
Row 14: Pink Pink Green Pink Green Pink Purple Pink Purple Pink Pink Gray Orange Green Purple Pink Orange Pink Pink Black Gray Red Pink Pink
Row 15: Purple Red Purple Orange Pink Pink Pink Purple Black Gray Pink Green Gray Pink Gray Pink Green Pink Pink Pink Orange Pink Pink Purple
Row 16: Pink Purple Pink Pink Black Pink Pink Pink Gray Pink Pink Pink Green Gray Gray Pink Pink Purple Green Gray Green Gray Pink Pink
Row 17: Gray Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Purple Pink Pink Black Orange Orange Pink Pink
Row 18: Red Gray Orange Pink Purple Gray Pink Pink Pink Red Pink Green Green Orange Pink Pink Gray Red Blue Orange Pink Pink Pink Pink
Row 19: Pink Pink Orange Pink Pink Orange Pink Red Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Orange Pink Pink Pink Orange Orange
Row 20: Pink Pink Pink Pink Pink Pink Green Green Pink Purple Green Green Gray Pink Gray Green Orange Orange Orange Pink Gray Pink Pink Red
Row 21: Red Black Pink Pink Orange Pink Purple Pink Orange Pink Black Pink Purple Orange Orange Pink Purple Orange Pink Purple Purple Pink Pink Green
Row 22: Pink Pink Gray Pink Pink Blue Pink Pink Gray Pink Red Pink Orange Pink Pink Pink Gray Gray Pink Orange Pink Pink Pink Pink
Row 23: Green Black Pink Gray Black Orange Pink Pink Pink Red Purple Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Orange Green Green
Row 24: Pink Black Pink Orange Pink Pink Gray Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Pink Pink Purple Pink Pink Purple
Row 25: Pink Pink Green Pink Orange Blue Orange Pink Gray Purple Gray Orange Pink Orange Green Pink Green Orange Pink Black Pink Pink Pink Black
Row 26: Pink Pink Pink Pink Pink Gray Pink Blue Pink Green Green Pink Pink Pink Orange Gray Pink Pink Purple Purple Orange Pink Orange Purple
Row 27: Orange Purple Green Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Orange Pink Pink Gray Pink Orange Pink Orange Pink Gray Pink
Row 28: Pink Orange Blue Pink Purple Pink Pink Black Pink Gray Green Pink Pink Pink Orange Pink Pink Gray Purple Pink Pink Red Gray Green
Here is the input grid for the test example:
Input:
Row 1: Green Gray
Row 2: Pink Orange
Row 3: Orange Red
Row 4: Black Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Orange Red Orange
Green Pink Orange Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 3: Black Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red
Row 2: Red Red Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Black Black Black Brown Brown Black Brown Green Green Brown
Row 2: Black Black Black Black Brown Black Black Green Black Black
Row 3: Black Brown Black Black Black Black Green Brown Black Black
Row 4: Brown Black Black Green Black Black Black Black Green Black
Row 5: Black Brown Black Black Green Black Black Black Brown Black
Row 6: Green Green Black Green Green Black Black Green Brown Green
Row 7: Green Green Black Brown Brown Brown Green Black Black Black
Row 8: Green Black Black Brown Black Brown Black Brown Brown Green
Row 9: Green Green Green Green Black Black Black Black Black Black
Row 10: Green Black Black Black Black Green Brown Black Black Green
Row 11: Green Black Black Black Black Black Brown Black Green Black
Row 12: Black Black Green Black Black Black Green Black Brown Brown
Row 13: Black Black Green Green Green Black Black Brown Black Black
Output:
Row 1: Red Red Red Brown Brown Red Brown Green Green Brown
Row 2: Red Red Red Red Brown Red Red Green Red Red
Row 3: Red Brown Red Red Red Red Green Brown Red Red
Row 4: Brown Red Red Green Red Red Red Red Green Red
Row 5: Red Brown Red Red Green Red Red Red Brown Red
Row 6: Green Green Red Green Green Red Red Green Brown Green
Row 7: Green Green Red Brown Brown Brown Green Red Red Red
Row 8: Green Red Red Brown Red Brown Red Brown Brown Green
Row 9: Green Green Green Green Red Red Red Red Red Red
Row 10: Green Red Red Red Red Green Brown Red Red Green
Row 11: Green Red Red Red Red Red Brown Red Green Red
Row 12: Red Red Green Red Red Red Green Red Brown Brown
Row 13: Red Red Green Green Green Red Red Brown Red Red
Example 3
Input:
Row 1: Green Green Green Green Pink Purple Purple Green Purple Green Green Purple Green Purple Pink Green Green Green Green Green Green Green Green Green Green Green Purple
Row 2: Green Green Green Green Green Green Purple Purple Green Green Green Pink Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Purple
Row 3: Green Pink Green Purple Purple Green Green Green Green Green Green Green Green Purple Green Green Green Purple Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Pink Green Pink Green Green Green Purple Green Green Green Pink Green Green Green Green Purple Green Pink Green Purple Green Green Green
Row 5: Green Green Green Green Pink Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Green Green Green
Row 6: Purple Purple Green Green Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Green
Row 7: Green Green Green Pink Green Purple Green Green Green Purple Green Green Green Pink Green Pink Green Green Green Green Pink Green Green Purple Green Purple Green
Output:
Row 1: Red Red Red Red Pink Purple Purple Red Purple Red Red Purple Red Purple Pink Red Red Red Red Red Red Red Red Red Red Red Purple
Row 2: Red Red Red Red Red Red Purple Purple Red Red Red Pink Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Purple
Row 3: Red Pink Red Purple Purple Red Red Red Red Red Red Red Red Purple Red Red Red Purple Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Pink Red Pink Red Red Red Purple Red Red Red Pink Red Red Red Red Purple Red Pink Red Purple Red Red Red
Row 5: Red Red Red Red Pink Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Red Red Red
Row 6: Purple Purple Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red
Row 7: Red Red Red Pink Red Purple Red Red Red Purple Red Red Red Pink Red Pink Red Red Red Red Pink Red Red Purple Red Purple Red
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Yellow Purple Purple Pink Pink Purple
Row 3: Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Purple Purple Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Red Purple Purple Pink Pink Purple
Red Red Red Red Red Purple Red Red Red Red Purple Red Red Red Red Red Yellow Purple Purple Red Red Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 2: Yellow Brown Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Brown Yellow Brown
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 5: Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow
Row 7: Yellow Brown Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 11: Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow
Row 14: Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 15: Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 16: Brown Brown Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 18: Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 19: Brown Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown
Row 21: Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Brown Brown Yellow Brown
Row 26: Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 2: Yellow Brown Green Brown Brown Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow
Row 3: Yellow Green Yellow Brown Green Green Brown Green Green Brown Brown Green Brown
Row 4: Yellow Green Yellow Green Green Yellow Green Brown Yellow Green Green Yellow Green
Row 5: Brown Green Green Green Brown Yellow Green Green Yellow Green Green Yellow Green
Row 6: Brown Green Green Green Green Green Green Green Green Brown Green Yellow Green
Row 7: Green Brown Green Brown Green Brown Green Green Yellow Green Green Yellow Green
Row 8: Green Green Yellow Brown Green Green Green Green Yellow Green Green Yellow Green
Row 9: Green Green Brown Green Green Green Green Green Green Green Green Brown Brown
Row 10: Green Green Green Green Green Green Green Brown Yellow Green Green Green Green
Row 11: Brown Green Green Green Green Green Brown Green Yellow Green Green Green Green
Row 12: Green Green Green Green Brown Green Green Green Green Green Green Brown Green
Row 13: Green Green Green Green Green Green Brown Green Green Brown Green Green Green
Row 14: Green Brown Green Green Green Brown Green Green Green Green Green Brown Brown
Row 15: Green Brown Green Green Green Green Green Green Green Green Green Brown Brown
Row 16: Brown Brown Green Green Green Green Brown Green Yellow Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Brown Green Green Green Green
Row 18: Green Brown Brown Green Green Green Green Green Green Green Green Brown Brown
Row 19: Brown Green Green Brown Brown Green Green Green Green Green Green Green Green
Row 20: Yellow Yellow Yellow Green Yellow Green Green Green Green Green Brown Green Brown
Row 21: Yellow Yellow Yellow Brown Green Green Green Green Brown Green Green Green Green
Row 22: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Brown Green Green Green
Row 23: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Brown Green Green
Row 24: Yellow Yellow Yellow Yellow Yellow Green Brown Green Brown Green Green Green Green
Row 25: Yellow Yellow Yellow Yellow Yellow Brown Green Brown Green Brown Brown Green Brown
Row 26: Yellow Yellow Yellow Yellow Yellow Brown Green Green Green Brown Yellow Green Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Example 2
Input:
Row 1: Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Red Brown Red Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown
Row 4: Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Red Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown
Row 14: Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Red Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Red
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Red Green Red Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Red Green Brown Brown Brown
Row 4: Brown Brown Brown Red Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 5: Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 6: Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 7: Brown Brown Brown Red Green Green Green Green Green Green Green Red Brown
Row 8: Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Green Brown
Row 9: Brown Brown Brown Red Brown Brown Brown Brown Brown Green Brown Green Brown
Row 10: Brown Brown Brown Red Green Green Red Brown Brown Green Brown Green Brown
Row 11: Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Green Red
Row 12: Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Green Green
Row 13: Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Red Green
Row 14: Brown Red Green Green Green Red Green Green Green Green Green Red Green
Row 15: Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Green Green
Row 16: Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Red Green
Row 17: Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown Brown Green
Row 18: Brown Brown Brown Brown Brown Brown Green Brown Brown Red Green Green Red
Row 19: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Brown Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Brown Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Row 3: Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Brown Brown Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Green Brown Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Brown Green Green Brown Green Brown Green Green Green Green Green Green Green Green Green Brown Purple Purple Purple Purple
Row 3: Purple Purple Purple Brown Green Green Green Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Green Brown Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Gray Red Gray Red Gray Gray Red Gray Gray Gray Gray
Row 2: Gray Red Gray Gray Gray Gray Gray Gray Red Gray Gray
Row 3: Gray Red Gray Gray Gray Red Gray Gray Gray Gray Gray
Row 4: Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red
Row 6: Gray Gray Gray Gray Red Gray Gray Gray Gray Red Gray
Row 7: Gray Gray Gray Red Red Gray Gray Gray Gray Red Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Red Green Red Green Green Red Gray Gray Gray Gray
Gray Red Green Green Green Green Green Green Red Gray Gray
Gray Red Green Green Green Red Gray Gray Gray Gray Gray
Red Red Gray Green Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Red
Gray Gray Gray Green Red Green Green Green Green Red Gray
Gray Gray Gray Red Red Green Green Green Green Red Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Yellow Orange Red Orange Gray Red Orange Yellow Red Gray Gray Orange Gray Red Orange Yellow Yellow Black Red Orange Blue
Row 2: Gray Black Gray Gray Red Black Yellow Red Gray Red Yellow Blue Gray Orange Red Gray Orange Orange Gray Gray Orange Orange
Row 3: Orange Red Yellow Gray Yellow Blue Yellow Gray Black Blue Gray Orange Gray Black Red Blue Gray Blue Red Black Black Orange
Row 4: Blue Orange Yellow Gray Orange Red Gray Red Gray Gray Gray Black Gray Yellow Yellow Gray Blue Blue Black Yellow Yellow Gray
Row 5: Red Gray Red Blue Orange Yellow Gray Red Red Black Gray Gray Yellow Black Gray Red Orange Blue Yellow Gray Black Red
Row 6: Gray Blue Yellow Orange Gray Black Blue Red Red Black Blue Red Gray Yellow Blue Gray Yellow Red Red Orange Orange Yellow
Row 7: Black Gray Yellow Yellow Blue Orange Gray Red Black Yellow Yellow Black Yellow Black Red Gray Orange Gray Black Yellow Blue Yellow
Row 8: Yellow Blue Yellow Yellow Red Black Orange Gray Blue Yellow Black Gray Gray Yellow Gray Blue Yellow Red Red Yellow Red Gray
Row 9: Black Yellow Yellow Gray Orange Yellow Orange Orange Blue Yellow Gray Red Orange Orange Yellow Red Gray Orange Orange Red Black Blue
Row 10: Gray Black Black Orange Yellow Red Red Orange Gray Gray Gray Red Black Black Orange Orange Red Gray Red Red Orange Gray
Row 11: Gray Blue Yellow Red Yellow Black Red Yellow Red Blue Blue Gray Gray Red Black Black Red Orange Gray Blue Gray Red
Row 12: Black Orange Red Gray Blue Red Gray Yellow Red Blue Gray Gray Blue Blue Yellow Red Black Blue Orange Blue Gray Blue
Row 13: Gray Red Blue Red Orange Gray Gray Blue Gray Yellow Yellow Black Black Orange Red Gray Orange Orange Yellow Blue Gray Yellow
Row 14: Red Gray Blue Red Yellow Red Orange Yellow Orange Gray Gray Black Blue Red Red Gray Red Yellow Gray Blue Blue Orange
Row 15: Blue Yellow Orange Red Orange Blue Orange Blue Red Yellow Red Gray Blue Gray Yellow Yellow Red Red Orange Orange Blue Black
Row 16: Blue Red Yellow Blue Orange Gray Blue Orange Yellow Orange Gray Red Yellow Gray Red Gray Gray Yellow Black Black Black Gray
Row 17: Red Gray Black Black Blue Orange Gray Red Blue Blue Orange Gray Blue Black Black Orange Gray Red Yellow Blue Blue Gray
Row 18: Gray Gray Red Gray Gray Red Orange Gray Blue Blue Blue Blue Yellow Black Blue Orange Yellow Blue Black Gray Blue Red
Row 19: Gray Black Black Black Yellow Yellow Black Yellow Blue Red Black Blue Red Yellow Gray Blue Orange Red Yellow Red Gray Red
Row 20: Blue Orange Gray Red Blue Blue Red Gray Orange Orange Yellow Red Gray Yellow Black Red Red Gray Gray Yellow Yellow Yellow
Row 21: Blue Blue Red Black Yellow Red Blue Gray Gray Orange Red Yellow Orange Yellow Orange Orange Gray Blue Black Gray Black Gray
Row 22: Red Orange Gray Orange Red Blue Red Gray Gray Red Orange Yellow Gray Gray Blue Gray Yellow Gray Gray Gray Black Gray
Row 23: Yellow Orange Gray Orange Red Red Gray Red Yellow Orange Red Blue Red Orange Blue Yellow Orange Blue Red Blue Orange Gray
Row 24: Gray Orange Orange Orange Black Orange Gray Red Gray Red Orange Red Gray Gray Red Gray Red Orange Gray Orange Orange Black
Row 25: Black Yellow Yellow Black Yellow Blue Orange Black Blue Red Gray Blue Red Gray Black Black Yellow Red Orange Gray Gray Red
Row 26: Gray Orange Red Yellow Orange Red Gray Red Black Yellow Black Blue Orange Gray Red Gray Blue Red Gray Red Orange Black
Row 27: Gray Gray Black Gray Black Yellow Gray Yellow Yellow Gray Blue Yellow Gray Black Black Gray Blue Gray Black Red Orange Black
Row 28: Gray Red Blue Blue Orange Blue Yellow Blue Black Gray Yellow Orange Blue Blue Orange Red Black Black Blue Yellow Gray Yellow
Row 29: Gray Gray Red Black Red Red Yellow Orange Black Blue Blue Gray Red Red Black Yellow Gray Red Blue Black Gray Orange
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Black Gray Gray Red Black Yellow Red Gray Red Yellow Blue Gray Orange Red Gray Orange Orange Gray Gray Orange Purple
Row 3: Purple Red Yellow Gray Yellow Blue Yellow Gray Black Blue Gray Orange Gray Black Red Blue Gray Blue Red Black Black Purple
Row 4: Purple Orange Yellow Gray Orange Red Gray Red Gray Gray Gray Black Gray Yellow Yellow Gray Blue Blue Black Yellow Yellow Purple
Row 5: Purple Gray Red Blue Orange Yellow Gray Red Red Black Gray Gray Yellow Black Gray Red Orange Blue Yellow Gray Black Purple
Row 6: Purple Blue Yellow Orange Gray Black Blue Red Red Black Blue Red Gray Yellow Blue Gray Yellow Red Red Orange Orange Purple
Row 7: Purple Gray Yellow Yellow Blue Orange Gray Red Black Yellow Yellow Black Yellow Black Red Gray Orange Gray Black Yellow Blue Purple
Row 8: Purple Blue Yellow Yellow Red Black Orange Gray Blue Yellow Black Gray Gray Yellow Gray Blue Yellow Red Red Yellow Red Purple
Row 9: Purple Yellow Yellow Gray Orange Yellow Orange Orange Blue Yellow Gray Red Orange Orange Yellow Red Gray Orange Orange Red Black Purple
Row 10: Purple Black Black Orange Yellow Red Red Orange Gray Gray Gray Red Black Black Orange Orange Red Gray Red Red Orange Purple
Row 11: Purple Blue Yellow Red Yellow Black Red Yellow Red Blue Blue Gray Gray Red Black Black Red Orange Gray Blue Gray Purple
Row 12: Purple Orange Red Gray Blue Red Gray Yellow Red Blue Gray Gray Blue Blue Yellow Red Black Blue Orange Blue Gray Purple
Row 13: Purple Red Blue Red Orange Gray Gray Blue Gray Yellow Yellow Black Black Orange Red Gray Orange Orange Yellow Blue Gray Purple
Row 14: Purple Gray Blue Red Yellow Red Orange Yellow Orange Gray Gray Black Blue Red Red Gray Red Yellow Gray Blue Blue Purple
Row 15: Purple Yellow Orange Red Orange Blue Orange Blue Red Yellow Red Gray Blue Gray Yellow Yellow Red Red Orange Orange Blue Purple
Row 16: Purple Red Yellow Blue Orange Gray Blue Orange Yellow Orange Gray Red Yellow Gray Red Gray Gray Yellow Black Black Black Purple
Row 17: Purple Gray Black Black Blue Orange Gray Red Blue Blue Orange Gray Blue Black Black Orange Gray Red Yellow Blue Blue Purple
Row 18: Purple Gray Red Gray Gray Red Orange Gray Blue Blue Blue Blue Yellow Black Blue Orange Yellow Blue Black Gray Blue Purple
Row 19: Purple Black Black Black Yellow Yellow Black Yellow Blue Red Black Blue Red Yellow Gray Blue Orange Red Yellow Red Gray Purple
Row 20: Purple Orange Gray Red Blue Blue Red Gray Orange Orange Yellow Red Gray Yellow Black Red Red Gray Gray Yellow Yellow Purple
Row 21: Purple Blue Red Black Yellow Red Blue Gray Gray Orange Red Yellow Orange Yellow Orange Orange Gray Blue Black Gray Black Purple
Row 22: Purple Orange Gray Orange Red Blue Red Gray Gray Red Orange Yellow Gray Gray Blue Gray Yellow Gray Gray Gray Black Purple
Row 23: Purple Orange Gray Orange Red Red Gray Red Yellow Orange Red Blue Red Orange Blue Yellow Orange Blue Red Blue Orange Purple
Row 24: Purple Orange Orange Orange Black Orange Gray Red Gray Red Orange Red Gray Gray Red Gray Red Orange Gray Orange Orange Purple
Row 25: Purple Yellow Yellow Black Yellow Blue Orange Black Blue Red Gray Blue Red Gray Black Black Yellow Red Orange Gray Gray Purple
Row 26: Purple Orange Red Yellow Orange Red Gray Red Black Yellow Black Blue Orange Gray Red Gray Blue Red Gray Red Orange Purple
Row 27: Purple Gray Black Gray Black Yellow Gray Yellow Yellow Gray Blue Yellow Gray Black Black Gray Blue Gray Black Red Orange Purple
Row 28: Purple Red Blue Blue Orange Blue Yellow Blue Black Gray Yellow Orange Blue Blue Orange Red Black Black Blue Yellow Gray Purple
Row 29: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Red Red Red Red Red Red Yellow Red Red Red Red Red Red
Row 2: Black Red Red Red Red Red Orange Red Red Red Brown Red Red
Row 3: Red Black Red Red Red Red Blue Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Green Pink
Row 5: Red Red Red Red Red Green Red Red Red Red Red Green Orange
Row 6: Gray Red Red Green Red Red Red Red Red Red Green Red Red
Row 7: Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 8: Red Red Red Red Brown Red Red Red Red Red Red Red Red
Row 9: Red Red Orange Red Red Red Red Green Red Red Red Orange Red
Row 10: Red Green Red Red Red Red Red Red Green Red Red Red Red
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Red Red Red Red Red Orange Red Red Red Brown Red Purple
Row 3: Purple Black Red Red Red Red Blue Red Red Red Red Red Purple
Row 4: Purple Red Red Red Red Red Red Red Red Red Red Green Purple
Row 5: Purple Red Red Red Red Green Red Red Red Red Red Green Purple
Row 6: Purple Red Red Green Red Red Red Red Red Red Green Red Purple
Row 7: Purple Red Red Red Red Yellow Red Red Red Red Red Red Purple
Row 8: Purple Red Red Red Brown Red Red Red Red Red Red Red Purple
Row 9: Purple Red Orange Red Red Red Red Green Red Red Red Orange Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Green Yellow Pink Black Red Green
Row 2: Red Black Pink Black Red Pink
Row 3: Red Blue Gray Brown Black Blue
Row 4: Black Pink Red Pink Pink Pink
Row 5: Black Red Green Red Pink Brown
Row 6: Brown Green Blue Red Pink Green
Row 7: Yellow Red Red Blue Red Brown
Row 8: Blue Black Pink Gray Blue Black
Row 9: Brown Brown Green Blue Black Brown
Row 10: Brown Red Red Green Red Gray
Row 11: Brown Pink Red Gray Black Red
Row 12: Red Pink Black Red Green Pink
Row 13: Brown Brown Black Black Black Pink
Row 14: Brown Gray Red Yellow Brown Gray
Row 15: Red Brown Red Gray Blue Red
Row 16: Blue Black Pink Green Brown Black
Row 17: Black Pink Black Black Pink Gray
Row 18: Green Gray Red Blue Gray Yellow
Row 19: Gray Pink Red Pink Brown Blue
Row 20: Gray Red Red Pink Red Brown
Row 21: Blue Gray Red Red Red Pink
Row 22: Red Red Black Yellow Black Yellow
Output:
Row 1: Purple Purple Purple Purple Purple Purple
Row 2: Purple Black Pink Black Red Purple
Row 3: Purple Blue Gray Brown Black Purple
Row 4: Purple Pink Red Pink Pink Purple
Row 5: Purple Red Green Red Pink Purple
Row 6: Purple Green Blue Red Pink Purple
Row 7: Purple Red Red Blue Red Purple
Row 8: Purple Black Pink Gray Blue Purple
Row 9: Purple Brown Green Blue Black Purple
Row 10: Purple Red Red Green Red Purple
Row 11: Purple Pink Red Gray Black Purple
Row 12: Purple Pink Black Red Green Purple
Row 13: Purple Brown Black Black Black Purple
Row 14: Purple Gray Red Yellow Brown Purple
Row 15: Purple Brown Red Gray Blue Purple
Row 16: Purple Black Pink Green Brown Purple
Row 17: Purple Pink Black Black Pink Purple
Row 18: Purple Gray Red Blue Gray Purple
Row 19: Purple Pink Red Pink Brown Purple
Row 20: Purple Red Red Pink Red Purple
Row 21: Purple Gray Red Red Red Purple
Row 22: Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Green Green Brown Green Brown Brown Green Pink Yellow
Row 2: Green Green Green Green Orange Green Yellow Green Green
Row 3: Green Orange Black Green Green Pink Green Green Green
Row 4: Yellow Green Green Green Green Yellow Blue Green Green
Row 5: Green Pink Green Orange Green Green Green Orange Green
Row 6: Green Green Green Green Green Blue Green Yellow Green
Row 7: Pink Green Green Green Green Green Pink Brown Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Green Green Orange Green Yellow Green Purple
Purple Orange Black Green Green Pink Green Green Purple
Purple Green Green Green Green Yellow Blue Green Purple
Purple Pink Green Orange Green Green Green Orange Purple
Purple Green Green Green Green Blue Green Yellow Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Pink Orange
Row 2: Orange Orange Red Orange Orange
Row 3: Red Orange Orange Orange Orange
Row 4: Orange Orange Orange Pink Orange
Row 5: Orange Orange Orange Orange Brown
Row 6: Orange Orange Black Orange Yellow
Row 7: Pink Purple Purple Purple Purple
Row 8: Purple Purple Gray Yellow Green
Row 9: Purple Purple Purple Pink Green
Row 10: Black Black Black Black Black
Row 11: Black Black Black Black Black
Row 12: Black Black Black Black Black
Row 13: Black Black Black Black Black
Row 14: Black Red Black Black Black
Row 15: Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue
Row 17: Blue Blue Purple Blue Blue
Row 18: Blue Yellow Blue Blue Blue
Row 19: Pink Pink Brown Pink Pink
Row 20: Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink
Output:
Row 1: Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange
Row 7: Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple
Row 10: Black Black Black Black Black
Row 11: Black Black Black Black Black
Row 12: Black Black Black Black Black
Row 13: Black Black Black Black Black
Row 14: Black Black Black Black Black
Row 15: Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue
Row 19: Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Pink Green Black Red Pink Purple Pink Pink Orange Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Blue Red Purple Brown Pink Pink Yellow Pink
Row 3: Green Pink Pink Pink Pink Pink Brown Pink Blue Pink Pink Pink Pink
Row 4: Pink Brown Pink Pink Pink Orange Pink Brown Pink Pink Pink Pink Pink
Row 5: Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Brown Orange
Row 6: Black Orange Orange Orange Orange Purple Orange Orange Orange Orange Blue Orange Black
Row 7: Orange Orange Orange Orange Orange Yellow Black Green Orange Orange Orange Green Orange
Row 8: Orange Black Orange Orange Orange Orange Blue Orange Orange Orange Orange Black Orange
Row 9: Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue
Row 10: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Brown Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 12: Purple Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 17: Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 18: Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Pink Yellow Yellow Yellow Yellow Pink Gray Blue Pink Brown Brown Blue Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 2: Yellow Brown Blue Yellow Yellow Pink Pink Purple Pink Black Blue Brown Brown Brown Purple Brown Blue Blue Blue Yellow Blue Blue Blue Pink Blue
Row 3: Yellow Orange Yellow Yellow Yellow Gray Pink Pink Pink Green Brown Brown Brown Brown Red Brown Yellow Brown Blue Blue Blue Blue Red Blue Brown
Row 4: Yellow Black Yellow Orange Yellow Pink Pink Pink Pink Brown Brown Pink Brown Brown Brown Brown Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 5: Blue Yellow Yellow Yellow Yellow Pink Pink Black Pink Red Brown Brown Green Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Yellow Yellow Yellow Pink Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Green Blue Blue Blue Blue Blue Brown Brown Blue
Row 7: Orange Yellow Yellow Red Blue Pink Pink Pink Pink Brown Orange Brown Brown Brown Brown Green Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Yellow Yellow Black Orange Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Pink Green Blue Blue Black Purple Blue Gray
Row 9: Purple Yellow Yellow Brown Yellow Pink Pink Green Pink Purple Brown Brown Brown Brown Brown Blue Blue Blue Yellow Blue Blue Green Blue Orange Blue
Row 10: Yellow Yellow Yellow Black Red Pink Pink Pink Pink Brown Brown Brown Brown Black Yellow Brown Red Blue Blue Brown Blue Blue Blue Purple Brown
Row 11: Yellow Yellow Yellow Black Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Purple Blue Black Blue Blue Blue Blue Orange Blue
Row 12: Yellow Yellow Black Yellow Yellow Red Pink Blue Green Brown Black Brown Brown Brown Brown Brown Green Blue Blue Blue Blue Blue Blue Brown Blue
Row 13: Red Yellow Yellow Yellow Blue Purple Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Black Blue Blue Blue Purple Yellow
Row 14: Green Yellow Green Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Pink Red Blue Blue Blue Orange Blue Blue
Row 15: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Purple Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Green Yellow Green Yellow Yellow Yellow Pink Pink Yellow Pink
Row 2: Brown Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Black Yellow Yellow Yellow Pink Yellow Yellow Purple
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 7: Red Red Red Gray Yellow Red Red Red Red Blue
Row 8: Green Black Green Red Red Red Purple Red Purple Black
Row 9: Red Red Red Purple Red Red Pink Red Red Red
Row 10: Black Black Red Red Red Red Pink Brown Blue Red
Row 11: Red Yellow Red Blue Brown Red Red Red Red Orange
Row 12: Pink Black Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Green Pink Pink Brown Pink Pink Pink
Row 14: Orange Pink Brown Pink Pink Black Pink Pink Pink Pink
Row 15: Pink Gray Pink Pink Pink Black Pink Pink Pink Pink
Row 16: Pink Yellow Pink Red Pink Gray Red Pink Pink Pink
Row 17: Purple Purple Purple Purple Purple Purple Purple Black Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple
Row 21: Black Gray Green Green Blue Blue Green Green Green Orange
Row 22: Green Green Orange Brown Green Green Green Green Green Green
Row 23: Green Green Green Blue Green Green Orange Orange Green Red
Row 24: Green Pink Green Green Green Green Green Green Green Green
Row 25: Blue Blue Blue Pink Pink Blue Blue Blue Blue Yellow
Row 26: Black Blue Orange Blue Blue Blue Blue Blue Pink Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Red Blue Blue
Row 28: Blue Black Blue Blue Blue Blue Blue Blue Pink Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Yellow Black
Row 2: Black Black Black
Row 3: Yellow Black Black
Row 4: Black Black Black
Row 5: Black Black Yellow
Output:
Row 1: Black Black Black Black Yellow Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Yellow Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Yellow Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black
Row 11: Black Yellow Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black
Row 13: Yellow Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black
Row 15: Black Black Yellow Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Yellow Black
Row 22: Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Yellow Black Black
Row 24: Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Yellow
Example 2
Input:
Row 1: Black Black Black
Row 2: Red Black Black
Row 3: Black Black Black
Row 4: Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black
Row 6: Red Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Black Black Black Black Gray
Row 2: Black Black Black Gray Black
Row 3: Black Black Black Gray Black
Row 4: Gray Gray Gray Black Black
Row 5: Black Black Gray Gray Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Black Black Black Black
Row 16: Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Gray Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Gray Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black
Row 19: Gray Gray Gray Black Black Gray Gray Gray Black Black Gray Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Gray Gray Black Black Black Gray Gray Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Gray Gray Gray Black Black Gray Gray Gray Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Black Gray Gray Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Pink Black
Row 2: Black Black
Row 3: Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Black Black Black
Black Black Black Black
Black Black Black Black
Black Black Black Black
Black Black Black Black
Black Black Black Black
Black Black Black Black
Black Black Black Black
Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Green Yellow
Row 2: Blue Yellow Gray Gray Purple
Row 3: Yellow Purple Yellow Purple Yellow
Row 4: Yellow Blue Brown Yellow Yellow
Row 5: Red Red Brown Blue Green
Output:
Row 1: Yellow Yellow Yellow Green Yellow Red Yellow Yellow Blue Yellow
Row 2: Blue Yellow Gray Gray Purple Red Blue Purple Yellow Yellow
Row 3: Yellow Purple Yellow Purple Yellow Brown Brown Yellow Gray Yellow
Row 4: Yellow Blue Brown Yellow Yellow Blue Yellow Purple Gray Green
Row 5: Red Red Brown Blue Green Green Yellow Yellow Purple Yellow
Row 6: Yellow Purple Yellow Yellow Green Green Blue Brown Red Red
Row 7: Green Gray Purple Yellow Blue Yellow Yellow Brown Blue Yellow
Row 8: Yellow Gray Yellow Brown Brown Yellow Purple Yellow Purple Yellow
Row 9: Yellow Yellow Purple Blue Red Purple Gray Gray Yellow Blue
Row 10: Yellow Blue Yellow Yellow Red Yellow Green Yellow Yellow Yellow
Example 2
Input:
Row 1: Black Blue Orange
Row 2: Purple Yellow Pink
Row 3: Green Gray Brown
Output:
Row 1: Black Blue Orange Green Purple Black
Row 2: Purple Yellow Pink Gray Yellow Blue
Row 3: Green Gray Brown Brown Pink Orange
Row 4: Orange Pink Brown Brown Gray Green
Row 5: Blue Yellow Gray Pink Yellow Purple
Row 6: Black Purple Green Orange Blue Black
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 2: Brown Orange Brown Brown Orange Purple Gray Purple Brown
Row 3: Yellow Gray Orange Orange Purple Brown Brown Purple Brown
Row 4: Purple Brown Brown Brown Brown Purple Yellow Brown Yellow
Row 5: Orange Yellow Yellow Brown Brown Brown Brown Purple Yellow
Row 6: Yellow Yellow Brown Brown Brown Brown Purple Brown Orange
Row 7: Brown Purple Gray Purple Purple Yellow Purple Yellow Brown
Row 8: Brown Brown Gray Orange Yellow Yellow Brown Brown Brown
Row 9: Brown Purple Orange Orange Brown Yellow Purple Orange Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Yellow Orange Purple Yellow Brown Brown
Row 2: Brown Orange Brown Brown Orange Purple Gray Purple Brown Purple Brown Purple Yellow Yellow Brown Gray Orange Brown
Row 3: Yellow Gray Orange Orange Purple Brown Brown Purple Brown Orange Gray Gray Brown Yellow Brown Orange Brown Brown
Row 4: Purple Brown Brown Brown Brown Purple Yellow Brown Yellow Orange Orange Purple Brown Brown Brown Orange Brown Brown
Row 5: Orange Yellow Yellow Brown Brown Brown Brown Purple Yellow Brown Yellow Purple Brown Brown Brown Purple Orange Brown
Row 6: Yellow Yellow Brown Brown Brown Brown Purple Brown Orange Yellow Yellow Yellow Brown Brown Purple Brown Purple Brown
Row 7: Brown Purple Gray Purple Purple Yellow Purple Yellow Brown Purple Brown Purple Purple Brown Yellow Brown Gray Purple
Row 8: Brown Brown Gray Orange Yellow Yellow Brown Brown Brown Orange Brown Yellow Brown Purple Brown Purple Purple Purple
Row 9: Brown Purple Orange Orange Brown Yellow Purple Orange Brown Brown Brown Brown Orange Yellow Yellow Brown Brown Purple
Row 10: Purple Brown Brown Yellow Yellow Orange Brown Brown Brown Brown Orange Purple Yellow Brown Orange Orange Purple Brown
Row 11: Purple Purple Purple Brown Purple Brown Yellow Brown Orange Brown Brown Brown Yellow Yellow Orange Gray Brown Brown
Row 12: Purple Gray Brown Yellow Brown Purple Purple Brown Purple Brown Yellow Purple Yellow Purple Purple Gray Purple Brown
Row 13: Brown Purple Brown Purple Brown Brown Yellow Yellow Yellow Orange Brown Purple Brown Brown Brown Brown Yellow Yellow
Row 14: Brown Orange Purple Brown Brown Brown Purple Yellow Brown Yellow Purple Brown Brown Brown Brown Yellow Yellow Orange
Row 15: Brown Brown Orange Brown Brown Brown Purple Orange Orange Yellow Brown Yellow Purple Brown Brown Brown Brown Purple
Row 16: Brown Brown Orange Brown Yellow Brown Gray Gray Orange Brown Purple Brown Brown Purple Orange Orange Gray Yellow
Row 17: Brown Orange Gray Brown Yellow Yellow Purple Brown Purple Brown Purple Gray Purple Orange Brown Brown Orange Brown
Row 18: Brown Brown Yellow Purple Orange Yellow Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Pink Orange Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Orange
Row 4: Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink
Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Yellow Blue Brown Brown Brown Brown Brown Brown Green Brown
Row 2: Orange Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Green Brown Blue Brown Yellow Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Orange Orange Brown Brown Brown Orange Brown Brown Blue Green Brown
Row 6: Orange Brown Green Brown Brown Green Orange Yellow Orange Brown Blue
Row 7: Brown Yellow Brown Brown Brown Brown Blue Orange Brown Brown Blue
Row 8: Brown Brown Brown Brown Brown Orange Orange Green Brown Brown Orange
Row 9: Brown Green Yellow Brown Brown Blue Green Green Green Brown Brown
Row 10: Brown Green Brown Orange Green Brown Brown Brown Brown Brown Brown
Row 11: Green Orange Brown Brown Green Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Yellow Blue Brown Brown Brown Brown Brown Brown Green Brown Green Brown Brown Brown Brown Orange Orange Brown Brown Orange Brown
Row 2: Orange Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Orange Green Green Brown Yellow Brown Orange Brown Brown Brown Yellow
Row 3: Brown Brown Brown Brown Brown Green Brown Blue Brown Yellow Brown Brown Brown Yellow Brown Brown Green Brown Brown Brown Brown Blue
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Orange Orange Brown Brown Brown Orange Brown Brown Blue Green Brown Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Orange Brown Green Brown Brown Green Orange Yellow Orange Brown Blue Brown Brown Blue Orange Brown Green Orange Brown Green Brown Brown
Row 7: Brown Yellow Brown Brown Brown Brown Blue Orange Brown Brown Blue Brown Brown Green Orange Blue Orange Brown Brown Brown Yellow Brown
Row 8: Brown Brown Brown Brown Brown Orange Orange Green Brown Brown Orange Brown Brown Green Green Orange Yellow Brown Brown Blue Brown Brown
Row 9: Brown Green Yellow Brown Brown Blue Green Green Green Brown Brown Brown Brown Green Brown Brown Orange Blue Brown Brown Brown Brown
Row 10: Brown Green Brown Orange Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Yellow Brown Green
Row 11: Green Orange Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Blue Blue Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Orange Green
Row 13: Green Brown Yellow Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Orange Brown Green Brown
Row 14: Brown Brown Brown Brown Blue Orange Brown Brown Green Brown Brown Brown Brown Green Green Green Blue Brown Brown Yellow Green Brown
Row 15: Brown Brown Blue Brown Brown Yellow Orange Green Green Brown Brown Orange Brown Brown Green Orange Orange Brown Brown Brown Brown Brown
Row 16: Brown Yellow Brown Brown Brown Orange Blue Orange Green Brown Brown Blue Brown Brown Orange Blue Brown Brown Brown Brown Yellow Brown
Row 17: Brown Brown Green Brown Orange Green Brown Orange Blue Brown Brown Blue Brown Orange Yellow Orange Green Brown Brown Green Brown Orange
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Green Blue Brown Brown Orange Brown Brown Brown Orange Orange
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Blue Brown Brown Brown Brown Green Brown Brown Yellow Brown Brown Brown Yellow Brown Blue Brown Green Brown Brown Brown Brown Brown
Row 21: Yellow Brown Brown Brown Orange Brown Yellow Brown Green Green Orange Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Orange
Row 22: Brown Orange Brown Brown Orange Orange Brown Brown Brown Brown Green Brown Green Brown Brown Brown Brown Brown Brown Blue Yellow Brown
Example 2
Input:
Row 1: Brown Green Red Brown
Row 2: Green Green Brown Brown
Row 3: Brown Brown Pink Green
Row 4: Green Red Red Brown
Output:
Row 1: Brown Green Red Brown Green Brown Green Brown
Row 2: Green Green Brown Brown Red Brown Green Green
Row 3: Brown Brown Pink Green Red Pink Brown Red
Row 4: Green Red Red Brown Brown Green Brown Brown
Row 5: Brown Brown Green Brown Brown Red Red Green
Row 6: Red Brown Pink Red Green Pink Brown Brown
Row 7: Green Green Brown Red Brown Brown Green Green
Row 8: Brown Green Brown Green Brown Red Green Brown
Example 3
Input:
Row 1: Gray
Output:
Row 1: Gray Gray
Row 2: Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Orange Orange
Row 2: Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange
Orange Orange Orange Orange
Orange Orange Orange Orange
Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Yellow Brown Brown Yellow Brown Brown
Row 4: Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow
Row 6: Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown
Row 8: Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown
Row 9: Brown Brown Yellow Brown Brown Brown Brown Brown Brown Yellow
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Orange Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 13: Black Brown Brown Yellow Brown Yellow Brown Brown Brown Brown
Row 14: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Yellow Brown Yellow
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Orange Brown Brown Orange Brown Brown
Row 3: Brown Orange Brown Brown Black Brown Brown Black Brown Brown
Row 4: Brown Black Brown Brown Red Brown Brown Red Brown Orange
Row 5: Brown Red Brown Orange Brown Brown Brown Brown Brown Black
Row 6: Brown Brown Brown Black Brown Brown Brown Orange Brown Red
Row 7: Orange Brown Brown Red Brown Orange Brown Black Brown Brown
Row 8: Black Brown Orange Brown Brown Black Brown Red Brown Orange
Row 9: Red Brown Black Brown Brown Red Brown Brown Brown Black
Row 10: Brown Brown Red Brown Brown Brown Brown Brown Brown Red
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 12: Orange Brown Brown Orange Brown Orange Brown Brown Black Brown
Row 13: Black Brown Brown Black Brown Black Brown Brown Red Brown
Row 14: Red Brown Brown Red Brown Red Brown Orange Brown Orange
Row 15: Brown Brown Brown Brown Brown Brown Brown Black Brown Black
Row 16: Brown Brown Brown Brown Brown Brown Brown Red Brown Red
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Yellow Gray Gray Gray
Row 8: Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Orange Pink Orange Gray Gray
Row 17: Gray Gray Gray Gray Gray Purple Black Gray Gray
Row 18: Gray Gray Gray Gray Green Green Orange Gray Gray
Row 19: Gray Gray Gray Gray Orange Orange Orange Gray Gray
Row 20: Gray Gray Gray Gray Orange Brown Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Yellow Gray
Row 28: Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 29: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 30: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Orange Pink Orange Gray Gray
Row 6: Orange Pink Orange Gray Gray Purple Black Gray Gray
Row 7: Gray Purple Black Gray Green Green Orange Gray Gray
Row 8: Green Green Orange Gray Orange Orange Orange Gray Gray
Row 9: Orange Orange Orange Gray Orange Brown Gray Gray Gray
Row 10: Orange Brown Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Orange Pink Orange Gray Gray Gray Gray Gray Gray
Row 14: Gray Purple Black Gray Gray Gray Gray Gray Gray
Row 15: Green Green Orange Gray Gray Gray Gray Gray Gray
Row 16: Orange Orange Orange Gray Orange Pink Orange Gray Gray
Row 17: Orange Brown Gray Gray Gray Purple Black Gray Gray
Row 18: Gray Gray Gray Gray Green Green Orange Gray Gray
Row 19: Gray Gray Gray Gray Orange Orange Orange Gray Gray
Row 20: Orange Pink Orange Gray Orange Brown Gray Gray Gray
Row 21: Gray Purple Black Gray Gray Gray Gray Gray Gray
Row 22: Green Green Orange Gray Gray Gray Gray Gray Gray
Row 23: Orange Orange Orange Gray Gray Gray Gray Gray Gray
Row 24: Orange Brown Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Orange Pink Orange
Row 26: Orange Pink Orange Gray Gray Gray Gray Purple Black
Row 27: Gray Purple Black Gray Gray Gray Green Green Orange
Row 28: Green Green Orange Gray Gray Gray Orange Orange Orange
Row 29: Orange Orange Orange Gray Gray Gray Orange Brown Gray
Row 30: Orange Brown Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Purple Blue Blue Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Purple Blue Blue Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Purple Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Purple Blue Blue Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Purple Black Black Red Gray
Row 9: Gray Gray Gray Gray Red Black Black Red Purple Gray
Row 10: Gray Gray Gray Gray Gray Gray Red Purple Black Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Purple Black Black Red
Gray Gray Gray Gray Gray Red Black Black Red Purple
Gray Purple Black Black Red Gray Gray Red Purple Black
Red Black Black Red Purple Gray Gray Gray Gray Gray
Gray Gray Red Purple Black Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Purple Black Black Red Gray
Gray Gray Gray Gray Red Black Black Red Purple Gray
Gray Gray Gray Gray Gray Gray Red Purple Black Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Purple Black Black Red
Gray Gray Gray Gray Gray Red Black Black Red Purple
Gray Gray Gray Gray Gray Gray Gray Red Purple Black
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Purple Black Black Red Gray Gray Gray Gray Gray
Red Black Black Red Purple Gray Gray Gray Gray Gray
Gray Gray Red Purple Black Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Green Green Green Green Green
Row 20: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Green Green Green Green Green
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Green Yellow
Output:
Row 1: Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Purple
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Green Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 12: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 13: Yellow Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 14: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 15: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 16: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue
Row 17: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Blue Blue Blue Blue Blue
Row 18: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Blue Blue Blue Blue Blue
Row 19: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Green Green Green Green Green
Row 20: Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Green Green Green Green Green
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Green Purple
Example 2
Input:
Row 1: Green Green Green Black Green Green Green Black Green Green Green Black Green Green Green Black Green Green Green
Row 2: Green Green Green Black Green Green Green Black Green Green Green Black Black Black Black Black Black Black Black
Row 3: Green Green Green Black Green Green Green Black Black Black Black Black Green Green Green Black Green Green Green
Row 4: Green Green Green Black Green Green Green Black Green Black Green Black Black Black Black Black Green Green Green
Row 5: Green Green Green Black Green Green Green Black Black Black Green Black Green Green Green Black Green Green Green
Row 6: Green Green Green Black Green Green Green Black Green Black Green Black Green Green Green Black Green Green Green
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Black Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Black Green Green Green
Row 11: Green Green Green Green Green Green Black Green Green Green Green Black Green Green Green Black Green Green Green
Row 12: Green Green Green Green Green Green Black Green Green Green Green Black Black Black Black Black Black Black Black
Row 13: Green Green Green Green Green Green Black Green Green Green Green Black Green Green Green Green Green Green Green
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Green Green Black Green Green Green Green Green Black Green Green Green Green Green Green Black Green Black Green
Row 16: Green Green Black Green Green Green Green Green Black Black Black Black Black Black Black Black Green Black Green
Row 17: Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black Green Black Green
Row 18: Green Green Green Green Green Green Green Green Black Black Black Black Black Black Black Black Green Black Green
Row 19: Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black Green Black Green
Row 20: Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Black Green Black Green
Row 21: Green Green Green Green Green Green Green Green Black Black Black Black Black Black Black Black Green Black Green
Row 22: Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Black Green Black Green
Row 23: Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Black Green Black Green
Output:
Row 1: Green Green Green Black Green Green Green Black Green Green Green Black Green Green Green Black Green Green Green
Row 2: Green Green Green Black Green Green Green Black Green Green Green Black Black Black Black Black Black Black Black
Row 3: Green Green Green Black Green Green Green Black Black Black Black Black Green Green Green Black Green Green Green
Row 4: Green Green Green Black Green Green Green Black Purple Black Green Black Black Black Black Black Green Green Green
Row 5: Green Green Green Black Green Green Green Black Black Black Green Black Green Green Green Black Green Green Green
Row 6: Green Green Green Black Green Green Green Black Purple Black Green Black Green Green Green Black Green Green Green
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Black Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green Black Green Green Green
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Black Green Green Green
Row 11: Green Green Green Green Green Green Black Green Green Green Green Black Green Green Green Black Green Green Green
Row 12: Green Green Green Green Green Green Black Green Green Green Green Black Black Black Black Black Black Black Black
Row 13: Green Green Green Green Green Green Black Green Green Green Green Black Green Green Green Green Green Green Green
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Green Green Black Green Green Green Green Green Black Green Green Green Green Green Green Black Green Black Green
Row 16: Green Green Black Green Green Green Green Green Black Black Black Black Black Black Black Black Green Black Green
Row 17: Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black Green Black Green
Row 18: Green Green Green Green Green Green Green Green Black Black Black Black Black Black Black Black Green Black Green
Row 19: Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Black Green Black Green
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Black Green Green Green Green Green Green Black Green Black Green
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Green Black Green
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Black Green Green Green Green Green Green Black Green Black Green
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Black Green Green Green Green Green Green Black Green Black Green
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Pink Pink Pink Orange Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Pink Pink Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Pink Pink Pink Orange Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink
Row 10: Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Orange Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Orange Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Orange Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Pink Pink Pink Pink Pink Pink Orange Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Pink Pink Pink Pink Pink Pink Orange Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Pink Pink Pink Orange Purple Purple Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Orange Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Pink Pink Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Orange Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Pink Pink Pink Orange Purple Purple Orange Purple Orange Blue Blue Blue Blue Blue Blue
Row 10: Orange Orange Orange Orange Orange Orange Orange Purple Orange Blue Blue Blue Blue Blue Blue
Row 11: Pink Pink Pink Orange Purple Purple Orange Purple Orange Blue Blue Blue Blue Blue Blue
Row 12: Pink Pink Pink Orange Purple Purple Orange Purple Orange Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Brown Brown Brown Brown Brown
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Brown Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Purple Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Brown Brown Brown Brown Brown
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Black Brown Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 25: Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Purple Brown Brown Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Purple Black Brown Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 3: Purple Black Brown Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Pink Orange Brown
Row 4: Purple Black Green Brown Blue Brown Red Brown Brown Brown Brown Brown Yellow Brown Pink Brown Brown
Row 5: Purple Black Green Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown
Row 6: Purple Black Green Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Purple Black Green Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Purple Brown Green Brown Blue Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Purple Brown Green Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Purple Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Purple Blue Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Purple Blue Red Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Purple Blue Red Green Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Purple Blue Red Green Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Purple Blue Red Green Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Purple Blue Red Green Black Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Purple Blue Red Green Black Pink Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Purple Blue Red Green Black Pink Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 29: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 30: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 28: Red Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 29: Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 30: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Purple Yellow Yellow Yellow Pink Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Yellow Yellow
Row 2: Purple Yellow Yellow Yellow Pink Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Yellow Yellow
Row 3: Purple Yellow Yellow Yellow Pink Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Yellow Yellow
Row 4: Purple Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Yellow Yellow
Row 5: Purple Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Yellow Yellow
Row 6: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Yellow Yellow
Row 7: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow
Row 8: Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Brown Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Brown Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Brown Black Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Brown Black Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Purple Red Brown Black Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Black Black Black Black Pink
Row 2: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Black Black Black Black Black Black Red
Row 3: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Black Black Black Black Black Black Black
Row 4: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Black Black Black Black Black Black Black
Row 5: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Black Black Black Black Black Black Black
Row 6: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Black Black Black Black Black Black Black
Row 7: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Black Black Black Black Black Black Black
Row 8: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Black Black Black Black Black Black Black
Row 9: Green Gray Green Green Red Brown Black Black Black Black Black Pink Green Gray Green Green Black Black Black Black Black
Row 10: Pink Gray Pink Pink Red Pink Black Black Black Black Black Pink Pink Gray Pink Pink Black Black Black Black Black
Row 11: Pink Green Pink Brown Pink Pink Black Black Black Black Black Brown Pink Green Pink Brown Black Black Black Black Black
Row 12: Red Pink Red Green Red Pink Black Black Black Black Black Pink Red Pink Red Green Black Black Black Black Black
Row 13: Green Gray Green Green Red Brown Black Black Black Black Black Pink Green Gray Green Green Red Brown Pink Green Pink
Row 14: Pink Black Black Black Black Black Black Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 15: Pink Black Black Black Black Black Black Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 16: Red Black Black Black Black Black Black Gray Pink Pink Black Black Red Pink Red Green Red Pink Pink Gray Pink
Row 17: Green Black Black Black Black Black Black Green Pink Brown Black Black Green Gray Green Green Red Brown Pink Green Pink
Row 18: Pink Black Black Black Black Black Black Pink Red Green Black Black Pink Gray Pink Pink Red Pink Red Pink Red
Row 19: Pink Green Pink Brown Pink Pink Green Gray Green Green Black Black Pink Black Black Black Black Black Green Gray Green
Row 20: Red Pink Red Green Red Pink Pink Gray Pink Pink Black Black Red Black Black Black Black Black Pink Gray Pink
Row 21: Green Gray Green Green Red Brown Pink Green Pink Brown Black Black Green Black Black Black Black Black Pink Green Pink
Row 22: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Black Black Black Black Black Red Pink Red
Row 23: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Black Black Black Black Black Green Gray Green
Row 24: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Black Black Black Black Black Pink Gray Pink
Row 25: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Black Black Black Black Pink Green Pink
Row 26: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Black Black Black Black Red Pink Red
Row 27: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 28: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Output:
Row 1: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 2: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 3: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 4: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Row 5: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 6: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 7: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 8: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Row 9: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 10: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 11: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 12: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Row 13: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 14: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 15: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 16: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Row 17: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 18: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 19: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 20: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Row 21: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 22: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 23: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 24: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Row 25: Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink
Row 26: Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red
Row 27: Pink Green Pink Brown Pink Pink Green Gray Green Green Red Brown Pink Green Pink Brown Pink Pink Green Gray Green
Row 28: Red Pink Red Green Red Pink Pink Gray Pink Pink Red Pink Red Pink Red Green Red Pink Pink Gray Pink
Example 2
Input:
Row 1: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 2: Red Purple Yellow Blue Blue Blue Blue Blue Yellow Red
Row 3: Yellow Red Red Blue Blue Blue Blue Blue Yellow Yellow
Row 4: Yellow Yellow Purple Blue Blue Blue Blue Blue Red Yellow
Row 5: Red Yellow Yellow Purple Red Purple Yellow Yellow Purple Yellow
Row 6: Purple Yellow Red Red Yellow Red Red Yellow Yellow Purple
Row 7: Yellow Purple Red Purple Yellow Yellow Purple Yellow Red Red
Row 8: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 9: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 10: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 11: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Row 12: Red Yellow Yellow Purple Red Purple Yellow Yellow Purple Yellow
Row 13: Purple Yellow Red Red Yellow Red Red Yellow Yellow Purple
Row 14: Yellow Purple Red Purple Yellow Yellow Purple Yellow Red Red
Row 15: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 16: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 17: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 18: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Row 19: Red Yellow Yellow Purple Red Purple Yellow Yellow Purple Yellow
Row 20: Purple Yellow Red Red Yellow Red Red Yellow Yellow Purple
Row 21: Yellow Purple Red Purple Yellow Yellow Purple Yellow Red Red
Row 22: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 23: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 24: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 25: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Output:
Row 1: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 2: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 3: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 4: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Row 5: Red Yellow Yellow Purple Red Purple Yellow Yellow Purple Yellow
Row 6: Purple Yellow Red Red Yellow Red Red Yellow Yellow Purple
Row 7: Yellow Purple Red Purple Yellow Yellow Purple Yellow Red Red
Row 8: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 9: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 10: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 11: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Row 12: Red Yellow Yellow Purple Red Purple Yellow Yellow Purple Yellow
Row 13: Purple Yellow Red Red Yellow Red Red Yellow Yellow Purple
Row 14: Yellow Purple Red Purple Yellow Yellow Purple Yellow Red Red
Row 15: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 16: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 17: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 18: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Row 19: Red Yellow Yellow Purple Red Purple Yellow Yellow Purple Yellow
Row 20: Purple Yellow Red Red Yellow Red Red Yellow Yellow Purple
Row 21: Yellow Purple Red Purple Yellow Yellow Purple Yellow Red Red
Row 22: Red Red Yellow Red Red Yellow Yellow Purple Red Purple
Row 23: Red Purple Yellow Yellow Purple Yellow Red Red Yellow Red
Row 24: Yellow Red Red Yellow Yellow Purple Red Purple Yellow Yellow
Row 25: Yellow Yellow Purple Yellow Red Red Yellow Red Red Yellow
Example 3
Input:
Row 1: Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange
Row 2: Brown Orange Brown Purple Gray Purple Red Red Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple
Row 3: Gray Pink Blue Purple Blue Black Red Red Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple
Row 4: Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown
Row 5: Black Pink Pink Black Gray Pink Red Red Red Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black
Row 6: Gray Purple Blue Gray Brown Orange Red Red Red Purple Red Red Red Red Red Purple Gray Purple Blue Gray
Row 7: Blue Black Purple Brown Gray Pink Red Red Red Black Red Red Red Red Red Purple Blue Black Red Red
Row 8: Gray Green Blue Blue Purple Pink Red Red Red Green Red Red Red Red Red Brown Gray Green Red Red
Row 9: Gray Pink Blue Orange Black Pink Red Red Red Pink Red Red Red Red Red Black Gray Pink Red Red
Row 10: Brown Red Red Red Red Purple Blue Gray Brown Orange Red Red Red Red Red Gray Brown Orange Red Red
Row 11: Gray Red Red Red Red Red Purple Brown Gray Pink Blue Red Red Black Purple Brown Gray Pink Red Red
Row 12: Purple Red Red Red Red Red Blue Blue Purple Red Red Red Red Red Blue Blue Purple Pink Red Red
Row 13: Black Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Orange Black Pink Red Red
Row 14: Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Purple Gray Purple Red Red
Row 15: Blue Black Purple Brown Gray Pink Blue Red Red Red Red Red Red Red Blue Purple Blue Black Purple Brown
Row 16: Gray Green Blue Blue Purple Pink Black Red Red Red Red Red Red Red Black Brown Gray Green Blue Blue
Row 17: Gray Pink Blue Orange Red Red Red Red Red Red Red Red Red Red Red Red Gray Pink Blue Orange
Row 18: Brown Orange Brown Purple Red Red Red Red Red Red Red Red Red Red Red Red Brown Orange Brown Purple
Row 19: Gray Pink Red Red Red Red Red Red Gray Pink Red Red Red Red Red Red Gray Pink Red Red
Row 20: Purple Pink Red Red Red Red Red Red Purple Pink Red Red Red Red Red Red Purple Pink Red Red
Row 21: Black Pink Red Red Red Red Red Red Black Pink Red Red Red Red Red Red Black Pink Red Red
Row 22: Gray Purple Red Red Red Red Red Red Gray Purple Blue Gray Brown Orange Red Red Red Purple Red Red
Row 23: Blue Black Red Red Red Red Red Red Blue Black Purple Brown Gray Pink Red Red Red Black Red Red
Row 24: Gray Green Red Red Red Red Red Red Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue
Row 25: Gray Pink Blue Orange Red Red Red Red Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange
Row 26: Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple
Output:
Row 1: Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange
Row 2: Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple
Row 3: Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple
Row 4: Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown
Row 5: Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black
Row 6: Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray
Row 7: Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown
Row 8: Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue
Row 9: Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange
Row 10: Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple
Row 11: Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple
Row 12: Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown
Row 13: Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black
Row 14: Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray
Row 15: Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown
Row 16: Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue
Row 17: Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange
Row 18: Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple
Row 19: Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple
Row 20: Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown
Row 21: Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black
Row 22: Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray
Row 23: Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown Gray Pink Blue Purple Blue Black Purple Brown
Row 24: Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue Purple Pink Black Brown Gray Green Blue Blue
Row 25: Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange Black Pink Pink Black Gray Pink Blue Orange
Row 26: Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple Gray Purple Blue Gray Brown Orange Brown Purple
Here is the input grid for the test example:
Input:
Row 1: Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue
Row 2: Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple
Row 3: Blue Green Gray Black Purple Brown Brown Brown Brown Brown Blue Blue Red Blue Purple Blue Green Gray Black Purple
Row 4: Black Gray Red Blue Blue Brown Brown Brown Brown Brown Blue Green Gray Brown Brown Brown Brown Brown Blue Blue
Row 5: Blue Blue Red Blue Purple Brown Brown Brown Brown Brown Black Gray Red Brown Brown Brown Brown Brown Blue Purple
Row 6: Blue Green Gray Black Purple Black Brown Brown Blue Blue Blue Blue Red Brown Brown Brown Brown Brown Black Purple
Row 7: Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Brown Brown Brown Brown Brown Brown Blue Blue
Row 8: Brown Brown Brown Brown Brown Blue Green Gray Brown Brown Black Gray Brown Brown Brown Brown Brown Brown Blue Purple
Row 9: Brown Brown Brown Brown Brown Black Gray Red Brown Brown Blue Blue Red Blue Purple Blue Green Gray Black Purple
Row 10: Brown Brown Brown Brown Brown Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue
Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple
Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple
Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue
Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple
Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple
Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue
Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple
Blue Green Gray Black Purple Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple
Black Gray Red Blue Blue Blue Blue Red Blue Purple Blue Green Gray Black Purple Black Gray Red Blue Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Red Red Red Red Green Red Red Green Red Red Red Red Red Red Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green
Row 13: Red Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Red
Row 14: Red Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Red
Row 15: Red Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Red
Row 16: Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Red
Row 17: Red Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Red
Row 18: Red Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Red
Row 19: Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Red Red Red Red Red Green Green Red Red Green Red Red Red Red Red Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Red Red Red Red Green Red Red Green Red Red Red Red Red Red Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Pink Red Red Red Red Pink Red Red Pink Red Red Red Red Red Red Pink Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green
Row 13: Red Green Green Green Green Green Green Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green Green Green Green Red
Row 14: Red Green Green Green Green Green Green Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green Green Green Green Red
Row 15: Red Green Green Green Green Green Green Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green Green Green Green Red
Row 16: Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green Green Green Green Red
Row 17: Red Green Green Green Green Green Green Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green Green Green Green Red
Row 18: Red Green Green Green Green Green Green Green Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Green Green Green Green Red
Row 19: Green Green Green Green Green Green Green Green Red Red Red Red Red Pink Pink Red Red Pink Red Red Red Red Red Pink Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Red Red Red Red Red Green Green Red Red Green Red Red Red Red Red Green Green Green Green Green Green
Example 2
Input:
Row 1: Gray Gray Gray Purple Yellow Gray Yellow Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 4: Gray Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Orange
Row 5: Gray Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 6: Yellow Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 7: Gray Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Purple Yellow Gray Yellow Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Pink Purple Yellow Pink Yellow Pink Gray Gray Gray Gray
Row 4: Gray Gray Pink Pink Pink Pink Pink Orange Gray Gray Gray Orange
Row 5: Gray Gray Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 6: Yellow Gray Yellow Pink Pink Pink Pink Pink Gray Gray Gray Gray
Row 7: Gray Gray Pink Yellow Pink Pink Pink Pink Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Red Red Red Pink Red Red
Row 2: Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red
Row 10: Red Red Brown Brown Red Red
Row 11: Yellow Red Brown Brown Red Red
Row 12: Black Red Brown Brown Red Yellow
Row 13: Red Red Brown Brown Red Yellow
Row 14: Black Red Brown Brown Red Yellow
Row 15: Pink Red Brown Brown Red Gray
Row 16: Pink Red Brown Brown Red Black
Row 17: Red Red Brown Brown Red Red
Row 18: Pink Red Brown Brown Red Yellow
Row 19: Red Red Brown Brown Red Gray
Row 20: Yellow Red Brown Brown Red Red
Row 21: Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red
Output:
Row 1: Red Red Red Pink Red Red
Row 2: Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red
Row 10: Red Red Brown Pink Red Red
Row 11: Yellow Red Yellow Brown Red Red
Row 12: Black Red Black Yellow Red Yellow
Row 13: Red Red Brown Yellow Red Yellow
Row 14: Black Red Black Yellow Red Yellow
Row 15: Pink Red Pink Gray Red Gray
Row 16: Pink Red Pink Black Red Black
Row 17: Red Red Brown Brown Red Red
Row 18: Pink Red Pink Yellow Red Yellow
Row 19: Red Red Brown Gray Red Gray
Row 20: Yellow Red Yellow Brown Red Red
Row 21: Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Purple Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Red Red Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Purple Red Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Purple Pink Pink Purple Blue Red Red Purple Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Red Red Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Gray
Row 2: Purple Brown
Row 3: Green Purple
Row 4: Green Brown
Row 5: Gray Purple
Row 6: Purple Orange
Row 7: Pink Purple
Row 8: Gray Purple
Row 9: Gray Purple
Row 10: Pink Green
Row 11: Orange Brown
Row 12: Pink Brown
Row 13: Orange Brown
Row 14: Green Purple
Row 15: Green Orange
Row 16: Green Green
Row 17: Brown Brown
Row 18: Brown Orange
Row 19: Brown Orange
Row 20: Brown Orange
Row 21: Orange Brown
Row 22: Brown Pink
Row 23: Orange Pink
Row 24: Orange Orange
Row 25: Pink Orange
Output:
Row 1: Brown Purple
Row 2: Gray Brown
Row 3: Green Gray
Row 4: Green Brown
Row 5: Purple Gray
Row 6: Gray Orange
Row 7: Pink Gray
Row 8: Purple Gray
Row 9: Purple Gray
Row 10: Pink Green
Row 11: Orange Brown
Row 12: Pink Brown
Row 13: Orange Brown
Row 14: Green Gray
Row 15: Green Orange
Row 16: Green Green
Row 17: Brown Brown
Row 18: Brown Orange
Row 19: Brown Orange
Row 20: Brown Orange
Row 21: Orange Brown
Row 22: Brown Pink
Row 23: Orange Pink
Row 24: Orange Orange
Row 25: Pink Orange
Example 2
Input:
Row 1: Purple Red Purple Red Orange Red Purple Purple Purple Orange Orange Purple Orange Red Orange Red Blue Purple Purple Blue Red Orange Red Blue Red Purple Red Orange Red Orange
Row 2: Purple Orange Red Purple Blue Purple Gray Red Blue Red Blue Blue Purple Blue Purple Blue Orange Red Red Blue Red Purple Purple Orange Red Purple Purple Orange Gray Gray
Row 3: Orange Red Blue Purple Purple Purple Purple Red Purple Blue Orange Blue Purple Blue Red Orange Purple Purple Purple Blue Blue Red Red Purple Orange Purple Orange Purple Purple Purple
Row 4: Red Purple Blue Purple Blue Purple Blue Orange Purple Orange Blue Red Orange Red Blue Purple Blue Blue Gray Red Blue Purple Purple Blue Red Red Orange Blue Red Red
Row 5: Purple Orange Red Orange Orange Purple Gray Orange Purple Purple Orange Purple Red Orange Red Blue Purple Blue Purple Red Orange Purple Purple Red Purple Red Red Purple Red Purple
Row 6: Orange Blue Purple Purple Purple Blue Red Purple Purple Blue Purple Red Red Orange Orange Purple Purple Blue Orange Red Blue Red Blue Purple Purple Purple Orange Orange Blue Orange
Row 7: Red Purple Purple Orange Red Red Red Blue Purple Purple Red Purple Red Blue Orange Blue Purple Purple Purple Red Red Purple Purple Purple Blue Blue Red Blue Blue Purple
Row 8: Red Red Purple Blue Gray Orange Purple Orange Purple Orange Gray Red Blue Orange Purple Red Red Purple Orange Blue Purple Orange Red Orange Red Gray Red Blue Purple Blue
Row 9: Purple Blue Blue Red Orange Purple Blue Red Purple Purple Red Blue Orange Blue Purple Gray Blue Purple Orange Orange Purple Orange Purple Blue Blue Orange Orange Red Purple Orange
Row 10: Orange Purple Blue Blue Blue Purple Red Orange Purple Orange Orange Blue Purple Red Orange Red Orange Orange Orange Red Red Purple Purple Gray Blue Purple Blue Orange Purple Blue
Row 11: Gray Red Purple Red Blue Purple Red Red Blue Purple Purple Blue Red Red Purple Gray Purple Blue Red Blue Purple Red Orange Gray Purple Red Blue Blue Red Orange
Row 12: Red Purple Red Blue Orange Blue Purple Purple Purple Gray Purple Purple Orange Blue Red Red Blue Purple Orange Orange Red Purple Gray Purple Blue Blue Purple Blue Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Blue Orange Orange Blue Orange Orange Purple Purple Purple Purple Purple Orange Red Orange Orange Purple Purple Purple Orange Purple Orange Purple Orange Purple
Row 14: Blue Blue Blue Orange Purple Red Red Gray Purple Purple Red Purple Red Purple Orange Blue Purple Red Orange Red Purple Purple Blue Gray Red Orange Blue Blue Orange Orange
Row 15: Red Orange Purple Purple Red Orange Orange Red Purple Purple Purple Orange Red Orange Blue Purple Red Purple Blue Orange Red Purple Orange Purple Gray Orange Blue Purple Purple Orange
Row 16: Purple Orange Purple Purple Red Purple Gray Red Red Red Purple Red Purple Red Purple Red Purple Blue Purple Purple Orange Purple Red Blue Purple Purple Red Blue Red Blue
Row 17: Blue Red Blue Purple Red Red Purple Purple Blue Orange Red Purple Blue Purple Red Red Purple Red Purple Red Red Orange Red Red Purple Purple Purple Purple Red Purple
Row 18: Orange Red Purple Red Purple Red Red Red Blue Purple Purple Purple Gray Blue Blue Purple Purple Orange Orange Red Blue Gray Orange Blue Orange Gray Blue Purple Blue Purple
Row 19: Red Blue Blue Orange Orange Gray Red Blue Purple Orange Blue Purple Orange Orange Gray Purple Purple Purple Blue Red Red Purple Orange Red Orange Purple Orange Blue Purple Red
Row 20: Orange Red Orange Purple Orange Purple Blue Purple Purple Orange Orange Blue Blue Blue Orange Blue Purple Red Red Purple Orange Purple Blue Purple Purple Purple Purple Red Red Purple
Row 21: Red Orange Purple Blue Purple Red Purple Purple Red Orange Purple Red Purple Purple Purple Red Red Purple Orange Blue Orange Purple Orange Blue Orange Red Blue Blue Blue Red
Row 22: Blue Blue Blue Blue Purple Blue Blue Blue Gray Red Red Orange Blue Purple Red Blue Purple Orange Orange Purple Purple Purple Purple Purple Blue Purple Orange Purple Purple Blue
Row 23: Orange Blue Purple Red Blue Orange Red Red Red Blue Blue Red Red Red Orange Blue Purple Purple Gray Purple Orange Orange Blue Blue Purple Purple Purple Purple Purple Blue
Row 24: Red Purple Purple Purple Orange Red Purple Purple Purple Purple Purple Orange Purple Purple Purple Blue Purple Purple Purple Red Blue Blue Orange Red Purple Purple Orange Orange Purple Orange
Row 25: Purple Orange Purple Red Red Red Blue Blue Purple Purple Blue Orange Blue Orange Blue Red Blue Purple Orange Orange Red Purple Purple Gray Red Purple Red Gray Purple Orange
Row 26: Purple Blue Purple Gray Purple Purple Orange Gray Purple Orange Purple Red Purple Purple Purple Blue Orange Blue Purple Blue Purple Orange Orange Blue Blue Purple Orange Blue Blue Orange
Row 27: Red Blue Orange Red Orange Orange Orange Purple Red Orange Purple Purple Purple Blue Orange Blue Purple Orange Purple Orange Red Purple Orange Blue Red Purple Blue Orange Purple Blue
Row 28: Purple Purple Purple Orange Orange Purple Purple Blue Purple Red Blue Purple Purple Purple Red Red Purple Red Purple Blue Blue Purple Purple Red Orange Orange Red Purple Blue Purple
Row 29: Orange Red Red Red Purple Purple Purple Blue Purple Gray Orange Blue Purple Purple Orange Gray Blue Blue Gray Orange Red Purple Purple Orange Red Purple Blue Red Red Red
Output:
Row 1: Gray Red Gray Red Orange Red Gray Gray Gray Orange Orange Gray Orange Red Orange Red Blue Gray Gray Blue Red Orange Red Blue Red Gray Red Orange Red Orange
Row 2: Gray Orange Red Gray Blue Gray Purple Red Blue Red Blue Blue Gray Blue Gray Blue Orange Red Red Blue Red Gray Gray Orange Red Gray Gray Orange Purple Purple
Row 3: Orange Red Blue Gray Gray Gray Gray Red Gray Blue Orange Blue Gray Blue Red Orange Gray Gray Gray Blue Blue Red Red Gray Orange Gray Orange Gray Gray Gray
Row 4: Red Gray Blue Gray Blue Gray Blue Orange Gray Orange Blue Red Orange Red Blue Gray Blue Blue Purple Red Blue Gray Gray Blue Red Red Orange Blue Red Red
Row 5: Gray Orange Red Orange Orange Gray Purple Orange Gray Gray Orange Gray Red Orange Red Blue Gray Blue Gray Red Orange Gray Gray Red Gray Red Red Gray Red Gray
Row 6: Orange Blue Gray Gray Gray Blue Red Gray Gray Blue Gray Red Red Orange Orange Gray Gray Blue Orange Red Blue Red Blue Gray Gray Gray Orange Orange Blue Orange
Row 7: Red Gray Gray Orange Red Red Red Blue Gray Gray Red Gray Red Blue Orange Blue Gray Gray Gray Red Red Gray Gray Gray Blue Blue Red Blue Blue Gray
Row 8: Red Red Gray Blue Purple Orange Gray Orange Gray Orange Purple Red Blue Orange Gray Red Red Gray Orange Blue Gray Orange Red Orange Red Purple Red Blue Gray Blue
Row 9: Gray Blue Blue Red Orange Gray Blue Red Gray Gray Red Blue Orange Blue Gray Purple Blue Gray Orange Orange Gray Orange Gray Blue Blue Orange Orange Red Gray Orange
Row 10: Orange Gray Blue Blue Blue Gray Red Orange Gray Orange Orange Blue Gray Red Orange Red Orange Orange Orange Red Red Gray Gray Purple Blue Gray Blue Orange Gray Blue
Row 11: Purple Red Gray Red Blue Gray Red Red Blue Gray Gray Blue Red Red Gray Purple Gray Blue Red Blue Gray Red Orange Purple Gray Red Blue Blue Red Orange
Row 12: Red Gray Red Blue Orange Blue Gray Gray Gray Purple Gray Gray Orange Blue Red Red Blue Gray Orange Orange Red Gray Purple Gray Blue Blue Gray Blue Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Blue Orange Orange Blue Orange Orange Gray Gray Gray Gray Gray Orange Red Orange Orange Gray Gray Gray Orange Gray Orange Gray Orange Gray
Row 14: Blue Blue Blue Orange Gray Red Red Purple Gray Gray Red Gray Red Gray Orange Blue Gray Red Orange Red Gray Gray Blue Purple Red Orange Blue Blue Orange Orange
Row 15: Red Orange Gray Gray Red Orange Orange Red Gray Gray Gray Orange Red Orange Blue Gray Red Gray Blue Orange Red Gray Orange Gray Purple Orange Blue Gray Gray Orange
Row 16: Gray Orange Gray Gray Red Gray Purple Red Red Red Gray Red Gray Red Gray Red Gray Blue Gray Gray Orange Gray Red Blue Gray Gray Red Blue Red Blue
Row 17: Blue Red Blue Gray Red Red Gray Gray Blue Orange Red Gray Blue Gray Red Red Gray Red Gray Red Red Orange Red Red Gray Gray Gray Gray Red Gray
Row 18: Orange Red Gray Red Gray Red Red Red Blue Gray Gray Gray Purple Blue Blue Gray Gray Orange Orange Red Blue Purple Orange Blue Orange Purple Blue Gray Blue Gray
Row 19: Red Blue Blue Orange Orange Purple Red Blue Gray Orange Blue Gray Orange Orange Purple Gray Gray Gray Blue Red Red Gray Orange Red Orange Gray Orange Blue Gray Red
Row 20: Orange Red Orange Gray Orange Gray Blue Gray Gray Orange Orange Blue Blue Blue Orange Blue Gray Red Red Gray Orange Gray Blue Gray Gray Gray Gray Red Red Gray
Row 21: Red Orange Gray Blue Gray Red Gray Gray Red Orange Gray Red Gray Gray Gray Red Red Gray Orange Blue Orange Gray Orange Blue Orange Red Blue Blue Blue Red
Row 22: Blue Blue Blue Blue Gray Blue Blue Blue Purple Red Red Orange Blue Gray Red Blue Gray Orange Orange Gray Gray Gray Gray Gray Blue Gray Orange Gray Gray Blue
Row 23: Orange Blue Gray Red Blue Orange Red Red Red Blue Blue Red Red Red Orange Blue Gray Gray Purple Gray Orange Orange Blue Blue Gray Gray Gray Gray Gray Blue
Row 24: Red Gray Gray Gray Orange Red Gray Gray Gray Gray Gray Orange Gray Gray Gray Blue Gray Gray Gray Red Blue Blue Orange Red Gray Gray Orange Orange Gray Orange
Row 25: Gray Orange Gray Red Red Red Blue Blue Gray Gray Blue Orange Blue Orange Blue Red Blue Gray Orange Orange Red Gray Gray Purple Red Gray Red Purple Gray Orange
Row 26: Gray Blue Gray Purple Gray Gray Orange Purple Gray Orange Gray Red Gray Gray Gray Blue Orange Blue Gray Blue Gray Orange Orange Blue Blue Gray Orange Blue Blue Orange
Row 27: Red Blue Orange Red Orange Orange Orange Gray Red Orange Gray Gray Gray Blue Orange Blue Gray Orange Gray Orange Red Gray Orange Blue Red Gray Blue Orange Gray Blue
Row 28: Gray Gray Gray Orange Orange Gray Gray Blue Gray Red Blue Gray Gray Gray Red Red Gray Red Gray Blue Blue Gray Gray Red Orange Orange Red Gray Blue Gray
Row 29: Orange Red Red Red Gray Gray Gray Blue Gray Purple Orange Blue Gray Gray Orange Purple Blue Blue Purple Orange Red Gray Gray Orange Red Gray Blue Red Red Red
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Gray Blue Purple Blue Blue Purple Purple Blue Blue Blue Purple
Row 2: Blue Blue Blue Gray Purple Blue Gray Purple Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Purple Blue Purple Gray Gray Blue Blue Blue Blue Gray Blue Gray Blue Blue Blue Blue
Row 4: Purple Blue Blue Blue Gray Purple Blue Blue Blue Purple Blue Purple Blue Purple Blue Blue
Row 5: Purple Blue Gray Blue Gray Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue
Row 6: Blue Blue Blue Blue Purple Blue Purple Gray Purple Purple Blue Gray Blue Blue Gray Blue
Row 7: Gray Purple Blue Blue Purple Blue Blue Gray Blue Blue Blue Blue Purple Blue Blue Blue
Row 8: Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue
Row 9: Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Gray Purple
Row 10: Blue Blue Blue Purple Purple Gray Blue Blue Blue Blue Blue Purple Gray Blue Purple Blue
Row 11: Blue Blue Blue Blue Blue Purple Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Purple Gray Blue Blue
Row 13: Blue Purple Purple Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 14: Blue Gray Purple Blue Purple Blue Blue Purple Blue Gray Purple Blue Blue Blue Blue Gray
Row 15: Blue Gray Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Purple Blue Purple
Row 16: Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Purple Purple
Row 17: Blue Blue Purple Purple Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 19: Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Purple Purple
Row 20: Blue Blue Blue Blue Blue Blue Gray Gray Purple Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Gray Blue Blue Blue Gray Gray Blue Blue Purple Blue Gray Blue Blue Purple Blue
Row 22: Purple Purple Blue Blue Blue Gray Blue Blue Blue Purple Blue Purple Gray Blue Blue Gray
Row 23: Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue
Row 24: Purple Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Purple Blue Purple Blue Blue Blue Blue Blue Purple Gray Blue Blue Purple Blue Blue
Row 26: Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue
Row 27: Blue Purple Blue Blue Blue Blue Gray Gray Purple Blue Gray Gray Blue Blue Purple Purple
Output:
Row 1: Blue Blue Blue Blue Blue Purple Blue Gray Blue Blue Gray Gray Blue Blue Blue Gray
Row 2: Blue Blue Blue Purple Gray Blue Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Gray Blue Gray Purple Purple Blue Blue Blue Blue Purple Blue Purple Blue Blue Blue Blue
Row 4: Gray Blue Blue Blue Purple Gray Blue Blue Blue Gray Blue Gray Blue Gray Blue Blue
Row 5: Gray Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue
Row 6: Blue Blue Blue Blue Gray Blue Gray Purple Gray Gray Blue Purple Blue Blue Purple Blue
Row 7: Purple Gray Blue Blue Gray Blue Blue Purple Blue Blue Blue Blue Gray Blue Blue Blue
Row 8: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue
Row 9: Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Gray
Row 10: Blue Blue Blue Gray Gray Purple Blue Blue Blue Blue Blue Gray Purple Blue Gray Blue
Row 11: Blue Blue Blue Blue Blue Gray Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Gray Purple Blue Blue
Row 13: Blue Gray Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue
Row 14: Blue Purple Gray Blue Gray Blue Blue Gray Blue Purple Gray Blue Blue Blue Blue Purple
Row 15: Blue Purple Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Gray Blue Gray
Row 16: Blue Blue Blue Purple Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Gray Gray
Row 17: Blue Blue Gray Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue
Row 19: Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple Purple Blue Blue Gray Gray
Row 20: Blue Blue Blue Blue Blue Blue Purple Purple Gray Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Purple Blue Blue Blue Purple Purple Blue Blue Gray Blue Purple Blue Blue Gray Blue
Row 22: Gray Gray Blue Blue Blue Purple Blue Blue Blue Gray Blue Gray Purple Blue Blue Purple
Row 23: Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue Blue
Row 24: Gray Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Gray Blue Gray Blue Blue Blue Blue Blue Gray Purple Blue Blue Gray Blue Blue
Row 26: Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue
Row 27: Blue Gray Blue Blue Blue Blue Purple Purple Gray Blue Purple Purple Blue Blue Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Orange Brown Yellow Brown Gray Orange Yellow Purple Orange Brown Yellow Orange Brown Brown Brown Orange Brown Yellow Yellow Yellow Yellow Yellow Orange
Row 2: Purple Purple Yellow Brown Yellow Orange Purple Brown Yellow Brown Yellow Brown Orange Brown Brown Yellow Yellow Brown Yellow Yellow Brown Brown Orange
Row 3: Orange Brown Yellow Brown Orange Brown Yellow Gray Orange Gray Brown Orange Brown Orange Yellow Brown Brown Brown Orange Orange Brown Brown Brown
Row 4: Yellow Brown Orange Brown Orange Brown Brown Brown Orange Orange Yellow Brown Orange Brown Gray Gray Orange Orange Gray Orange Yellow Yellow Brown
Row 5: Orange Orange Orange Brown Brown Orange Brown Gray Orange Yellow Brown Brown Orange Yellow Brown Brown Orange Brown Brown Brown Brown Yellow Brown
Row 6: Yellow Yellow Orange Yellow Yellow Brown Brown Yellow Orange Orange Yellow Yellow Yellow Yellow Orange Orange Orange Gray Yellow Yellow Yellow Purple Gray
Row 7: Purple Yellow Orange Yellow Yellow Yellow Brown Gray Yellow Brown Brown Orange Orange Brown Yellow Brown Brown Purple Orange Gray Brown Orange Brown
Row 8: Orange Brown Brown Yellow Gray Yellow Brown Brown Gray Yellow Orange Yellow Orange Brown Yellow Orange Orange Yellow Brown Brown Brown Yellow Brown
Row 9: Purple Yellow Orange Orange Yellow Yellow Brown Yellow Orange Orange Purple Yellow Yellow Orange Yellow Yellow Orange Orange Yellow Orange Yellow Brown Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Brown Yellow Brown Purple Orange Yellow Gray Orange Brown Yellow Orange Brown Brown Brown Orange Brown Yellow Yellow Yellow Yellow Yellow Orange
Gray Gray Yellow Brown Yellow Orange Gray Brown Yellow Brown Yellow Brown Orange Brown Brown Yellow Yellow Brown Yellow Yellow Brown Brown Orange
Orange Brown Yellow Brown Orange Brown Yellow Purple Orange Purple Brown Orange Brown Orange Yellow Brown Brown Brown Orange Orange Brown Brown Brown
Yellow Brown Orange Brown Orange Brown Brown Brown Orange Orange Yellow Brown Orange Brown Purple Purple Orange Orange Purple Orange Yellow Yellow Brown
Orange Orange Orange Brown Brown Orange Brown Purple Orange Yellow Brown Brown Orange Yellow Brown Brown Orange Brown Brown Brown Brown Yellow Brown
Yellow Yellow Orange Yellow Yellow Brown Brown Yellow Orange Orange Yellow Yellow Yellow Yellow Orange Orange Orange Purple Yellow Yellow Yellow Gray Purple
Gray Yellow Orange Yellow Yellow Yellow Brown Purple Yellow Brown Brown Orange Orange Brown Yellow Brown Brown Gray Orange Purple Brown Orange Brown
Orange Brown Brown Yellow Purple Yellow Brown Brown Purple Yellow Orange Yellow Orange Brown Yellow Orange Orange Yellow Brown Brown Brown Yellow Brown
Gray Yellow Orange Orange Yellow Yellow Brown Yellow Orange Orange Gray Yellow Yellow Orange Yellow Yellow Orange Orange Yellow Orange Yellow Brown Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Brown Brown Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Brown Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow
Row 7: Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow
Row 8: Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Yellow Yellow
Row 9: Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow
Row 11: Brown Brown Yellow Brown Brown Brown Brown Yellow Yellow Brown Yellow
Row 12: Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow
Row 13: Brown Brown Yellow Yellow Brown Brown Brown Brown Yellow Yellow Yellow
Row 14: Brown Brown Yellow Brown Yellow Yellow Brown Brown Yellow Yellow Yellow
Row 15: Yellow Brown Brown Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 16: Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Red Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Red Red Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Red Red Red Yellow Red Red Yellow Yellow Yellow Yellow Yellow
Row 8: Red Red Red Red Red Yellow Yellow Red Red Yellow Yellow
Row 9: Red Red Red Red Yellow Red Red Red Yellow Yellow Yellow
Row 10: Red Red Red Red Red Red Red Yellow Red Red Yellow
Row 11: Red Red Red Red Red Red Red Red Red Yellow Yellow
Row 12: Red Red Yellow Red Red Red Red Yellow Yellow Red Yellow
Row 13: Yellow Red Red Red Red Red Red Red Yellow Yellow Yellow
Row 14: Red Red Yellow Yellow Red Red Red Red Yellow Yellow Yellow
Row 15: Red Red Yellow Red Yellow Yellow Red Red Yellow Yellow Yellow
Row 16: Yellow Red Red Red Yellow Yellow Red Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Black Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Red Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green
Row 13: Green Green Green Green Gray Green Green
Row 14: Green Green Green Green Green Gray Green
Row 15: Green Green Green Gray Gray Green Green
Row 16: Green Green Green Gray Green Gray Green
Row 17: Green Green Gray Gray Gray Gray Gray
Row 18: Green Green Gray Gray Gray Gray Green
Row 19: Green Green Gray Green Gray Gray Gray
Row 20: Green Green Gray Gray Gray Gray Gray
Row 21: Green Green Green Gray Gray Green Gray
Row 22: Green Green Green Gray Green Green Gray
Row 23: Green Green Green Gray Green Green Green
Row 24: Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green
Row 28: Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green
Row 14: Green Green Green Green Red Green Green
Row 15: Green Green Green Green Green Red Green
Row 16: Green Green Green Red Red Green Green
Row 17: Green Green Green Red Green Red Green
Row 18: Green Green Red Red Red Red Red
Row 19: Green Green Red Red Red Red Green
Row 20: Green Green Red Green Red Red Red
Row 21: Green Green Red Red Red Red Red
Row 22: Green Green Green Red Red Green Red
Row 23: Green Green Green Red Green Green Red
Row 24: Green Green Green Red Green Green Green
Row 25: Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green
Row 27: Green Green Green Green Green Green Green
Row 28: Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown
Row 2: Brown Brown Orange Brown Brown Orange Orange Orange Orange Brown Brown Brown
Row 3: Brown Brown Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown
Row 4: Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown
Row 5: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 6: Brown Brown Brown Orange Orange Brown Brown Orange Orange Orange Orange Brown
Row 7: Brown Brown Orange Brown Orange Orange Orange Brown Brown Orange Orange Brown
Row 8: Brown Brown Brown Orange Brown Orange Orange Orange Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Orange Brown Orange Orange Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Brown
Row 11: Brown Brown Brown Brown Brown Orange Brown Brown Orange Brown Orange Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Red Red Red Red Red Red Brown
Brown Brown Red Brown Brown Red Red Red Red Brown Brown Brown
Brown Brown Red Red Red Red Brown Red Red Red Red Brown
Brown Red Red Red Red Red Red Red Red Red Brown Brown
Brown Brown Brown Red Red Red Red Red Red Red Red Brown
Brown Brown Brown Red Red Brown Brown Red Red Red Red Brown
Brown Brown Red Brown Red Red Red Brown Brown Red Red Brown
Brown Brown Brown Red Brown Red Red Red Brown Brown Brown Brown
Brown Brown Brown Brown Brown Red Brown Red Red Brown Brown Brown
Brown Brown Brown Brown Brown Red Brown Red Red Red Red Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Red Blue Blue Red
Row 2: Blue Red Blue Orange
Row 3: Red Orange Orange Red
Row 4: Blue Blue Blue Blue
Row 5: Red Blue Blue Blue
Row 6: Blue Red Orange Red
Row 7: Blue Orange Blue Orange
Row 8: Blue Red Red Red
Row 9: Red Blue Blue Blue
Row 10: Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue
Row 12: Red Red Blue Red
Row 13: Orange Blue Orange Blue
Row 14: Orange Blue Blue Blue
Row 15: Red Blue Blue Blue
Row 16: Red Red Blue Blue
Row 17: Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue
Row 19: Blue Red Blue Orange
Row 20: Orange Blue Orange Blue
Row 21: Red Blue Blue Blue
Row 22: Red Blue Blue Blue
Row 23: Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue
Row 25: Blue Red Blue Blue
Output:
Row 1: Purple Purple Purple Purple
Row 2: Purple Red Blue Purple
Row 3: Purple Orange Orange Purple
Row 4: Purple Blue Blue Purple
Row 5: Purple Blue Blue Purple
Row 6: Purple Red Orange Purple
Row 7: Purple Orange Blue Purple
Row 8: Purple Red Red Purple
Row 9: Purple Blue Blue Purple
Row 10: Purple Blue Blue Purple
Row 11: Purple Blue Blue Purple
Row 12: Purple Red Blue Purple
Row 13: Purple Blue Orange Purple
Row 14: Purple Blue Blue Purple
Row 15: Purple Blue Blue Purple
Row 16: Purple Red Blue Purple
Row 17: Purple Blue Blue Purple
Row 18: Purple Blue Blue Purple
Row 19: Purple Red Blue Purple
Row 20: Purple Blue Orange Purple
Row 21: Purple Blue Blue Purple
Row 22: Purple Blue Blue Purple
Row 23: Purple Blue Blue Purple
Row 24: Purple Blue Blue Purple
Row 25: Purple Purple Purple Purple
Example 2
Input:
Row 1: Yellow Yellow Yellow Black Yellow Yellow Green Green Black Yellow Green Black Green Black Black Black Yellow Green Green Green Black Black Yellow Green Green Black Green Black Green
Row 2: Black Yellow Black Yellow Green Green Green Green Yellow Yellow Black Yellow Green Green Yellow Yellow Black Black Black Black Black Yellow Black Yellow Black Black Black Green Green
Row 3: Black Black Green Yellow Green Green Black Yellow Yellow Green Black Black Yellow Black Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Black Black Green Green Black Green
Row 4: Green Green Black Green Yellow Black Yellow Green Black Black Green Green Green Green Black Black Green Green Green Green Black Yellow Black Black Black Yellow Black Yellow Green
Row 5: Yellow Black Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Black Green Black Yellow Yellow Green Yellow Green Black Green Black Black Green
Row 6: Yellow Green Black Black Black Yellow Yellow Green Green Black Green Green Green Green Green Yellow Green Yellow Black Black Black Green Black Yellow Yellow Green Green Green Yellow
Row 7: Black Black Green Green Black Black Green Yellow Green Yellow Yellow Green Black Green Green Green Yellow Yellow Green Green Green Green Green Yellow Black Green Yellow Yellow Green
Row 8: Yellow Green Green Black Black Green Black Green Yellow Black Black Green Yellow Black Green Yellow Yellow Green Green Green Green Green Green Yellow Green Green Green Black Green
Row 9: Green Yellow Green Yellow Green Green Black Black Black Yellow Green Yellow Yellow Green Yellow Black Black Green Black Yellow Black Yellow Green Green Green Black Yellow Green Yellow
Row 10: Green Black Black Black Green Black Green Yellow Black Yellow Yellow Green Black Black Yellow Yellow Black Yellow Green Black Black Green Green Black Green Black Green Green Yellow
Row 11: Yellow Green Green Yellow Green Green Yellow Black Yellow Yellow Black Yellow Black Green Green Green Yellow Black Yellow Yellow Green Black Green Green Black Yellow Green Green Yellow
Row 12: Green Green Yellow Black Black Black Green Yellow Yellow Black Yellow Green Green Green Yellow Black Black Yellow Green Green Black Green Yellow Black Black Black Black Yellow Black
Row 13: Green Green Yellow Green Black Yellow Yellow Yellow Green Yellow Green Yellow Green Yellow Green Green Black Black Black Yellow Black Yellow Black Yellow Green Black Black Yellow Black
Row 14: Yellow Black Green Green Black Green Yellow Yellow Green Yellow Green Black Yellow Black Yellow Black Green Green Black Green Green Green Green Green Black Green Yellow Black Black
Row 15: Yellow Green Black Green Black Green Yellow Yellow Yellow Green Green Yellow Black Green Green Yellow Green Green Black Yellow Green Yellow Green Green Black Yellow Green Yellow Green
Row 16: Yellow Green Green Green Green Black Green Black Black Black Yellow Green Yellow Black Yellow Green Yellow Green Yellow Yellow Yellow Black Black Green Yellow Green Black Yellow Yellow
Row 17: Black Green Yellow Black Green Yellow Black Yellow Yellow Green Yellow Black Yellow Green Green Black Green Black Green Yellow Green Black Green Green Green Black Black Green Black
Row 18: Green Yellow Green Yellow Green Yellow Green Green Black Black Yellow Yellow Black Green Green Yellow Green Yellow Black Black Green Yellow Black Black Green Yellow Yellow Green Yellow
Row 19: Black Black Yellow Yellow Green Green Green Green Green Yellow Black Green Black Green Yellow Yellow Yellow Yellow Black Black Yellow Green Green Yellow Green Green Black Green Yellow
Row 20: Yellow Green Yellow Yellow Green Green Yellow Black Yellow Black Yellow Black Green Green Green Yellow Yellow Yellow Yellow Yellow Black Yellow Green Yellow Green Green Black Green Green
Row 21: Green Black Yellow Yellow Yellow Yellow Yellow Green Black Yellow Black Black Yellow Yellow Green Yellow Black Black Yellow Black Black Black Black Yellow Yellow Yellow Green Yellow Black
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Yellow Black Yellow Green Green Green Green Yellow Yellow Black Yellow Green Green Yellow Yellow Black Black Black Black Black Yellow Black Yellow Black Black Black Green Purple
Row 3: Purple Black Green Yellow Green Green Black Yellow Yellow Green Black Black Yellow Black Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Black Black Green Green Black Purple
Row 4: Purple Green Black Green Yellow Black Yellow Green Black Black Green Green Green Green Black Black Green Green Green Green Black Yellow Black Black Black Yellow Black Yellow Purple
Row 5: Purple Black Yellow Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Black Green Black Yellow Yellow Green Yellow Green Black Green Black Black Purple
Row 6: Purple Green Black Black Black Yellow Yellow Green Green Black Green Green Green Green Green Yellow Green Yellow Black Black Black Green Black Yellow Yellow Green Green Green Purple
Row 7: Purple Black Green Green Black Black Green Yellow Green Yellow Yellow Green Black Green Green Green Yellow Yellow Green Green Green Green Green Yellow Black Green Yellow Yellow Purple
Row 8: Purple Green Green Black Black Green Black Green Yellow Black Black Green Yellow Black Green Yellow Yellow Green Green Green Green Green Green Yellow Green Green Green Black Purple
Row 9: Purple Yellow Green Yellow Green Green Black Black Black Yellow Green Yellow Yellow Green Yellow Black Black Green Black Yellow Black Yellow Green Green Green Black Yellow Green Purple
Row 10: Purple Black Black Black Green Black Green Yellow Black Yellow Yellow Green Black Black Yellow Yellow Black Yellow Green Black Black Green Green Black Green Black Green Green Purple
Row 11: Purple Green Green Yellow Green Green Yellow Black Yellow Yellow Black Yellow Black Green Green Green Yellow Black Yellow Yellow Green Black Green Green Black Yellow Green Green Purple
Row 12: Purple Green Yellow Black Black Black Green Yellow Yellow Black Yellow Green Green Green Yellow Black Black Yellow Green Green Black Green Yellow Black Black Black Black Yellow Purple
Row 13: Purple Green Yellow Green Black Yellow Yellow Yellow Green Yellow Green Yellow Green Yellow Green Green Black Black Black Yellow Black Yellow Black Yellow Green Black Black Yellow Purple
Row 14: Purple Black Green Green Black Green Yellow Yellow Green Yellow Green Black Yellow Black Yellow Black Green Green Black Green Green Green Green Green Black Green Yellow Black Purple
Row 15: Purple Green Black Green Black Green Yellow Yellow Yellow Green Green Yellow Black Green Green Yellow Green Green Black Yellow Green Yellow Green Green Black Yellow Green Yellow Purple
Row 16: Purple Green Green Green Green Black Green Black Black Black Yellow Green Yellow Black Yellow Green Yellow Green Yellow Yellow Yellow Black Black Green Yellow Green Black Yellow Purple
Row 17: Purple Green Yellow Black Green Yellow Black Yellow Yellow Green Yellow Black Yellow Green Green Black Green Black Green Yellow Green Black Green Green Green Black Black Green Purple
Row 18: Purple Yellow Green Yellow Green Yellow Green Green Black Black Yellow Yellow Black Green Green Yellow Green Yellow Black Black Green Yellow Black Black Green Yellow Yellow Green Purple
Row 19: Purple Black Yellow Yellow Green Green Green Green Green Yellow Black Green Black Green Yellow Yellow Yellow Yellow Black Black Yellow Green Green Yellow Green Green Black Green Purple
Row 20: Purple Green Yellow Yellow Green Green Yellow Black Yellow Black Yellow Black Green Green Green Yellow Yellow Yellow Yellow Yellow Black Yellow Green Yellow Green Green Black Green Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Brown Red Brown Black Red Brown Black Black Black Black Red Green Black Brown Green Green Red Gray
Row 2: Black Green Black Black Black Gray Green Gray Gray Green Black Red Black Black Green Gray Black Green
Row 3: Black Black Black Gray Red Black Gray Gray Brown Brown Black Green Red Green Black Brown Red Black
Row 4: Black Gray Gray Black Gray Brown Black Black Black Black Brown Red Brown Red Red Black Red Gray
Row 5: Red Black Red Black Green Black Gray Gray Black Brown Black Red Red Black Green Green Green Black
Row 6: Black Black Black Red Gray Green Green Gray Green Brown Black Black Black Black Brown Black Black Green
Row 7: Red Brown Black Black Red Brown Green Red Red Black Red Brown Green Brown Gray Red Red Black
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Green Black Black Black Gray Green Gray Gray Green Black Red Black Black Green Gray Black Purple
Row 3: Purple Black Black Gray Red Black Gray Gray Brown Brown Black Green Red Green Black Brown Red Purple
Row 4: Purple Gray Gray Black Gray Brown Black Black Black Black Brown Red Brown Red Red Black Red Purple
Row 5: Purple Black Red Black Green Black Gray Gray Black Brown Black Red Red Black Green Green Green Purple
Row 6: Purple Black Black Red Gray Green Green Gray Green Brown Black Black Black Black Brown Black Black Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Blue Green Green Green Blue Green Green Green Green Green Green Green Green Green Green
Row 5: Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Blue Red Green
Row 7: Blue Green Green Green Green Green Gray Green Green Green Green Gray Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Brown Green Green Green Green Green Green Green Yellow Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Blue Green Green
Row 13: Green Green Green Green Green Black Green Green Green Green Green Green Yellow Green Blue
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Black Green Green Green Blue Green Green
Row 16: Green Green Green Green Green Yellow Green Green Green Green Green Gray Green Brown Green
Row 17: Blue Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Yellow Green Green Green Green Green Green Green Green Green Yellow Green Brown Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Green Green Brown Green Green Green Green Green Green Green Green Green Purple
Purple Green Blue Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Blue Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Blue Red Purple
Purple Green Green Green Green Green Gray Green Green Green Green Gray Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Brown Green Green Green Green Green Green Green Yellow Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Blue Green Purple
Purple Green Green Green Green Black Green Green Green Green Green Green Yellow Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Green Green Green Green Black Green Green Green Blue Green Purple
Purple Green Green Green Green Yellow Green Green Green Green Green Gray Green Brown Purple
Purple Brown Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Purple Black Black Purple Black
Row 2: Black Black Black Black Purple Black Black Purple Black
Row 3: Black Black Black Black Purple Black Black Purple Black
Row 4: Black Black Black Black Purple Black Black Purple Black
Row 5: Black Black Black Black Purple Black Black Purple Black
Row 6: Black Black Black Black Purple Black Black Purple Black
Row 7: Black Black Black Black Purple Black Black Purple Black
Row 8: Black Black Black Black Purple Black Black Purple Black
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Black Black Black Black Purple Black Black Purple Black
Row 11: Black Black Black Black Purple Black Black Purple Black
Row 12: Black Black Black Black Purple Black Black Purple Black
Row 13: Black Black Black Black Purple Black Black Purple Black
Row 14: Black Black Black Black Purple Black Black Purple Black
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Black Black Black Black Purple Black Black Purple Black
Row 17: Black Black Black Black Purple Black Black Purple Black
Row 18: Black Black Black Black Purple Black Black Purple Black
Row 19: Black Black Black Black Purple Black Black Purple Black
Row 20: Black Black Black Black Purple Black Black Purple Black
Row 21: Black Black Black Black Purple Black Black Purple Black
Row 22: Black Black Black Black Purple Black Black Purple Black
Row 23: Black Black Black Black Purple Black Black Purple Black
Row 24: Black Black Black Black Purple Black Black Purple Black
Row 25: Black Black Black Black Purple Black Black Purple Black
Row 26: Black Black Black Black Purple Black Black Purple Black
Row 27: Black Black Black Black Purple Black Black Purple Black
Row 28: Black Black Black Black Purple Black Black Purple Black
Row 29: Black Black Black Black Purple Black Black Purple Black
Row 30: Black Black Black Black Purple Black Black Purple Black
Output:
Row 1: Black Black Black Black Purple Red Red Purple Black
Row 2: Black Black Black Black Purple Red Red Purple Black
Row 3: Black Black Black Black Purple Red Red Purple Black
Row 4: Black Black Black Black Purple Red Red Purple Black
Row 5: Black Black Black Black Purple Red Red Purple Black
Row 6: Black Black Black Black Purple Red Red Purple Black
Row 7: Black Black Black Black Purple Red Red Purple Black
Row 8: Black Black Black Black Purple Red Red Purple Black
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Yellow Yellow Yellow Yellow Purple Pink Pink Purple Green
Row 11: Yellow Yellow Yellow Yellow Purple Pink Pink Purple Green
Row 12: Yellow Yellow Yellow Yellow Purple Pink Pink Purple Green
Row 13: Yellow Yellow Yellow Yellow Purple Pink Pink Purple Green
Row 14: Yellow Yellow Yellow Yellow Purple Pink Pink Purple Green
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Black Black Black Black Purple Blue Blue Purple Black
Row 17: Black Black Black Black Purple Blue Blue Purple Black
Row 18: Black Black Black Black Purple Blue Blue Purple Black
Row 19: Black Black Black Black Purple Blue Blue Purple Black
Row 20: Black Black Black Black Purple Blue Blue Purple Black
Row 21: Black Black Black Black Purple Blue Blue Purple Black
Row 22: Black Black Black Black Purple Blue Blue Purple Black
Row 23: Black Black Black Black Purple Blue Blue Purple Black
Row 24: Black Black Black Black Purple Blue Blue Purple Black
Row 25: Black Black Black Black Purple Blue Blue Purple Black
Row 26: Black Black Black Black Purple Blue Blue Purple Black
Row 27: Black Black Black Black Purple Blue Blue Purple Black
Row 28: Black Black Black Black Purple Blue Blue Purple Black
Row 29: Black Black Black Black Purple Blue Blue Purple Black
Row 30: Black Black Black Black Purple Blue Blue Purple Black
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Brown Red Red Red Red Red Red Red Red Red Brown Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Brown Red Red Red Red Red Red Red Red Red Brown Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Brown Red Red Red Red Red Red Red Red Red Brown Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Brown Red Red Red Red Red Red Red Red Red Brown Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Brown Red Red Red Red Red Red Red Red Red Brown Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Brown Red Red Red Red Red Red Red Red Red Brown Purple
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Green
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Green
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Green
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Green
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Green
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Purple Purple Purple Purple Purple Purple Purple Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Purple
Example 3
Input:
Row 1: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 2: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 3: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 4: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 5: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 6: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 7: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 8: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 9: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 10: Black Black Black Black Black Black Black Black Black Black
Row 11: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 12: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 13: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 14: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 15: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 16: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 17: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 18: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 19: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 20: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 21: Black Black Black Black Black Black Black Black Black Black
Row 22: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 23: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Row 24: Gray Black Gray Gray Gray Gray Black Gray Gray Gray
Output:
Row 1: Gray Black Red Red Red Red Black Gray Gray Gray
Row 2: Gray Black Red Red Red Red Black Gray Gray Gray
Row 3: Gray Black Red Red Red Red Black Gray Gray Gray
Row 4: Gray Black Red Red Red Red Black Gray Gray Gray
Row 5: Gray Black Red Red Red Red Black Gray Gray Gray
Row 6: Gray Black Red Red Red Red Black Gray Gray Gray
Row 7: Gray Black Red Red Red Red Black Gray Gray Gray
Row 8: Gray Black Red Red Red Red Black Gray Gray Gray
Row 9: Gray Black Red Red Red Red Black Gray Gray Gray
Row 10: Black Black Black Black Black Black Black Black Black Black
Row 11: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 12: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 13: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 14: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 15: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 16: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 17: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 18: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 19: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 20: Yellow Black Pink Pink Pink Pink Black Green Green Green
Row 21: Black Black Black Black Black Black Black Black Black Black
Row 22: Gray Black Blue Blue Blue Blue Black Gray Gray Gray
Row 23: Gray Black Blue Blue Blue Blue Black Gray Gray Gray
Row 24: Gray Black Blue Blue Blue Blue Black Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Purple Purple Purple
Purple Purple Purple Purple Purple Purple Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Purple Purple Purple
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Green Green Green
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Purple Purple Purple Purple Purple Purple Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Purple Purple Purple
Purple Purple Purple Purple Purple Purple Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Red
Row 2: Brown Brown Brown Brown Brown Brown Red
Row 3: Brown Brown Brown Brown Brown Brown Red
Row 4: Brown Brown Blue Blue Brown Brown Red
Row 5: Brown Brown Blue Blue Brown Brown Red
Row 6: Brown Brown Blue Blue Brown Brown Red
Row 7: Brown Brown Blue Blue Brown Brown Red
Row 8: Brown Brown Blue Blue Brown Brown Red
Row 9: Brown Brown Blue Blue Brown Brown Red
Output:
Row 1: Brown Brown Brown Purple Brown Brown Red
Row 2: Brown Brown Brown Purple Brown Brown Red
Row 3: Brown Brown Brown Purple Brown Brown Red
Row 4: Brown Brown Brown Purple Blue Blue Red
Row 5: Brown Brown Brown Purple Blue Blue Red
Row 6: Brown Brown Brown Purple Blue Blue Red
Row 7: Brown Brown Brown Purple Blue Blue Red
Row 8: Brown Brown Brown Purple Blue Blue Red
Row 9: Brown Brown Brown Purple Blue Blue Red
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Gray Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Gray Green Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Gray Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Gray Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Gray Green Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Gray Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Brown Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Brown Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Brown Brown Brown Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Brown Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Purple Black Brown Brown Brown Red Black Black Black Black Black Black Black Black Black Black Black Black Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Orange Black Orange Black Black Green Green Black Green Green Green
Row 2: Orange Orange Orange Orange Black Orange Black Orange Green Black Black Green Black Black Green Black
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Green Black Black
Row 4: Black Yellow Yellow Black Black Black Yellow Black Black Gray Black Black Black Gray Black Black
Row 5: Yellow Black Yellow Yellow Black Yellow Yellow Black Black Black Black Black Black Black Black Gray
Row 6: Yellow Yellow Black Black Yellow Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Orange Yellow Green Green Orange Green Green Green
Row 2: Green Orange Yellow Green Black Yellow Green Gray
Row 3: Yellow Yellow Orange Orange Yellow Green Orange Orange
Example 2
Input:
Row 1: Black Black Orange Orange Purple Black Black Black
Row 2: Black Black Black Black Black Black Purple Purple
Row 3: Black Black Black Orange Purple Black Black Purple
Row 4: Black Orange Orange Orange Black Purple Black Black
Row 5: Black Orange Orange Black Black Purple Black Purple
Row 6: Black Orange Black Black Purple Black Purple Purple
Row 7: Black Orange Orange Black Black Purple Black Black
Row 8: Black Black Orange Black Purple Black Purple Purple
Row 9: Orange Black Orange Orange Purple Purple Purple Purple
Row 10: Black Black Orange Orange Purple Purple Purple Purple
Row 11: Black Red Black Red Blue Blue Blue Blue
Row 12: Red Red Black Black Blue Blue Blue Black
Row 13: Red Black Red Black Blue Blue Blue Blue
Row 14: Black Black Red Black Black Blue Blue Blue
Row 15: Black Black Red Black Blue Blue Blue Blue
Row 16: Red Black Red Black Blue Black Blue Black
Row 17: Red Red Black Black Blue Blue Blue Blue
Row 18: Red Black Black Black Blue Blue Blue Blue
Row 19: Red Red Red Black Blue Blue Blue Blue
Row 20: Red Black Red Red Black Blue Blue Blue
Output:
Row 1: Purple Red Blue Red
Row 2: Red Red Purple Purple
Row 3: Purple Blue Red Purple
Row 4: Black Purple Red Blue
Row 5: Blue Purple Red Purple
Row 6: Purple Orange Purple Purple
Row 7: Red Purple Blue Blue
Row 8: Purple Blue Purple Purple
Row 9: Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple
Example 3
Input:
Row 1: Gray Gray Gray Red Gray Red Red Red Brown Red
Row 2: Gray Gray Red Gray Gray Brown Red Red Red Brown
Row 3: Gray Red Red Gray Red Red Red Red Red Red
Row 4: Gray Gray Red Gray Gray Brown Brown Brown Brown Brown
Row 5: Gray Red Gray Gray Gray Brown Red Red Red Red
Row 6: Gray Gray Red Gray Gray Red Red Red Brown Red
Row 7: Gray Gray Red Gray Gray Brown Red Brown Brown Red
Row 8: Gray Gray Gray Gray Gray Red Brown Brown Red Red
Row 9: Gray Gray Red Red Gray Brown Red Brown Red Red
Row 10: Gray Gray Red Gray Gray Brown Brown Red Red Brown
Row 11: Gray Red Gray Gray Gray Brown Red Brown Brown Brown
Row 12: Red Gray Gray Gray Gray Brown Red Brown Red Brown
Row 13: Green Red Green Green Red Red Red Orange Orange Red
Row 14: Green Green Green Green Green Orange Orange Orange Orange Red
Row 15: Green Green Green Green Green Orange Orange Orange Orange Red
Row 16: Green Green Green Red Green Orange Orange Orange Orange Red
Row 17: Green Green Green Green Green Orange Orange Red Orange Red
Row 18: Red Green Green Red Green Orange Orange Orange Orange Red
Row 19: Green Green Green Green Green Orange Orange Orange Red Orange
Row 20: Green Red Red Red Green Orange Orange Orange Orange Orange
Row 21: Green Red Green Green Green Orange Orange Orange Red Orange
Row 22: Red Green Red Red Red Orange Orange Orange Orange Red
Row 23: Red Green Green Red Green Orange Orange Red Orange Orange
Row 24: Green Green Red Green Red Red Red Orange Red Orange
Output:
Row 1: Green Gray Green Brown Gray
Row 2: Brown Green Green Green Brown
Row 3: Green Green Green Green Green
Row 4: Brown Brown Brown Brown Brown
Row 5: Brown Green Green Green Green
Row 6: Orange Green Green Brown Green
Row 7: Brown Green Brown Brown Green
Row 8: Green Brown Brown Orange Green
Row 9: Brown Orange Brown Green Green
Row 10: Brown Brown Orange Orange Brown
Row 11: Brown Green Brown Brown Brown
Row 12: Brown Green Brown Green Brown
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Orange Yellow Orange Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow
Row 10: Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 11: Yellow Yellow Yellow Orange Yellow Orange Yellow Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 12: Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Yellow Orange Yellow Orange Yellow Yellow Yellow Black Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Orange Yellow Black Yellow Yellow Orange Orange Yellow Gray Yellow
Yellow Orange Yellow Gray Yellow Yellow Yellow Black Yellow Yellow Yellow Gray
Yellow Yellow Yellow Orange Yellow Orange Yellow Orange Orange Orange Yellow Yellow
Orange Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Gray Red Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Purple Gray Orange Red Purple
Row 2: Gray Gray Black Gray Black Gray Gray Red Gray Red Gray Gray Gray Gray Gray Gray Orange Gray Black Orange Gray Gray Black
Row 3: Gray Red Gray Black Gray Black Gray Gray Gray Black Gray Gray Gray Red Purple Black Gray Red Gray Gray Gray Purple Gray
Row 4: Gray Purple Orange Gray Gray Red Orange Gray Gray Gray Black Purple Gray Gray Black Gray Gray Gray Gray Red Purple Black Red
Row 5: Purple Gray Gray Gray Red Gray Gray Black Gray Orange Black Red Gray Gray Gray Black Gray Red Red Black Gray Gray Purple
Row 6: Black Purple Gray Red Gray Gray Gray Red Gray Gray Black Purple Gray Gray Gray Black Gray Gray Gray Gray Orange Gray Red
Row 7: Red Gray Red Gray Red Black Gray Black Red Gray Gray Red Orange Gray Gray Gray Gray Purple Gray Gray Gray Gray Black
Row 8: Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Red Gray Red Orange Orange Gray Gray Orange Gray
Row 9: Gray Gray Orange Yellow Orange Black Gray Purple Gray Gray Gray Gray Gray Red Black Gray Red Black Gray Orange Black Gray Gray
Row 10: Gray Gray Orange Black Gray Gray Gray Red Gray Gray Yellow Black Gray Red Gray Purple Gray Gray Gray Red Purple Orange Gray
Row 11: Gray Gray Orange Black Gray Gray Gray Gray Gray Gray Purple Red Black Gray Gray Red Gray Gray Gray Gray Red Gray Black
Row 12: Gray Purple Orange Gray Gray Gray Gray Orange Gray Orange Gray Gray Gray Black Gray Orange Black Red Gray Orange Gray Gray Black
Row 13: Orange Red Orange Gray Gray Orange Gray Gray Black Purple Purple Gray Black Gray Gray Gray Orange Black Gray Red Purple Gray Red
Row 14: Red Black Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Red Red Red Purple Black Red Gray Purple Gray
Row 15: Gray Red Gray Red Black Orange Red Gray Red Gray Red Gray Gray Black Red Black Gray Black Black Red Orange Red Gray
Row 16: Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Purple Gray Gray Gray Gray Red Gray Gray Orange Black Orange Gray Gray
Row 17: Red Red Red Black Gray Red Gray Purple Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Black Gray Black
Row 18: Black Red Gray Gray Gray Purple Gray Gray Gray Gray Black Black Gray Black Gray Gray Purple Gray Gray Gray Black Gray Gray
Row 19: Gray Black Gray Black Gray Black Gray Gray Black Purple Red Gray Black Red Gray Gray Gray Gray Red Gray Red Gray Gray
Output:
Row 1: Purple Red Orange Gray Purple Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Gray Red Gray Black
Row 2: Black Gray Gray Orange Black Gray Orange Gray Gray Gray Gray Gray Gray Red Gray Red Gray Gray Black Gray Black Gray Gray
Row 3: Gray Purple Gray Gray Gray Red Gray Black Purple Red Gray Gray Gray Black Gray Gray Gray Black Gray Black Gray Red Gray
Row 4: Red Black Purple Red Gray Gray Gray Gray Black Gray Gray Purple Black Gray Gray Gray Orange Red Gray Gray Orange Purple Gray
Row 5: Purple Gray Gray Black Red Red Gray Black Gray Gray Gray Red Black Orange Gray Black Gray Gray Red Gray Gray Gray Purple
Row 6: Red Gray Orange Gray Gray Gray Gray Black Gray Gray Gray Purple Black Gray Gray Red Gray Gray Gray Red Gray Purple Black
Row 7: Black Gray Gray Gray Gray Purple Gray Gray Gray Gray Orange Red Gray Gray Red Black Gray Black Red Gray Red Gray Red
Row 8: Gray Orange Gray Gray Orange Orange Red Gray Red Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black
Row 9: Gray Gray Black Orange Gray Black Red Gray Black Red Gray Gray Gray Gray Gray Purple Gray Black Orange Yellow Orange Gray Gray
Row 10: Gray Orange Purple Red Gray Gray Gray Purple Gray Red Gray Black Yellow Gray Gray Red Gray Gray Gray Black Orange Gray Gray
Row 11: Black Gray Red Gray Gray Gray Gray Red Gray Gray Black Red Purple Gray Gray Gray Gray Gray Gray Black Orange Gray Gray
Row 12: Black Gray Gray Orange Gray Red Black Orange Gray Black Gray Gray Gray Orange Gray Orange Gray Gray Gray Gray Orange Purple Gray
Row 13: Red Gray Purple Red Gray Black Orange Gray Gray Gray Black Gray Purple Purple Black Gray Gray Orange Gray Gray Orange Red Orange
Row 14: Gray Purple Gray Red Black Purple Red Red Red Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Black Red
Row 15: Gray Red Orange Red Black Black Gray Black Red Black Gray Gray Red Gray Red Gray Red Orange Black Red Gray Red Gray
Row 16: Gray Gray Orange Black Orange Gray Gray Red Gray Gray Gray Gray Purple Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray
Row 17: Black Gray Black Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Purple Gray Red Gray Black Red Red Red
Row 18: Gray Gray Black Gray Gray Gray Purple Gray Gray Black Gray Black Black Gray Gray Gray Gray Purple Gray Gray Gray Red Black
Row 19: Gray Gray Red Gray Red Gray Gray Gray Gray Red Black Gray Red Purple Black Gray Gray Black Gray Black Gray Black Gray
Example 2
Input:
Row 1: Orange Gray Gray Gray Gray
Row 2: Gray Gray Orange Orange Brown
Row 3: Gray Brown Gray Brown Gray
Row 4: Gray Orange Brown Gray Orange
Row 5: Brown Brown Gray Gray Gray
Row 6: Brown Brown Pink Gray Brown
Row 7: Gray Gray Pink Pink Brown
Row 8: Gray Gray Gray Pink Gray
Row 9: Orange Gray Orange Orange Pink
Row 10: Orange Pink Gray Orange Brown
Row 11: Gray Brown Gray Gray Gray
Row 12: Gray Brown Gray Gray Gray
Row 13: Gray Brown Gray Brown Brown
Row 14: Gray Gray Brown Brown Gray
Row 15: Brown Brown Brown Brown Gray
Row 16: Orange Brown Brown Gray Gray
Row 17: Brown Brown Orange Gray Gray
Row 18: Pink Gray Brown Pink Gray
Row 19: Brown Orange Orange Brown Gray
Output:
Row 1: Gray Gray Gray Gray Orange
Row 2: Brown Orange Orange Gray Gray
Row 3: Gray Brown Gray Brown Gray
Row 4: Orange Gray Brown Orange Gray
Row 5: Gray Gray Gray Brown Brown
Row 6: Brown Gray Pink Brown Brown
Row 7: Brown Pink Pink Gray Gray
Row 8: Gray Pink Gray Gray Gray
Row 9: Pink Orange Orange Gray Orange
Row 10: Brown Orange Gray Pink Orange
Row 11: Gray Gray Gray Brown Gray
Row 12: Gray Gray Gray Brown Gray
Row 13: Brown Brown Gray Brown Gray
Row 14: Gray Brown Brown Gray Gray
Row 15: Gray Brown Brown Brown Brown
Row 16: Gray Gray Brown Brown Orange
Row 17: Gray Gray Orange Brown Brown
Row 18: Gray Pink Brown Gray Pink
Row 19: Gray Brown Orange Orange Brown
Example 3
Input:
Row 1: Purple Brown Brown Blue Brown Red Red Brown Purple Brown Purple Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Blue Brown
Row 2: Brown Blue Purple Brown Blue Red Yellow Brown Brown Brown Purple Brown Brown Red Brown Brown Yellow Red Brown Purple Red Red Purple Red Brown
Row 3: Purple Brown Brown Brown Brown Brown Yellow Yellow Brown Blue Purple Purple Black Brown Brown Yellow Brown Green Brown Brown Yellow Purple Brown Red Brown
Row 4: Brown Brown Yellow Brown Brown Purple Yellow Red Brown Brown Brown Blue Brown Brown Purple Brown Purple Brown Purple Brown Brown Brown Red Brown Purple
Row 5: Purple Yellow Brown Brown Brown Brown Blue Brown Green Brown Brown Brown Brown Brown Brown Brown Red Brown Red Brown Purple Brown Brown Brown Yellow
Row 6: Brown Purple Brown Brown Purple Blue Brown Brown Yellow Brown Brown Brown Brown Brown Yellow Brown Brown Red Brown Purple Brown Brown Brown Brown Yellow
Row 7: Brown Purple Brown Red Yellow Brown Brown Brown Brown Brown Green Red Brown Brown Purple Brown Red Brown Blue Brown Brown Brown Brown Brown Brown
Row 8: Brown Yellow Brown Brown Brown Brown Red Brown Purple Brown Brown Brown Brown Brown Brown Blue Purple Brown Brown Purple Yellow Blue Purple Yellow Brown
Row 9: Brown Brown Purple Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Purple Red Red Brown Brown Brown Blue Yellow Yellow
Row 10: Yellow Brown Black Yellow Brown Brown Yellow Purple Brown Brown Brown Brown Yellow Brown Brown Yellow Blue Brown Brown Green Red Red Brown Gray Yellow
Row 11: Brown Brown Brown Brown Blue Yellow Black Brown Purple Brown Green Brown Brown Yellow Red Red Red Brown Purple Purple Blue Brown Purple Yellow Brown
Row 12: Brown Red Brown Blue Brown Yellow Brown Blue Brown Brown Brown Brown Brown Yellow Red Brown Red Green Purple Brown Brown Green Brown Brown Brown
Row 13: Brown Brown Red Brown Brown Yellow Brown Brown Blue Brown Purple Brown Brown Brown Brown Yellow Brown Brown Brown Blue Brown Purple Black Brown Brown
Row 14: Brown Brown Purple Red Purple Brown Brown Brown Brown Brown Brown Green Brown Black Blue Brown Brown Brown Brown Red Yellow Brown Brown Purple Brown
Row 15: Blue Brown Yellow Brown Brown Brown Yellow Purple Brown Brown Brown Brown Yellow Brown Brown Brown Purple Brown Yellow Brown Purple Brown Brown Brown Purple
Row 16: Brown Brown Green Brown Brown Purple Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Red Brown Green Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Red Brown Brown Brown Purple Red Brown Brown Brown Brown Yellow Brown Brown Brown Red Red Brown Brown Brown Brown Brown
Row 18: Brown Red Brown Purple Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Red Brown Blue Brown Gray Red Brown Brown Purple Brown
Row 19: Brown Blue Brown Brown Brown Purple Brown Brown Purple Red Blue Purple Gray Yellow Yellow Brown Yellow Green Brown Brown Brown Purple Brown Brown Brown
Output:
Row 1: Brown Blue Brown Brown Brown Brown Brown Brown Brown Red Red Brown Brown Brown Purple Brown Purple Brown Red Red Brown Blue Brown Brown Purple
Row 2: Brown Red Purple Red Red Purple Brown Red Yellow Brown Brown Red Brown Brown Purple Brown Brown Brown Yellow Red Blue Brown Purple Blue Brown
Row 3: Brown Red Brown Purple Yellow Brown Brown Green Brown Yellow Brown Brown Black Purple Purple Blue Brown Yellow Yellow Brown Brown Brown Brown Brown Purple
Row 4: Purple Brown Red Brown Brown Brown Purple Brown Purple Brown Purple Brown Brown Blue Brown Brown Brown Red Yellow Purple Brown Brown Yellow Brown Brown
Row 5: Yellow Brown Brown Brown Purple Brown Red Brown Red Brown Brown Brown Brown Brown Brown Brown Green Brown Blue Brown Brown Brown Brown Yellow Purple
Row 6: Yellow Brown Brown Brown Brown Purple Brown Red Brown Brown Yellow Brown Brown Brown Brown Brown Yellow Brown Brown Blue Purple Brown Brown Purple Brown
Row 7: Brown Brown Brown Brown Brown Brown Blue Brown Red Brown Purple Brown Brown Red Green Brown Brown Brown Brown Brown Yellow Red Brown Purple Brown
Row 8: Brown Yellow Purple Blue Yellow Purple Brown Brown Purple Blue Brown Brown Brown Brown Brown Brown Purple Brown Red Brown Brown Brown Brown Yellow Brown
Row 9: Yellow Yellow Blue Brown Brown Brown Red Red Purple Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Purple Brown Brown
Row 10: Yellow Gray Brown Red Red Green Brown Brown Blue Yellow Brown Brown Yellow Brown Brown Brown Brown Purple Yellow Brown Brown Yellow Black Brown Yellow
Row 11: Brown Yellow Purple Brown Blue Purple Purple Brown Red Red Red Yellow Brown Brown Green Brown Purple Brown Black Yellow Blue Brown Brown Brown Brown
Row 12: Brown Brown Brown Green Brown Brown Purple Green Red Brown Red Yellow Brown Brown Brown Brown Brown Blue Brown Yellow Brown Blue Brown Red Brown
Row 13: Brown Brown Black Purple Brown Blue Brown Brown Brown Yellow Brown Brown Brown Brown Purple Brown Blue Brown Brown Yellow Brown Brown Red Brown Brown
Row 14: Brown Purple Brown Brown Yellow Red Brown Brown Brown Brown Blue Black Brown Green Brown Brown Brown Brown Brown Brown Purple Red Purple Brown Brown
Row 15: Purple Brown Brown Brown Purple Brown Yellow Brown Purple Brown Brown Brown Yellow Brown Brown Brown Brown Purple Yellow Brown Brown Brown Yellow Brown Blue
Row 16: Brown Brown Brown Brown Green Brown Red Brown Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Purple Brown Brown Green Brown Brown
Row 17: Brown Brown Brown Brown Brown Red Red Brown Brown Brown Yellow Brown Brown Brown Brown Red Purple Brown Brown Brown Red Brown Brown Brown Brown
Row 18: Brown Purple Brown Brown Red Gray Brown Blue Brown Red Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Purple Brown Red Brown
Row 19: Brown Brown Brown Purple Brown Brown Brown Green Yellow Brown Yellow Yellow Gray Purple Blue Red Purple Brown Brown Purple Brown Brown Brown Blue Brown
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Yellow Yellow Orange Purple Gray Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Gray Purple Orange Yellow Yellow Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Gray Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Gray Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Red Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Black Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Red Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Black Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Black Purple Purple Purple Purple Purple
Row 4: Purple Purple Black Green Purple Purple Purple
Row 5: Purple Purple Red Black Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Black Purple Purple Purple Purple Purple Purple
Row 3: Purple Black Purple Purple Purple Purple Purple
Row 4: Purple Purple Black Green Purple Purple Purple
Row 5: Purple Purple Red Black Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Yellow Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Yellow Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Black Black Black Red Red Red Red Red Red Red Red
Row 2: Brown Brown Orange Brown Brown Black Orange Black Red Red Red Red Red Red Red Red
Row 3: Brown Brown Brown Brown Brown Black Black Black Red Red Red Red Red Orange Red Red
Row 4: Brown Orange Brown Brown Brown Black Black Black Red Red Red Red Red Red Red Red
Row 5: Brown Brown Brown Brown Brown Black Black Black Red Red Red Red Red Red Red Red
Row 6: Brown Brown Brown Brown Brown Black Black Black Red Red Red Red Red Red Red Red
Row 7: Gray Gray Gray Gray Gray Black Black Black Red Red Red Red Red Red Red Red
Row 8: Gray Gray Gray Gray Gray Black Orange Black Red Red Red Red Red Red Orange Red
Row 9: Gray Gray Orange Gray Gray Black Black Black Red Red Red Red Red Red Red Red
Row 10: Gray Gray Orange Orange Gray Black Orange Black Red Red Red Red Red Orange Red Red
Row 11: Gray Gray Gray Orange Gray Black Black Black Red Red Red Red Red Red Red Red
Row 12: Gray Gray Gray Gray Gray Black Black Black Red Red Red Red Red Red Red Red
Row 13: Gray Gray Gray Gray Gray Black Black Black Red Red Red Red Red Red Red Red
Row 14: Gray Gray Gray Orange Gray Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Gray Gray Gray Gray Gray Black Orange Black Purple Orange Purple Purple Purple Orange Purple Purple
Row 16: Gray Gray Gray Gray Gray Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Gray
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Red Red Red Gray Gray Gray Gray Blue Gray Blue Gray Gray
Row 20: Red Blue Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Purple Purple Purple Purple Orange Orange Orange Orange Pink Pink Pink Pink
Row 23: Purple Purple Blue Purple Orange Orange Orange Orange Pink Blue Pink Pink
Row 24: Purple Purple Purple Purple Orange Orange Orange Orange Pink Pink Pink Pink
Output:
Row 1: Brown
Example 3
Input:
Row 1: Red Red Red Red Red Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 2: Red Red Red Red Red Green Gray Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 3: Red Red Red Red Red Green Green Green Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Gray Orange Orange Orange
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Orange Gray Orange Orange Orange Gray Orange
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Orange Gray Orange Orange Orange Orange Orange
Row 7: Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray Blue Blue Blue Blue Orange Orange Orange Orange Orange Gray Orange
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Gray Gray Orange Orange Orange Orange
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Gray Orange Orange
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Gray Brown Brown Gray Brown Gray Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Blue
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Brown Pink Brown Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red
Row 4: Brown Brown Pink Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Black Black Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Black Black Pink Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Black Black Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange
Row 14: Green Pink Green Green Green Green Green Green Green Green Pink Green Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Green Pink Pink Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Green Pink Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Pink Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Green Green Gray Gray
Row 3: Green Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Red Gray Gray Gray Gray Gray Gray Gray Black
Row 5: Gray Gray Green Gray Red Gray Gray Gray Gray
Row 6: Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Green Gray Gray Gray
Row 8: Gray Red Gray Gray Gray Gray Gray Gray Gray
Row 9: Green Gray Gray Gray Gray Green Gray Gray Gray
Row 10: Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Red Gray Gray Gray Gray Gray
Row 14: Gray Gray Red Gray Gray Gray Gray Gray Gray
Row 15: Red Gray Red Red Gray Gray Green Gray Gray
Row 16: Gray Gray Gray Green Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Black Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Red Gray Gray Gray Gray Gray Red
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Black Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Black Gray Gray Gray Red Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Green Green Gray Gray
Row 3: Purple Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Black
Row 5: Gray Gray Green Gray Red Gray Gray Gray Gray
Row 6: Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Green Gray Gray Gray
Row 8: Gray Red Gray Gray Gray Gray Gray Gray Gray
Row 9: Green Gray Gray Gray Gray Green Gray Gray Gray
Row 10: Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Red Gray Gray Gray Gray Gray
Row 14: Gray Gray Red Gray Gray Gray Gray Gray Gray
Row 15: Red Gray Red Gray Gray Gray Green Gray Gray
Row 16: Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Black Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Red Gray Gray Gray Gray Gray Red
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Black Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 26: Gray Black Gray Gray Gray Red Gray Gray Gray
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Blue Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 13: Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 18: Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Green Orange Orange Orange Orange Red Blue
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Blue Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 13: Purple Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 18: Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Green Orange Orange Orange Orange Red Blue
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Brown Red Orange Orange Green Orange Orange Orange Orange Brown Brown Orange Orange Red Orange Red
Row 3: Orange Orange Orange Orange Orange Brown Orange Orange Brown Red Red Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Brown Orange Orange
Row 4: Orange Orange Brown Orange Brown Green Orange Orange Orange Orange Red Green Orange Brown Red Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Row 5: Orange Orange Orange Orange Green Orange Orange Red Orange Orange Orange Red Orange Orange Orange Brown Red Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Green Orange Brown Orange Red Orange Orange Orange Brown Green Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Brown Red Orange Orange Green Orange Orange Brown Orange Orange Orange Orange Orange Orange Green Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Brown Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Green Red Orange Red Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Brown Orange Green Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown Orange Orange Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 10: Green Red Orange Red Orange Red Brown Orange Green Orange Brown Orange Brown Orange Orange Orange Orange Orange Brown Orange Orange Red Brown Red Brown Orange Green
Row 11: Orange Orange Orange Green Orange Orange Brown Orange Orange Orange Red Orange Orange Red Orange Orange Green Orange Orange Orange Brown Orange Brown Orange Orange Green Orange
Row 12: Orange Brown Orange Orange Orange Green Orange Orange Orange Orange Green Orange Orange Brown Orange Red Green Orange Orange Brown Orange Orange Orange Orange Orange Green Orange
Row 13: Orange Orange Orange Green Green Orange Orange Red Brown Orange Red Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Green Red Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Red Brown Orange Orange Orange Orange Orange Red Brown Orange Brown Orange Orange Green Brown Orange Orange Orange Orange Orange Orange
Row 15: Brown Orange Orange Red Brown Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Brown Orange Orange Red Brown Orange Orange Orange Brown Orange Orange Orange
Row 16: Red Orange Orange Orange Orange Green Orange Orange Red Green Orange Orange Orange Orange Orange Orange Orange Orange Green Red Orange Orange Green Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Red Red Orange Green Orange Orange Orange Orange Red Green Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Brown Red Orange Orange Green Orange Orange Orange Orange Brown Brown Orange Orange Red Orange Red
Row 3: Orange Orange Orange Orange Orange Brown Orange Orange Brown Red Red Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Brown Orange Orange
Row 4: Orange Orange Brown Orange Brown Green Orange Orange Orange Orange Orange Purple Orange Brown Red Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Row 5: Orange Orange Orange Orange Green Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Brown Red Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Green Orange Brown Orange Red Orange Orange Orange Brown Green Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Brown Red Orange Orange Green Orange Orange Brown Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Brown Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Red Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Brown Orange Purple Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown Orange Orange Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 10: Purple Orange Orange Orange Orange Red Brown Orange Green Orange Brown Orange Brown Orange Orange Orange Orange Orange Brown Orange Orange Red Brown Red Brown Orange Green
Row 11: Orange Orange Orange Purple Orange Orange Brown Orange Orange Orange Orange Orange Orange Red Orange Orange Green Orange Orange Orange Brown Orange Brown Orange Orange Green Orange
Row 12: Orange Brown Orange Orange Orange Green Orange Orange Orange Orange Purple Orange Orange Brown Orange Orange Purple Orange Orange Brown Orange Orange Orange Orange Orange Green Orange
Row 13: Orange Orange Orange Green Green Orange Orange Red Brown Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Red Brown Orange Orange Orange Orange Orange Red Brown Orange Brown Orange Orange Green Brown Orange Orange Orange Orange Orange Orange
Row 15: Brown Orange Orange Red Brown Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Orange
Row 16: Red Orange Orange Orange Orange Purple Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Green Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Red Orange Orange Green Orange Orange Orange Orange Orange Purple Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Red Brown Brown
Row 3: Green Brown Brown Red Brown Green Orange Brown Green Orange Brown Brown Brown Brown Brown Brown Orange Brown Orange Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown
Row 4: Brown Brown Green Red Red Brown Brown Red Brown Brown Brown Brown Brown Red Green Orange Green Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown Red Brown Brown
Row 5: Red Orange Red Brown Brown Orange Brown Orange Brown Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Orange Green Brown Brown Brown Brown
Row 6: Brown Green Brown Brown Brown Brown Green Brown Green Brown Brown Brown Brown Brown Green Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 7: Red Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Green Green Orange Brown Red Brown Brown Green Brown Red
Row 9: Brown Brown Brown Green Red Orange Green Green Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Green Brown Brown
Row 10: Brown Brown Brown Brown Brown Red Brown Orange Brown Brown Green Red Green Brown Brown Brown Brown Green Brown Brown Brown Green Brown Brown Brown Orange Brown Brown Brown Brown
Row 11: Red Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Red Brown Red Brown Brown Brown Red Green Red Brown
Row 12: Green Brown Brown Red Red Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Red
Row 13: Green Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Red Brown Green Green Brown Brown Brown Brown Green Brown Brown Red Brown Brown Green Brown Brown Red Brown
Row 14: Brown Brown Orange Brown Brown Red Red Red Brown Green Brown Green Brown Brown Brown Brown Brown Brown Brown Green Brown Green Red Brown Orange Brown Brown Brown Brown Green
Row 15: Brown Brown Red Brown Brown Red Orange Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown
Row 16: Orange Brown Brown Green Green Brown Brown Orange Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Green Brown Brown Brown Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Purple Brown Brown
Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Green Brown Brown Red Brown Green Orange Brown Green Orange Brown Brown Brown Brown Brown Brown Orange Brown Orange Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown
Brown Brown Purple Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Purple Orange Green Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown Red Brown Brown
Red Orange Brown Brown Brown Orange Brown Orange Brown Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Orange Green Brown Brown Brown Brown
Brown Green Brown Brown Brown Brown Green Brown Green Brown Brown Brown Brown Brown Green Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Red Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Green Green Orange Brown Red Brown Brown Green Brown Red
Brown Brown Brown Purple Brown Orange Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Green Brown Brown
Brown Brown Brown Brown Brown Red Brown Orange Brown Brown Purple Brown Purple Brown Brown Brown Brown Green Brown Brown Brown Green Brown Brown Brown Orange Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Red Brown Red Brown Brown Brown Brown Purple Brown Brown
Purple Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Red
Green Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Green Green Brown Brown Brown Brown Green Brown Brown Red Brown Brown Green Brown Brown Red Brown
Brown Brown Orange Brown Brown Red Red Red Brown Green Brown Purple Brown Brown Brown Brown Brown Brown Brown Green Brown Purple Brown Brown Orange Brown Brown Brown Brown Green
Brown Brown Red Brown Brown Red Orange Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown
Orange Brown Brown Green Green Brown Brown Orange Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Green Brown Brown Brown Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Black Purple Green Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Black Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Black Purple Black Purple Green Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Green Purple Black Purple Black Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Black Purple Black Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Black Purple Black Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Black Purple Black Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Black Purple Black Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Black Purple Black Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Black Purple Black Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Black Purple Black Purple Green Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Green Purple Black Purple Black Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Yellow Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Brown Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Yellow Pink Green Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Orange Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Orange Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Orange Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Yellow Pink Green Pink Brown Pink Brown Pink Brown Pink Brown Pink Brown Pink Brown Pink Brown Pink Green Pink Yellow Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Yellow Pink Brown Pink Pink Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Brown Pink Yellow Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Yellow Pink Brown Pink Yellow Pink Pink Pink Purple Pink Purple Pink Purple Pink Pink Pink Yellow Pink Brown Pink Yellow Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Yellow Pink Brown Pink Yellow Pink Purple Pink Pink Pink Pink Pink Pink Pink Purple Pink Yellow Pink Brown Pink Yellow Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Yellow Pink Brown Pink Yellow Pink Purple Pink Pink Pink Pink Pink Pink Pink Purple Pink Yellow Pink Brown Pink Yellow Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Yellow Pink Brown Pink Yellow Pink Pink Pink Purple Pink Purple Pink Purple Pink Pink Pink Yellow Pink Brown Pink Yellow Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Yellow Pink Brown Pink Pink Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Pink Pink Brown Pink Yellow Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Yellow Pink Green Pink Brown Pink Brown Pink Brown Pink Brown Pink Brown Pink Brown Pink Brown Pink Green Pink Yellow Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Orange Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Yellow Pink Orange Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Green Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Green Black Green Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Green Black Green Black Green Black Green Black Green Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Green Black Black Black Black Black Black Black Green Black
Row 5: Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Green Black Black Black Black Black Black Black Green Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Green Black Black Black Black Black Black Black Green Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Green Black Black Black Black Black Black Black Green Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Green Black Black Black Black Black Black Black Green Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Green Black Black Black Black Black Black Black Green Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Green Black Green Black Green Black Green Black Green Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Blue Purple Blue Purple Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Blue Purple Blue Purple Blue Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red
Row 2: Red Red Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 3: Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 4: Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 5: Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 6: Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 7: Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 8: Red Red Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red Green Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red Green Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Green Red Green Red Green Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Green Red Green Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Green Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown
Row 17: Orange Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown
Row 18: Orange Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown
Row 19: Orange Brown Brown Orange Brown Brown Orange Brown Brown Orange Brown Brown
Row 20: Orange Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown
Row 21: Orange Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown
Row 22: Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown
Row 23: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 28: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Red Red Red Red Red Black
Row 2: Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red
Row 9: Red Red Red Red Red Black
Row 10: Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red
Row 17: Red Red Red Red Red Black
Row 18: Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Black
Row 2: Red Red Red Red Red Black
Row 3: Red Red Red Red Red Black
Row 4: Red Red Red Red Red Black
Row 5: Red Red Red Red Red Black
Row 6: Red Red Red Red Red Black
Row 7: Red Red Red Red Red Black
Row 8: Red Red Red Red Red Black
Row 9: Red Red Red Red Red Black
Row 10: Red Red Red Red Red Black
Row 11: Red Red Red Red Red Black
Row 12: Red Red Red Red Red Black
Row 13: Red Red Red Red Red Black
Row 14: Red Red Red Red Red Black
Row 15: Red Red Red Red Red Black
Row 16: Red Red Red Red Red Black
Row 17: Red Red Red Red Red Black
Row 18: Red Red Red Red Red Black
Row 19: Red Red Red Red Red Black
Row 20: Red Red Red Red Red Black
Row 21: Red Red Red Red Red Black
Row 22: Red Red Red Red Red Black
Row 23: Red Red Red Red Red Black
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Black Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Black Black Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Black Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Black Black Gray Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Black Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Black Black Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange
Row 7: Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Pink Gray Gray Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Gray Orange Orange
Row 12: Pink Orange Orange Orange Orange Orange Orange Orange Gray Gray Black Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Black Orange Orange Orange Orange Pink Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Pink Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Black Gray Gray Orange Orange
Row 4: Orange Orange Gray Gray Black Orange Orange Orange Gray Orange Gray Gray Orange
Row 5: Orange Gray Gray Orange Gray Orange Orange Orange Gray Gray Orange Gray Orange
Row 6: Orange Gray Orange Gray Gray Orange Orange Orange Orange Gray Gray Pink Orange
Row 7: Orange Pink Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Pink Gray Gray Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Gray Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Gray Orange Orange
Row 12: Pink Gray Gray Orange Orange Orange Orange Orange Gray Gray Black Orange Orange
Row 13: Gray Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Gray Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Gray Gray Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Gray Gray Black Orange Orange Gray Gray Pink Orange Orange Orange
Row 18: Orange Gray Gray Orange Gray Orange Gray Gray Orange Gray Orange Orange Orange
Row 19: Orange Gray Orange Gray Gray Orange Gray Orange Gray Gray Orange Orange Orange
Row 20: Orange Pink Gray Gray Orange Orange Black Gray Gray Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Black Gray Gray Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Gray Orange Gray Gray Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Gray Gray Orange Gray Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Gray Gray Pink Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue
Row 2: Blue Gray Blue Blue Blue Blue Blue Orange Orange Orange Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Orange
Row 3: Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Orange Blue Blue Blue Blue Blue Blue Orange Orange Orange Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue
Row 5: Blue Gray Blue Orange Blue Blue Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Gray Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Blue Blue
Row 9: Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Orange Orange Blue Blue
Row 10: Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Gray Gray
Row 11: Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray
Row 12: Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Orange Blue Blue Black Gray Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Gray Blue Orange Black Blue Blue Gray Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue
Row 18: Gray Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Orange Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Orange Orange Blue Blue Blue Orange Blue Blue Blue Blue Gray Blue Blue Blue Blue Gray
Row 21: Blue Blue Blue Blue Blue Orange Orange Blue Blue Blue Blue Gray Blue Blue Blue Blue Orange Blue Blue Orange Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Gray Blue Gray Black
Row 2: Black Gray Blue Blue Blue Blue Blue Orange Orange Orange Black Black Black Blue Blue Blue Orange Black Blue Black Orange
Row 3: Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Orange Black Blue Blue Blue Blue Blue Orange Orange Orange Black Black Black Blue Blue Orange Black Blue Blue Blue Blue
Row 5: Black Gray Blue Orange Black Blue Blue Black Black Black Gray Gray Gray Blue Blue Black Gray Blue Blue Blue Blue
Row 6: Blue Blue Blue Black Gray Blue Blue Black Black Black Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Black Black Black Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Black Black
Row 9: Gray Gray Gray Gray Black Black Black Black Blue Blue Blue Blue Blue Black Gray Blue Blue Orange Orange Black Black
Row 10: Gray Gray Gray Gray Black Black Black Black Blue Blue Blue Blue Blue Orange Black Blue Blue Black Black Gray Gray
Row 11: Gray Gray Gray Gray Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Gray Gray
Row 12: Gray Gray Gray Gray Black Black Black Black Blue Blue Blue Blue Blue Black Gray Blue Blue Blue Blue Blue Blue
Row 13: Black Black Black Black Orange Orange Orange Orange Blue Blue Blue Blue Blue Orange Black Blue Blue Blue Blue Blue Blue
Row 14: Black Black Black Black Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Black Black Black Black Orange Orange Orange Orange Blue Blue Orange Black Blue Black Gray Blue Blue Blue Blue Blue Blue
Row 16: Black Black Black Black Orange Orange Orange Orange Blue Blue Black Gray Blue Orange Black Blue Blue Gray Black Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Orange Blue Blue
Row 18: Gray Black Blue Blue Blue Black Black Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Black Orange Blue Blue Blue Black Black Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Orange Orange Black Black Blue Orange Black Blue Blue Blue Gray Black Blue Blue Black Gray
Row 21: Blue Blue Blue Blue Blue Orange Orange Black Black Blue Black Gray Blue Blue Blue Black Orange Blue Blue Orange Black
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Brown Brown Orange Orange
Row 2: Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Brown Orange Orange
Row 3: Orange Orange Orange Brown Brown Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
Row 4: Orange Orange Orange Brown Brown Orange Orange Orange Brown Orange Orange Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Gray
Row 5: Gray Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange
Row 6: Orange Brown Orange Orange Orange Gray Gray Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange Gray Orange Orange Orange
Row 9: Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange Orange Brown Orange Orange
Row 10: Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Gray Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Gray Gray Orange Orange Orange Brown Orange Orange Orange Orange Orange Gray Gray Orange Brown Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Brown Orange
Row 13: Brown Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Brown Blue Orange Orange Orange Orange Orange Orange Gray
Row 14: Orange Gray Orange Orange Gray Gray Gray Orange Orange Orange Orange Brown Orange Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Gray Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange
Row 17: Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Brown Orange Orange Orange Gray Gray Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Orange Orange Gray Orange Orange Orange Orange Brown Brown Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange
Row 20: Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Gray Orange Orange Orange Brown Brown Orange Brown Brown Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Brown Brown Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange
Row 23: Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange
Row 24: Orange Brown Orange Orange Gray Gray Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Gray Gray Orange Orange Orange Brown Orange
Row 25: Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange Gray Orange Orange
Row 26: Orange Orange Orange Orange Gray Orange Orange Brown Orange Orange Brown Orange Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Brown Orange Orange Gray Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Blue Orange Orange Orange Brown Brown Blue Blue
Brown Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Brown Orange Orange Orange Brown Brown Blue Blue
Orange Orange Orange Brown Brown Blue Blue Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Gray Gray
Orange Orange Orange Brown Brown Blue Blue Orange Brown Blue Orange Gray Blue Orange Orange Orange Blue Gray Orange Blue Blue Gray Gray
Gray Blue Orange Blue Blue Gray Gray Orange Orange Orange Orange Blue Brown Orange Orange Orange Brown Blue Orange Orange Orange Orange Orange
Blue Brown Orange Blue Blue Gray Gray Orange Brown Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Brown Brown Blue Blue Orange Orange Orange Orange Orange Orange Orange Brown Brown Blue Blue Orange Orange Gray Blue Orange Orange
Orange Orange Brown Brown Blue Blue Orange Orange Orange Orange Orange Orange Orange Brown Brown Blue Blue Orange Orange Blue Brown Orange Orange
Orange Orange Blue Blue Gray Gray Orange Orange Orange Blue Gray Orange Orange Blue Blue Gray Gray Orange Orange Orange Orange Orange Orange
Orange Orange Blue Blue Gray Gray Orange Orange Orange Brown Blue Orange Orange Blue Blue Gray Gray Orange Brown Blue Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Gray Orange Brown Blue
Brown Blue Orange Orange Gray Gray Gray Blue Blue Blue Orange Orange Orange Orange Brown Blue Orange Orange Orange Orange Orange Blue Gray
Blue Gray Orange Orange Gray Gray Gray Blue Blue Blue Orange Brown Blue Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Gray Gray Gray Blue Blue Blue Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Blue Gray Orange Orange Blue Blue Blue Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Gray Gray Blue Blue Orange Orange
Brown Blue Orange Orange Blue Blue Blue Brown Brown Brown Orange Orange Orange Brown Blue Orange Orange Gray Gray Blue Blue Orange Orange
Orange Orange Orange Orange Blue Blue Blue Brown Brown Brown Orange Orange Orange Blue Gray Orange Orange Blue Blue Brown Brown Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Brown Brown Orange Orange
Orange Brown Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Brown Orange Orange Orange Orange Orange Orange Orange
Orange Blue Gray Orange Blue Blue Brown Brown Orange Brown Brown Blue Blue Orange Gray Blue Orange Orange Orange Gray Blue Orange Orange
Orange Orange Orange Orange Blue Blue Brown Brown Orange Brown Brown Blue Blue Orange Orange Orange Orange Orange Orange Blue Brown Orange Orange
Orange Orange Orange Orange Gray Gray Blue Blue Orange Blue Blue Gray Gray Orange Blue Blue Gray Gray Orange Orange Orange Orange Orange
Orange Brown Blue Orange Gray Gray Blue Blue Orange Blue Blue Gray Gray Orange Blue Blue Gray Gray Orange Orange Blue Brown Orange
Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Blue Blue Orange Orange Gray Blue Orange
Orange Orange Orange Orange Gray Blue Orange Brown Blue Orange Brown Blue Orange Orange Brown Brown Blue Blue Orange Orange Orange Orange Orange
Orange Orange Orange Orange Blue Brown Orange Blue Gray Orange Blue Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Blue Blue Gray Gray Gray Orange
Row 2: Gray Blue Brown Gray Blue Gray Blue
Row 3: Orange Gray Gray Gray Yellow Gray Gray
Output:
Row 1: Gray Gray Yellow Gray Gray Gray Orange
Row 2: Blue Gray Blue Gray Brown Blue Gray
Row 3: Orange Gray Gray Gray Blue Blue Gray
Example 2
Input:
Row 1: Yellow Purple Yellow Black Purple Green Yellow Green Yellow Yellow Blue Purple
Row 2: Yellow Green Black Black Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Black Purple Green Yellow Yellow Yellow Black Black Black Yellow Yellow
Row 4: Yellow Green Yellow Purple Yellow Yellow Yellow Green Green Green Purple Yellow
Row 5: Yellow Yellow Yellow Black Yellow Yellow Yellow Purple Yellow Yellow Yellow Black
Row 6: Yellow Yellow Black Yellow Yellow Green Yellow Black Green Yellow Yellow Yellow
Row 7: Black Green Yellow Black Purple Yellow Black Black Yellow Yellow Purple Yellow
Row 8: Black Yellow Yellow Green Blue Purple Yellow Purple Yellow Black Blue Yellow
Row 9: Black Green Yellow Yellow Yellow Black Yellow Green Purple Yellow Yellow Yellow
Row 10: Black Black Yellow Purple Black Yellow Purple Yellow Yellow Black Blue Yellow
Row 11: Purple Yellow Black Black Yellow Yellow Yellow Yellow Green Purple Yellow Black
Row 12: Black Black Yellow Yellow Yellow Yellow Purple Green Black Yellow Yellow Yellow
Row 13: Yellow Yellow Purple Black Yellow Yellow Yellow Black Yellow Black Yellow Purple
Row 14: Yellow Green Green Purple Black Purple Black Yellow Black Yellow Blue Black
Row 15: Yellow Blue Green Green Black Black Green Yellow Green Black Black Yellow
Row 16: Yellow Green Green Yellow Purple Black Black Yellow Black Purple Green Purple
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Blue Yellow Yellow Purple
Row 18: Green Green Black Black Yellow Purple Yellow Green Green Yellow Purple Yellow
Row 19: Yellow Green Black Yellow Black Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 20: Yellow Purple Yellow Black Black Green Purple Green Black Purple Purple Yellow
Output:
Row 1: Yellow Purple Purple Black Green Purple Green Black Black Yellow Purple Yellow
Row 2: Yellow Yellow Yellow Yellow Green Yellow Yellow Black Yellow Black Green Yellow
Row 3: Yellow Purple Yellow Green Green Yellow Purple Yellow Black Black Green Green
Row 4: Purple Yellow Yellow Blue Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Purple Green Purple Black Yellow Black Black Purple Yellow Green Green Yellow
Row 6: Yellow Black Black Green Yellow Green Black Black Green Green Blue Yellow
Row 7: Black Blue Yellow Black Yellow Black Purple Black Purple Green Green Yellow
Row 8: Purple Yellow Black Yellow Black Yellow Yellow Yellow Black Purple Yellow Yellow
Row 9: Yellow Yellow Yellow Black Green Purple Yellow Yellow Yellow Yellow Black Black
Row 10: Black Yellow Purple Green Yellow Yellow Yellow Yellow Black Black Yellow Purple
Row 11: Yellow Blue Black Yellow Yellow Purple Yellow Black Purple Yellow Black Black
Row 12: Yellow Yellow Yellow Purple Green Yellow Black Yellow Yellow Yellow Green Black
Row 13: Yellow Blue Black Yellow Purple Yellow Purple Blue Green Yellow Yellow Black
Row 14: Yellow Purple Yellow Yellow Black Black Yellow Purple Black Yellow Green Black
Row 15: Yellow Yellow Yellow Green Black Yellow Green Yellow Yellow Black Yellow Yellow
Row 16: Black Yellow Yellow Yellow Purple Yellow Yellow Yellow Black Yellow Yellow Yellow
Row 17: Yellow Purple Green Green Green Yellow Yellow Yellow Purple Yellow Green Yellow
Row 18: Yellow Yellow Black Black Black Yellow Yellow Yellow Green Purple Black Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Black Black Green Yellow
Row 20: Purple Blue Yellow Yellow Green Yellow Green Purple Black Yellow Purple Yellow
Example 3
Input:
Row 1: Orange Brown Brown Brown Brown Brown Brown Black Orange Orange Black Brown
Row 2: Black Brown Orange Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Orange Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Brown
Row 4: Orange Brown Orange Pink Black Orange Brown Black Orange Brown Black Pink
Row 5: Orange Brown Orange Pink Brown Brown Pink Black Orange Black Pink Orange
Row 6: Brown Brown Black Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 7: Orange Brown Brown Brown Brown Orange Brown Brown Brown Black Orange Orange
Row 8: Brown Brown Brown Orange Brown Brown Brown Brown Orange Orange Orange Brown
Row 9: Orange Black Orange Brown Brown Brown Orange Brown Brown Orange Orange Brown
Row 10: Brown Brown Orange Brown Orange Brown Brown Orange Black Brown Black Brown
Row 11: Brown Orange Brown Orange Brown Brown Orange Black Brown Brown Brown Brown
Row 12: Brown Brown Black Orange Orange Brown Orange Orange Orange Brown Brown Brown
Output:
Row 1: Brown Brown Brown Orange Orange Orange Brown Orange Orange Black Brown Brown
Row 2: Brown Brown Brown Brown Black Orange Brown Brown Orange Brown Orange Brown
Row 3: Brown Black Brown Black Orange Brown Brown Orange Brown Orange Brown Brown
Row 4: Brown Orange Orange Brown Brown Orange Brown Brown Brown Orange Black Orange
Row 5: Brown Orange Orange Orange Brown Brown Brown Brown Orange Brown Brown Brown
Row 6: Orange Orange Black Brown Brown Brown Orange Brown Brown Brown Brown Orange
Row 7: Brown Brown Brown Brown Brown Brown Orange Orange Orange Black Brown Brown
Row 8: Orange Pink Black Orange Black Pink Brown Brown Pink Orange Brown Orange
Row 9: Pink Black Brown Orange Black Brown Orange Black Pink Orange Brown Orange
Row 10: Brown Orange Orange Orange Orange Brown Orange Brown Brown Brown Brown Orange
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Black Orange Brown Black
Row 12: Brown Black Orange Orange Black Brown Brown Brown Brown Brown Brown Orange
Here is the input grid for the test example:
Input:
Row 1: Brown Blue Brown Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Brown Blue Blue Brown Blue
Row 2: Brown Blue Brown Blue Blue Brown Blue Blue Brown Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue
Row 3: Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Brown Blue Blue Blue Brown Brown Blue Brown Brown
Row 4: Blue Brown Brown Blue Brown Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue
Row 5: Brown Blue Blue Brown Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Blue Blue
Row 6: Blue Blue Blue Brown Blue Brown Brown Brown Blue Brown Blue Blue Blue Brown Blue Blue Brown Blue Brown
Row 7: Brown Blue Blue Brown Blue Blue Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Brown Blue Brown Blue Blue Blue Blue Brown Blue Brown Blue Brown Blue Blue Brown Blue Brown Blue Blue
Row 9: Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Blue
Row 10: Blue Brown Brown Blue Blue Brown Blue Brown Blue Brown Blue Blue Brown Blue Blue Brown Blue Brown Brown
Row 11: Blue Blue Brown Blue Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Blue Blue
Row 12: Brown Blue Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Brown Blue Brown Blue Brown
Row 13: Brown Brown Blue Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue
Row 14: Blue Brown Blue Blue Brown Brown Brown Blue Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Blue Brown Blue Blue Brown Blue Blue Brown Brown Brown Blue Blue Blue Brown Blue Blue Blue Blue Brown
Row 16: Brown Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Brown Blue Blue Brown Brown Brown Brown
Row 17: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Brown
Row 18: Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown Brown Blue Brown Blue Brown Blue Brown Brown Brown
Row 19: Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Brown Brown Brown Blue Brown Brown Blue Blue Brown
Row 20: Blue Brown Blue Blue Brown Blue Blue Blue Brown Blue Brown Blue Blue Brown Brown Blue Blue Blue Blue
Row 21: Blue Blue Blue Brown Blue Blue Brown Brown Brown Blue Blue Brown Brown Blue Brown Blue Blue Blue Blue
Row 22: Blue Brown Brown Blue Blue Brown Blue Blue Blue Blue Brown Brown Blue Brown Blue Brown Blue Blue Brown
Row 23: Brown Blue Blue Brown Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Brown Brown
Row 24: Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Brown Blue Blue Brown Brown Blue Blue Blue Blue
Row 25: Brown Blue Blue Brown Brown Brown Brown Blue Blue Brown Blue Brown Blue Brown Brown Brown Blue Blue Brown
Row 26: Blue Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Blue Brown Brown Brown Blue Blue Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Blue Blue Brown Brown Brown Blue Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Blue
Brown Blue Blue Brown Brown Brown Blue Brown Blue Brown Blue Blue Brown Brown Brown Brown Blue Blue Brown
Blue Blue Blue Blue Brown Brown Blue Blue Brown Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue
Brown Brown Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Brown Blue Blue Brown
Brown Blue Blue Brown Blue Brown Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue Brown Brown Blue
Blue Blue Blue Blue Brown Blue Brown Brown Blue Blue Brown Brown Brown Blue Blue Brown Blue Blue Blue
Blue Blue Blue Blue Brown Brown Blue Blue Brown Blue Brown Blue Blue Blue Brown Blue Blue Brown Blue
Brown Blue Blue Brown Brown Blue Brown Brown Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue
Brown Brown Brown Blue Brown Blue Brown Blue Brown Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue
Brown Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue
Brown Brown Brown Brown Blue Blue Brown Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Blue Brown
Brown Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Brown Blue Blue Brown Blue Blue Brown Blue
Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Blue Blue Brown Brown Brown Blue Blue Brown Blue
Blue Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Blue Blue Brown Blue Brown Blue Brown Brown
Brown Blue Brown Blue Brown Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Brown Blue Blue Brown
Blue Blue Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown Blue Blue Brown Blue Blue
Brown Brown Blue Brown Blue Blue Brown Blue Blue Brown Blue Brown Blue Brown Blue Blue Brown Brown Blue
Blue Brown Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown
Blue Blue Brown Blue Brown Blue Blue Brown Blue Brown Blue Brown Blue Blue Blue Blue Brown Blue Brown
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Blue Blue Blue Brown Blue Blue Brown
Brown Blue Brown Blue Blue Brown Blue Blue Blue Brown Blue Brown Brown Brown Blue Brown Blue Blue Blue
Blue Blue Brown Brown Blue Blue Blue Blue Brown Brown Brown Brown Blue Blue Blue Brown Blue Blue Brown
Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown Brown Blue Brown Brown Blue
Brown Brown Blue Brown Brown Blue Blue Blue Brown Brown Blue Blue Blue Brown Blue Blue Blue Brown Blue
Blue Brown Blue Brown Blue Blue Blue Brown Blue Brown Brown Blue Blue Brown Blue Blue Brown Blue Brown
Blue Brown Blue Blue Brown Blue Brown Blue Blue Brown Blue Blue Blue Blue Blue Blue Brown Blue Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Red Yellow Red Red
Row 2: Brown Red Red Orange Green
Row 3: Red Red Red Green Red
Row 4: Brown Red Pink Red Red
Row 5: Green Yellow Red Orange Brown
Output:
Row 1: Black Black Black Black Black Orange Red Yellow Red Red Black Black Black Black Black Orange Red Yellow Red Red Orange Red Yellow Red Red
Row 2: Black Black Black Black Black Brown Red Red Orange Green Black Black Black Black Black Brown Red Red Orange Green Brown Red Red Orange Green
Row 3: Black Black Black Black Black Red Red Red Green Red Black Black Black Black Black Red Red Red Green Red Red Red Red Green Red
Row 4: Black Black Black Black Black Brown Red Pink Red Red Black Black Black Black Black Brown Red Pink Red Red Brown Red Pink Red Red
Row 5: Black Black Black Black Black Green Yellow Red Orange Brown Black Black Black Black Black Green Yellow Red Orange Brown Green Yellow Red Orange Brown
Row 6: Black Black Black Black Black Orange Red Yellow Red Red Orange Red Yellow Red Red Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Brown Red Red Orange Green Brown Red Red Orange Green Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Red Red Red Green Red Red Red Red Green Red Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Brown Red Pink Red Red Brown Red Pink Red Red Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Green Yellow Red Orange Brown Green Yellow Red Orange Brown Black Black Black Black Black Black Black Black Black Black
Row 11: Orange Red Yellow Red Red Orange Red Yellow Red Red Orange Red Yellow Red Red Black Black Black Black Black Orange Red Yellow Red Red
Row 12: Brown Red Red Orange Green Brown Red Red Orange Green Brown Red Red Orange Green Black Black Black Black Black Brown Red Red Orange Green
Row 13: Red Red Red Green Red Red Red Red Green Red Red Red Red Green Red Black Black Black Black Black Red Red Red Green Red
Row 14: Brown Red Pink Red Red Brown Red Pink Red Red Brown Red Pink Red Red Black Black Black Black Black Brown Red Pink Red Red
Row 15: Green Yellow Red Orange Brown Green Yellow Red Orange Brown Green Yellow Red Orange Brown Black Black Black Black Black Green Yellow Red Orange Brown
Row 16: Black Black Black Black Black Orange Red Yellow Red Red Black Black Black Black Black Orange Red Yellow Red Red Orange Red Yellow Red Red
Row 17: Black Black Black Black Black Brown Red Red Orange Green Black Black Black Black Black Brown Red Red Orange Green Brown Red Red Orange Green
Row 18: Black Black Black Black Black Red Red Red Green Red Black Black Black Black Black Red Red Red Green Red Red Red Red Green Red
Row 19: Black Black Black Black Black Brown Red Pink Red Red Black Black Black Black Black Brown Red Pink Red Red Brown Red Pink Red Red
Row 20: Black Black Black Black Black Green Yellow Red Orange Brown Black Black Black Black Black Green Yellow Red Orange Brown Green Yellow Red Orange Brown
Row 21: Black Black Black Black Black Black Black Black Black Black Orange Red Yellow Red Red Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Brown Red Red Orange Green Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Red Red Red Green Red Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Brown Red Pink Red Red Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Black Black Black Black Black Green Yellow Red Orange Brown Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Blue Green Green Green
Row 2: Green Green Green Green
Row 3: Green Green Green Green
Output:
Row 1: Black Black Black Black Blue Green Green Green Blue Green Green Green Blue Green Green Green
Row 2: Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Blue Green Green Green Blue Green Green Green Blue Green Green Green Blue Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Blue Green Green Green Blue Green Green Green Blue Green Green Green Blue Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Blue Gray Blue
Row 2: Yellow Green Blue
Output:
Row 1: Blue Gray Blue Black Black Black Blue Gray Blue
Row 2: Yellow Green Blue Black Black Black Yellow Green Blue
Row 3: Black Black Black Black Black Black Blue Gray Blue
Row 4: Black Black Black Black Black Black Yellow Green Blue
Here is the input grid for the test example:
Input:
Row 1: Gray Gray
Row 2: Gray Orange
Row 3: Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray
Gray Orange Gray Orange
Gray Gray Gray Gray
Gray Gray Black Black
Gray Orange Black Black
Gray Gray Black Black
Gray Gray Gray Gray
Gray Orange Gray Orange
Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Red Red Red Red Red Red Red Red Red
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Red Red Red Red Red Red Red Red Red
Row 21: Yellow Black Purple Black Blue Black Purple Black Blue
Row 22: Purple Purple Purple Blue Purple Blue Black Black Blue
Row 23: Black Black Purple Purple Blue Purple Black Blue Blue
Row 24: Black Black Purple Black Purple Blue Black Black Purple
Row 25: Purple Black Blue Purple Purple Black Blue Blue Blue
Row 26: Black Purple Purple Purple Black Purple Black Blue Purple
Row 27: Black Black Purple Purple Purple Blue Black Blue Yellow
Row 28: Blue Black Black Black Blue Black Blue Purple Black
Row 29: Purple Purple Purple Purple Yellow Blue Blue Black Blue
Output:
Row 1: Blue Black Blue Blue Yellow Purple Purple Purple Purple
Row 2: Black Purple Blue Black Blue Black Black Black Blue
Row 3: Yellow Blue Black Blue Purple Purple Purple Black Black
Row 4: Purple Blue Black Purple Black Purple Purple Purple Black
Row 5: Blue Blue Blue Black Purple Purple Blue Black Purple
Row 6: Purple Black Black Blue Purple Black Purple Black Black
Row 7: Blue Blue Black Purple Blue Purple Purple Black Black
Row 8: Blue Black Black Blue Purple Blue Purple Purple Purple
Row 9: Blue Black Purple Black Blue Black Purple Black Yellow
Row 10: Red Red Red Red Red Red Red Red Red
Row 11: Blue Blue Blue Purple Blue Purple Yellow Black Blue
Row 12: Black Black Blue Black Blue Blue Blue Purple Black
Row 13: Purple Black Black Black Blue Black Black Blue Blue
Row 14: Black Blue Purple Blue Black Purple Blue Black Blue
Row 15: Blue Purple Blue Purple Purple Black Purple Blue Yellow
Row 16: Black Blue Purple Black Purple Purple Purple Black Purple
Row 17: Purple Purple Purple Purple Blue Purple Purple Black Purple
Row 18: Black Purple Black Black Black Purple Black Black Purple
Row 19: Yellow Purple Black Black Purple Black Black Blue Purple
Row 20: Red Red Red Red Red Red Red Red Red
Row 21: Yellow Black Purple Black Blue Black Purple Black Blue
Row 22: Purple Purple Purple Blue Purple Blue Black Black Blue
Row 23: Black Black Purple Purple Blue Purple Black Blue Blue
Row 24: Black Black Purple Black Purple Blue Black Black Purple
Row 25: Purple Black Blue Purple Purple Black Blue Blue Blue
Row 26: Black Purple Purple Purple Black Purple Black Blue Purple
Row 27: Black Black Purple Purple Purple Blue Black Blue Yellow
Row 28: Blue Black Black Black Blue Black Blue Purple Black
Row 29: Purple Purple Purple Purple Yellow Blue Blue Black Blue
Example 2
Input:
Row 1: Green Green Green
Row 2: Green Green Green
Row 3: Green Green Green
Row 4: Orange Orange Orange
Row 5: Green Green Green
Row 6: Green Green Green
Row 7: Green Green Green
Row 8: Orange Orange Orange
Row 9: Green Green Green
Row 10: Gray Black Green
Row 11: Green Red Green
Output:
Row 1: Green Red Green
Row 2: Green Black Gray
Row 3: Green Green Green
Row 4: Orange Orange Orange
Row 5: Green Green Green
Row 6: Green Black Red
Row 7: Green Gray Green
Row 8: Orange Orange Orange
Row 9: Green Green Green
Row 10: Gray Black Green
Row 11: Green Red Green
Example 3
Input:
Row 1: Black Black Black Black Yellow Green
Row 2: Red Black Black Red Black Black
Row 3: Green Green Red Red Black Yellow
Row 4: Black Black Black Green Black Red
Row 5: Yellow Black Red Yellow Red Black
Row 6: Black Black Green Black Black Black
Row 7: Purple Purple Purple Purple Purple Purple
Row 8: Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Yellow Green
Row 2: Red Black Black Red Black Black
Row 3: Green Green Red Red Black Yellow
Row 4: Black Black Black Green Black Red
Row 5: Yellow Black Red Yellow Red Black
Row 6: Black Black Green Black Black Black
Row 7: Purple Purple Purple Purple Purple Purple
Row 8: Black Yellow Black Green Red Black
Row 9: Black Black Black Green Black Black
Row 10: Green Red Black Red Black Black
Row 11: Black Yellow Green Red Red Black
Row 12: Black Red Black Black Black Yellow
Row 13: Black Black Red Yellow Black Green
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Blue Brown Brown Brown Blue Brown Purple Brown
Row 2: Brown Brown Brown Blue Brown Brown Brown Blue Yellow Gray Brown
Row 3: Brown Brown Brown Blue Brown Brown Brown Blue Brown Gray Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Gray Brown Blue Brown Brown Brown Blue Brown Purple Brown
Brown Gray Yellow Blue Purple Gray Gray Blue Yellow Gray Brown
Brown Purple Brown Blue Brown Yellow Brown Blue Brown Gray Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 2: Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 5: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 8: Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow
Row 10: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 13: Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown
Row 14: Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Output:
Row 1: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Blue Black Black Black Black Brown Brown Black Black Yellow Yellow Black
Row 2: Black Black Black Blue Brown Black Brown Brown Yellow Black Yellow Yellow
Row 3: Black Blue Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Brown Black Black Black Yellow Black
Row 5: Black Black Black Blue Brown Black Brown Black Yellow Black Yellow Black
Row 6: Black Blue Black Blue Black Black Brown Brown Black Black Yellow Yellow
Row 7: Black Black Black Black Brown Brown Black Brown Yellow Yellow Black Yellow
Row 8: Black Black Black Black Black Black Black Brown Black Black Black Yellow
Row 9: Black Blue Black Black Black Black Black Brown Black Black Black Yellow
Row 10: Black Blue Blue Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Brown Black Brown Black Yellow Black Yellow
Row 12: Blue Black Black Black Black Brown Brown Brown Black Yellow Yellow Yellow
Row 13: Black Blue Black Black Brown Black Black Black Yellow Black Black Black
Output:
Row 1: Blue Black Black Black
Row 2: Black Black Black Blue
Row 3: Black Blue Black Black
Row 4: Black Black Black Black
Row 5: Black Black Black Blue
Row 6: Black Blue Black Blue
Row 7: Black Black Black Black
Row 8: Black Black Black Black
Row 9: Black Blue Black Black
Row 10: Black Blue Blue Black
Row 11: Black Black Black Black
Row 12: Blue Black Black Black
Row 13: Black Blue Black Black
Example 3
Input:
Row 1: Black Orange Black Purple Black Green Black Yellow
Row 2: Black Orange Black Purple Black Green Black Yellow
Row 3: Orange Orange Purple Black Green Black Yellow Black
Row 4: Orange Black Purple Black Green Black Yellow Black
Row 5: Black Orange Black Purple Black Green Black Yellow
Row 6: Black Orange Black Purple Black Green Black Yellow
Row 7: Black Orange Black Purple Black Green Black Yellow
Row 8: Orange Orange Purple Black Green Black Yellow Black
Row 9: Orange Orange Purple Black Green Black Yellow Black
Row 10: Black Orange Black Black Black Black Black Black
Row 11: Orange Black Purple Black Green Black Yellow Black
Row 12: Orange Black Purple Black Green Black Yellow Black
Row 13: Orange Orange Black Purple Black Green Black Yellow
Row 14: Orange Orange Purple Purple Green Green Yellow Yellow
Row 15: Orange Black Purple Black Green Black Yellow Black
Row 16: Orange Black Black Black Black Black Black Black
Row 17: Black Black Black Purple Black Green Black Yellow
Row 18: Orange Black Purple Purple Green Green Yellow Yellow
Row 19: Orange Orange Black Purple Black Green Black Yellow
Row 20: Black Black Black Black Black Black Black Black
Row 21: Orange Black Purple Purple Green Green Yellow Yellow
Row 22: Orange Orange Purple Purple Green Green Yellow Yellow
Row 23: Black Orange Purple Purple Green Green Yellow Yellow
Output:
Row 1: Black Orange
Row 2: Black Orange
Row 3: Orange Orange
Row 4: Orange Black
Row 5: Black Orange
Row 6: Black Orange
Row 7: Black Orange
Row 8: Orange Orange
Row 9: Orange Orange
Row 10: Black Orange
Row 11: Orange Black
Row 12: Orange Black
Row 13: Orange Orange
Row 14: Orange Orange
Row 15: Orange Black
Row 16: Orange Black
Row 17: Black Black
Row 18: Orange Black
Row 19: Orange Orange
Row 20: Black Black
Row 21: Orange Black
Row 22: Orange Orange
Row 23: Black Orange
Here is the input grid for the test example:
Input:
Row 1: Red Red Yellow Yellow Yellow Red Yellow Yellow Red Red Red Yellow Yellow Yellow Red Red Red Yellow Red Red Red Yellow Red Red Red Red Red
Row 2: Yellow Red Red Yellow Red Red Yellow Red Yellow Red Yellow Red Red Red Red Red Red Red Red Yellow Red Red Yellow Red Yellow Red Red
Row 3: Red Yellow Red Yellow Red Yellow Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Red Red
Row 4: Yellow Yellow Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Red Red Red Red Red Red Yellow Red
Row 5: Red Red Brown Brown Brown Red Brown Brown Red Red Red Brown Brown Brown Red Red Red Brown Red Red Red Brown Red Red Red Red Red
Row 6: Brown Red Red Brown Red Red Brown Red Brown Red Brown Red Red Red Red Red Red Red Red Brown Red Red Brown Red Brown Red Red
Row 7: Red Brown Red Brown Red Brown Red Red Red Red Red Red Red Red Red Red Brown Brown Brown Red Brown Red Brown Brown Brown Red Red
Row 8: Brown Brown Red Red Red Red Red Red Brown Brown Brown Brown Brown Red Brown Red Red Red Red Red Red Red Red Red Red Brown Red
Row 9: Red Red Green Green Green Red Green Green Red Red Red Green Green Green Red Red Red Green Red Red Red Green Red Red Red Red Red
Row 10: Green Red Red Green Red Red Green Red Green Red Green Red Red Red Red Red Red Red Red Green Red Red Green Red Green Red Red
Row 11: Red Green Red Green Red Green Red Red Red Red Red Red Red Red Red Red Green Green Green Red Green Red Green Green Green Red Red
Row 12: Green Green Red Red Red Red Red Red Green Green Green Green Green Red Green Red Red Red Red Red Red Red Red Red Red Green Red
Row 13: Red Red Orange Orange Orange Red Orange Orange Red Red Red Orange Orange Orange Red Red Red Orange Red Red Red Orange Red Red Red Red Red
Row 14: Orange Red Red Orange Red Red Orange Red Orange Red Orange Red Red Red Red Red Red Red Red Orange Red Red Orange Red Orange Red Red
Row 15: Red Orange Red Orange Red Orange Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Red Orange Red Orange Orange Orange Red Red
Row 16: Orange Orange Red Red Red Red Red Red Orange Orange Orange Orange Orange Red Orange Red Red Red Red Red Red Red Red Red Red Orange Red
Row 17: Red Red Purple Purple Purple Red Purple Purple Red Red Red Purple Purple Purple Red Red Red Purple Red Red Red Purple Red Red Red Red Red
Row 18: Purple Red Red Purple Red Red Purple Red Purple Red Purple Red Red Red Red Red Red Red Red Purple Red Red Purple Red Purple Red Red
Row 19: Red Purple Red Purple Red Purple Red Red Red Red Red Red Red Red Red Red Purple Purple Purple Red Purple Red Purple Purple Purple Red Red
Row 20: Purple Purple Red Red Red Red Red Red Purple Purple Purple Purple Purple Red Purple Red Red Red Red Red Red Red Red Red Red Purple Red
Row 21: Red Red Red Pink Red Red Red Pink Red Red Red Pink Pink Pink Red Red Red Pink Pink Red Red Red Red Red Red Red Red
Row 22: Pink Red Red Pink Red Pink Pink Pink Pink Red Pink Red Red Pink Red Red Red Red Red Pink Red Red Pink Red Pink Red Red
Row 23: Red Red Red Pink Pink Pink Pink Red Red Red Pink Red Red Pink Red Red Pink Pink Pink Red Red Red Pink Pink Pink Pink Red
Row 24: Red Pink Red Red Red Red Red Red Pink Red Pink Pink Pink Red Pink Red Red Red Red Red Red Red Red Red Pink Pink Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Red Red Pink Red Red Red Pink Red Red Red Pink Pink Pink Red Red Red Pink Pink Red Red Red Red Red Red Red Red
Pink Red Red Pink Red Pink Pink Pink Pink Red Pink Red Red Pink Red Red Red Red Red Pink Red Red Pink Red Pink Red Red
Red Red Red Pink Pink Pink Pink Red Red Red Pink Red Red Pink Red Red Pink Pink Pink Red Red Red Pink Pink Pink Pink Red
Red Pink Red Red Red Red Red Red Pink Red Pink Pink Pink Red Pink Red Red Red Red Red Red Red Red Red Pink Pink Pink |
Subsets and Splits