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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: Orange Green Green Green Green Green Green Green Black Green Green
Row 2: Red Green Green Orange Green Green Green Orange Green Green Green
Row 3: Green Green Green Green Green Green Black Green Black Green Green
Row 4: Green Green Green Orange Green Green Orange Green Orange Orange Orange
Row 5: Orange Green Green Green Green Green Green Green Green Green Orange
Row 6: Brown Green Green Brown Orange Green Green Black Green Green Black
Row 7: Green Green Orange Green Orange Green Orange Orange Green Green Orange
Row 8: Green Green Black Green Green Orange Green Green Green Green Green
Row 9: Green Green Black Green Green Green Brown Green Green Green Black
Row 10: Black Black Green Green Green Green Green Orange Green Green Orange
Row 11: Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Brown Black Green Green Green Green Green Green
Row 13: Green Green Orange Green Green Green Green Black Green Green Green
Row 14: Orange Green Green Green Green Green Green Green Black Green Green
Row 15: Red Green Green Orange Green Green Green Orange Green Green Green
Row 16: Green Green Green Green Green Green Black Green Black Green Green
Row 17: Green Green Green Orange Green Green Orange Green Orange Orange Orange
Row 18: Orange Green Green Green Green Green Green Green Green Green Orange
Row 19: Brown Green Green Brown Orange Green Green Black Green Green Black
Row 20: Green Green Orange Green Orange Green Orange Orange Green Green Orange
Row 21: Green Green Black Green Green Orange Green Green Green Green Green
Row 22: Green Green Black Green Green Green Brown Green Green Green Black
Row 23: Black Black Green Green Green Green Green Orange Green Green Orange
Row 24: Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Brown Black Green Green Green Green Green Green
Row 26: Green Green Orange Green Green Green Green Black Green Green Green
Output:
Row 1: Orange Green Green Green Green Green Green Green Black Green Green
Row 2: Red Green Green Orange Green Green Green Orange Green Green Green
Row 3: Green Green Green Green Green Green Black Green Black Green Green
Row 4: Green Green Green Orange Green Green Orange Green Orange Orange Orange
Row 5: Orange Green Green Green Green Green Green Green Green Green Orange
Row 6: Brown Green Green Brown Orange Green Green Black Green Green Black
Row 7: Green Green Orange Green Orange Green Orange Orange Green Green Orange
Row 8: Green Green Black Green Green Orange Green Green Green Green Green
Row 9: Green Green Black Green Green Green Brown Green Green Green Black
Row 10: Black Black Green Green Green Green Green Orange Green Green Orange
Row 11: Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Brown Black Green Green Green Green Green Green
Row 13: Green Green Orange Green Green Green Green Black Green Green Green
Example 2
Input:
Row 1: Brown Green Black Black Brown Brown Brown Red Brown Brown Brown Yellow Blue Pink Brown Brown
Row 2: Brown Brown Gray Brown Brown Brown Black Brown Brown Brown Brown Gray Yellow Red Brown Brown
Row 3: Blue Gray Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Red Brown Black Brown
Row 4: Black Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Red Brown Brown Brown Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Red Brown Brown Brown Red Brown Green Green Yellow Brown Brown Brown Red Brown Red
Row 8: Brown Red Brown Red Brown Yellow Brown Brown Brown Brown Pink Brown Brown Brown Brown Red
Row 9: Brown Brown Red Brown Brown Pink Blue Brown Brown Brown Brown Brown Brown Black Green Blue
Row 10: Brown Brown Brown Gray Brown Blue Brown Brown Brown Brown Brown Brown Brown Red Pink Brown
Row 11: Brown Brown Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 12: Brown Red Brown Brown Pink Brown Red Brown Brown Red Brown Brown Brown Brown Brown Yellow
Row 13: Brown Green Black Black Brown Brown Brown Red Brown Brown Brown Yellow Blue Pink Brown Brown
Row 14: Brown Brown Gray Brown Brown Brown Black Brown Brown Brown Brown Gray Yellow Red Brown Brown
Row 15: Blue Gray Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Red Brown Black Brown
Row 16: Black Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Red Brown Brown Brown Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Red Brown Brown Brown Red Brown Green Green Yellow Brown Brown Brown Red Brown Red
Row 20: Brown Red Brown Red Brown Yellow Brown Brown Brown Brown Pink Brown Brown Brown Brown Red
Row 21: Brown Brown Red Brown Brown Pink Blue Brown Brown Brown Brown Brown Brown Black Green Blue
Row 22: Brown Brown Brown Gray Brown Blue Brown Brown Brown Brown Brown Brown Brown Red Pink Brown
Row 23: Brown Brown Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 24: Brown Red Brown Brown Pink Brown Red Brown Brown Red Brown Brown Brown Brown Brown Yellow
Output:
Row 1: Brown Green Black Black Brown Brown Brown Red Brown Brown Brown Yellow Blue Pink Brown Brown
Row 2: Brown Brown Gray Brown Brown Brown Black Brown Brown Brown Brown Gray Yellow Red Brown Brown
Row 3: Blue Gray Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Red Brown Black Brown
Row 4: Black Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Red Brown Brown Brown Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Red Brown Brown Brown Red Brown Green Green Yellow Brown Brown Brown Red Brown Red
Row 8: Brown Red Brown Red Brown Yellow Brown Brown Brown Brown Pink Brown Brown Brown Brown Red
Row 9: Brown Brown Red Brown Brown Pink Blue Brown Brown Brown Brown Brown Brown Black Green Blue
Row 10: Brown Brown Brown Gray Brown Blue Brown Brown Brown Brown Brown Brown Brown Red Pink Brown
Row 11: Brown Brown Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 12: Brown Red Brown Brown Pink Brown Red Brown Brown Red Brown Brown Brown Brown Brown Yellow
Example 3
Input:
Row 1: Gray Gray Gray Yellow Gray Gray Gray Red Gray Brown Brown Gray Gray Gray Yellow Gray Gray Gray Red Gray Brown Brown
Row 2: Gray Pink Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Green Gray Gray Gray Gray Gray
Row 3: Blue Gray Black Orange Blue Gray Gray Gray Gray Gray Orange Blue Gray Black Orange Blue Gray Gray Gray Gray Gray Orange
Row 4: Gray Gray Gray Purple Gray Yellow Purple Gray Pink Pink Gray Gray Gray Gray Purple Gray Yellow Purple Gray Pink Pink Gray
Row 5: Pink Gray Orange Pink Gray Gray Yellow Gray Purple Gray Gray Pink Gray Orange Pink Gray Gray Yellow Gray Purple Gray Gray
Row 6: Gray Gray Gray Pink Brown Gray Gray Blue Gray Orange Pink Gray Gray Gray Pink Brown Gray Gray Blue Gray Orange Pink
Row 7: Gray Gray Gray Purple Black Pink Gray Gray Gray Gray Orange Gray Gray Gray Purple Black Pink Gray Gray Gray Gray Orange
Row 8: Gray Pink Gray Gray Orange Gray Orange Purple Gray Gray Blue Gray Pink Gray Gray Orange Gray Orange Purple Gray Gray Blue
Row 9: Black Gray Gray Gray Red Orange Purple Gray Gray Black Pink Black Gray Gray Gray Red Orange Purple Gray Gray Black Pink
Row 10: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Pink
Row 11: Gray Purple Gray Gray Black Gray Gray Orange Pink Gray Gray Gray Purple Gray Gray Black Gray Gray Orange Pink Gray Gray
Row 12: Gray Gray Gray Brown Gray Gray Orange Pink Gray Green Gray Gray Gray Gray Brown Gray Gray Orange Pink Gray Green Gray
Row 13: Gray Orange Red Gray Gray Orange Gray Gray Gray Gray Purple Gray Orange Red Gray Gray Orange Gray Gray Gray Gray Purple
Row 14: Gray Gray Orange Gray Black Black Gray Gray Pink Gray Gray Gray Gray Orange Gray Black Black Gray Gray Pink Gray Gray
Row 15: Brown Gray Pink Gray Gray Brown Gray Orange Pink Gray Gray Brown Gray Pink Gray Gray Brown Gray Orange Pink Gray Gray
Row 16: Red Black Black Brown Gray Gray Yellow Pink Gray Gray Gray Red Black Black Brown Gray Gray Yellow Pink Gray Gray Gray
Row 17: Blue Gray Orange Gray Black Gray Blue Gray Gray Gray Pink Blue Gray Orange Gray Black Gray Blue Gray Gray Gray Pink
Row 18: Gray Gray Gray Orange Gray Yellow Pink Orange Yellow Orange Orange Gray Gray Gray Orange Gray Yellow Pink Orange Yellow Orange Orange
Row 19: Gray Gray Red Pink Blue Red Gray Gray Yellow Gray Gray Gray Gray Red Pink Blue Red Gray Gray Yellow Gray Gray
Row 20: Blue Purple Gray Gray Gray Purple Gray Black Orange Blue Gray Blue Purple Gray Gray Gray Purple Gray Black Orange Blue Gray
Row 21: Gray Black Gray Gray Gray Purple Orange Purple Pink Gray Gray Gray Black Gray Gray Gray Purple Orange Purple Pink Gray Gray
Row 22: Gray Pink Yellow Red Gray Red Purple Yellow Brown Purple Gray Gray Pink Yellow Red Gray Red Purple Yellow Brown Purple Gray
Output:
Row 1: Gray Gray Gray Yellow Gray Gray Gray Red Gray Brown Brown
Row 2: Gray Pink Gray Gray Gray Green Gray Gray Gray Gray Gray
Row 3: Blue Gray Black Orange Blue Gray Gray Gray Gray Gray Orange
Row 4: Gray Gray Gray Purple Gray Yellow Purple Gray Pink Pink Gray
Row 5: Pink Gray Orange Pink Gray Gray Yellow Gray Purple Gray Gray
Row 6: Gray Gray Gray Pink Brown Gray Gray Blue Gray Orange Pink
Row 7: Gray Gray Gray Purple Black Pink Gray Gray Gray Gray Orange
Row 8: Gray Pink Gray Gray Orange Gray Orange Purple Gray Gray Blue
Row 9: Black Gray Gray Gray Red Orange Purple Gray Gray Black Pink
Row 10: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Pink
Row 11: Gray Purple Gray Gray Black Gray Gray Orange Pink Gray Gray
Row 12: Gray Gray Gray Brown Gray Gray Orange Pink Gray Green Gray
Row 13: Gray Orange Red Gray Gray Orange Gray Gray Gray Gray Purple
Row 14: Gray Gray Orange Gray Black Black Gray Gray Pink Gray Gray
Row 15: Brown Gray Pink Gray Gray Brown Gray Orange Pink Gray Gray
Row 16: Red Black Black Brown Gray Gray Yellow Pink Gray Gray Gray
Row 17: Blue Gray Orange Gray Black Gray Blue Gray Gray Gray Pink
Row 18: Gray Gray Gray Orange Gray Yellow Pink Orange Yellow Orange Orange
Row 19: Gray Gray Red Pink Blue Red Gray Gray Yellow Gray Gray
Row 20: Blue Purple Gray Gray Gray Purple Gray Black Orange Blue Gray
Row 21: Gray Black Gray Gray Gray Purple Orange Purple Pink Gray Gray
Row 22: Gray Pink Yellow Red Gray Red Purple Yellow Brown Purple Gray
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Orange Black Black Black Gray Yellow Green Black Green Black Black Black Orange Black Black Black Black Black
Row 2: Yellow Yellow Black Black Blue Black Red Gray Blue Pink Orange Black Black Black Black Black Blue Black Black Black Blue
Row 3: Black Red Black Orange Green Black Black Red Green Black Black Yellow Yellow Brown Black Black Yellow Gray Black Green Red
Row 4: Black Black Black Orange Black Black Black Gray Yellow Green Black Green Black Black Black Orange Black Black Black Black Black
Row 5: Yellow Yellow Black Black Blue Black Red Gray Blue Pink Orange Black Black Black Black Black Blue Black Black Black Blue
Row 6: Black Red Black Orange Green Black Black Red Green Black Black Yellow Yellow Brown Black Black Yellow Gray Black Green Red
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 Orange Black Black Black Gray Yellow Green Black Green Black Black Black Orange Black Black Black Black Black
Yellow Yellow Black Black Blue Black Red Gray Blue Pink Orange Black Black Black Black Black Blue Black Black Black Blue
Black Red Black Orange Green Black Black Red Green Black Black Yellow Yellow Brown Black Black Yellow Gray Black Green 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: Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 2: Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Green Green Blue Green
Row 3: Green Blue Yellow Yellow Yellow Yellow Blue Blue Blue Green Yellow Yellow Yellow Yellow Green Blue Blue Green Yellow Yellow Yellow Yellow Blue Blue
Row 4: Blue Blue Yellow Yellow Yellow Yellow Green Blue Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Blue Blue
Row 5: Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Green Blue Blue Green Yellow Yellow Yellow Yellow Blue Blue
Row 6: Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue Green Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Green Blue Blue Blue Green Green Blue
Row 8: Blue Blue Blue Blue Blue Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Green Green Blue Blue Blue Green Green
Row 9: Green Blue Green Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Green Blue Green Blue Blue Blue
Row 10: Blue Blue Green Green Blue Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Green Blue Blue Green Blue Blue Blue Blue Blue
Row 11: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Green Blue Yellow Yellow Yellow Yellow Blue Blue Blue Green Blue Blue
Row 12: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Green Yellow Yellow Yellow Yellow Blue Blue Blue Green Green Blue
Row 13: Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Green Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 14: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 16: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Blue Blue Blue Green
Row 17: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Green Blue Blue Blue
Row 18: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Green Blue Blue Blue Blue Blue Green
Row 20: Green Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Green Green Blue Blue Blue Blue
Row 21: Green Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Green Blue
Row 22: Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Green Blue Green Blue Blue Green Blue Blue Green Blue Green Blue
Row 23: Blue Green Blue Green Blue Green Blue Blue Blue Blue Blue Green Green Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Output:
Row 1: Green Blue Green Blue Green
Row 2: Blue Green Green Blue Blue
Row 3: Green Green Blue Green Blue
Row 4: Green Green Green Green Blue
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 2: Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Pink Orange Orange Orange
Row 3: Orange Orange Orange Purple Purple Purple Purple Orange Orange Pink Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Pink Orange
Row 4: Orange Orange Orange Purple Purple Purple Purple Pink Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Pink Orange
Row 5: Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Pink Orange Orange Pink
Example 3
Input:
Row 1: Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Red Purple Red Red Red Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Red
Row 3: Purple Purple Purple Purple Purple Red Purple Purple Purple Gray Gray Gray Gray Purple Red Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Red
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Red Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Red Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Red Purple Gray Gray Gray Gray Red Purple Purple Purple Purple Purple
Row 6: Purple Red Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Red Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Red Purple Purple Gray Gray Gray Gray Purple Purple Purple Red Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 8: Red Purple Red Purple Red Gray Gray Gray Gray Red Purple Purple Purple Gray Gray Gray Gray Purple Red Purple Purple Purple Purple Purple Purple Purple Red
Row 9: Red Purple Purple Red Purple Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Row 10: Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Red Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple
Row 11: Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Red Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple
Row 12: Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Purple Purple Purple Gray Gray Gray Gray Purple Red Purple Purple Purple Purple
Row 13: Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Red Purple Purple Gray Gray Gray Gray Purple Purple Purple Red Purple Purple
Row 14: Purple Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Red Purple Purple Purple Purple
Row 15: Red Gray Gray Gray Gray Gray Gray Gray Gray Purple Red Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Red Red Purple Purple Purple Purple
Row 16: Purple Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Red Gray Gray Gray Gray Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Red Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Red Gray Gray Gray Gray Purple Purple Purple Red Purple Purple Red Purple Purple Red
Row 18: Purple Purple Purple Red Red Red Red Purple Purple Red Purple Purple Purple Purple Red Red Purple Purple Purple Red Purple Purple Purple Red Red Purple Red
Row 19: Red Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple
Row 20: Red Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Purple Purple Purple Purple Purple Purple Purple Purple Red Red
Row 21: Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Red Red Purple
Row 22: Purple Purple Red Purple Red Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Red Purple Red Red Red Purple Red Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Red Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Red Red
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Red Purple Purple Purple Purple Red Red Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Red Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Purple Purple Purple Purple Red Purple Red Red
Row 26: Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Red Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple
Output:
Row 1: Purple Purple Red Purple Red
Row 2: Purple Red Purple Red Purple
Row 3: Red Red Red Purple Red
Row 4: Red Red Purple Red Purple
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
Row 2: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Gray Gray Gray Pink Pink
Row 3: Pink Pink Pink Green Green Green Green Green Green Green Green Gray Pink Pink Pink Pink Pink Gray Pink Pink
Row 4: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Gray Pink Pink Pink Pink
Row 5: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Green Green Green Green Green Green Green Green Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray 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
Row 12: Pink Gray 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 Gray Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray 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
Row 18: Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 19: Pink Pink Gray Pink Gray Gray Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Green Green Green Green Green Green Green Green Pink
Row 25: Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Gray
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Gray Gray Pink Pink Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Pink
Pink Pink
Pink 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 Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Black Black Orange Orange Orange Orange Black Orange Pink Pink Orange Orange Orange Pink Orange Orange Pink
Row 3: Black Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Pink Pink
Row 4: Black Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Pink
Row 5: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 6: Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink
Row 7: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink
Row 8: Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 9: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink
Row 10: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink
Row 11: Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink
Row 12: Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 13: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink
Row 14: Black Black Orange Orange Orange Orange Black Black Pink Orange Pink Orange Orange Orange Orange Orange Pink
Row 15: Black Black Black Orange Orange Orange Black Black Pink Orange Pink Orange Orange Orange Pink Orange Pink
Row 16: Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Black Black Orange Green Green Green Black Orange Pink Pink Orange Green Green Pink Orange Orange Pink
Row 3: Black Orange Orange Green Green Green Orange Orange Pink Pink Orange Green Green Orange Orange Pink Pink
Row 4: Black Orange Orange Green Green Green Orange Orange Pink Pink Orange Green Green Orange Orange Orange Pink
Row 5: Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 6: Black Black Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Pink Pink
Row 7: Black Orange Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Pink Pink Pink
Row 8: Black Black Black Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Orange Pink
Row 9: Black Orange Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Pink Pink
Row 10: Black Orange Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Pink Pink Pink
Row 11: Black Black Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Pink Pink
Row 12: Black Black Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Orange Pink
Row 13: Black Orange Orange Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Pink Pink
Row 14: Black Black Orange Green Green Green Black Black Pink Orange Pink Green Green Orange Orange Orange Pink
Row 15: Black Black Black Green Green Green Black Black Pink Orange Pink Green Green Orange Pink Orange Pink
Row 16: Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
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 Orange Orange Orange
Row 2: Orange Orange Orange Orange Red Red Orange Orange Red Orange Orange Red Red Orange Orange Orange Red Red Red Orange Red Orange Red Orange Red Red Orange Orange Red Orange
Row 3: Orange Red Orange Orange Red Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Orange Red Orange
Row 4: Orange Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Black Black Black
Row 5: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 6: Orange Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 7: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Black Black
Row 8: Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 9: Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Black
Row 10: Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 11: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 12: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Black
Row 13: Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 14: Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 15: Orange Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 16: Orange Red Red Red Red Black Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Black Red Red Red Red Red Red Red Black
Row 17: Orange Black Red Black Red Black Black Red Black Black Black Red Black Red Red Red Black Red Red Red Black Black Red Black Black Black Red Red 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 Black Black Black Black
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 Orange Orange Orange
Row 2: Orange Orange Orange Orange Green Red Orange Orange Red Orange Orange Green Red Orange Orange Orange Red Green Green Orange Red Orange Green Orange Red Red Orange Orange Red Orange
Row 3: Orange Red Orange Orange Green Red Red Orange Red Red Red Green Red Red Red Red Red Green Green Orange Red Red Green Red Red Red Red Orange Red Orange
Row 4: Orange Red Red Orange Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Orange Red Red Green Red Red Red Red Black Black Black
Row 5: Orange Green Green Green Green 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
Row 6: Orange Orange Orange Orange Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Red Black
Row 7: Orange Red Red Red Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Black Black Black
Row 8: Orange Orange Red Red Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Red Black
Row 9: Orange Orange Orange Red Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Black Black
Row 10: Orange Orange Red Red Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Red Black
Row 11: Orange Green Green Green Green 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
Row 12: Orange Red Red Red Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Black Black
Row 13: Orange Green Green Green Green 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
Row 14: Orange Orange Red Red Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Red Black
Row 15: Orange Orange Orange Orange Green Red Red Red Red Red Red Green Red Red Red Red Red Green Green Red Red Red Green Red Red Red Red Red Red Black
Row 16: Orange Red Red Red Green Black Red Red Red Black Red Green Red Red Red Red Black Green Green Red Red Black Green Red Red Red Red Red Red Black
Row 17: Orange Black Red Black Green Black Black Red Black Black Black Green Black Red Red Red Black Green Green Red Black Black Green Black Black Black Red Red 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 Black Black Black Black
Example 3
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
Row 2: Gray Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Gray Gray Gray Gray Brown Brown Gray Brown Gray Gray Brown Brown Gray
Row 3: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray
Row 4: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 5: Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 6: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 7: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 8: Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 9: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 10: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple
Row 11: Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown 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
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
Row 2: Gray Brown Green Green Green Green Green Green Gray Green Green Green Gray Gray Gray Gray Green Green Gray Green Gray Gray Green Green Gray
Row 3: Gray Gray Green Green Green Green Green Green Brown Green Green Green Brown Brown Brown Brown Green Green Brown Green Brown Brown Green Green Gray
Row 4: Gray Gray Green Green Green Green Green Green Brown Green Green Green Brown Brown Brown Brown Green Green Brown Green Brown Brown Green Green Purple
Row 5: Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 6: Gray Gray Green Green Green Green Green Green Brown Green Green Green Brown Brown Brown Brown Green Green Brown Green Brown Brown Green Green Purple
Row 7: Gray Gray Green Green Green Green Green Green Brown Green Green Green Brown Brown Brown Brown Green Green Brown Green Brown Brown Green Green Purple
Row 8: Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 9: Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 10: Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 11: Purple Purple Green Green Green Green Green Green Brown Green Green Green Brown Brown Brown Brown Green Green Brown Green Brown Brown Green Green 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
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Black Gray Black Black Gray Black Black Black Black Gray Gray
Row 3: Gray Gray Black Black Black Black Black Black Black Black Gray Orange
Row 4: Gray Black Black Black Black Black Black Black Black Black Orange Orange
Row 5: Gray Black Black Black Black Black Black Black Black Black Black Orange
Row 6: Gray Black Black Black Black Black Black Black Black Black Black Orange
Row 7: Gray Gray Gray Black Black Black Black Black Black Black Black Orange
Row 8: Gray Black Black Black Black Black Black Black Black Orange Orange Orange
Row 9: Gray Gray Black Black Black Black Black Black Black Black Orange Orange
Row 10: Gray Black Black Black Black Black Black Black Black Black Orange Orange
Row 11: Gray Black Black Black Black Black Black Black Black Black Black Orange
Row 12: Gray Gray Black Black Black Black Black Black Black Black Orange Orange
Row 13: Gray Gray Gray Black Black Black Black Black Black Orange Orange Orange
Row 14: Gray Black Black Black Black Black Black Black Black Black Black Orange
Row 15: Gray Gray Black Black Black Black Black Black Black Orange Orange Orange
Row 16: Gray Gray Gray Gray Black Black Black Black Black Orange Orange Orange
Row 17: Gray Gray Black Black Black Black Black Black Black Black Black Orange
Row 18: Gray Black Black Black Black Black Black Black Black Black Black Orange
Row 19: Gray Gray Black Black Black Black Black Black Black Black Black Orange
Row 20: Gray Gray Gray Gray Black Black Black Black Black Black Black Orange
Row 21: Gray Black Black Black Black Black Black Black Black Black Black Orange
Row 22: Gray Gray Black Black Black Black Black Black Black Black Black Orange
Row 23: Orange Orange Black Black Black Black Black Black Black Black Black Orange
Row 24: Orange Black Black Orange Black Black Orange Black Black Black Orange Orange
Row 25: Orange Orange Black Orange Black Orange Orange Orange Orange Black Black Orange
Row 26: 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>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Black Gray Black Green Gray Black Black Black Black Gray Gray
Gray Gray Black Black Green Black Black Black Black Black Gray Orange
Gray Black Black Black Green Black Black Black Black Black Orange Orange
Gray Green Green Green Green Green Green Green Green Green Green Orange
Gray Green Green Green Green Green Green Green Green Green Green Orange
Gray Gray Gray Black Green Black Black Black Black Black Black Orange
Gray Black Black Black Green Black Black Black Black Orange Orange Orange
Gray Gray Black Black Green Black Black Black Black Black Orange Orange
Gray Black Black Black Green Black Black Black Black Black Orange Orange
Gray Green Green Green Green Green Green Green Green Green Green Orange
Gray Gray Black Black Green Black Black Black Black Black Orange Orange
Gray Gray Gray Black Green Black Black Black Black Orange Orange Orange
Gray Green Green Green Green Green Green Green Green Green Green Orange
Gray Gray Black Black Green Black Black Black Black Orange Orange Orange
Gray Gray Gray Gray Green Black Black Black Black Orange Orange Orange
Gray Gray Black Black Green Black Black Black Black Black Black Orange
Gray Green Green Green Green Green Green Green Green Green Green Orange
Gray Gray Black Black Green Black Black Black Black Black Black Orange
Gray Gray Gray Gray Green Black Black Black Black Black Black Orange
Gray Green Green Green Green Green Green Green Green Green Green Orange
Gray Gray Black Black Green Black Black Black Black Black Black Orange
Orange Orange Black Black Green Black Black Black Black Black Black Orange
Orange Black Black Orange Green Black Orange Black Black Black Orange Orange
Orange Orange Black Orange Green Orange Orange Orange Orange Black Black 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: 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
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: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Green Blue Yellow Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue Blue Blue Blue
Row 14: 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
Row 16: 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
Row 18: 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
Row 20: 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
Row 22: 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
Row 24: 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
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Green Blue Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Row 7: Green Blue Blue Blue Blue Blue Yellow Blue Yellow Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Green Green Blue Blue Yellow Yellow Blue Blue Blue Blue
Row 10: Blue Blue Green Blue Green Blue Yellow Blue Yellow Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue Blue Blue Blue
Row 14: 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
Row 16: 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
Row 18: 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
Row 20: 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
Row 22: 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
Row 24: 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
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 29: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
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 Purple Purple Purple Purple Purple
Row 2: 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 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 Orange 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 Orange Orange Purple Purple Pink Pink 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 Black Black Black 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 Black Black 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 Black Black Black Purple Pink 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 Black Black Black 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 Pink Pink Pink Purple Yellow Yellow Yellow 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow 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 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 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Pink Pink Pink 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 Orange Orange Purple Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Pink Pink Pink 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 Black Black Black Purple Pink Pink Pink Purple Pink Pink Pink Purple Pink
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Pink Pink Purple Purple Pink Pink Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Purple Pink Pink Pink Purple Pink Pink Pink Purple Pink
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Purple Pink Pink Pink Purple Pink Pink Pink Purple Pink
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 Pink Pink Pink Purple Yellow Yellow Yellow 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 Pink Pink Purple Purple Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Yellow Yellow Yellow 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 Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Brown Gray Black Black Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Pink Pink Gray Yellow Yellow Gray Gray Gray Gray Gray
Row 5: Gray Pink Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Brown Brown Gray Black Black Gray Gray Gray Gray Gray
Row 8: Gray Brown Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Green Green Gray Blue Blue Gray Gray
Row 11: Gray Gray Gray Gray Green Gray Gray Blue Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Green Green Gray Gray Gray Gray Blue
Row 14: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Blue
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Green Green Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Green Green Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray 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 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
Row 3: 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
Row 5: 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 Brown 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
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray 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 Orange Orange Orange
Row 11: Orange Orange Orange Orange 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 Brown 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
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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown
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 Brown Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown 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 Orange Orange Orange Orange Orange Orange Orange Orange Gray 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 Brown Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown 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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow 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 Yellow Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Red Orange Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Orange 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 Yellow Yellow 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 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 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 Yellow Yellow Yellow Yellow Yellow Yellow 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
Example 2
Input:
Row 1: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Yellow Black Red Yellow Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 3
Input:
Row 1: Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 8: Orange Orange Orange Orange 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
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red 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 Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red 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: 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: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red 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
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
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green 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 Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow 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
Row 13: Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Gray Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 2: 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
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow
Row 8: Yellow Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow
Row 9: Yellow Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Yellow
Row 10: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue
Row 3: 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
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Red
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
Output:
Row 1: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Row 2: 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
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 7: Blue Blue Blue Blue Blue Green Green Green Red Red Red Blue
Row 8: Blue Blue Blue Blue Blue Green Green Green Red Red Red Blue
Row 9: Blue Blue Blue Blue Blue Green Green Green Red Red Red Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown
Example 3
Input:
Row 1: Purple Purple Brown Red Orange 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 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 3: 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 Yellow
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
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 Red Red Orange Orange 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 Red Red Orange Orange 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
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
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
Row 11: 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 Yellow
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
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
Output:
Row 1: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
Row 2: 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
Row 4: Purple Purple Purple Purple Purple Purple Brown Brown Red Red Orange Orange Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Brown Brown Red Red Orange Orange Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow
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 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 Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red 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: 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
Row 10: Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red 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 Blue Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Black Blue Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Gray Blue 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red
Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Gray Gray Gray Gray Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Gray Gray Gray Gray Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Gray Gray Gray Gray Blue Blue Blue Blue Green Green
Green Green Green Green Blue Blue Blue Blue Gray Gray Gray Gray Blue Blue Blue Blue Green Green
Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange
Row 2: Red Orange Orange Orange Orange Green Purple Purple Orange Orange Orange Orange Orange Black
Row 3: Red Orange Green Green Orange Black Orange Red Brown Orange Gray Orange Orange Black
Row 4: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Black
Row 5: Red Orange Black Purple Orange Orange Yellow Orange Orange Red Orange Orange Pink Black
Row 6: Red Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Pink Purple Black
Row 7: Red Orange Orange Blue Orange Purple Orange Black Green Yellow Orange Gray Orange Black
Row 8: Red Orange Orange Orange Blue Orange Orange Green Orange Brown Orange Yellow Orange Black
Row 9: Red Green Orange Orange Black Orange Red Orange Orange Orange Green Orange Orange Black
Row 10: Red Orange Orange Orange Orange Brown Red Orange Orange Orange Black Brown Orange Black
Row 11: Red Orange Orange Orange Brown Orange Blue Orange Yellow Red Blue Orange Orange Black
Row 12: Red Orange Orange Orange Orange Red Orange Orange Pink Orange Orange Yellow Orange Black
Row 13: Red Orange Orange Orange Orange Orange Black Orange Orange Orange Brown Orange Gray Black
Row 14: Red Orange Orange Orange Purple Purple Red Brown Orange Orange Orange Orange Orange Black
Row 15: Red Orange Blue Orange Gray Blue Orange Blue Orange Orange Orange Orange Orange Black
Row 16: Red Orange Red Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Black
Row 17: Red Orange Orange Orange Orange Yellow Green Orange Orange Gray Yellow Orange Orange Black
Row 18: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink
Output:
Row 1: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange
Row 2: Red Orange Orange Orange Brown Brown Orange Brown Brown Brown Brown Brown Orange Black
Row 3: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 4: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 5: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 6: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 7: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 8: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 9: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 10: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 11: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 12: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 13: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 14: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 15: Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 16: Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 17: Red Orange Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Orange Black
Row 18: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange
Example 2
Input:
Row 1: Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 2: Red Brown Black Black Black Black Black Black Black Pink
Row 3: Red Black Black Red Black Green Black Black Brown Pink
Row 4: Red Black Black Blue Blue Brown Black Orange Black Pink
Row 5: Red Gray Black Black Black Pink Black Red Black Pink
Row 6: Red Black Black Black Yellow Red Black Green Black Pink
Row 7: Red Black Black Black Black Orange Red Gray Black Pink
Row 8: Red Black Black Pink Black Gray Black Black Black Pink
Row 9: Red Black Black Blue Black Red Black Black Purple Pink
Row 10: Red Black Black Pink Black Black Purple Black Black Pink
Row 11: Red Black Black Red Black Black Black Gray Purple Pink
Row 12: Red Black Orange Black Blue Red Black Black Black Pink
Row 13: Red Black Pink Black Red Black Black Black Black Pink
Row 14: Red Black Red Black Black Black Black Black Black Pink
Row 15: Red Brown Black Black Pink Black Black Black Green Pink
Row 16: Red Black Black Orange Black Black Brown Black Black Pink
Row 17: Red Black Yellow Black Black Pink Red Black Black Pink
Row 18: Red Black Black Black Pink Yellow Black Black Black Pink
Row 19: Red Black Black Black Black Black Black Black Black Pink
Row 20: Red Black Black Black Red Black Black Black Black Pink
Row 21: Red Black Red Black Black Black Black Black Black Pink
Row 22: Red Black Black Black Black Black Black Red Brown Pink
Row 23: Red Black Black Black Red Pink Yellow Yellow Black Pink
Row 24: Red Black Black Black Black Black Orange Pink Green Pink
Row 25: Red Black Black Red Black Black Black Purple Brown Pink
Row 26: Red Black Black Black Black Black Black Black Black Pink
Row 27: Black Orange Orange Orange Orange Orange Orange Orange Orange Gray
Output:
Row 1: Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 2: Red Black Yellow Black Yellow Yellow Yellow Yellow Black Pink
Row 3: Red Red Black Black Black Black Black Black Black Pink
Row 4: Red Black Black Black Black Black Black Black Black Pink
Row 5: Red Red Black Black Black Black Black Black Pink Pink
Row 6: Red Red Black Black Black Black Black Black Black Pink
Row 7: Red Red Black Black Black Black Black Black Black Pink
Row 8: Red Black Black Black Black Black Black Black Pink Pink
Row 9: Red Red Black Black Black Black Black Black Black Pink
Row 10: Red Black Black Black Black Black Black Black Pink Pink
Row 11: Red Red Black Black Black Black Black Black Black Pink
Row 12: Red Red Black Black Black Black Black Black Black Pink
Row 13: Red Red Black Black Black Black Black Black Pink Pink
Row 14: Red Red Black Black Black Black Black Black Black Pink
Row 15: Red Black Black Black Black Black Black Black Pink Pink
Row 16: Red Black Black Black Black Black Black Black Black Pink
Row 17: Red Red Black Black Black Black Black Black Pink Pink
Row 18: Red Black Black Black Black Black Black Black Pink Pink
Row 19: Red Black Black Black Black Black Black Black Black Pink
Row 20: Red Red Black Black Black Black Black Black Black Pink
Row 21: Red Red Black Black Black Black Black Black Black Pink
Row 22: Red Red Black Black Black Black Black Black Black Pink
Row 23: Red Red Black Black Black Black Black Black Pink Pink
Row 24: Red Black Black Black Black Black Black Black Pink Pink
Row 25: Red Red Black Black Black Black Black Black Black Pink
Row 26: Red Black Orange Orange Black Orange Orange Orange Black Pink
Row 27: Black Orange Orange Orange Orange Orange Orange Orange Orange Black
Example 3
Input:
Row 1: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 2: Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Black
Row 3: Brown Pink Pink Pink Green Pink Pink Yellow Pink Pink Pink Orange Pink Pink Pink Pink Yellow Pink Pink Pink Black Pink Yellow Pink Black
Row 4: Brown Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Green Green Pink Pink Brown Pink Pink Pink Black Pink Pink Pink Black
Row 5: Brown Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Brown Pink Pink Black Pink Yellow Pink Pink Yellow Green Green Pink Black
Row 6: Brown Pink Yellow Pink Yellow Pink Pink Pink Brown Purple Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Green Orange Pink Pink Pink Black
Row 7: Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Row 8: Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Output:
Row 1: Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 2: Brown Pink Yellow Pink Yellow Pink Pink Yellow Yellow Pink Yellow Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Yellow Pink Yellow Pink Black
Row 3: Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black
Row 4: Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black
Row 5: Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black
Row 6: Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black
Row 7: Brown Pink Pink Pink Green Pink Green Pink Pink Pink Pink Pink Green Green Pink Pink Pink Pink Pink Green Pink Green Green Pink Black
Row 8: Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Here is the input grid for the test example:
Input:
Row 1: Yellow Green Green Green Green Green Green Yellow
Row 2: Pink Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 3: Pink Yellow Yellow Yellow Yellow Red Yellow Red
Row 4: Pink Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 5: Pink Yellow Yellow Gray Red Pink Yellow Red
Row 6: Pink Yellow Gray Yellow Yellow Pink Yellow Red
Row 7: Pink Yellow Blue Blue Pink Yellow Yellow Red
Row 8: Pink Yellow Yellow Red Yellow Yellow Yellow Red
Row 9: Pink Yellow Yellow Yellow Green Yellow Yellow Red
Row 10: Pink Yellow Yellow Yellow Yellow Pink Yellow Red
Row 11: Pink Yellow Pink Yellow Yellow Red Yellow Red
Row 12: Pink Yellow Yellow Yellow Pink Yellow Yellow Red
Row 13: Pink Yellow Yellow Yellow Red Yellow Yellow Red
Row 14: Pink Yellow Yellow Pink Red Yellow Yellow Red
Row 15: Pink Yellow Yellow Red Yellow Green Yellow Red
Row 16: Pink Yellow Red Pink Yellow Yellow Yellow Red
Row 17: Pink Yellow Yellow Yellow Yellow Pink Yellow Red
Row 18: Pink Yellow Yellow Red Gray Pink Yellow Red
Row 19: Pink Yellow Yellow Pink Yellow Yellow Yellow Red
Row 20: Pink Yellow Yellow Pink Yellow Yellow Yellow Red
Row 21: Pink Yellow Yellow Pink Yellow Yellow Yellow Red
Row 22: Pink Yellow Red Green Yellow Yellow Yellow Red
Row 23: Pink Yellow Yellow Yellow Yellow Yellow Yellow Red
Row 24: Yellow Gray Gray Gray Gray Gray Gray Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Green Green Green Green Green Green Yellow
Pink Yellow Yellow Green Green Green Yellow Red
Pink Yellow Yellow Yellow Yellow Yellow Red Red
Pink Yellow Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Red Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Yellow Yellow Yellow Yellow Yellow Red Red
Pink Yellow Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Red Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Yellow Yellow Yellow Yellow Yellow Red Red
Pink Pink Yellow Yellow Yellow Yellow Red Red
Pink Yellow Yellow Yellow Yellow Yellow Red Red
Pink Pink Yellow Yellow Yellow Yellow Red Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Red Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Pink Yellow Yellow Yellow Yellow Yellow Red
Pink Yellow Yellow Yellow Yellow Yellow Red Red
Pink Yellow Gray Gray Gray Yellow Yellow Red
Yellow Gray Gray Gray Gray Gray Gray 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: Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Yellow Gray Gray Gray Gray
Row 3: Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 4: Gray Yellow Gray Gray Gray Yellow Gray Gray Yellow
Row 5: Yellow Yellow Gray Gray Gray Gray Gray Yellow Gray
Row 6: Gray Yellow Gray Gray Gray Gray Yellow Gray Gray
Row 7: Gray Yellow Gray Gray Gray Yellow Yellow Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Yellow Gray Gray Gray Gray Gray Yellow
Row 10: Yellow Gray Yellow Gray Yellow Gray Yellow Gray Gray
Row 11: Gray Gray Gray Yellow Yellow Gray Gray Yellow Gray
Row 12: Gray Gray Yellow Gray Yellow Gray Yellow Yellow Gray
Row 13: Pink Pink Yellow Pink Pink Pink Pink Pink Pink
Row 14: Yellow Yellow Yellow Yellow Pink Pink Yellow Pink Pink
Row 15: Pink Yellow Pink Yellow Pink Yellow Yellow Pink Pink
Row 16: Pink Pink Pink Pink Yellow Pink Pink Yellow Pink
Row 17: Pink Pink Pink Pink Pink Pink Yellow Pink Yellow
Row 18: Yellow Pink Pink Pink Pink Yellow Pink Pink Yellow
Row 19: Pink Pink Pink Pink Pink Pink Yellow Yellow Pink
Row 20: Yellow Yellow Yellow Pink Pink Pink Pink Yellow Pink
Row 21: Pink Pink Yellow Pink Pink Pink Pink Pink Yellow
Row 22: Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Yellow Pink Pink Pink Yellow Yellow Pink Yellow
Row 24: Pink Pink Yellow Pink Pink Yellow Yellow Pink Yellow
Output:
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 Red Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Red
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Yellow
Example 2
Input:
Row 1: Yellow Orange Yellow Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange
Row 2: Yellow Orange Yellow Orange Orange Orange Orange Yellow Orange Yellow Orange Yellow Orange
Row 3: Yellow Yellow Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Yellow Yellow
Row 4: Yellow Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Yellow Yellow
Row 5: Yellow Yellow Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Yellow Orange
Row 7: Yellow Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Blue Orange Blue Blue Orange Orange Orange Orange Orange Orange Blue Orange
Row 10: Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Orange Blue Orange
Row 11: Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Blue Blue Blue
Row 12: Orange Orange Orange Orange Blue Blue Orange Orange Orange Orange Blue Blue Orange
Row 13: Orange Blue Orange Orange Orange Blue Blue Orange Orange Orange Orange Orange Blue
Row 14: Orange Orange Orange Orange Blue Orange Orange Blue Blue Orange Orange Blue Blue
Row 15: Orange Blue Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Blue
Row 16: Orange Orange Blue Orange Orange Orange Orange Blue Orange Orange Orange Blue Blue
Output:
Row 1: Orange Orange Orange Orange Orange Red Orange Orange Red Red Red Orange Red
Row 2: Orange Red Orange Orange Orange Red Red Orange Red Orange Red Orange Red
Row 3: Orange Orange Red Orange Red Red Orange Orange Red Orange Orange Orange Orange
Row 4: Orange Red Red Red Orange Orange Red Red Red Red Orange Orange Orange
Row 5: Orange Orange Red Red Red Orange Orange Red Red Red Orange Red Orange
Row 6: Red Red Red Red Orange Red Orange Orange Orange Red Red Orange Orange
Row 7: Orange Orange Orange Red Orange Red Orange Red Red Red Red Red Orange
Row 8: Red Red Orange Orange Red Orange Red Orange Red Red Red Orange Orange
Example 3
Input:
Row 1: Yellow Yellow Yellow Brown Brown Brown Black Black Black Brown
Row 2: Yellow Yellow Brown Yellow Yellow Black Black Black Brown Brown
Row 3: Yellow Yellow Yellow Brown Yellow Black Black Black Black Black
Row 4: Yellow Yellow Brown Yellow Yellow Black Black Brown Brown Brown
Row 5: Yellow Brown Brown Brown Yellow Black Brown Brown Black Brown
Row 6: Yellow Yellow Yellow Yellow Yellow Black Black Brown Brown Black
Row 7: Yellow Yellow Brown Yellow Brown Black Brown Brown Black Black
Row 8: Yellow Brown Brown Yellow Yellow Black Black Brown Black Brown
Row 9: Yellow Brown Yellow Yellow Brown Black Black Black Black Brown
Row 10: Brown Yellow Yellow Brown Yellow Black Black Black Black Black
Row 11: Brown Yellow Brown Yellow Brown Brown Black Brown Black Brown
Row 12: Yellow Brown Brown Brown Brown Brown Brown Black Black Brown
Row 13: Yellow Yellow Yellow Yellow Yellow Black Brown Black Black Brown
Row 14: Brown Yellow Yellow Yellow Yellow Brown Brown Black Black Black
Row 15: Yellow Yellow Brown Yellow Yellow Black Black Black Brown Brown
Row 16: Brown Yellow Brown Yellow Yellow Black Brown Black Black Brown
Row 17: Brown Yellow Brown Yellow Yellow Black Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Red
Row 2: Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown
Row 4: Brown Brown Red Brown Brown
Row 5: Brown Red Red Brown Brown
Row 6: Brown Brown Brown Brown Brown
Row 7: Brown Brown Red Brown Brown
Row 8: Brown Brown Red Brown Brown
Row 9: Brown Brown Brown Brown Red
Row 10: Brown Brown Brown Brown Brown
Row 11: Red Brown Red Brown Red
Row 12: Brown Red Brown Brown Red
Row 13: Brown Brown Brown Brown Brown
Row 14: Red Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown
Row 17: Brown Brown Red Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Black Orange Black Orange Orange Orange Black Black Orange Gray Gray Gray Gray Orange Gray Gray Orange Gray
Row 2: Orange Black Black Black Black Black Orange Orange Black Orange Gray Orange Orange Orange Gray Orange Gray Orange
Row 3: Black Black Orange Black Black Black Black Black Black Orange Orange Orange Gray Gray Orange Orange Orange Orange
Row 4: Black Black Black Orange Orange Orange Black Black Orange Orange Gray Orange Gray Orange Gray Orange Orange Orange
Row 5: Black Orange Black Black Orange Orange Black Orange Orange Orange Gray Orange Gray Gray Orange Orange Orange Orange
Row 6: Orange Orange Black Black Orange Orange Black Orange Black Orange Orange Orange Gray Gray Orange Gray Orange Orange
Row 7: Black Black Orange Black Black Black Black Black Black Orange Orange Gray Gray Gray Orange Gray Gray Gray
Row 8: Black Orange Black Black Black Orange Black Black Black Orange Orange Orange Orange Gray Gray Gray Orange Orange
Row 9: Orange Black Black Black Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray 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 Red Orange Orange Orange Orange
Red Orange Orange Orange Orange Orange Red Orange Orange
Orange Orange Red Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Red Orange Orange Orange Red
Orange Orange Orange Orange Orange Red Orange Red Red
Red Red Orange Orange Orange Red Orange Red Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Red Orange Orange Orange Orange Orange Orange Orange
Red Orange Orange Orange Red Orange Orange 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: 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
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Gray Gray 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: Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
Row 5: Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
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
Example 2
Input:
Row 1: Blue Blue Blue Blue
Row 2: Blue Blue Blue Orange
Row 3: Blue Blue Pink Blue
Row 4: Black Blue Black Blue
Row 5: Blue Blue Blue Pink
Row 6: Pink Gray Pink Blue
Row 7: Brown Yellow Brown Brown
Row 8: Black Yellow Blue Blue
Row 9: Blue Blue Blue Blue
Row 10: Pink Brown Orange Blue
Row 11: Blue Blue Blue Yellow
Row 12: Blue Blue Blue Blue
Row 13: Brown Blue Blue Pink
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Orange Orange Blue Blue Blue
Row 3: Blue Blue Pink Blue Blue Pink Blue Blue
Row 4: Black Blue Black Blue Blue Black Blue Black
Row 5: Blue Blue Blue Pink Pink Blue Blue Blue
Row 6: Pink Gray Pink Blue Blue Pink Gray Pink
Row 7: Brown Yellow Brown Brown Brown Brown Yellow Brown
Row 8: Black Yellow Blue Blue Blue Blue Yellow Black
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Pink Brown Orange Blue Blue Orange Brown Pink
Row 11: Blue Blue Blue Yellow Yellow Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Brown Blue Blue Pink Pink Blue Blue Brown
Row 14: Brown Blue Blue Pink Pink Blue Blue Brown
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Yellow Yellow Blue Blue Blue
Row 17: Pink Brown Orange Blue Blue Orange Brown Pink
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Black Yellow Blue Blue Blue Blue Yellow Black
Row 20: Brown Yellow Brown Brown Brown Brown Yellow Brown
Row 21: Pink Gray Pink Blue Blue Pink Gray Pink
Row 22: Blue Blue Blue Pink Pink Blue Blue Blue
Row 23: Black Blue Black Blue Blue Black Blue Black
Row 24: Blue Blue Pink Blue Blue Pink Blue Blue
Row 25: Blue Blue Blue Orange Orange Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Green Brown Pink Brown Green
Row 2: Green Green Purple Brown Pink
Row 3: Pink Brown Pink Green Pink
Row 4: Green Green Green Pink Pink
Row 5: Green Green Brown Green Brown
Row 6: Green Brown Brown Purple Brown
Output:
Row 1: Green Brown Pink Brown Green Green Brown Pink Brown Green
Row 2: Green Green Purple Brown Pink Pink Brown Purple Green Green
Row 3: Pink Brown Pink Green Pink Pink Green Pink Brown Pink
Row 4: Green Green Green Pink Pink Pink Pink Green Green Green
Row 5: Green Green Brown Green Brown Brown Green Brown Green Green
Row 6: Green Brown Brown Purple Brown Brown Purple Brown Brown Green
Row 7: Green Brown Brown Purple Brown Brown Purple Brown Brown Green
Row 8: Green Green Brown Green Brown Brown Green Brown Green Green
Row 9: Green Green Green Pink Pink Pink Pink Green Green Green
Row 10: Pink Brown Pink Green Pink Pink Green Pink Brown Pink
Row 11: Green Green Purple Brown Pink Pink Brown Purple Green Green
Row 12: Green Brown Pink Brown Green Green Brown Pink Brown Green
Here is the input grid for the test example:
Input:
Row 1: Brown Blue Blue Blue Yellow Yellow Brown Brown Blue Gray
Row 2: Yellow Pink Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow
Row 3: Blue Yellow Brown Brown Brown Blue Yellow Yellow Yellow Brown
Row 4: Yellow Gray Yellow Yellow Brown Yellow Gray Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Brown Gray Yellow Yellow Gray Yellow
Row 6: Brown Yellow Yellow Pink Yellow Yellow Gray Brown Gray Gray
Row 7: Yellow Brown Yellow Yellow Yellow Yellow Pink Brown Brown Yellow
Row 8: Yellow Gray Yellow Gray Yellow Yellow Gray Brown Yellow Yellow
Row 9: Blue Yellow Yellow Yellow Yellow Pink Brown Yellow Pink Yellow
Row 10: Yellow Gray Yellow Blue Yellow Brown Brown 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>
| Brown Blue Blue Blue Yellow Yellow Brown Brown Blue Gray Gray Blue Brown Brown Yellow Yellow Blue Blue Blue Brown
Yellow Pink Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Pink Yellow
Blue Yellow Brown Brown Brown Blue Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Blue Brown Brown Brown Yellow Blue
Yellow Gray Yellow Yellow Brown Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Brown Yellow Yellow Gray Yellow
Yellow Yellow Yellow Yellow Brown Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Brown Yellow Yellow Yellow Yellow
Brown Yellow Yellow Pink Yellow Yellow Gray Brown Gray Gray Gray Gray Brown Gray Yellow Yellow Pink Yellow Yellow Brown
Yellow Brown Yellow Yellow Yellow Yellow Pink Brown Brown Yellow Yellow Brown Brown Pink Yellow Yellow Yellow Yellow Brown Yellow
Yellow Gray Yellow Gray Yellow Yellow Gray Brown Yellow Yellow Yellow Yellow Brown Gray Yellow Yellow Gray Yellow Gray Yellow
Blue Yellow Yellow Yellow Yellow Pink Brown Yellow Pink Yellow Yellow Pink Yellow Brown Pink Yellow Yellow Yellow Yellow Blue
Yellow Gray Yellow Blue Yellow Brown Brown Yellow Yellow Blue Blue Yellow Yellow Brown Brown Yellow Blue Yellow Gray Yellow
Yellow Gray Yellow Blue Yellow Brown Brown Yellow Yellow Blue Blue Yellow Yellow Brown Brown Yellow Blue Yellow Gray Yellow
Blue Yellow Yellow Yellow Yellow Pink Brown Yellow Pink Yellow Yellow Pink Yellow Brown Pink Yellow Yellow Yellow Yellow Blue
Yellow Gray Yellow Gray Yellow Yellow Gray Brown Yellow Yellow Yellow Yellow Brown Gray Yellow Yellow Gray Yellow Gray Yellow
Yellow Brown Yellow Yellow Yellow Yellow Pink Brown Brown Yellow Yellow Brown Brown Pink Yellow Yellow Yellow Yellow Brown Yellow
Brown Yellow Yellow Pink Yellow Yellow Gray Brown Gray Gray Gray Gray Brown Gray Yellow Yellow Pink Yellow Yellow Brown
Yellow Yellow Yellow Yellow Brown Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Brown Yellow Yellow Yellow Yellow
Yellow Gray Yellow Yellow Brown Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Brown Yellow Yellow Gray Yellow
Blue Yellow Brown Brown Brown Blue Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Blue Brown Brown Brown Yellow Blue
Yellow Pink Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Pink Yellow
Brown Blue Blue Blue Yellow Yellow Brown Brown Blue Gray Gray Blue Brown Brown Yellow Yellow Blue Blue 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 Blue Orange
Row 2: Black Orange Orange
Row 3: Yellow Pink Gray
Output:
Row 1: Orange Blue Orange Yellow Black Orange
Row 2: Black Orange Orange Pink Orange Blue
Row 3: Yellow Pink Gray Gray Orange Orange
Row 4: Orange Orange Gray Gray Pink Yellow
Row 5: Blue Orange Pink Orange Orange Black
Row 6: Orange Black Yellow Orange Blue Orange
Example 2
Input:
Row 1: Purple Purple Pink Green Purple
Row 2: Purple Purple Purple Blue Purple
Row 3: Purple Red Brown Blue Purple
Row 4: Purple Purple Purple Black Gray
Row 5: Purple Black Green Brown Gray
Output:
Row 1: Purple Purple Pink Green Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Blue Purple Black Purple Red Purple Purple
Row 3: Purple Red Brown Blue Purple Green Purple Brown Purple Pink
Row 4: Purple Purple Purple Black Gray Brown Black Blue Blue Green
Row 5: Purple Black Green Brown Gray Gray Gray Purple Purple Purple
Row 6: Purple Purple Purple Gray Gray Gray Brown Green Black Purple
Row 7: Green Blue Blue Black Brown Gray Black Purple Purple Purple
Row 8: Pink Purple Brown Purple Green Purple Blue Brown Red Purple
Row 9: Purple Purple Red Purple Black Purple Blue Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Green Pink Purple Purple
Example 3
Input:
Row 1: Green Green Brown Red Red
Row 2: Brown Red Brown Brown Brown
Row 3: Brown Red Brown Brown Brown
Row 4: Brown Purple Brown Green Red
Row 5: Red Brown Brown Red Brown
Output:
Row 1: Green Green Brown Red Red Red Brown Brown Brown Green
Row 2: Brown Red Brown Brown Brown Brown Purple Red Red Green
Row 3: Brown Red Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Purple Brown Green Red Red Green Brown Brown Red
Row 5: Red Brown Brown Red Brown Brown Red Brown Brown Red
Row 6: Red Brown Brown Red Brown Brown Red Brown Brown Red
Row 7: Red Brown Brown Green Red Red Green Brown Purple Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Red Brown
Row 9: Green Red Red Purple Brown Brown Brown Brown Red Brown
Row 10: Green Brown Brown Brown Red Red Red Brown Green Green
Here is the input grid for the test example:
Input:
Row 1: Red Gray
Row 2: 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 Gray Red Red
Red Gray Gray Gray
Gray Gray Gray Red
Red Red 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: 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 Green Green Orange Red Red Red Red Red Red Red
Row 4: Red Red Red Blue Blue Purple Blue Red Red Red Red Red Red
Row 5: Red Red Red Orange Pink Black Red Red Red Red Red Red Red
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
Row 8: Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 9: Gray Gray Gray Gray Red Gray Gray Gray Red Red Red Red Red
Row 10: Gray Gray Gray Red Red Gray Gray Gray Gray Red Red Red Red
Row 11: Red Red Red Red Red Gray Gray Gray Red Red Red Red Red
Row 12: 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
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 Green Green Orange Red Red Red Red Red Red Red
Row 4: Red Red Red Blue Blue Purple Blue Red Red Red Red Red Red
Row 5: Red Red Red Orange Pink Black Red Red Red Red Red Red Red
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
Row 8: Green Green Orange Red Red Red Red Red Red Red Red Red Red
Row 9: Blue Blue Purple Blue Red Green Green Orange Red Red Red Red Red
Row 10: Orange Pink Black Red Red Blue Blue Purple Blue Red Red Red Red
Row 11: Red Red Red Red Red Orange Pink Black Red Red Red Red Red
Row 12: 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
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Yellow Green Green Green Green Green Green
Row 3: Yellow Green Green Green Yellow Yellow Green Green Green Green Green
Row 4: Yellow Yellow Green Green Yellow Yellow Yellow Green Green Green Green
Row 5: Yellow Yellow Yellow Green Yellow Green Green Green Green Green Green
Row 6: Yellow Green Green Green Green Green Yellow Green Green Green Green
Row 7: Green Green Green Green Green Green Yellow Yellow Green Green Green
Row 8: Green Green Green Green Green Green Yellow Yellow Yellow Green Green
Row 9: Green Yellow Green Green Green Green Yellow Green Green Green Green
Row 10: Green Yellow Yellow Green Green Green Green Green Green Green Green
Row 11: Green Yellow Yellow Yellow Green Green Green Green Green Green Green
Row 12: Green Yellow Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Yellow Green Green Green Green
Row 14: Green Green Green Green Green Green Yellow Yellow Green Green Green
Row 15: Green Green Yellow Green Green Green Yellow Yellow Yellow Green Green
Row 16: Green Green Yellow Yellow Green Green Yellow Green Green Green Green
Row 17: Green Green Yellow Yellow Yellow Green Green Green Green Green Green
Row 18: Green Green Yellow Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green
Row 20: Gray Green Green Green Green Green Green Green Green Green Green
Row 21: Orange Red Green Green Green Green Green Green Green Green Green
Row 22: Pink Red Pink Green Green Green Green Green Green Green Green
Row 23: Pink Green Green Green Green Green Green Green Green Green Green
Row 24: 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 Gray Green Green Green Green Green Green
Row 3: Gray Green Green Green Orange Red Green Green Green Green Green
Row 4: Orange Red Green Green Pink Red Pink Green Green Green Green
Row 5: Pink Red Pink Green Pink Green Green Green Green Green Green
Row 6: Pink Green Green Green Green Green Gray Green Green Green Green
Row 7: Green Green Green Green Green Green Orange Red Green Green Green
Row 8: Green Green Green Green Green Green Pink Red Pink Green Green
Row 9: Green Gray Green Green Green Green Pink Green Green Green Green
Row 10: Green Orange Red Green Green Green Green Green Green Green Green
Row 11: Green Pink Red Pink Green Green Green Green Green Green Green
Row 12: Green Pink Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Gray Green Green Green Green
Row 14: Green Green Green Green Green Green Orange Red Green Green Green
Row 15: Green Green Gray Green Green Green Pink Red Pink Green Green
Row 16: Green Green Orange Red Green Green Pink Green Green Green Green
Row 17: Green Green Pink Red Pink Green Green Green Green Green Green
Row 18: Green Green Pink Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green
Row 20: Gray Green Green Green Green Green Green Green Green Green Green
Row 21: Orange Red Green Green Green Green Green Green Green Green Green
Row 22: Pink Red Pink Green Green Green Green Green Green Green Green
Row 23: Pink Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Brown Gray Gray Gray Gray Brown Gray Gray Gray Gray Brown Brown Brown Brown Brown
Row 3: Brown Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Brown Brown Brown Brown
Row 4: Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray 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
Row 9: Brown Brown Brown Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray Brown Brown Gray Gray Brown Gray Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray Brown Brown Gray Gray Brown Gray 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 Red Orange Brown Yellow
Row 13: Gray Gray Brown Gray Brown Brown Gray Gray Brown Gray Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray Brown Brown Orange Orange Orange Yellow
Row 14: Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Brown Gray Gray Brown Gray Brown Gray Gray Gray Gray Brown Brown Orange Yellow Brown Red
Row 15: Gray Gray Brown Gray Brown Brown Gray Gray Brown Gray Brown Gray Gray Gray Gray Brown Gray Gray Brown Gray Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray 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
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
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray Brown Brown Gray Gray Brown Gray Brown Brown Brown Brown
Row 20: Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray Brown Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown
Row 21: Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray Brown Gray Gray Brown Gray Brown Brown Gray Gray Brown Gray Brown Brown Brown Brown
Row 22: Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray 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 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 Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Red Orange Brown Yellow Brown Red Orange Brown Yellow Brown Red Orange Brown Yellow Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Yellow Brown Orange Orange Orange Yellow Brown Orange Orange Orange Yellow Brown Brown Brown Brown Brown
Row 3: Brown Brown Red Orange Brown Yellow Brown Orange Yellow Brown Red Brown Orange Yellow Brown Red Brown Orange Yellow Brown Red Brown Brown Brown Brown Brown
Row 4: Brown Brown Orange Orange Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Orange Yellow Brown Red Brown Red Orange Brown Yellow Brown Brown Brown Red Orange Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Yellow Brown Brown Brown Orange Orange Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Orange Yellow Brown Red Brown Brown Brown Orange Yellow Brown Red 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
Row 9: Brown Brown Brown Red Orange Brown Yellow Brown Brown Brown Red Orange Brown Yellow Brown Brown Red Orange Brown Yellow Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Orange Orange Orange Yellow Brown Brown Brown Orange Orange Orange Yellow Brown Brown Orange Orange Orange Yellow Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Orange Yellow Brown Red Brown Brown Brown Orange Yellow Brown Red Brown Brown Orange Yellow Brown Red 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 Red Orange Brown Yellow
Row 13: Red Orange Brown Yellow Brown Brown Red Orange Brown Yellow Brown Brown Brown Brown Brown Brown Red Orange Brown Yellow Brown Brown Orange Orange Orange Yellow
Row 14: Orange Orange Orange Yellow Brown Brown Orange Orange Orange Yellow Brown Red Orange Brown Yellow Brown Orange Orange Orange Yellow Brown Brown Orange Yellow Brown Red
Row 15: Orange Yellow Brown Red Brown Brown Orange Yellow Brown Red Brown Orange Orange Orange Yellow Brown Orange Yellow Brown Red Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Yellow Brown Red 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
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
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Orange Brown Yellow Brown Brown Red Orange Brown Yellow Brown Brown Brown Brown
Row 20: Red Orange Brown Yellow Brown Brown Brown Red Orange Brown Yellow Brown Orange Orange Orange Yellow Brown Brown Orange Orange Orange Yellow Brown Brown Brown Brown
Row 21: Orange Orange Orange Yellow Brown Brown Brown Orange Orange Orange Yellow Brown Orange Yellow Brown Red Brown Brown Orange Yellow Brown Red Brown Brown Brown Brown
Row 22: Orange Yellow Brown Red Brown Brown Brown Orange Yellow Brown Red 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 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 Brown Brown
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
Row 2: Black Black Black Black Black Pink Pink Pink Black Black Pink Pink Pink Black Black Black
Row 3: Pink Pink Pink Black Black Pink Pink Pink Black Black Pink Pink Pink Black Black Black
Row 4: Pink Pink Pink Black Black Pink Black Black Black Black Pink Black Black Black Black Black
Row 5: Pink Black Black Black Black Pink Pink Black Black Black Pink Pink Black Black Black Black
Row 6: Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Pink Pink Pink Black Black Black Black Black
Row 8: Black Black Purple Orange Brown Black Black Black Pink Pink Pink Black Black Black Black Black
Row 9: Black Black Yellow Purple Brown Black Black Black Pink Black Black Black Black Black Black Black
Row 10: Black Black Brown Black Black Black Black Black Pink Pink Black Black Black Black Black Black
Row 11: Black Black Orange 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 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 Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Purple Orange Brown Black Black Purple Orange Brown Black Black Black
Purple Orange Brown Black Black Yellow Purple Brown Black Black Yellow Purple Brown Black Black Black
Yellow Purple Brown Black Black Brown Black Black Black Black Brown Black Black Black Black Black
Brown Black Black Black Black Orange Yellow Black Black Black Orange Yellow Black Black Black Black
Orange Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Purple Orange Brown Black Black Black Black Black
Black Black Purple Orange Brown Black Black Black Yellow Purple Brown Black Black Black Black Black
Black Black Yellow Purple Brown Black Black Black Brown Black Black Black Black Black Black Black
Black Black Brown Black Black Black Black Black Orange Yellow Black Black Black Black Black Black
Black Black Orange 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 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 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: Blue Blue Yellow Green Yellow Brown Red
Row 2: Blue Blue Red Brown Red Blue Blue
Row 3: Yellow Red Yellow Green Blue Red Green
Row 4: Green Brown Green Blue Black Yellow Green
Row 5: Yellow Red Blue Black Black Blue Brown
Row 6: Brown Blue Red Yellow Blue Brown Blue
Row 7: Red Blue Green Green Brown Blue Black
Row 8: Pink Purple Yellow Purple Purple Yellow Red
Row 9: Purple Brown Yellow Red Yellow Red Pink
Row 10: Pink Yellow Red Red Blue Brown Brown
Row 11: Purple Red Red Purple Purple Blue Red
Row 12: Purple Red Blue Purple Purple Pink Brown
Row 13: Yellow Red Brown Brown Pink Purple Yellow
Row 14: Red Pink Brown Brown Pink Yellow Blue
Row 15: Pink Brown Blue Red Brown Brown Orange
Row 16: Brown Orange Red Orange Purple Blue Blue
Row 17: Blue Red Orange Pink Pink Orange Orange
Row 18: Red Orange Pink Blue Red Red Blue
Row 19: Brown Purple Pink Red Red Brown Red
Row 20: Brown Blue Orange Red Brown Orange Purple
Row 21: Orange Blue Orange Blue Red Purple Brown
Output:
Row 1: Pink Purple Yellow Purple Purple Yellow Red
Row 2: Purple Brown Yellow Red Yellow Red Pink
Row 3: Pink Yellow Red Red Blue Brown Brown
Row 4: Purple Red Red Purple Purple Blue Red
Row 5: Purple Red Blue Purple Purple Pink Brown
Row 6: Yellow Red Brown Brown Pink Purple Yellow
Row 7: Red Pink Brown Brown Pink Yellow Blue
Example 2
Input:
Row 1: Purple Black Purple
Row 2: Black Purple Brown
Row 3: Purple Brown Brown
Row 4: Black Pink Black
Row 5: Pink Yellow Black
Row 6: Black Black Blue
Row 7: Black Yellow Yellow
Row 8: Yellow Yellow Yellow
Row 9: Blue Green Green
Row 10: Orange Gray Orange
Row 11: Gray Black Pink
Row 12: Orange Pink Orange
Row 13: Green Pink Orange
Row 14: Pink Green Red
Row 15: Orange Red Orange
Output:
Row 1: Black Yellow Yellow
Row 2: Yellow Yellow Yellow
Row 3: Blue Green Green
Example 3
Input:
Row 1: Yellow Purple Yellow Yellow
Row 2: Purple Purple Yellow Yellow
Row 3: Yellow Yellow Yellow Purple
Row 4: Yellow Yellow Purple Yellow
Row 5: Pink Pink Pink Pink
Row 6: Pink Pink Orange Orange
Row 7: Pink Pink Orange Pink
Row 8: Pink Orange Pink Pink
Row 9: Yellow Blue Yellow Blue
Row 10: Blue Yellow Blue Blue
Row 11: Yellow Blue Yellow Yellow
Row 12: Blue Blue Yellow Blue
Row 13: Blue Blue Orange Orange
Row 14: Blue Orange Blue Orange
Row 15: Orange Blue Orange Orange
Row 16: Orange Orange Orange Blue
Row 17: Gray Orange Orange Orange
Row 18: Orange Gray Gray Gray
Row 19: Orange Gray Gray Gray
Row 20: Orange Gray Gray Orange
Row 21: Black Gray Gray Black
Row 22: Gray Black Black Black
Row 23: Gray Black Gray Black
Row 24: Black Black Black Gray
Output:
Row 1: Pink Pink Pink Pink
Row 2: Pink Pink Orange Orange
Row 3: Pink Pink Orange Pink
Row 4: Pink Orange Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Pink Red Orange Brown Blue
Row 2: Red Yellow Green Blue Orange
Row 3: Orange Green Brown Red Gray
Row 4: Brown Blue Red Orange Brown
Row 5: Blue Orange Gray Brown Pink
Row 6: Pink Blue Blue Pink Black
Row 7: Blue Purple Green Green Pink
Row 8: Blue Green Pink Pink Yellow
Row 9: Pink Green Pink Pink Orange
Row 10: Black Pink Yellow Orange Yellow
Row 11: Gray Red Black Red Purple
Row 12: Red Purple Gray Brown Purple
Row 13: Brown Gray Green Purple Brown
Row 14: Red Brown Purple Gray Red
Row 15: Purple Black Brown Red Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Red Black Red Purple
Red Purple Gray Brown Purple
Brown Gray Green Purple Brown
Red Brown Purple Gray Red
Purple Black Brown Red 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 Blue Blue Blue Black Blue Black
Row 2: Blue Blue Pink Blue Blue Blue Blue Blue Black
Row 3: Blue Pink Blue Blue Blue Pink Blue Blue Blue
Row 4: Blue Blue Black Blue Blue Black Blue Blue Black
Row 5: Blue Black Blue Blue Blue Black Blue Black Blue
Row 6: Blue Blue Blue Blue Blue Blue Black Black Blue
Row 7: Blue Pink Black Black Black Blue Blue Blue Black
Row 8: Blue Blue Black Pink Black Black Pink Black Blue
Row 9: Blue Blue Black Black Black Black Blue Black Pink
Row 10: Blue Black Blue Black Blue Blue Black Blue Pink
Row 11: Blue Black Blue Blue Black Blue Blue Blue Blue
Row 12: Pink Blue Black Blue Pink Blue Black Blue Blue
Row 13: Black Blue Blue Blue Black Blue Blue Blue Pink
Row 14: Blue Black Black Blue Blue Blue Black Blue Blue
Row 15: Pink Blue Blue Pink Black Blue Black Blue Blue
Row 16: Blue Blue Black Pink Blue Black Blue Black Blue
Row 17: Blue Blue Blue Blue Blue Pink Blue Pink Blue
Row 18: Blue Blue Blue Black Blue Blue Blue Blue Blue
Row 19: Blue Black Blue Blue Blue Blue Black Black Pink
Row 20: Blue Black Blue Blue Blue Blue Blue Black Pink
Row 21: Blue Black Blue Blue Black Blue Blue Blue Black
Row 22: Pink Blue Black Black Blue Blue Blue Blue Pink
Row 23: Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Black Blue Black Black Blue Black Blue Blue Blue
Row 25: Black Blue Blue Black Blue Blue Blue Blue Blue
Row 26: Blue Black Black Black Blue Black Pink Blue Black
Output:
Row 1: Pink
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Blue Blue Blue Green Purple Purple Purple Purple Purple Purple
Row 3: Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Blue Purple Blue Purple Purple Blue Green Blue Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Blue Blue Blue Purple Purple Purple Purple Purple Blue Purple
Row 5: Green Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Blue Purple Purple Blue Purple Blue Purple
Row 6: Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 8: Purple Green Purple Purple Purple Purple Green Purple Purple Purple Blue Green Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Green Purple Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple
Row 10: Green Purple Purple Purple Purple Purple Blue Blue Purple Purple Green Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Blue Purple
Row 11: Purple Blue Purple Blue Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Green
Row 12: Purple Purple Purple Purple Green 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 Green Purple Purple Blue Purple Purple Purple Purple Purple Purple Green Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue
Row 14: Purple Purple Purple Purple Purple Blue Purple Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple
Row 15: Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple
Output:
Row 1: Green
Example 3
Input:
Row 1: Green Green Black Green Green Green Green Black Blue Green Black Blue Green Black Green Green Green Blue Green Black Blue Green Green Green Green Blue Black Green
Row 2: Green Black Green Green Black Blue Blue Blue Green Green Green Green Green Green Blue Green Green Green Black Green Green Blue Blue Blue Black Green Green Black
Row 3: Black Black Green Green Black Green Green Green Green Blue Blue Blue Green Green Black Green Blue Green Black Green Green Blue Black Blue Blue Blue Green Green
Row 4: Green Black Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Black Green Green Blue Green Blue Blue Blue Green Green Green Blue
Row 5: Green Blue Black Green Green Blue Black Black Black Green Blue Black Black Green Black Green Green Blue Blue Black Green Green Green Green Green Blue Green Blue
Row 6: Green Black Blue Blue Green Green Green Blue Green Black Blue Black Black Green Green Green Blue Blue Green Black Black Green Green Black Black Green Blue Blue
Row 7: Green Green Black Green Blue Blue Black Black Black Black Green Green Black Black Green Green Green Blue Black Green Blue Black Blue Blue Green Black Blue Green
Output:
Row 1: Black
Here is the input grid for the test example:
Input:
Row 1: Black Blue Blue Black Yellow Black Blue Black
Row 2: Black Blue Blue Black Black Yellow Black Yellow
Row 3: Black Black Black Black Blue Black Black Black
Row 4: Yellow Blue Yellow Black Black Black Yellow Black
Row 5: Blue Blue Yellow Blue Black Black Blue Blue
Row 6: Black Black Yellow Yellow Black Black Blue Black
Row 7: Black Blue Blue Blue Black Black Black Black
Row 8: Yellow Black Black Yellow Yellow Yellow Black Black
Row 9: Blue Yellow Black Yellow Blue Yellow Blue Black
Row 10: Yellow Black Black Yellow Yellow Yellow Black Black
Row 11: Black Black Black Black Yellow Black Black Black
Row 12: Black Black Black Black Black Black Black Yellow
Row 13: Black Black Yellow Black Black Yellow Black Black
Row 14: Black Black Black Black Black Blue Black Black
Row 15: Black Yellow Black Yellow Black Black 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 |
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 Brown Yellow Yellow Yellow Pink Green Purple Pink Pink
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Purple Pink Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Yellow Yellow Purple Green Pink Purple Pink
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Green Yellow Yellow Yellow Yellow Purple Green
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Green Yellow Green Purple Green Purple Pink Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Purple Purple Yellow Yellow Purple Yellow Green Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Pink Purple Pink Pink Pink Green
Output:
Row 1: Pink Yellow Yellow Pink Green Yellow Yellow Green Brown Yellow Yellow Yellow Pink Green Purple Pink Pink
Row 2: Pink Yellow Yellow Purple Purple Pink Green Pink Brown Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 3: Purple Yellow Yellow Pink Yellow Purple Yellow Pink Brown Yellow Yellow Yellow Purple Pink Yellow Yellow Yellow
Row 4: Green Yellow Pink Green Yellow Green Purple Pink Brown Pink Yellow Yellow Purple Green Pink Purple Pink
Row 5: Pink Yellow Purple Purple Yellow Purple Yellow Purple Brown Pink Green Yellow Yellow Yellow Yellow Purple Green
Row 6: Yellow Purple Yellow Yellow Yellow Green Yellow Pink Brown Green Yellow Green Purple Green Purple Pink Yellow
Row 7: Yellow Purple Yellow Yellow Green Yellow Purple Yellow Brown Purple Purple Yellow Yellow Purple Yellow Green Yellow
Row 8: Yellow Purple Yellow Pink Pink Green Purple Yellow Brown Yellow Yellow Pink Purple Pink Pink Pink Green
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange
Row 7: Pink Pink Pink Pink Pink Pink
Row 8: Orange Orange Orange Orange Orange Red
Row 9: Orange Orange Orange Orange Orange Orange
Row 10: Orange Red Orange Orange Orange Orange
Row 11: Orange Brown Orange Orange Orange Brown
Row 12: Orange Orange Orange Orange Orange Orange
Row 13: Green Orange Brown Orange Orange Orange
Row 14: Pink Pink Pink Pink Pink Pink
Row 15: Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange
Row 21: Pink Pink Pink Pink Pink Pink
Row 22: Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange
Output:
Row 1: Red Orange Orange Brown Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Brown
Row 5: Orange Orange Red Brown Orange Orange
Row 6: Orange Orange Orange Orange Orange Green
Row 7: Pink Pink Pink Pink Pink Pink
Row 8: Orange Orange Orange Orange Orange Red
Row 9: Orange Orange Orange Orange Orange Orange
Row 10: Orange Red Orange Orange Orange Orange
Row 11: Orange Brown Orange Orange Orange Brown
Row 12: Orange Orange Orange Orange Orange Orange
Row 13: Green Orange Brown Orange Orange Orange
Row 14: Pink Pink Pink Pink Pink Pink
Row 15: Green Orange Orange Orange Orange Orange
Row 16: Orange Orange Brown Red Orange Orange
Row 17: Brown Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Brown Orange Orange Red
Row 21: Pink Pink Pink Pink Pink Pink
Row 22: Orange Orange Orange Brown Orange Green
Row 23: Orange Orange Orange Orange Orange Orange
Row 24: Brown Orange Orange Orange Brown Orange
Row 25: Orange Orange Orange Orange Red Orange
Row 26: Orange Orange Orange Orange Orange Orange
Row 27: Red Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Purple Pink Pink Pink Pink Pink Pink
Row 21: Pink Purple Pink Pink Pink Pink Pink Pink
Row 22: Gray Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Green Pink Pink Gray Pink
Row 24: Pink Pink Pink Pink Pink Gray Pink Pink
Row 25: Pink Pink Pink Pink Gray Pink Pink Gray
Row 26: Pink Pink Purple Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Purple Pink Pink
Row 2: Gray Pink Pink Gray Pink Pink Pink Pink
Row 3: Pink Pink Gray Pink Pink Pink Pink Pink
Row 4: Pink Gray Pink Pink Green Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Gray
Row 6: Pink Pink Pink Pink Pink Pink Purple Pink
Row 7: Pink Pink Pink Pink Pink Pink Purple Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Pink Pink Pink Pink Pink Gray Pink
Row 11: Pink Pink Pink Pink Gray Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Gray Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Gray Pink
Row 14: Pink Pink Pink Pink Green Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Purple
Row 16: Pink Purple Purple Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Gray Pink Pink Pink Pink
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Purple Pink Pink Pink Pink Pink Pink
Row 21: Pink Purple Pink Pink Pink Pink Pink Pink
Row 22: Gray Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Green Pink Pink Gray Pink
Row 24: Pink Pink Pink Pink Pink Gray Pink Pink
Row 25: Pink Pink Pink Pink Gray Pink Pink Gray
Row 26: Pink Pink Purple Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Gray Pink Yellow Yellow Gray Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Gray Pink Red Red Gray Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Gray Yellow Yellow Red Gray 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 Red Red Gray Pink Yellow Yellow Gray Yellow Pink Pink
Yellow Red Yellow Gray Pink Red Red Gray Yellow Red Yellow
Pink Pink Yellow Gray Yellow Yellow Red Gray Red Red 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: 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
Row 3: 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
Row 5: 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
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: 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: 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
Row 14: Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 15: 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
Row 17: 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
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: 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
Row 2: 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
Row 4: 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
Row 6: 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
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 Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: 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
Row 14: Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Red Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: 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
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Purple 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
Row 6: 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
Row 8: 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
Row 10: Red 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
Row 12: 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
Row 14: 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
Row 16: 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 Gray
Row 18: Gray Gray 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 Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray 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
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray 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 Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: 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
Row 2: 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
Row 4: Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Red Yellow Yellow 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
Row 12: 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
Row 14: 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
Row 16: 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 Gray
Row 18: Gray Gray 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 Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray 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
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray 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 Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
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
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
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 Red 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
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
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple 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
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
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
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
Row 12: Blue Blue 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 13: Blue Blue 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 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 Blue Blue
Row 15: Blue Blue 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 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 Blue Blue
Row 17: Blue Blue 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 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
Row 19: Blue Blue 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 20: Blue Blue 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 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
Row 22: Blue Blue 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 23: Blue Blue 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 24: Blue Blue 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 25: Blue Blue 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
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
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 Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Yellow 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 Yellow 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 Purple 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
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
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
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
Row 12: Blue Blue 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 13: Blue Blue 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 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 Blue Blue
Row 15: Blue Blue 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 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 Blue Blue
Row 17: Blue Blue 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 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
Row 19: Blue Blue 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 20: Blue Blue 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 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
Row 22: Blue Blue 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 23: Blue Blue 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 24: Blue Blue 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 25: Blue Blue Blue Blue Blue 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: 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: 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 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 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 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 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 Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray 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
Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Yellow 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 Yellow 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 Yellow 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 Purple Gray 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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: 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
Row 3: 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
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Gray Black Black Black Black Black
Row 2: Black Black Black Black Black Black
Row 3: Black Black Black Black Orange Black
Row 4: Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black
Row 6: Black Black Black Pink Black Green
Row 7: Black Black Gray Black Black Brown
Row 8: Black Black Black Black Gray Black
Row 9: Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black
Row 11: Black Brown Black Black Black Black
Row 12: Black Black Gray Black Black Black
Output:
Row 1: Gray Black Black Black Black Black Gray Black Black Black Black Black
Row 2: Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple
Row 3: Black Black Black Black Orange Black Black Black Black Black Orange Black
Row 4: Black Black Black Purple Black Purple Black Black Black Purple Black Purple
Row 5: Black Black Purple Black Purple Black Purple Black Purple Black Purple Black
Row 6: Black Purple Black Pink Purple Green Purple Purple Black Pink Purple Green
Row 7: Black Black Gray Purple Purple Brown Purple Black Gray Purple Purple Brown
Row 8: Black Purple Black Purple Gray Black Purple Purple Black Purple Gray Black
Row 9: Black Black Black Purple Black Purple Black Black Black Purple Black Purple
Row 10: Purple Black Purple Black Black Black Purple Black Purple Black Black Black
Row 11: Black Brown Black Purple Black Black Black Brown Black Purple Black Black
Row 12: Purple Purple Gray Black Black Purple Purple Purple Gray Black Black Black
Row 13: Gray Purple Black Purple Black Black Gray Purple Black Purple Black Black
Row 14: Black Purple Black Purple Black Purple Black Purple Black Purple Black Purple
Row 15: Black Black Black Black Orange Black Black Black Black Black Orange Black
Row 16: Black Black Black Purple Black Purple Black Black Black Purple Black Purple
Row 17: Black Black Purple Black Purple Black Purple Black Purple Black Purple Black
Row 18: Black Purple Black Pink Purple Green Purple Purple Black Pink Purple Green
Row 19: Black Black Gray Purple Purple Brown Purple Black Gray Purple Purple Brown
Row 20: Black Purple Black Purple Gray Black Purple Purple Black Purple Gray Black
Row 21: Black Black Black Purple Black Purple Black Black Black Purple Black Purple
Row 22: Purple Black Purple Black Black Black Purple Black Purple Black Black Black
Row 23: Black Brown Black Purple Black Black Black Brown Black Purple Black Black
Row 24: Purple Black Gray Black Black Black Purple Black Gray Black Black Black
Example 3
Input:
Row 1: Black Black Black Black
Row 2: Black Black Black Black
Row 3: Black Black Black Black
Row 4: Black Black Black Black
Row 5: Black Pink Black Black
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: Purple Black Purple Black Purple Black Purple Black
Row 5: Black Pink Black Black Black Pink Black Black
Row 6: Purple Black Purple Black Purple Black Purple Black
Row 7: Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black
Row 9: Purple Black Purple Black Purple Black Purple Black
Row 10: Black Pink Black Black Black Pink Black Black
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown
Row 2: Brown Brown Brown
Row 3: Brown Brown Green
Row 4: Brown Brown Brown
Row 5: 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 Purple Brown Purple Purple Brown
Brown Brown Green Brown Brown Green
Brown Purple Brown Purple Purple Brown
Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown
Brown Purple Brown Purple Purple Brown
Brown Brown Green Brown Brown Green
Brown Purple Brown Purple Purple 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: 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 Brown Green Green Black Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Brown Black Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Yellow Blue 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
Output:
Row 1: Green Green Green Green Brown Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Brown Green Green Black Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Brown Black Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Yellow Blue 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
Example 2
Input:
Row 1: 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
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 Green Green Green Green Green Green
Row 12: 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
Row 14: 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 Gray Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Gray Yellow Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Brown Yellow Green Green
Row 18: Green Green Green Green Green Green Green Green Green Brown Green Green Green Green
Row 19: 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
Row 21: 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
Row 23: 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
Row 25: 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
Row 27: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 28: 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
Row 2: 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
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: Gray Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Gray Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Gray Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Gray Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Gray Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Gray Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Gray Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Gray Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Gray Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Gray Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Gray Yellow Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Brown Yellow Green Green
Row 18: Green Green Green Green Green Green Green Green Green Brown Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Brown Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Brown Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Brown Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Brown Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Brown Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Brown Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Brown Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Brown Green Green Green Green Green Green Green Green Green Green Green Green
Row 27: Brown Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 28: Green Green 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 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 Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Green Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Green 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 Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Green Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Green 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: Blue Blue 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 Purple 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 Orange Purple 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 Black Red 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 Black Blue Blue Red 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
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
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
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
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
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
Row 12: Blue Blue 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 13: Blue Blue 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 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 Blue Blue
Row 15: Blue Blue 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange 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 Black Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Red Blue 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 Red 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 Red 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 Red Blue Blue Blue
Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue
Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue
Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red
Blue Blue Blue Black 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: Green Green Brown Brown Black Green Green Green
Row 2: Green Green Brown Brown Green Green Green Green
Row 3: Green Green Black Green Green Green Green Black
Row 4: Black Black Green Green Green Black Green Green
Row 5: Black Green Green Green Green Green Black Green
Row 6: Green Black Green Green Green Green Green Black
Row 7: Green Black Green Green Black Black Green Green
Row 8: Green Green Black Green Green Green Green Green
Row 9: Green Green Black Green Green Black Black Black
Row 10: Black Black Green Green Green Black Black Green
Row 11: Green Black Green Green Green Green Green Green
Row 12: Black Green Green Green Green Green Black Green
Row 13: Black Green Green Green Green Green Brown Brown
Row 14: Green Green Green Black Black Green Brown Brown
Row 15: Green Green Black Black Green Green Black Green
Row 16: Black Black Black Black Green Green Green Black
Row 17: Black Green Green Black Green Green Black Black
Row 18: Green Green Green Green Green Black Black Green
Row 19: Green Black Green Green Green Green Green Black
Row 20: Black Black Green Green Green Green Green Green
Row 21: Green Green Green Green Green Black Green Black
Row 22: Green Green Green Black Green Green Black Black
Row 23: Green Green Green Green Green Black Black Green
Row 24: Black Green Green Green Black Green Green Green
Row 25: Green Green Green Black Green Green Black Black
Row 26: Green Black Green Green Black Black Green Green
Row 27: Black Green Green Black Green Green Green Black
Row 28: Black Black Black Green Green Green Green Green
Row 29: Green Green Green Green Green Green Black Green
Output:
Row 1: Green
Example 2
Input:
Row 1: Black Yellow Black Yellow Yellow Black Black Black Yellow Black Yellow Black
Row 2: Yellow Black Yellow Yellow Black Yellow Black Yellow Yellow Yellow Black Yellow
Row 3: Yellow Black Yellow Yellow Black Yellow Yellow Black Black Black Yellow Yellow
Row 4: Black Black Yellow Black Black Yellow Black Yellow Black Yellow Black Black
Row 5: Black Yellow Black Black Black Orange Orange Black Yellow Yellow Black Black
Row 6: Black Black Yellow Yellow Yellow Orange Orange Yellow Orange Orange Yellow Yellow
Row 7: Black Black Yellow Yellow Black Yellow Yellow Black Orange Orange Black Black
Row 8: Black Yellow Yellow Yellow Yellow Black Black Yellow Yellow Yellow Black Black
Output:
Row 1: Yellow
Example 3
Input:
Row 1: Blue Black Black Black Black Black Black Black
Row 2: Blue Blue Blue Black Black Blue Black Black
Row 3: Blue Black Black Black Blue Black Black Black
Row 4: Black Black Blue Black Black Black Black Black
Row 5: Blue Black Blue Blue Blue Blue Black Black
Row 6: Blue Blue Black Black Blue Blue Black Black
Row 7: Blue Blue Black Black Black Black Black Blue
Row 8: Black Black Blue Blue Blue Blue Black Black
Row 9: Black Black Black Orange Orange Black Black Black
Row 10: Black Blue Black Orange Orange Blue Black Black
Row 11: Orange Orange Blue Black Black Blue Blue Blue
Row 12: Orange Orange Black Blue Black Black Black Black
Row 13: Black Black Blue Black Black Black Black Black
Row 14: Black Blue Black Blue Black Black Black Blue
Row 15: Blue Blue Blue Black Black Black Black Blue
Row 16: Blue 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 Blue Black Blue Black Blue Black
Row 20: Black Blue Black Black Black Black Black Blue
Row 21: Black Black Black Black Black Black Black Black
Row 22: Black Blue Black Black Black Blue Blue Black
Row 23: Blue Black Black Black Blue Blue Black Black
Row 24: Black Blue Black Blue Black Blue Black Blue
Row 25: Black Blue Blue Blue Blue Black Black Blue
Row 26: Blue Blue Blue Black Black Black Black Blue
Row 27: Blue Black Black Black Blue Black Black Black
Row 28: Blue Black Black Black Black Blue Black Black
Output:
Row 1: Black
Here is the input grid for the test example:
Input:
Row 1: Black Blue Black Blue Black Black Blue Blue Blue Black Black Blue Black Blue Blue Blue Black Blue Black Black Blue Black Black
Row 2: Blue Black Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Black Blue Black Blue Blue Blue Blue Blue Black Black
Row 3: Black Black Blue Blue Blue Blue Blue Black Black Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue Black Blue Black
Row 4: Black Blue Black Blue Blue Blue Black Blue Black Blue Black Black Black Blue Blue Blue Blue Black Black Blue Black Blue Black
Row 5: Blue Blue Blue Blue Black Black Blue Black Blue Black Blue Black Blue Blue Blue Blue Black Blue Blue Blue Black Black Blue
Row 6: Black Black Black Blue Blue Blue Blue Black Black Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue Black Blue
Row 7: Blue Blue Black Black Blue Black Black Black Black Blue Black Black Black Black Black Black Black Black Black Blue Blue Black Black
Row 8: Black Blue Blue Blue Blue Black Black Black Black Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 9: Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Black Blue Blue Black Black Black Blue Blue Black Gray Gray Black Blue
Row 10: Black Blue Blue Black Blue Black Black Black Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue Gray Gray Blue Black
Row 11: Blue Blue Black Blue Black Blue Blue Blue Black Blue Black Blue Blue Blue Blue Black Blue Black Black Blue Black Blue Blue
Row 12: Blue Blue Gray Gray Blue Black Blue Blue Blue Black Black Black Black Black Blue Black Black Black Blue Blue Black Black Black
Row 13: Blue Blue Gray Gray Black Blue Black Blue Blue Blue Blue Black Black Blue Blue Blue Black Black Blue Blue Black Black Black
Row 14: Blue Black Blue Black Blue Blue Blue Black Blue Black Black Blue Blue Black Blue Blue Blue Blue Black Black Blue Blue Black
Row 15: Blue Blue Black Black Black Blue Blue Blue Black Blue Black Blue Black Black Blue Black Blue Black Blue Blue Blue Black Blue
Row 16: Black Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue Black Black Blue Blue
Row 17: Black Blue Blue Blue Blue Blue Blue Black Blue Blue Black Blue Blue Blue Blue Blue Blue Black Blue Black Black Blue Black
Row 18: Blue Blue Blue Black Black Black Blue Blue Black Blue Blue Blue Black Blue Blue Blue Blue Blue Black Black 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 |
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 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 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 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 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 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 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 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 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 Purple 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 Purple Purple 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 Purple Purple Purple Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Purple Purple Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Purple Purple Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Yellow 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 Gray Pink Pink Pink Yellow 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 Gray Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Yellow 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 Orange Orange Orange 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 Pink Pink Pink Pink Pink Pink 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 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 Pink 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Brown Brown Brown Pink
Row 2: Gray Pink Brown Pink Yellow
Row 3: Gray Pink Purple Yellow Yellow
Row 4: Gray Gray Purple Yellow Yellow
Row 5: Gray Gray Purple Pink Yellow
Row 6: Gray Gray Purple Pink Yellow
Row 7: Gray Gray Purple Yellow Yellow
Row 8: Gray Gray Purple Yellow Yellow
Row 9: Gray Purple Orange Purple Yellow
Row 10: Pink Orange Orange Orange Pink
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Black Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Black Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Black Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Black Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Black Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Yellow Yellow Yellow 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
Row 11: 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
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown
Row 19: 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
Row 21: 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
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Red Red Red Brown
Row 2: Black Green Red Green Purple
Row 3: Black Black Green Purple Purple
Row 4: Black Brown Green Brown Purple
Row 5: Black Black Brown Brown Purple
Row 6: Black Brown Green Brown Purple
Row 7: Black Green Brown Brown Purple
Row 8: Brown Yellow Yellow Yellow Brown
Example 3
Input:
Row 1: 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
Row 3: 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 Orange Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Red Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Red Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Red Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Purple Purple
Row 13: 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
Row 15: 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
Output:
Row 1: Purple Black Black Purple
Row 2: Brown Purple Orange Red
Row 3: Brown Purple Red Red
Row 4: Brown Orange Orange Red
Row 5: Purple Pink Pink Purple
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 Blue Blue
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Gray Gray Gray Blue Blue Blue Orange Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Gray Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 13: Blue Gray Blue Gray Blue Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Gray Blue Gray 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 Blue Blue
Row 16: 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 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 Blue Blue Blue
Row 19: Blue Blue Blue 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 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Purple Purple Purple Purple Blue
Orange Blue Purple Purple Gray Yellow
Orange Blue Gray Blue Blue Yellow
Orange Orange Blue Gray Blue Yellow
Orange Gray Blue Black Blue Yellow
Blue Black Black Black Black 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: Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow
Row 6: Green Green Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow
Row 8: Yellow Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Green
Row 9: Yellow Green Green Yellow Yellow Yellow Green Green Yellow Green Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Green Yellow
Row 11: Yellow Yellow Green Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Green Yellow Yellow
Row 15: Yellow Yellow Green Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 17: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow
Row 18: Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green
Row 21: Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Yellow
Row 22: Green Green Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 23: Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Green Blue Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Blue Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow
Row 6: Green Green Yellow Green Green Yellow Yellow Yellow Green Blue Yellow Yellow
Row 7: Yellow Yellow Yellow Green Blue Yellow Yellow Yellow Yellow Yellow Green Blue
Row 8: Yellow Green Blue Yellow Yellow Yellow Green Blue Yellow Yellow Green Green
Row 9: Yellow Green Green Yellow Yellow Yellow Green Green Yellow Green Blue Yellow
Row 10: Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Green Yellow
Row 11: Yellow Blue Green Yellow Green Blue Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Green Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Blue Green Yellow Yellow Green Green Yellow Yellow
Row 15: Yellow Yellow Green Blue Green Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Green Green Yellow Yellow Yellow Green Blue Yellow Yellow Yellow
Row 17: Blue Green Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow
Row 18: Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green
Row 21: Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Green Blue
Row 22: Green Green Yellow Yellow Yellow Blue Green Yellow Yellow Yellow Yellow Yellow
Row 23: Green Blue Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 2: Purple Purple Green Green Green Green Green Green Purple Green Green Green Green Green Green Green Green Green Purple Green
Row 3: Green Purple Green Green Green Green Green Green Purple Purple Green Green Green Green Purple Green Green Green Purple Purple
Row 4: Green Green Green Green Purple Purple Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green
Row 5: Green Green Green Purple Green Purple Green Green Green Green Purple Purple Green Green Green Green Green Green Green Green
Row 6: Green Green Green Purple Purple Green Green Green Green Green Green Purple 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 Purple Green Green
Row 8: Green Green Green Green Green Purple Purple Green Purple Purple Green Green Green Green Green Green Purple Purple Green Green
Row 9: Purple Purple Green Green Green Green Purple Green Purple Green Purple Purple Green Purple Purple Green Green Green Green Green
Row 10: Green Purple Green Green Green Green Green Green Green Green Purple Green Green Purple Green Green Green Purple Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Purple Purple Green
Row 12: Green Green Purple Green Green Green Purple Green Green Green Green Green Green Purple Purple Green Green Green Green Green
Row 13: Green Green Purple Purple Green Purple Purple Green Green Green Purple Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green Green Green Purple Green
Row 15: Green Green Green Green Purple Purple Green Green Purple Green Green Green Green Green Green Green Green Green Purple Purple
Row 16: Green Green Green Green Purple Green Green Green Purple Purple Green Purple Purple Green Green Green Purple Purple Green Green
Row 17: Green Green Purple Purple Green Green Green Green Green Green Green Purple Green Green Green Green Green Purple Green Green
Row 18: Green Green Purple Green Green Purple Green Green Green Green Green Green Purple Green Green Green Green Green Green Green
Row 19: Green Green Green Green Purple Purple Green Green Green Green Green Green Purple Purple 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
Row 21: Purple Purple Green Green Green Purple Purple Green Green Purple Purple Green Green Purple Purple Green Green Green Green Green
Row 22: Purple Green Green Green Green Green Purple Green Green Green Purple Green Green Purple 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
Row 24: Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green Purple Green Green Green
Row 25: Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green Green Purple Purple 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
Row 2: Purple Purple Green Green Green Green Green Green Purple Blue Green Green Green Green Green Green Green Green Purple Blue
Row 3: Blue Purple Green Green Green Green Green Green Purple Purple Green Green Green Green Purple Blue Green Green Purple Purple
Row 4: Green Green Green Green Purple Purple Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green
Row 5: Green Green Green Purple Blue Purple Green Green Green Green Purple Purple Green Green Green Green Green Green Green Green
Row 6: Green Green Green Purple Purple Green Green Green Green Green Blue Purple 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 Blue Purple Green Green
Row 8: Green Green Green Green Green Purple Purple Green Purple Purple Green Green Green Green Green Green Purple Purple Green Green
Row 9: Purple Purple Green Green Green Blue Purple Green Purple Blue Purple Purple Green Purple Purple Green Green Green Green Green
Row 10: Blue Purple Green Green Green Green Green Green Green Green Purple Blue Green Purple Blue Green Green Purple Blue Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Purple Green Green Purple Purple Green
Row 12: Green Green Purple Blue Green Blue Purple Green Green Green Green Green Green Purple Purple Green Green Green Green Green
Row 13: Green Green Purple Purple Green Purple Purple Green Green Green Purple Blue Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green Green Green Purple Blue
Row 15: Green Green Green Green Purple Purple Green Green Purple Blue Green Green Green Green Green Green Green Green Purple Purple
Row 16: Green Green Green Green Purple Blue Green Green Purple Purple Green Purple Purple Green Green Green Purple Purple Green Green
Row 17: Green Green Purple Purple Green Green Green Green Green Green Green Purple Blue Green Green Green Blue Purple Green Green
Row 18: Green Green Purple Blue Blue Purple Green Green Green Green Green Green Purple Blue Green Green Green Green Green Green
Row 19: Green Green Green Green Purple Purple Green Green Green Green Green Green Purple Purple 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
Row 21: Purple Purple Green Green Green Purple Purple Green Green Purple Purple Green Green Purple Purple Green Green Green Green Green
Row 22: Purple Blue Green Green Green Blue Purple Green Green Blue Purple Green Green Purple Blue 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
Row 24: Green Green Green Green Green Green Green Green Blue Purple Green Green Green Green Green Blue Purple Green Green Green
Row 25: Green Green Green Green Green Green Green Green Purple Purple Green Green Green Green Green Purple Purple Green Green Green
Example 3
Input:
Row 1: Red Red Red Yellow Yellow Red Red Yellow Red Red Red Red Red Red Red Yellow Red
Row 2: Red Red Red Yellow Red Red Red Yellow Yellow Red Yellow Red Red Red Yellow Yellow Red
Row 3: Red Yellow Yellow Red Yellow Yellow Red Red Red Red Yellow Yellow Red Red Red Red Red
Row 4: Red Yellow Red Red Yellow Red Red Red Yellow Yellow Red Red Yellow Yellow Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Yellow Red Red Red Yellow Red Red Red
Output:
Row 1: Red Red Red Yellow Yellow Red Red Yellow Blue Red Red Red Red Red Blue Yellow Red
Row 2: Red Red Red Yellow Blue Red Red Yellow Yellow Red Yellow Blue Red Red Yellow Yellow Red
Row 3: Red Yellow Yellow Red Yellow Yellow Red Red Red Red Yellow Yellow Red Red Red Red Red
Row 4: Red Yellow Blue Red Yellow Blue Red Red Yellow Yellow Red Red Yellow Yellow Red Red Red
Row 5: Red Red Red Red Red Red Red Red Blue Yellow Red Red Blue Yellow Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Yellow Orange Orange Yellow Yellow Orange
Row 2: Yellow Orange Orange Yellow Orange Orange Yellow Yellow Orange Orange Yellow Orange Orange Yellow Orange Orange Orange Yellow Yellow Orange Orange Yellow Orange
Row 3: Orange Orange Orange Yellow Yellow Orange Orange Orange Yellow Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Yellow Orange Yellow Yellow Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Yellow Orange Yellow Yellow
Row 5: Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Yellow Orange Yellow Yellow Orange Orange Yellow
Row 6: Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Yellow Orange Orange Orange Yellow Yellow Orange Orange Yellow Orange Orange
Row 7: Orange Yellow Orange Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Yellow Orange Orange Orange Orange Yellow Blue Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Yellow Blue Orange Yellow Yellow Orange
Yellow Blue Orange Yellow Blue Orange Yellow Yellow Orange Orange Yellow Blue Orange Yellow Blue Orange Orange Yellow Yellow Orange Blue Yellow Orange
Orange Orange Orange Yellow Yellow Orange Orange Blue Yellow Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Yellow Blue Yellow Yellow Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Blue Yellow Orange Yellow Yellow
Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Yellow Blue Yellow Blue Orange Yellow Blue Yellow Yellow Orange Blue Yellow
Orange Yellow Yellow Orange Orange Orange Orange Orange Blue Yellow Orange Yellow Yellow Orange Orange Orange Yellow Yellow Orange Orange Yellow Blue Orange
Orange Yellow Blue Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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 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
Row 3: 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
Row 5: 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
Row 7: 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
Row 9: 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
Row 11: 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
Row 13: Gray Red 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
Row 15: 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
Row 17: 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 Purple 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 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
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: 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
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: 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
Row 10: 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
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Red Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Purple 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 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
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
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 Red 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 Purple
Row 13: Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green
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
Row 20: Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green
Row 24: 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 Red Yellow Yellow Yellow
Row 9: Green Green Green Green Green Green Yellow
Row 10: Green Green Green Green Green Green Yellow
Row 11: Green Green Green Green Green Green Yellow
Row 12: Green Green Green Green Green Green Purple
Row 13: Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green
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
Row 20: Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Red 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
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Purple 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
Output:
Row 1: Red Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Purple 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
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
Row 2: 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
Row 4: 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
Row 6: Blue Blue Blue Blue Blue Blue Red 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 Purple 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
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 27: 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 Yellow Yellow Red Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue 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
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue 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: Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray
Row 2: Yellow Yellow Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Purple Purple Gray Gray
Row 3: Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Purple 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 Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray
Row 6: Gray Green Green Green Gray Gray Gray Green Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Yellow Gray Gray Gray Gray
Row 7: Gray Green Green Green Gray Gray Gray Yellow Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Yellow Gray Gray Gray Gray
Row 8: Gray Green Green Green Gray Gray Gray Yellow Green Green Gray Gray Gray Green Green Green Green Green Green Green Green Yellow Gray Gray Gray Gray
Row 9: Gray Green Pink Green Gray Gray Gray Yellow Green Green Gray Gray Gray Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray
Row 10: Gray Pink Pink Pink Gray Gray Gray Yellow Yellow Green 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 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
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 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 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
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 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 Gray 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 20: Gray Yellow Yellow Green Gray Gray Gray Gray Gray Orange Orange Orange Gray Gray Green Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray
Row 21: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Orange Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 22: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 23: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 24: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 25: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 26: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 27: Gray Yellow Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Purple Gray Gray Gray
Row 28: Gray Green Green Green Gray Gray Gray Gray Gray Green Green Green Gray Gray Green Green Green Green Green Green Green Green Green Gray Gray Gray
Output:
Row 1: Yellow Yellow Green Orange Orange Orange Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Yellow Green Green Green Orange Green Green Green Green Green Green Green Green Green Purple
Row 3: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 4: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 5: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 6: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 7: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 8: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 11: Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Purple Purple
Row 12: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow
Row 15: Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow
Row 16: Yellow Green Green Green Pink Green Green Green Green Green Green Green Green Green Yellow
Row 17: Yellow Yellow Green Pink Pink Pink Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Brown Brown Green Green Green Brown Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Green Brown Brown
Row 2: Brown Brown Pink Green Green Brown Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Purple Brown Brown
Row 3: Brown Brown Pink Green Green Brown Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Purple Brown Brown
Row 4: Brown Brown Pink Green Green Brown Green Black Green Green Brown Green Green Green Green Green Green Green Green Green Green Purple Brown Brown
Row 5: Brown Brown Pink Pink Green Brown Black Black Black Black Brown Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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 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
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
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
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
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
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
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
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 Purple Purple Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Purple Green Green Brown Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Green Green Green Brown Brown Brown Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Pink Brown Brown
Row 25: Black Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink Brown Brown
Row 26: Black Black Green Brown Brown Brown Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Pink Brown Brown
Row 27: Black Green Green Brown Brown Brown Green Green Green Green Brown Brown Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 28: Brown Brown Brown Brown Brown Brown Green Green Green Green Brown Brown Green Green Green Green Green Green Green Green Green Green Purple Brown
Row 29: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Brown
Output:
Row 1: Purple Purple Green Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Green Green Green Purple 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
Row 4: Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 5: Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink
Row 6: Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 9: Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 10: Pink Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 11: Pink Pink Green Black Black Black Black Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Pink 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 Purple Pink Pink Pink Purple Purple Purple Black Black Black Black Black
Row 3: Black Black Yellow Yellow Yellow Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 4: Black Black Pink Yellow Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 5: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 6: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 7: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 8: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 9: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 10: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Purple Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 11: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Purple Black Black Black Black Black
Row 12: Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Black Black Black Black Black
Row 13: Black Black Pink Pink Pink 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 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
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 Pink Pink Pink Black Black Black Black Black Black Black Black Black Pink Pink Pink Brown Black Black Black Black Black
Row 20: Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Orange Pink Pink Pink Pink Pink Brown Black Black Black Black Black
Row 21: Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Orange Pink Pink Pink Pink Brown Brown Black Black Black Black Black
Row 22: Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Orange Orange Pink Pink Pink Pink Brown Black Black Black Black Black
Row 23: Black Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Orange Pink Pink Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Pink Yellow Pink Black Black Black Black Black Black Black Black Pink Pink Pink Pink Black Black Black Black Black Black
Row 25: Black Black Black Black Black Yellow Yellow Yellow Black Black Black Black Black Pink Pink Pink Pink Pink Pink Yellow Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Pink Pink Pink Yellow Yellow Yellow Black Black Black Black Black Black
Row 27: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Pink Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Purple Purple Pink Yellow Yellow Yellow Pink Purple Purple Purple
Row 2: Purple Pink Pink Pink Yellow Pink Pink Pink Pink Purple
Row 3: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 4: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 5: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 6: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 7: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 8: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 9: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 10: Purple Pink Pink Pink Pink Pink Pink Pink Pink Purple
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Orange Pink Pink Pink Pink Pink Pink Pink Pink Brown
Row 13: Orange Pink Pink Pink Pink Pink Pink Pink Pink Brown
Row 14: Orange Orange Pink Pink Pink Pink Pink Pink Brown Brown
Row 15: Orange Pink Pink Pink Pink Pink Pink Pink Pink Brown
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Gray Pink Pink Pink Yellow Pink Pink Pink Pink Yellow
Row 18: Gray Gray Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow
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 Gray Gray Gray Gray Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Red Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Yellow
Row 3: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Gray Red Red Red Yellow
Row 4: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Red Yellow
Row 5: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Red Yellow
Row 6: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Red Yellow
Row 7: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Red Yellow
Row 8: Red Red Red Gray 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 Yellow
Row 9: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Gray Gray 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
Row 14: Red Red Red Gray 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 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 Yellow 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 Yellow 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 Yellow Yellow Yellow
Row 18: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Red Red Red Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Red Red Red Red Gray Red Red Red
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 Gray Gray Gray Gray Gray Gray Gray
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 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 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 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 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 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 Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Red Gray Gray Gray
Gray Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Gray
Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray
Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray
Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray
Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray
Gray 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
Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray
Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray
Gray Gray Red Red Red Red 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 Gray
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 Brown
Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown
Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown
Brown Red Red Red Red Red Red Red Gray Red Red Red Red Red Red Brown
Brown Brown Brown Brown Red Gray Gray Gray Gray Gray Gray Gray Red 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Orange Orange 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 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
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Output:
Row 1: 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
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Orange Brown Orange Orange Brown Orange Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown
Row 6: 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
Row 8: 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
Row 10: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Example 2
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 Brown Brown Brown Green Green Green Green
Row 4: Green Green Green Green Brown 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: Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Red Green Green Green Green
Row 12: Green Green Green Green Red Red Red Green Green Green Green
Row 13: Green Green Green Green Green Red 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 Brown Brown Brown Brown Brown Brown Green
Row 4: Green Green Green Green Brown Green Green Green Green Brown 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: Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Red Green Green Green Green
Row 12: Green Green Green Green Red Red Red Green Green Green Green
Row 13: Green Green Green Green Green Red Green Green Green Green Green
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue 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 Yellow Blue Blue Red Blue Blue Red Blue
Row 6: Yellow Yellow Blue Blue Blue Red Red Blue Blue
Row 7: Blue Yellow Yellow Blue Blue Blue Blue Red 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
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue 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 Yellow Blue Blue Red Blue Blue Red Blue
Row 6: Yellow Yellow Blue Blue Blue Red Red Blue Blue
Row 7: Blue Yellow Yellow Blue Blue Blue Blue Red Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Red Blue
Row 9: Blue Blue Blue Blue Blue Red Red Blue Blue
Row 10: Blue Blue Blue Blue Red Blue Blue Red Blue
Row 11: Blue 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 Pink Pink Pink Pink Pink Pink Pink
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: 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
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Gray Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Pink
Row 12: Gray Gray Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Row 13: Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Yellow 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
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink 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 Pink Pink Pink Pink Pink Pink Yellow Yellow Pink
Gray Gray Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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 Red Yellow
Row 2: Pink Red Pink
Row 3: Brown Pink Gray
Row 4: Brown Gray Yellow
Row 5: Pink Brown Pink
Row 6: Red Gray Gray
Row 7: Red Gray Red
Row 8: Gray Black Gray
Row 9: Brown Brown Pink
Row 10: Pink Red Gray
Row 11: Pink Yellow Gray
Row 12: Red Brown Brown
Row 13: Red Red Pink
Row 14: Brown Red Brown
Row 15: Yellow Brown Brown
Output:
Row 1: Brown Red Yellow
Row 2: Pink Red Pink
Row 3: Brown Pink Gray
Row 4: Brown Gray Yellow
Row 5: Pink Brown Pink
Row 6: Red Gray Gray
Row 7: Black Gray Black
Row 8: Gray Black Gray
Row 9: Black Brown Black
Row 10: Pink Red Gray
Row 11: Pink Yellow Gray
Row 12: Red Brown Brown
Row 13: Red Red Pink
Row 14: Brown Red Brown
Row 15: Yellow Brown Brown
Example 2
Input:
Row 1: Blue Pink Blue
Row 2: Blue Yellow Blue
Row 3: Blue Pink Pink
Output:
Row 1: Yellow Pink Yellow
Row 2: Blue Yellow Blue
Row 3: Yellow Pink Yellow
Example 3
Input:
Row 1: Orange Gray Brown Green Brown Gray Gray Gray Gray
Row 2: Green Brown Blue Black Blue Blue Black Green Brown
Row 3: Purple Purple Gray Orange Black Brown Blue Green Orange
Row 4: Purple Black Black Pink Purple Black Brown Pink Orange
Row 5: Brown Black Blue Purple Red Black Purple Gray Green
Row 6: Orange Orange Black Blue Blue Orange Black Blue Blue
Row 7: Purple Pink Blue Green Black Black Blue Green Brown
Row 8: Orange Orange Black Purple Pink Blue Black Black Purple
Row 9: Black Blue Brown Black Brown Black Pink Green Black
Output:
Row 1: Red Gray Brown Green Brown Gray Gray Gray Red
Row 2: Green Red Blue Black Blue Blue Black Red Brown
Row 3: Purple Purple Red Orange Black Brown Red Green Orange
Row 4: Purple Black Black Red Purple Red Brown Pink Orange
Row 5: Brown Black Blue Purple Red Black Purple Gray Green
Row 6: Orange Orange Black Red Blue Red Black Blue Blue
Row 7: Purple Pink Red Green Black Black Red Green Brown
Row 8: Orange Red Black Purple Pink Blue Black Red Purple
Row 9: Red Blue Brown Black Brown Black Pink Green 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
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: 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
Row 10: 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
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow 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
Row 14: 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
Row 16: 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
Row 18: Pink Pink Pink 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 Pink Pink Pink
Row 20: Pink Pink 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
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 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
Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink
Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink
Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink
Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink
Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink
Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink
Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow
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: Green Green Black Green
Row 2: Green Green Green Green
Row 3: Green Green Green Green
Row 4: Green Green Green Black
Output:
Row 1: Green Green Black Green Green Green Black Green Black Black Black Black Green Green Black Green
Row 2: Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Black Black Black Black Green Green Green Green
Row 4: Green Green Green Black Green Green Green Black Black Black Black Black Green Green Green Black
Row 5: Green Green Black Green Green Green Black Green Green Green Black Green Green Green Black Green
Row 6: 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
Row 8: Green Green Green Black Green Green Green Black Green Green Green Black Green Green Green Black
Row 9: Green Green Black Green Green Green Black Green Green Green Black Green Green Green Black Green
Row 10: 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
Row 12: Green Green Green Black Green Green Green Black Green Green Green Black Green Green Green Black
Row 13: Green Green Black Green Green Green Black Green Green Green Black Green Black Black Black Black
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black
Row 16: Green Green Green Black Green Green Green Black Green Green Green Black Black Black Black Black
Example 2
Input:
Row 1: Black Blue Blue
Row 2: Blue Blue Blue
Row 3: Blue Black Blue
Output:
Row 1: Black Black Black Black Blue Blue Black Blue Blue
Row 2: Black Black Black Blue Blue Blue Blue Blue Blue
Row 3: Black Black Black Blue Black Blue Blue Black Blue
Row 4: Black Blue Blue Black Blue Blue Black Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Black Blue Blue Black Blue Blue Black Blue
Row 7: Black Blue Blue Black Black Black Black Blue Blue
Row 8: Blue Blue Blue Black Black Black Blue Blue Blue
Row 9: Blue Black Blue Black Black Black Blue Black Blue
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Black Purple
Row 3: Purple Black 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 Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple
Row 3: Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Black Black Black Black Black Purple Purple Purple Black Purple
Row 6: Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Black Black Black Black Black Purple Black Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Black Purple Black Black Black Black Black Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple
Row 9: Purple Black Purple Purple Purple Black Black Black Black Black Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Black Purple Black
Row 2: 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 Black Black Black Purple 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: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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 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
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
Row 12: 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 13: 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 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: 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 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 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 Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Orange Orange Orange 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
Row 6: 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
Example 2
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
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
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
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
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
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
Row 7: Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Red Red Red
Row 8: Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray 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
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
Output:
Row 1: Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Red Red Red Red Red
Row 2: Red Red Red Red Red
Row 3: Orange Orange Red Red Red
Row 4: Brown Brown Red Red Red
Row 5: Brown Brown Red Red Red
Row 6: Brown Brown Red Red Red
Row 7: Red Red Red Red Red
Row 8: Red Red Red Red Red
Row 9: Red Red Red Red Red
Row 10: Red Red Red Red Red
Row 11: Red Red Red Red Red
Row 12: Red Red Red Red Red
Row 13: Red Red Red Red Red
Row 14: Red Red Red Red Red
Row 15: Red Red Red Red Red
Row 16: Red Red Red Red Red
Row 17: Red Red Red Red Red
Row 18: Red Red Red Red Red
Row 19: Red Red Red Red Red
Row 20: Red Red Red Red Red
Row 21: Red Red Red Red Red
Row 22: Red Red Red Red Red
Row 23: Red Red Red Red Red
Output:
Row 1: Orange Orange
Row 2: Brown Brown
Row 3: Brown Brown
Row 4: Brown Brown
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 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
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 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
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
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
Row 8: Blue Blue Black Black Black Black Black Black Black Black Purple Black Purple Black Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Black Black Black Black Black Black Black Black Purple Black Black Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black 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 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 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 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 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 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 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 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 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 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 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 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>
| Purple Black Purple Black Purple Black Black Black Black Black Black Black Black
Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Black
Purple Purple Black Black Purple Black Black Black Black Black Black Black Black
Purple 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: Black Black Black Black Orange Blue Orange Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Blue Orange Orange Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Blue Orange Pink Orange Blue Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Orange Orange Blue Orange Blue Blue Blue Pink Blue Blue Blue Orange Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Blue Orange Orange Orange Pink Orange Orange Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black Blue Pink Blue Orange Blue Blue Orange Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black Blue Pink Blue Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Orange Orange Blue Orange Blue Blue Blue Blue
Row 2: Black Black Black Black Black Black Black Black Black Blue Orange
Row 3: Black Black Black Black Orange Orange Blue Orange Blue Blue Blue
Row 4: Black Black Black Black Black Black Black Blue Orange Orange Orange
Row 5: Black Black Black Black Black Black Orange Blue Blue Orange Blue
Row 6: Black Black Black Black Black Black Black Black Black Black Blue
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Yellow Yellow Yellow Red Yellow Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Yellow Yellow Red Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Yellow Yellow Yellow Red Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 10: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 11: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 12: Blue Blue Blue Blue Blue Yellow Yellow Yellow Red Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Yellow Yellow Red Yellow Yellow Yellow Yellow Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Yellow Yellow Red Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Yellow Red Yellow Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Yellow Yellow Yellow
Row 3: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Yellow Yellow
Row 8: Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 9: Blue Blue Blue Blue Blue Yellow Yellow Yellow
Row 10: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Blue Blue Blue Blue Blue Yellow Yellow Yellow
Row 13: Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 16: Blue Blue Blue Blue Blue Blue Yellow Yellow
Row 17: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 18: Blue Blue Blue Blue Blue Blue Blue Yellow
Row 19: Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Brown Pink Brown Gray Brown Pink Brown Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Red Purple Gray Purple Red Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Green Pink Orange Green Gray Green Orange Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Orange Purple Purple Gray Purple Purple Orange Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Brown Green Gray Green Brown Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Orange Pink Green Purple Gray Purple Green Pink Orange Green Brown Blue Blue
Row 7: Blue Blue Blue Red Pink Green Purple Orange Gray Orange Purple Green Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Pink Green Green Gray Green Green Pink Brown Brown Purple Blue Blue
Row 9: Blue Blue Blue Blue Brown Green Pink Brown Gray Brown Pink Green Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Brown Gray Brown Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Green Gray Green Brown Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Orange Red Pink Brown Pink Gray Pink Brown Pink Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Brown Brown Red Pink Red Gray Red Pink Red Brown Brown Orange Blue Blue
Row 14: Blue Blue Blue Blue Blue Pink Red Brown Gray Brown Red Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Pink Red Green Gray Green Red Pink Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Green Gray Green Green Orange Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Orange Brown Gray Brown Orange Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Green Green Brown Pink Gray Pink Brown Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Brown Red Red Purple Green Red Gray Red Green Purple Red Red Brown Blue Blue
Row 20: Blue Blue Blue Red Green Pink Orange Brown Gray Brown Orange Pink Green Red Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Purple Red Gray Red Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Green Red Gray Red Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Purple Purple Red Gray Red Purple Purple Brown Green Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Brown Pink Brown
Row 2: Blue Blue Blue Blue Blue Blue Red Purple
Row 3: Blue Blue Blue Blue Green Pink Orange Green
Row 4: Blue Blue Blue Blue Blue Orange Purple Purple
Row 5: Blue Blue Blue Blue Blue Blue Brown Green
Row 6: Blue Blue Brown Green Orange Pink Green Purple
Row 7: Blue Blue Blue Red Pink Green Purple Orange
Row 8: Blue Blue Purple Brown Brown Pink Green Green
Row 9: Blue Blue Blue Blue Brown Green Pink Brown
Row 10: Blue Blue Blue Blue Blue Blue Blue Brown
Row 11: Blue Blue Blue Blue Blue Blue Brown Green
Row 12: Blue Blue Blue Orange Red Pink Brown Pink
Row 13: Blue Blue Orange Brown Brown Red Pink Red
Row 14: Blue Blue Blue Blue Blue Pink Red Brown
Row 15: Blue Blue Blue Blue Blue Pink Red Green
Row 16: Blue Blue Blue Blue Blue Orange Green Green
Row 17: Blue Blue Blue Blue Blue Blue Orange Brown
Row 18: Blue Blue Blue Blue Green Green Brown Pink
Row 19: Blue Blue Brown Red Red Purple Green Red
Row 20: Blue Blue Blue Red Green Pink Orange Brown
Row 21: Blue Blue Blue Blue Blue Blue Purple Red
Row 22: Blue Blue Blue Blue Blue Blue Green Red
Row 23: Blue Blue Blue Green Brown Purple Purple Red
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Black Gray Black Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Orange Yellow Black Gray Black Yellow Orange Yellow Red Red Red Red
Row 3: Red Red Blue Blue Purple Purple Brown Pink Gray Pink Brown Purple Red Red Red Red Red
Row 4: Red Red Red Red Red Purple Blue Yellow Gray Yellow Blue Purple Green Brown Red Red Red
Row 5: Red Red Red Red Red Pink Orange Yellow Gray Yellow Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Blue Purple Blue Gray Blue Purple Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Purple Black Gray Black Purple Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Yellow Gray Yellow Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Purple Gray Purple Brown Pink Blue Red Red Red Red
Row 10: Red Red Red Yellow Green Black Yellow Black Gray Black Yellow Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Blue Gray Blue Brown Red Red Red Red Red Red
Row 12: Red Orange Black Green Yellow Brown Pink Brown Gray Brown Pink Red Red Red Red Red Red
Row 13: Red Red Red Red Green Orange Black Pink Gray Pink Black Orange Green Black Blue 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 Black
Red Red Red Red Yellow Orange Yellow Black
Red Red Blue Blue Purple Purple Brown Pink
Red Red Red Brown Green Purple Blue Yellow
Red Red Red Red Red Pink Orange Yellow
Red Red Red Red Red Blue Purple Blue
Red Red Red Red Red Red Purple Black
Red Red Red Red Red Red Red Yellow
Red Red Red Red Blue Pink Brown Purple
Red Red Red Yellow Green Black Yellow Black
Red Red Red Red Red Red Brown Blue
Red Orange Black Green Yellow Brown Pink Brown
Red Red Blue Black Green Orange Black 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: Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Orange Orange Pink Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange
Row 2: Pink Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Orange Pink
Row 3: Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange Pink
Row 4: Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange
Row 5: Orange Orange Orange Orange Pink Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Orange Pink Pink Orange Orange Orange Orange Pink Orange Orange Pink Orange
Row 6: Pink Orange Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Orange Pink Orange Orange Orange Pink Pink Orange Orange Orange Pink Pink Orange Orange Orange Pink Orange Orange
Row 7: Pink Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Pink Orange Orange Orange
Row 8: Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Orange Pink Orange Orange Pink Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Pink Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange
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 Brown Brown Brown Brown Brown Brown
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Orange Red Red Orange Red Red Red Red
Row 12: Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Orange Red Red Red Red Orange Orange Red Red Red Red Red
Row 14: Orange Red Red Red Red Red Red Red Red Red Red Orange Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red
Row 15: Red Red Red Orange Red Red Red Red Red Red Red Orange Red Orange Red Red Red Red Red Red Red Orange Red Orange Red Red Orange Red Red Red
Row 16: Red Orange Red Red Orange Red Red Red Red Red Red Orange Orange Red Red Orange Red Red Red Red Red Red Red Red Red Orange Orange Red Red Red
Row 17: Orange Red Red Red Red Orange Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Orange Red Red Red Orange Red Red Orange Orange Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red
Row 19: Red Orange Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Red
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 Green Orange Orange Green Orange Orange Orange Orange
Row 2: 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 Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange
Row 4: Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange Green Orange Orange Orange
Row 6: Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Green Orange Orange 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
Example 2
Input:
Row 1: Pink Pink Purple Pink Pink Purple Purple Pink Pink Pink Purple Purple Pink Pink Pink Purple Purple
Row 2: Purple Purple Purple Pink Pink Pink Purple Pink Purple Purple Pink Purple Purple Pink Purple Pink Pink
Row 3: Purple Pink Pink Purple Purple Pink Pink Pink Purple Purple Purple Pink Purple Purple Purple Purple Pink
Row 4: Pink Purple Purple Pink Pink Pink Pink Pink Purple Pink Purple Pink Purple Pink Pink Pink Pink
Row 5: Purple Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Pink Purple Purple Pink Pink
Row 6: Pink Purple Purple Pink Pink Purple Purple Pink Purple Purple Pink Purple Pink Pink Pink Purple Pink
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Black Purple Purple Black Black Black Black Black Black Black Purple Purple Purple Black Black Black Black
Row 9: Black Purple Black Black Purple Purple Purple Black Black Purple Black Black Black Black Purple Black Black
Row 10: Black Black Black Black Black Black Purple Black Purple Black Purple Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Purple Purple Black Black Black Black Purple Black Black
Row 12: Black Black Black Black Purple Black Black Black Black Black Purple Black Black Black Purple Purple Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black
Output:
Row 1: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Green Green Purple Purple Purple Purple Purple
Row 2: Purple Green Purple Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple Green Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Green Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Brown Brown Black Brown Brown Brown Brown Brown Black Brown Black Brown Brown Brown Brown Black Brown Black Brown Brown Black Brown Black Brown Black Brown Black Black Brown
Row 2: Brown Brown Black Brown Brown Black Brown Black Brown Brown Brown Brown Brown Brown Black Brown Black Black Black Black Black Brown Black Brown Black Brown Brown Black Black
Row 3: Black Brown Brown Black Brown Brown Brown Black Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown Brown Black Black Black Brown Black Brown Black Brown Brown
Row 4: Black Brown Brown Brown Brown Brown Black Black Black Brown Brown Brown Brown Black Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Black Brown Brown Black Brown
Row 5: Brown Brown Brown Black Brown Black Brown Black Brown Brown Brown Black Brown Black Brown Brown Brown Brown Black Brown Brown Brown Brown Black Black Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Black Brown Black Brown Brown Brown Brown Brown Brown Brown Black Brown Black Brown Black Brown
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 Pink Pink Pink
Row 8: Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Brown Brown Gray Gray Brown Gray Brown
Row 9: Brown Gray Gray Brown Gray Gray Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Brown Gray Brown Gray Gray Brown Brown Brown Brown Brown
Row 10: Gray Brown Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray Brown Gray Gray Brown Brown Brown Gray Gray Gray Brown Gray
Row 11: Gray Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Gray
Row 12: Brown Brown Brown Gray Brown Gray Brown Brown Gray Gray Brown Gray Brown Gray Brown Brown Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Brown Brown Brown
Row 13: Gray Brown Gray Gray Brown Gray Brown Brown Gray Brown Brown Gray Brown Gray Gray Brown Brown Brown Brown Brown Gray Brown Gray Gray Gray Brown Gray Gray Gray
Output:
Row 1: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Green Green Brown Green Brown Brown Brown Brown Green Brown Green Brown Brown Brown Brown Green
Row 2: Green Brown Brown Green Brown Brown Green Brown Green Green Green Brown Green Green Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Green Green Brown Brown
Row 3: Brown Green Green Brown Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Green Brown Brown Brown Brown Green Brown Brown Brown Green Brown
Row 4: Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Green Green Brown Brown
Row 5: Green Green Green Brown Green Brown Green Brown Brown Brown Green Brown Green Brown Green Green Brown Brown Brown Brown Brown Brown Green Brown Brown Green Green Green Green
Row 6: Brown Green Brown Brown Green Brown Green Green Brown Brown Green Brown Green Brown Brown Brown Green Green Green Green Brown Green Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Red Gray Gray Brown Red Orange Orange Orange Orange Orange Orange Orange Red
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Red Orange Orange Orange Red Red Orange Red Orange
Row 3: Gray Gray Gray Red Gray Gray Gray Gray Gray Brown Red Orange Orange Orange Orange Orange Red Orange Orange
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 5: Gray Gray Gray Gray Gray Gray Gray Red Gray Brown Orange Orange Red Orange Orange Red Orange Red Orange
Row 6: Gray Gray Gray Gray Gray Red Gray Gray Gray Brown Orange Orange Red Orange Orange Orange Red Orange Orange
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Red Orange Red Orange Orange Orange Orange Orange
Row 9: Gray Gray Gray Gray Gray Red Red Gray Gray Brown Red Orange Red Orange Orange Orange Orange Orange Orange
Row 10: Gray Red Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Red Orange Orange Orange Orange Orange Red
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Red Orange Orange Red Red Orange Orange Orange Red
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Red Red Orange Orange Orange Orange Orange
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Gray Gray Gray Gray Gray Gray Red Gray Gray Brown Orange Orange Orange Orange Red Orange Orange Orange Orange
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Orange Orange Red Orange Red Orange Orange
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Red Red Orange Orange Red Orange Orange Orange Red
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Orange Orange Red Orange Red Orange Orange
Row 18: Gray Gray Gray Gray Gray Red Gray Gray Gray Brown Orange Orange Orange Red Orange Orange Orange Red Orange
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Orange Orange Orange Red Orange Orange Red
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Red Orange Red Orange Red Red Orange Orange Red
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Red Red Orange Orange Orange Orange Orange Red
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Orange Orange Red Red Orange Red Orange Orange Red
Row 23: Gray Red Gray Gray Gray Gray Gray Gray Gray Brown Red Orange Orange Orange Orange Orange Orange Red 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 Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red 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
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red
Red Red Red 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: Brown Brown Brown Blue Brown Brown
Row 2: Blue Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Red Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Blue
Row 6: Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Blue Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Green Brown Brown
Row 12: Brown Brown Red Brown Brown Blue
Row 13: Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Green Brown Brown
Row 16: Brown Brown Green Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Green
Row 22: Brown Brown Green Brown Brown Brown
Row 23: Blue Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue
Row 3: Brown Brown Red Red Brown Brown
Row 4: Brown Brown Red Red Brown Brown
Row 5: Blue Blue Blue Blue Blue Blue
Row 6: Brown Brown Red Red Brown Brown
Row 7: Blue Blue Blue Blue Blue Blue
Row 8: Brown Brown Red Red Brown Brown
Row 9: Brown Brown Red Red Brown Brown
Row 10: Brown Brown Red Red Brown Brown
Row 11: Green Green Green Green Green Green
Row 12: Blue Blue Blue Blue Blue Blue
Row 13: Brown Brown Red Red Brown Brown
Row 14: Brown Brown Red Red Brown Brown
Row 15: Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green
Row 17: Brown Brown Red Red Brown Brown
Row 18: Brown Brown Red Red Brown Brown
Row 19: Brown Brown Red Red Brown Brown
Row 20: Brown Brown Red Red Brown Brown
Row 21: Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green
Row 23: Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Black Black Black Red Black Black Black Black Black Black Black Blue Black Black Black Black
Row 2: Black Black Green Black Black Black Black Black Black Black Red Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Blue Black Red Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Blue Black Black Black
Row 5: Black Black Black Black Red 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
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red
Row 8: Black Black Black Black Black Black Red Black Black Black Black Blue Black Black Red Black
Row 9: Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Black Black
Row 11: Black Red Black Black Black Black Black Black Black Red 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 Red Blue Black Black
Row 14: Black Black Blue Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 15: Red Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
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: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Row 6: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Row 7: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Row 12: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Row 13: 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
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Red Red Black Red Red Black Red Red Red Red Red Red Red Black Red Red
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue 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 Red Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red 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 Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray
Row 6: Gray Gray Gray Red 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 Red 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 Gray
Row 9: Gray Gray Red 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 Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: 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
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 Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green 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 Blue
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 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
Row 18: 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 19: Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Green 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 Gray
Row 21: 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 22: 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 23: 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 24: Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: 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 26: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Red Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
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
Row 2: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 3: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 4: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
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
Row 6: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 7: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 8: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 9: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 10: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
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
Row 12: Blue 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 13: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
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
Row 15: Blue 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 16: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 17: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 18: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
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
Row 20: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 21: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 22: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 23: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 24: Blue 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 25: Gray Red Red Red Gray Gray Gray Gray Gray Gray Red Gray Gray Gray Red Gray Gray Gray Gray Red Gray Gray Red Gray Gray
Row 26: Blue 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 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
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red 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
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Blue Pink
Row 7: Pink Pink Green 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
Row 9: Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Red 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>
| Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Pink Pink Red Pink Red Red Pink Pink Pink Red Pink Pink Red Pink Red Red Pink Red Pink Pink
Pink Pink Red Pink Red Red Pink Pink Pink Red Pink Pink Red Pink Red Red Pink Red Pink Pink
Pink Pink Red Pink Red Red Pink Pink Pink Red Pink Pink Red Pink Red Red Pink Red 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 Blue Blue Blue Blue Blue 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
Pink Pink Red Pink Red Red Pink Pink Pink Red Pink Pink Red Pink Red Red Pink Red Pink Pink
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: 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
Row 3: Yellow Yellow Yellow 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 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
Row 6: Yellow Yellow Yellow 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 Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green 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
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow Green Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow 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
Row 15: Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 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
Row 3: Yellow Yellow Yellow 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 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
Row 6: Yellow Yellow Yellow 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 Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Green Green Green Green Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Yellow Green Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow 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
Row 15: Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange 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 Yellow Orange Yellow Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 13: Yellow Orange Yellow Yellow Yellow Yellow Orange Orange Orange Orange
Row 14: Orange Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange
Row 15: Yellow Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange
Row 16: Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange 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 Yellow Orange Yellow Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 13: Yellow Orange Yellow Yellow Yellow Yellow Orange Orange Orange Orange
Row 14: Orange Yellow Yellow Yellow Yellow Yellow Orange Red Orange Orange
Row 15: Yellow Orange Yellow Yellow Yellow Red Red Orange Orange Orange
Row 16: Orange Orange Yellow Yellow Yellow Red Orange Red Orange Orange
Row 17: Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Brown Orange Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Brown Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Orange Orange Orange Orange Brown Orange Brown Orange Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Orange Brown Orange Orange Brown Orange Orange Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange 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 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 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 Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Brown Orange Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Brown Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Red Red Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Red Red Orange Orange Orange Orange Orange Orange Orange Red Brown Brown Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Red Red Red Red Brown Red Red Brown Red Orange Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Red Red Red Red Brown Red Red Red Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Red Red Red Brown Red Red Red Red Orange Orange Brown Orange Orange Orange Orange Brown Orange Brown Orange Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Red Brown Red Red Red Red Red Brown Red Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Red Red Red Red Brown Red Red Red Red Red Orange Brown Orange Orange Brown Orange Orange Brown Orange Orange Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Red Red Red Red Red Red Brown Brown Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange 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 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 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 Brown Brown Brown Brown Brown Brown
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 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: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Yellow Yellow Yellow Yellow 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 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: 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
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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Yellow Yellow Yellow Yellow Gray Gray Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Red 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: Red Brown Yellow Red Purple Red Brown Yellow Blue Blue Yellow Yellow Red Gray Yellow Yellow Purple Blue Green Brown Green Green Green Gray Blue
Row 2: Yellow Green Red Green Green Yellow Brown Green Red Green Red Purple Green Pink Green Gray Brown Brown Blue Blue Green Blue Red Gray Red
Row 3: Purple Blue Yellow Red Gray Blue Green Yellow Brown Blue Gray Gray Pink Red Gray Yellow Blue Green Red Gray Purple Red Yellow Yellow Yellow
Row 4: Brown Green Yellow Yellow Yellow Red Blue Green Purple Red Red Gray Gray Gray Red Gray Red Blue Blue Green Blue Brown Brown Green Red
Output:
Row 1: Red Green Yellow Blue Gray Brown Purple Pink
Row 2: Red Green Yellow Blue Gray Brown Purple Pink
Row 3: Red Green Yellow Blue Gray Brown Purple Black
Row 4: Red Green Yellow Blue Gray Brown Purple Black
Row 5: Red Green Yellow Blue Gray Brown Purple Black
Row 6: Red Green Yellow Blue Gray Brown Purple Black
Row 7: Red Green Yellow Blue Gray Brown Black Black
Row 8: Red Green Yellow Blue Gray Brown Black Black
Row 9: Red Green Yellow Blue Gray Brown Black Black
Row 10: Red Green Yellow Blue Gray Brown Black Black
Row 11: Red Green Yellow Blue Gray Black Black Black
Row 12: Red Green Yellow Blue Gray Black Black Black
Row 13: Red Green Yellow Blue Gray Black Black Black
Row 14: Red Green Yellow Blue Black Black Black Black
Row 15: Red Green Yellow Blue Black Black Black Black
Row 16: Red Green Yellow Black Black Black Black Black
Row 17: Red Green Yellow Black Black Black Black Black
Row 18: Red Green Black Black Black Black Black Black
Row 19: Red Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Yellow Yellow Brown Purple Orange Brown Purple Purple Yellow
Row 2: Yellow Purple Brown Pink Purple Orange Brown Red Pink
Row 3: Pink Orange Brown Red Yellow Brown Pink Yellow Yellow
Row 4: Brown Purple Orange Purple Pink Red Red Purple Brown
Row 5: Orange Red Yellow Yellow Yellow Red Pink Brown Brown
Row 6: Yellow Red Yellow Red Brown Red Orange Brown Brown
Row 7: Brown Pink Orange Yellow Red Yellow Brown Red Pink
Row 8: Orange Red Pink Brown Red Red Red Orange Brown
Row 9: Pink Purple Brown Yellow Pink Red Orange Orange Yellow
Row 10: Orange Yellow Red Orange Pink Brown Pink Pink Red
Row 11: Red Orange Pink Pink Pink Orange Yellow Orange Brown
Output:
Row 1: Brown Red Yellow Pink Orange Purple
Row 2: Brown Red Yellow Pink Orange Purple
Row 3: Brown Red Yellow Pink Orange Purple
Row 4: Brown Red Yellow Pink Orange Purple
Row 5: Brown Red Yellow Pink Orange Purple
Row 6: Brown Red Yellow Pink Orange Purple
Row 7: Brown Red Yellow Pink Orange Purple
Row 8: Brown Red Yellow Pink Orange Purple
Row 9: Brown Red Yellow Pink Orange Purple
Row 10: Brown Red Yellow Pink Orange Black
Row 11: Brown Red Yellow Pink Orange Black
Row 12: Brown Red Yellow Pink Orange Black
Row 13: Brown Red Yellow Pink Orange Black
Row 14: Brown Red Yellow Pink Orange Black
Row 15: Brown Red Yellow Pink Orange Black
Row 16: Brown Red Yellow Pink Orange Black
Row 17: Brown Red Yellow Pink Black Black
Row 18: Brown Red Yellow Black Black Black
Row 19: Brown Red Black Black Black Black
Row 20: Brown Black Black Black Black Black
Example 3
Input:
Row 1: Gray Green Gray Gray Gray Orange Orange Red
Row 2: Orange Green Red Orange Purple Brown Red Brown
Row 3: Red Red Green Purple Purple Gray Red Brown
Row 4: Orange Red Gray Purple Purple Brown Brown Green
Row 5: Brown Red Red Green Orange Red Orange Red
Row 6: Red Green Gray Red Red Green Gray Red
Row 7: Orange Orange Brown Brown Orange Gray Gray Purple
Row 8: Orange Purple Green Brown Brown Gray Red Green
Row 9: Gray Orange Green Purple Orange Gray Orange Brown
Row 10: Brown Purple Purple Red Gray Green Gray Brown
Row 11: Orange Gray Gray Gray Gray Red Red Purple
Row 12: Gray Purple Purple Orange Gray Purple Purple Purple
Row 13: Red Red Green Brown Purple Gray Orange Brown
Row 14: Gray Purple Green Purple Purple Orange Gray Gray
Row 15: Brown Green Green Gray Orange Gray Orange Green
Row 16: Green Brown Green Brown Orange Red Red Orange
Row 17: Red Brown Gray Green Gray Brown Green Purple
Row 18: Orange Purple Orange Brown Orange Brown Red Orange
Row 19: Brown Brown Orange Red Brown Purple Orange Orange
Row 20: Brown Purple Purple Brown Gray Red Purple Brown
Output:
Row 1: Gray Orange Brown Red Purple Green
Row 2: Gray Orange Brown Red Purple Green
Row 3: Gray Orange Brown Red Purple Green
Row 4: Gray Orange Brown Red Purple Green
Row 5: Gray Orange Brown Red Purple Green
Row 6: Gray Orange Brown Red Purple Green
Row 7: Gray Orange Brown Red Purple Green
Row 8: Gray Orange Brown Red Purple Green
Row 9: Gray Orange Brown Red Purple Green
Row 10: Gray Orange Brown Red Purple Green
Row 11: Gray Orange Brown Red Purple Green
Row 12: Gray Orange Brown Red Purple Green
Row 13: Gray Orange Brown Red Purple Green
Row 14: Gray Orange Brown Red Purple Green
Row 15: Gray Orange Brown Red Purple Green
Row 16: Gray Orange Brown Red Purple Green
Row 17: Gray Orange Brown Red Purple Green
Row 18: Gray Orange Brown Red Purple Green
Row 19: Gray Orange Brown Red Purple Green
Row 20: Gray Orange Brown Red Purple Green
Row 21: Gray Orange Brown Red Purple Black
Row 22: Gray Orange Brown Red Purple Black
Row 23: Gray Orange Brown Red Purple Black
Row 24: Gray Orange Brown Red Purple Black
Row 25: Gray Orange Brown Red Purple Black
Row 26: Gray Orange Brown Red Purple Black
Row 27: Gray Orange Brown Red Black Black
Row 28: Gray Orange Brown Black Black Black
Row 29: Gray Orange Black Black Black Black
Row 30: Gray Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Green Pink
Row 2: Orange Pink Pink Pink
Row 3: Green Green Pink Orange
Row 4: Green Orange Orange Orange
Row 5: Pink Orange Pink Pink
Row 6: Orange Green 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 Green
Pink Orange Green
Pink Orange Green
Pink Orange Green
Pink Orange Green
Pink Orange Black
Pink Orange Black
Pink Black Black
Pink Black Black
Pink Black Black
Pink Black Black
Pink 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: 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
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Purple Black Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Pink Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Pink Purple Purple
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Orange Purple Purple
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Purple Brown Purple
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 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
Row 11: Green Green Green Green Blue Purple 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 Purple Blue Green Green Green Green
Row 13: Green Green Green Green Green Green Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Purple Purple Green Green Green Green Purple Purple Green Green Green Green Green Green
Row 15: Green Green Green Green Green Purple Green Purple Green Green Green Green Purple Purple Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Purple 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
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 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 Green Green Green Green Green Green Green Green Green Blue Purple Black Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Pink Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Pink Purple Purple
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Orange Purple Purple
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Purple Brown Purple
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 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
Row 11: Green Green Green Green Blue Purple Black Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Orange Pink Green Green Green Green Green Green Green Black Purple Blue Green Green Green Green
Row 13: Green Green Green Green Brown Pink Purple Purple Green Green Green Green Green Green Pink Orange Green Green Green Green
Row 14: Green Green Green Green Yellow Orange Purple Purple Green Green Green Green Purple Purple Pink Brown Green Green Green Green
Row 15: Green Green Green Green Brown Purple Brown Purple Green Green Green Green Purple Purple Orange Yellow Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Purple Brown Purple Brown 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
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Blue Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Green Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Orange Green Blue Orange Orange Orange
Row 6: Orange Orange Orange Green Pink Orange Orange Green Orange Orange Orange Orange Orange Green Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Green Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Green Blue Orange Orange Orange Green 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 Green Orange Green Blue Orange Orange Orange Orange Orange Orange Green Orange Green Blue Orange
Row 11: Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Orange Orange Orange Orange Green Orange
Row 12: Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange
Row 14: Blue Green Orange Orange Orange Orange Orange Orange Orange Blue Green Orange Orange Orange Orange Orange Orange
Row 15: Green Orange Orange Orange Orange Orange Green Blue Orange Orange Orange Orange Orange Orange Green Orange Orange
Row 16: Orange Orange Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Green
Row 17: Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Blue Green Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: 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 Green Orange Green Blue Gray Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Green Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Green Blue Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Orange Green Blue Orange Orange Orange
Row 6: Orange Orange Orange Green Pink Orange Orange Green Pink Orange Orange Orange Orange Green Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Green Pink Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Green Blue Orange Orange Orange Green Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Green Orange Green Blue Gray Orange Orange Orange Orange Orange Green Orange Green Blue Gray
Row 11: Orange Orange Orange Pink Orange Green Orange Orange Orange Green Orange Orange Orange Pink Orange Green Orange
Row 12: Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Pink Green Orange Green Orange Orange Orange
Row 13: Gray Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange
Row 14: Blue Green Orange Orange Orange Orange Orange Gray Orange Blue Green Orange Orange Orange Orange Orange Orange
Row 15: Green Orange Orange Orange Orange Orange Green Blue Orange Gray Orange Orange Orange Orange Green Orange Orange
Row 16: Orange Pink Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Pink Green
Row 17: Green Orange Orange Orange Orange Green Pink Orange Orange Orange Orange Orange Orange Orange Green Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Blue Green Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Gray Black Black Black Black
Row 3: Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Pink Gray Black Black Black Black
Row 4: Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Gray Gray 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 Gray Pink Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Gray Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Gray Gray 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
Row 11: Black Black Black Black Gray Gray Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Gray 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 Gray Black Gray Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Pink Gray Black Black Black Black Black Black Pink Black Black Black Gray Gray Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Black Black Black Pink Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Black Black
Row 19: Black Black Black Black Black Black Brown Orange Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Gray Gray Blue Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Green Pink Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Gray Black Green 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
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Green Gray Brown Black Black Black
Row 3: Black Black Black Black Green Black Gray Black Black Black Black Black Black Black Black Black Pink Gray Orange Black Black Black
Row 4: Black Black Black Black Green Pink Green Black Black Black Black Black Black Black Black Green Green Blue Green Black Black Black
Row 5: Black Black Black Black Blue Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Green Orange Brown Black Black Black Black Black Black Green Blue Green Green Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Gray Pink Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Brown Orange Green Black Black Brown Gray Green Gray Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Gray Gray Blue Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Green Orange Brown Black Black Green Pink Green Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Blue Gray Gray Black Black Gray Black Green Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Green Pink Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Green Black Gray 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 Gray Green Gray Brown Black Black Black Black Green Black Gray Black Black Brown Orange Green Black Black Black
Row 16: Black Black Black Black Pink Gray Orange Black Black Black Black Green Pink Green Black Black Gray Gray Blue Black Black Black
Row 17: Black Black Black Green Green Blue Green Black Black Black Black Blue Gray Gray Black Black Green Pink Green Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Green Orange Brown Black Black Gray Black Green Black Black Black
Row 19: Black Black Black Black Black Black Brown Orange Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Gray Gray Blue Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Black Black Green Pink Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Black Gray Black Green 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 Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Purple Purple Purple Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Blue Gray Purple
Row 4: Gray Red Purple Purple Green Gray Purple Purple Purple Purple
Row 5: Gray Pink Purple Brown Purple Gray Purple Purple Gray Gray
Row 6: Gray Purple Purple Blue Purple Gray Gray Gray Gray Gray
Row 7: Gray Purple Purple Yellow Purple Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Purple Gray Purple Purple Gray Gray Gray Purple Purple Purple
Row 10: Purple Blue Purple Purple Gray Gray Purple Gray Blue Gray
Row 11: Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple
Row 12: Gray Purple Purple Gray Gray Gray Gray Gray Purple 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 Purple Purple Purple Green
Gray Gray Gray Gray Gray Gray Yellow Blue Brown Purple
Gray Red Purple Purple Green Gray Purple Purple Purple Purple
Gray Pink Purple Brown Purple Gray Purple Purple Pink Red
Gray Purple Purple Blue Purple Gray Gray Gray Gray Gray
Gray Purple Purple Yellow Purple Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Purple Yellow Purple Purple Gray Gray Green Purple Purple Purple
Purple Blue Purple Purple Gray Gray Purple Brown Blue Yellow
Purple Brown Purple Pink Gray Gray Purple Purple Purple Purple
Green Purple Purple Red Gray Gray Red Pink 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
Row 2: Green Green Gray Pink
Row 3: Green Green Green Green
Row 4: Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Gray Pink Green Green Gray Pink Green Green Gray Pink Green Green Gray Pink
Row 3: 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
Row 5: Green Green Green Green Green Green Green Green Black Black Black Black Black Black Black Black
Row 6: Green Green Gray Pink Green Green Gray Pink Black Black Black Black Black Black Black Black
Row 7: Green Green Green Green Green Green Green Green Black Black Black Black Black Black Black Black
Row 8: Green Green Green Green Green Green Green Green Black Black Black Black Black Black Black Black
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Gray Pink Green Green Gray Pink Green Green Gray Pink Green Green Gray Pink
Row 11: 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
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Gray Pink Green Green Gray Pink Green Green Gray Pink Green Green Gray Pink
Row 15: 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
Example 2
Input:
Row 1: Red Red Pink Red
Row 2: Red Green Red Red
Output:
Row 1: Red Red Pink Red Red Red Pink Red Black Black Black Black Red Red Pink Red
Row 2: Red Green Red Red Red Green Red Red Black Black Black Black Red Green Red Red
Row 3: Red Red Pink Red Black Black Black Black Red Red Pink Red Red Red Pink Red
Row 4: Red Green Red Red Black Black Black Black Red Green Red Red Red Green Red Red
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple
Row 3: Yellow Pink Yellow 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: Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple Yellow Pink Yellow 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: Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Pink Yellow Purple Purple Yellow Pink Yellow Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Green Green
Row 2: Green Green
Row 3: 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 |
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 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 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 Brown Brown Pink Brown Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown 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 Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Brown 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 Brown 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 Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink
Row 15: Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown 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 Brown Brown Brown Brown 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 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 Pink Pink Pink
Row 20: Pink Pink 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 21: Pink Pink 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 22: Pink Pink 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 23: Pink Pink 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 24: Pink Pink 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 25: Pink Pink Pink 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 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 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 Red Red Pink Red Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red 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 Red Red Red Red Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Red 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 Red 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 Blue Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Pink Pink
Row 15: Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue 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 Blue Blue Blue Blue 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 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 Pink Pink Pink
Row 20: Pink Pink 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 21: Pink Pink 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 22: Pink Pink 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 23: Pink Pink 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 24: Pink Pink 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 25: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 2
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 Brown Brown Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange
Row 4: 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
Row 6: 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
Row 8: 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 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 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 Orange
Row 13: Orange Orange 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 Orange Orange
Row 15: Orange 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 Orange
Row 17: Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange 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
Row 23: 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
Row 25: 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 Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Brown Brown Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown 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
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange
Row 4: 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
Row 6: 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
Row 8: 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 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 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 Orange
Row 13: Orange Orange 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 Orange Orange
Row 15: Orange 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 Orange
Row 17: Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange 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
Row 23: 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
Row 25: 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 Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Red Red Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple
Row 2: Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Black Purple Purple
Row 3: Purple Purple Purple Black 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
Row 5: 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
Row 7: Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Black Black 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
Row 10: 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
Row 12: 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 Blue Blue Purple
Row 2: Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Blue Purple Purple
Row 3: Purple Purple Purple Blue 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
Row 5: 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
Row 7: Purple Purple Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Red 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
Row 10: 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
Row 12: 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: 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
Row 3: 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 Orange Black Black
Row 5: Black Black Black Black Black Black Black Black Black Orange Orange Black Black
Row 6: Black Black Orange Orange Black Black Black Black Black Black Black Black Black
Row 7: Black Black Orange Orange Black Black Black Black Black Black Black Black Black
Row 8: Black Black Orange 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 Orange Black Black Black Black Black Black Black Black
Row 12: Black Black Black Orange Orange 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
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 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 Black Black Black Black Blue Black Black
Black Black Black Black Black Black Black Black Black Blue Blue Black Black
Black Black Red Red Black Black Black Black Black Black Black Black Black
Black Black Red Red Black Black Black Black Black Black Black Black Black
Black Black 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 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 Blue 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 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
Row 2: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Purple
Row 3: Purple Purple Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Purple
Row 4: Purple Purple Green Green Green Green Green Green Green Green Green Green Green Purple
Row 5: 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
Output:
Row 1: Purple Purple Purple Purple Purple
Row 2: Purple Green Green Green Purple
Row 3: Purple Green Yellow Green Purple
Row 4: Purple Green Green Green Purple
Row 5: Purple Purple Purple Purple Purple
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 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 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 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 Black Black Black
Row 5: Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 6: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black
Row 7: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black
Row 8: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Brown Black
Row 9: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Brown Black
Row 10: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Brown Black
Row 11: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Brown Black
Row 12: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Brown Black
Row 13: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Blue Blue Brown Black
Row 14: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Yellow Yellow Yellow Yellow Yellow Pink Purple Blue Blue Brown Black
Row 15: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Yellow Yellow Yellow Yellow Yellow Pink Purple Blue Blue Brown Black
Row 16: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Yellow Red Red Red Yellow Pink Purple Blue Blue Brown Black
Row 17: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Yellow Yellow Yellow Yellow Yellow Pink Purple Blue Blue Brown Black
Row 18: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Yellow Yellow Yellow Yellow Yellow Pink Purple Blue Blue Brown Black
Row 19: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Yellow Yellow Yellow Yellow Yellow Pink Purple Blue Blue Brown Black
Row 20: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Blue Blue Brown Black
Row 21: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Brown Black
Row 22: Black Black Black Black Black Black Black Black Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black
Row 23: Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown 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 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 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 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 Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 3: Black Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black
Row 4: Black Brown Blue Purple Purple Purple Purple Purple Purple Purple Blue Brown Black
Row 5: Black Brown Blue Purple Pink Pink Pink Pink Pink Purple Blue Brown Black
Row 6: Black Brown Blue Purple Pink Yellow Yellow Yellow Pink Purple Blue Brown Black
Row 7: Black Brown Blue Purple Pink Yellow Red Yellow Pink Purple Blue Brown Black
Row 8: Black Brown Blue Purple Pink Yellow Yellow Yellow Pink Purple Blue Brown Black
Row 9: Black Brown Blue Purple Pink Pink Pink Pink Pink Purple Blue Brown Black
Row 10: Black Brown Blue Purple Purple Purple Purple Purple Purple Purple Blue Brown Black
Row 11: Black Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Black
Row 12: Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
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 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 Gray Gray Gray
Row 3: 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 Gray Gray Gray
Row 4: Gray Green 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 Gray Gray Gray
Row 5: Gray Green 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 Gray Gray Gray
Row 6: Gray Green Purple Purple Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 7: Gray Green Purple Purple Purple Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 8: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 9: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 10: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 11: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Brown Blue Brown Brown Brown Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 12: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 13: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 14: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 15: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 16: Gray Green Purple Purple Purple Black Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 17: Gray Green Purple Purple Purple Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 18: Gray Green Purple Purple Purple Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 19: Gray Green Purple Purple Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Green Green Gray Gray Gray
Row 20: Gray Green 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 Gray Gray Gray
Row 21: Gray Green 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 Gray Gray Gray
Row 22: 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 Gray Gray Gray
Row 23: 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
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Gray
Row 3: Gray Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Gray
Row 4: Gray Green Purple Black Black Black Black Black Black Black Black Black Purple Green Gray
Row 5: Gray Green Purple Black Orange Orange Orange Orange Orange Orange Orange Black Purple Green Gray
Row 6: Gray Green Purple Black Orange Yellow Yellow Yellow Yellow Yellow Orange Black Purple Green Gray
Row 7: Gray Green Purple Black Orange Yellow Brown Brown Brown Yellow Orange Black Purple Green Gray
Row 8: Gray Green Purple Black Orange Yellow Brown Blue Brown Yellow Orange Black Purple Green Gray
Row 9: Gray Green Purple Black Orange Yellow Brown Brown Brown Yellow Orange Black Purple Green Gray
Row 10: Gray Green Purple Black Orange Yellow Yellow Yellow Yellow Yellow Orange Black Purple Green Gray
Row 11: Gray Green Purple Black Orange Orange Orange Orange Orange Orange Orange Black Purple Green Gray
Row 12: Gray Green Purple Black Black Black Black Black Black Black Black Black Purple Green Gray
Row 13: Gray Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Gray
Row 14: Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
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 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 Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 4: Black Black Black Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black
Row 5: Black Black Black Red Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Red Black
Row 6: Black Black Black Red Yellow Yellow Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Yellow Red Black
Row 7: Black Black Black Red Yellow Yellow Purple Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 8: Black Black Black Red Yellow Yellow Purple Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 9: Black Black Black Red Yellow Yellow Purple Blue Orange Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 10: Black Black Black Red Yellow Yellow Purple Blue Orange Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 11: Black Black Black Red Yellow Yellow Purple Blue Orange Gray Gray Pink Pink Gray Gray Gray Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 12: Black Black Black Red Yellow Yellow Purple Blue Orange Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 13: Black Black Black Red Yellow Yellow Purple Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Purple Purple Yellow Red Black
Row 14: Black Black Black Red Yellow Yellow Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Yellow Red Black
Row 15: Black Black Black Red Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Red Black
Row 16: Black Black Black Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black
Row 17: Black Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red 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
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 Black Black Black Black Black
Black Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Black Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black
Black Red Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Red Black
Black Red Yellow Purple Blue Blue Blue Blue Blue Blue Blue Purple Yellow Red Black
Black Red Yellow Purple Blue Orange Orange Orange Orange Orange Blue Purple Yellow Red Black
Black Red Yellow Purple Blue Orange Gray Gray Gray Orange Blue Purple Yellow Red Black
Black Red Yellow Purple Blue Orange Gray Pink Gray Orange Blue Purple Yellow Red Black
Black Red Yellow Purple Blue Orange Gray Gray Gray Orange Blue Purple Yellow Red Black
Black Red Yellow Purple Blue Orange Orange Orange Orange Orange Blue Purple Yellow Red Black
Black Red Yellow Purple Blue Blue Blue Blue Blue Blue Blue Purple Yellow Red Black
Black Red Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Red Black
Black Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black
Black Red Red Red Red Red Red Red Red Red Red Red Red Red 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: Brown Brown Brown Black Black Brown Brown Brown Brown
Row 2: Brown Brown Brown Black Black Brown Brown Brown Brown
Row 3: Brown Brown Black Brown Brown Black Brown Brown Brown
Row 4: Brown Black Brown Brown Brown Brown Black Brown Brown
Row 5: Black Brown Brown Brown Brown Brown Brown Black Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Black Black Brown Brown Brown Brown
Row 2: Brown Brown Brown Black Black Brown Brown Brown Brown
Row 3: Brown Brown Black Black Black Black Brown Brown Brown
Row 4: Brown Black Black Black Black Black Black Brown Brown
Row 5: Black Black Black Black Black Black Black Black Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown
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
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
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
Row 4: Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Purple Gray Gray Gray
Row 5: Brown Gray Gray Gray Gray Gray Gray Brown Pink Gray Gray Gray Gray Pink Gray Gray Gray Gray Purple Gray Gray Gray Gray
Row 6: Gray Brown Gray Gray Gray Gray Brown Gray Gray Pink Gray Gray Pink Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray
Row 7: Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray
Row 9: Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple 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
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
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
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
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
Row 4: Gray Gray Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Purple Gray Gray Gray
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Purple Purple Gray Gray Gray
Row 6: Gray Brown Brown Brown Brown Brown Brown Gray Gray Pink Pink Pink Pink Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray
Row 7: Gray Gray Brown Brown Brown Brown Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray
Row 8: Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray
Row 9: Gray Gray Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple 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
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
Example 3
Input:
Row 1: 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
Row 3: 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
Row 5: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Red Pink Pink Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Red Blue Pink Pink Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Red Red Blue Pink Blue Blue Pink Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Red Red Pink Blue Blue Blue Blue Pink Blue Blue Blue
Row 9: 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
Row 11: Black Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Black Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Black Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Black Black 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
Row 2: 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
Row 4: 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 Red Red Red Red Red Red Pink Pink Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Pink Pink Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Red Red Blue Pink Pink Pink Pink Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Red Red Pink Pink Pink Pink Pink Pink Blue Blue Blue
Row 9: 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
Row 11: Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Black Black 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: 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
Row 3: 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
Row 5: 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
Row 7: 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 Yellow Blue Blue Blue Blue Yellow Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow 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 Blue Blue
Row 13: Blue Blue Blue Blue Blue 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 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 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
Row 17: Blue Blue Blue Blue Blue 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 Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue 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 Blue Blue 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 Purple
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Gray Blue Purple Purple Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Purple Purple Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Purple Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
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 Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 Yellow Yellow Yellow Yellow Yellow Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Blue Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Purple Purple Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Purple Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 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
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green 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 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
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 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 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 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
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 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
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 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
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
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 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 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 Red 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 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 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 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 Green 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple 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 Purple Purple Red 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 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 Black
Example 2
Input:
Row 1: 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
Row 3: 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
Row 5: 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
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: 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 Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: 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
Row 14: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray
Row 15: 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
Row 17: 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
Row 19: 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
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: 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
Row 2: 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
Row 4: 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
Row 6: 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
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 Red Purple Purple Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray
Row 15: 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
Row 17: 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
Row 19: 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
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black
Row 2: Black Black Red Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Green Black Black Black
Row 5: Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black
Row 2: Black Black Red Purple Purple Black Black Black
Row 3: Black Black Black Black Purple Black Black Black
Row 4: Black Black Black Black Green Black Black Black
Row 5: Black Black Black Black Black Black Black Black
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
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
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
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
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
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
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
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
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
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
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
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
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
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow 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
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
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
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
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 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 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 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 Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green 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 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 |
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 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 Green Green Green
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
Row 20: Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green
Row 23: Green Green Green Green 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: Gray Purple Purple Purple Purple Purple Purple
Row 2: Purple Gray Purple Purple Purple Purple Purple
Row 3: Purple Purple Gray Purple Purple Purple Purple
Row 4: Purple Purple Purple Gray Purple Purple Purple
Row 5: Purple Purple Purple Purple Gray Purple Purple
Row 6: Purple Purple Purple Purple Purple Gray Purple
Row 7: Purple Purple Purple Purple Purple Purple Gray
Row 8: Purple Purple Purple Purple Purple Gray Purple
Row 9: Purple Purple Purple Purple Gray Purple Purple
Row 10: Purple Purple Purple Gray Purple Purple Purple
Row 11: Purple Purple Gray Purple Purple Purple Purple
Row 12: Purple Gray Purple Purple Purple Purple Purple
Row 13: Gray Purple Purple Purple Purple Purple Purple
Row 14: Purple Gray Purple Purple Purple Purple Purple
Row 15: Purple Purple Gray Purple Purple Purple Purple
Row 16: Purple Purple Purple Gray Purple Purple Purple
Row 17: Purple Purple Purple Purple Gray Purple Purple
Row 18: Purple Purple Purple Purple Purple Gray Purple
Row 19: Purple Purple Purple Purple Purple Purple Gray
Row 20: Purple Purple Purple Purple Purple Gray Purple
Row 21: Purple Purple Purple Purple Gray Purple Purple
Row 22: Purple Purple Purple Gray Purple Purple Purple
Row 23: Purple Purple Gray Purple Purple Purple Purple
Row 24: Purple Gray Purple Purple Purple Purple Purple
Row 25: Gray Purple Purple Purple Purple Purple Purple
Row 26: Purple Gray Purple Purple Purple Purple Purple
Row 27: Purple Purple Gray Purple Purple Purple Purple
Row 28: Purple Purple Purple Gray Purple Purple Purple
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 Red
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red
Row 2: Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple Red Purple
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow
Output:
Row 1: Yellow Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Yellow
Row 2: Purple Yellow Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Yellow Purple
Row 3: Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Yellow Purple Purple
Row 4: Purple Purple Purple Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Purple Purple Purple
Row 5: Purple Purple Purple Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Purple Purple Purple
Row 6: Purple Purple Yellow Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Yellow Purple Purple
Row 7: Purple Yellow Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Yellow Purple
Row 8: Yellow Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Yellow
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Pink
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 Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Pink Purple Purple Pink
Purple Pink Purple Purple Pink Purple
Pink Purple Purple Pink Purple Purple
Purple Pink Pink Purple Purple Purple
Purple Pink Pink Purple Purple Purple
Pink Purple Purple Pink Purple Purple
Purple Pink Purple Purple Pink Purple
Purple Purple Pink Purple Purple 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 Gray Brown Brown Green Brown Green Green Green Green Green Green Green Orange Orange Purple Green Green Orange
Row 2: Green Yellow Green Purple Green Green Green Purple Purple Green Green Green Green Yellow Green Yellow Green Green Green
Row 3: Green Green Green Green Yellow Green Purple Green Purple Purple Green Green Purple Green Black Green Green Black Black
Row 4: Green Green Orange Green Black Green Green Green Yellow Green Green Orange Green Gray Green Green Purple Green Green
Row 5: Green Orange Green Green Green Green Green Green Green Black Green Purple Green Green Green Purple Green Green Green
Row 6: Green Green Yellow Green Green Black Green Green Yellow Green Purple Green Green Orange Black Orange Green Green Green
Row 7: Purple Green Green Yellow Yellow Green Orange Green Green Green Yellow Green Green Green Brown Green Green Orange Green
Row 8: Green Green Green Green Black Purple Orange Green Green Green Green Green Orange Yellow Gray Orange Yellow Green Green
Row 9: Green Green Green Green Orange Green Black Green Black Brown Green Yellow Green Black Orange Orange Orange Green Green
Row 10: Green Purple Green Green Green Green Green Green Yellow Purple Green Green Gray Green Green Green Green Black Green
Output:
Row 1: Black Black Gray
Row 2: Black Black Gray
Row 3: Gray Gray Gray
Example 2
Input:
Row 1: Gray Green Green Green Green Pink Green Green Pink Pink Green Green Green Green Green Green Green Green Gray Gray Green
Row 2: Green Green Green Green Green Pink Green Green Pink Pink Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Pink 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 Pink Green Green Pink Green Green Green Green Gray Green Green Green
Row 5: Green Green Green Green Green Green Pink Green Green Green Green Pink Green Green Gray Green Gray Green Green Green Green
Row 6: Green Green Pink Green Pink Green Green Green Green Green Gray Green Green Gray Gray Green Green Green Green Pink Pink
Row 7: Green Green Green Green Green Green Green Green Green Gray Green Green Green Green Pink Green Green Green Pink Green Pink
Row 8: Pink Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Pink Green Gray Gray Green Green Green Green Green
Row 10: Pink Green Green Green Green Pink Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Gray Pink Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green
Row 12: Green Green Pink Green Green Pink Green Gray Green Green Green Green Green Pink Green Pink Green Gray Green Green Green
Output:
Row 1: Black Black Gray
Row 2: Black Black Gray
Row 3: Gray Gray Gray
Example 3
Input:
Row 1: Green Purple Purple Gray Purple
Row 2: Gray Brown Brown Purple Gray
Row 3: Gray Brown Purple Gray Purple
Row 4: Green Brown Brown Gray Purple
Row 5: Brown Purple Brown Purple Purple
Row 6: Brown Purple Gray Brown Gray
Row 7: Gray Purple Gray Purple Gray
Row 8: Brown Gray Gray Brown Gray
Row 9: Purple Gray Brown Green Purple
Row 10: Purple Gray Green Purple Brown
Row 11: Brown Gray Brown Gray Brown
Row 12: Brown Green Green Gray Gray
Row 13: Brown Brown Brown Purple Purple
Row 14: Purple Purple Purple Gray Brown
Row 15: Gray Brown Gray Brown Brown
Row 16: Brown Gray Brown Brown Brown
Row 17: Brown Green Green Purple Gray
Row 18: Purple Purple Purple Purple Purple
Row 19: Brown Gray Gray Brown Green
Row 20: Purple Gray Green Gray Purple
Row 21: Green Purple Purple Brown Gray
Row 22: Gray Brown Purple Brown Gray
Row 23: Green Brown Gray Purple Gray
Row 24: Brown Purple Purple Green Gray
Row 25: Green Green Gray Gray Brown
Row 26: Gray Gray Green Purple Gray
Row 27: Gray Gray Purple Purple Brown
Row 28: Gray Brown Green Purple Gray
Output:
Row 1: Black Black Gray
Row 2: Black Black Gray
Row 3: Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Black Orange Blue Brown Blue Blue Brown Blue Blue Brown Black Black Black Blue Brown Blue Brown Blue Brown Blue Blue Blue
Row 2: Orange Brown Blue Blue Orange Black Blue Blue Black Blue Orange Blue Black Blue Blue Black Blue Orange Blue Blue Blue Blue
Row 3: Blue Blue Black Black Blue Blue Blue Black Black Blue Orange Black Black Brown Blue Black Orange Blue Blue Black Orange Blue
Row 4: Brown Blue Black Blue Brown Blue Blue Blue Brown Blue Brown Blue Black Orange Orange Orange Black Blue Blue Blue Blue Blue
Row 5: Blue Blue Black Black Blue Blue Brown Orange Black Blue Brown Blue Blue Black Brown Orange Blue Brown Black Blue Brown Brown
Row 6: Brown Blue Blue Black Blue Blue Black Blue Blue Brown Blue Brown Blue Blue Blue Blue Orange Blue Blue Orange Blue Brown
Row 7: Blue Orange Brown Brown Blue Blue Black Blue Blue Orange Brown Blue Black Blue Black Blue Orange Orange Black Blue Blue Brown
Row 8: Brown Blue Blue Orange Orange Orange Black Orange Black Orange Blue Blue Brown Black Black Blue Blue Black Orange Blue Blue Orange
Row 9: Blue Blue Brown Brown Black Brown Black Black Blue Brown Orange Blue Brown Brown Black Black Blue Blue Black Orange Blue Blue
Row 10: Blue Brown Black Orange Orange Blue Blue Brown Black Blue Blue Brown Black Blue Blue Black Black Black Brown Black Orange Black
Row 11: Blue Black Orange Blue Black Blue Black Orange Black Orange Orange Brown Brown Orange Orange Blue Brown Black Black Black Blue Orange
Row 12: Blue Blue Blue Orange Black Brown Brown Brown Brown Blue Brown Blue Brown Orange Blue Orange Blue Black Blue Black Blue Brown
Row 13: Blue Blue Orange Black Blue Brown Blue Blue Black Brown Blue Orange Orange Orange Orange Blue Brown Blue Orange Blue Blue Blue
Row 14: Blue Blue Brown Orange Blue Brown Blue Blue Blue Black Blue Blue Blue Blue Blue Brown Blue Brown Blue Blue Blue Brown
Row 15: Blue Blue Blue Brown Blue Orange Orange Blue Blue Blue Black Black Orange Blue Blue Brown Brown Blue Blue Orange Orange Orange
Row 16: Blue Blue Blue Brown Blue Blue Blue Brown Blue Brown Blue Blue Brown Orange Orange Blue Blue Brown Brown Blue Black Blue
Row 17: Blue Blue Brown Blue Blue Black Blue Orange Black Orange Blue Blue Blue Blue Blue Blue Brown Brown Brown Black Brown Brown
Row 18: Blue Blue Brown Orange Blue Blue Black Blue Brown Orange Blue Orange Blue Orange Blue Blue Blue Blue Brown Blue Brown Black
Row 19: Black Blue Black Brown Blue Blue Blue Orange Blue Brown Blue Blue Blue Orange Orange Orange Blue Blue Blue Black Brown Blue
Row 20: Brown Orange Orange Black Brown Blue Black Blue Brown Brown Black Blue Blue Brown Brown Black Blue Black Orange Blue Blue Blue
Row 21: Brown Blue Brown Blue Black Blue Brown Blue Blue Blue Blue Blue Blue Orange Orange Blue Black Brown Black Blue Blue Brown
Row 22: Blue Blue Blue Brown Blue Blue Black Blue Black Blue Orange Blue Blue Orange Black Brown Blue Blue Orange Blue Blue Orange
Row 23: Black Blue Brown Black Blue Blue Black Orange Black Blue Blue Blue Orange Black Black Brown Blue Brown Blue Blue Black Orange
Row 24: Blue Blue Blue Brown Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue
Row 25: Orange Brown Blue Black Brown Brown Blue Blue Orange Black Blue Black Blue Orange Blue Blue Blue Orange Brown Orange Blue Black
Row 26: Blue Black Blue Orange Brown Brown Blue Blue Blue Blue Black Brown Black Brown Blue Blue Blue Black Blue Brown Blue Blue
Row 27: Black Black Orange Brown Black Blue Black Brown Blue Brown Black Orange Black Blue Blue Blue Blue Blue Orange Black Black 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 Black
Gray Gray Gray
Black Gray 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: Pink Pink Pink Pink Pink Pink 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 Yellow Pink Orange Pink Yellow 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 Yellow Pink Yellow 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 Yellow Pink Orange 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 Yellow Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Yellow Pink Red Pink Yellow 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 Orange Pink Blue Pink Orange Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow 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 Orange Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Blue Pink Yellow Pink Blue Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Blue Pink Red Pink Blue Pink Yellow Pink Blue Pink Yellow Pink Pink Orange Pink Red Pink Orange Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink
Row 14: Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Red Pink Yellow Pink Red Pink Blue Pink Yellow Pink Blue Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Yellow Pink 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 Blue Pink Red Pink Blue Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Blue Pink Yellow Pink Pink Orange Pink Pink Pink Orange Pink Pink 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 Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Orange Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Red 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 Orange Pink Pink Pink Orange Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red 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
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 Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Yellow Pink Orange Pink Yellow 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 Yellow Pink Yellow 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 Orange Pink Yellow Pink Orange 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 Yellow Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Yellow Pink Orange Pink Yellow Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Yellow Pink Red Pink Yellow 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 Orange Pink Blue Pink Orange Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow 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 Orange Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Blue Pink Yellow Pink Blue Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Blue Pink Red Pink Blue Pink Yellow Pink Blue Pink Yellow Pink Pink Orange Pink Red Pink Orange Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink
Row 14: Pink Pink Yellow Pink Yellow Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Red Pink Yellow Pink Red Pink Blue Pink Yellow Pink Blue Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Yellow Pink Yellow Pink 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 Blue Pink Red Pink Blue Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Blue Pink Yellow Pink Pink Orange Pink Red Pink Orange Pink Pink 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 Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Red Pink Orange Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Orange Pink Pink Pink Orange Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink Red 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 Orange Pink Pink Pink Orange Pink Pink
Row 28: Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red 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
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 Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple 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 Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Green Orange Red Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple 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 Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple 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 Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Green Orange Green Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Purple Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange
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 Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Purple Orange Gray 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 Red Orange Red Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange
Row 16: Orange Red Orange Orange Orange Red Orange Orange Purple Orange Green Orange Purple 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 Red Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Green Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Purple Orange Gray Orange Orange 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 Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange
Row 20: Orange Red Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange
Row 22: Orange Orange Green Orange Purple Orange Green Orange Pink Orange Red Orange Pink Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Red Orange Red Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange
Row 24: Orange Orange Purple Orange Yellow Orange Purple Orange Green Orange Pink Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Red Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange
Row 26: Orange Orange Orange Orange Purple Orange Green 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 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 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 Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple 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 Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Green Orange Red Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple 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 Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Purple 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 Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Green Orange Green Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Purple Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Orange Orange
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 Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Purple Orange Gray 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 Red Orange Red Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange
Row 16: Orange Red Orange Orange Orange Red Orange Orange Purple Orange Green Orange Purple 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 Red Orange Red Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Green Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Gray Orange Orange Orange Orange Gray Orange Purple Orange Gray Orange Orange 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 Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange
Row 20: Orange Red Orange Orange Orange Red Orange Orange Green Orange Pink Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange
Row 22: Orange Orange Green Orange Purple Orange Green Orange Pink Orange Red Orange Pink Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Red Orange Red Orange Orange Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange
Row 24: Orange Orange Purple Orange Yellow Orange Purple Orange Green Orange Pink Orange Green Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Red Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange
Row 26: Orange Orange Green Orange Purple Orange Green 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 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 Orange Orange Orange Orange Orange Orange Orange
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
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 Red Purple Red Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Black Purple Red 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 Red Purple Purple Purple Red Purple Purple Purple Black Purple Red Purple Black Purple Purple
Row 9: Purple Black Purple Red Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple
Row 10: Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Red Purple Purple
Row 11: Purple Red Purple Black Purple Red 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 Black Purple Red Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Black Purple Purple Purple Black 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 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Black Purple Purple Purple Black 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 Black Purple Red Purple Black 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
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Black Purple Red Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Black 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
Row 24: 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
Row 26: Purple Purple 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 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
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 Red Purple Red Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Red Purple Black Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Black Purple Black Purple Purple Red Purple Purple Purple Red Purple Purple Purple Black Purple Red Purple Black Purple Purple
Row 9: Purple Black Purple Red Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple
Row 10: Purple Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Red Purple Purple
Row 11: Purple Red Purple Black Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Red Purple Black Purple Purple
Row 13: Purple Purple Purple Purple Black Purple Purple Purple Black 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 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Black Purple Purple Purple Black 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 Black Purple Red Purple Black Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Black Purple Red Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Red Purple Black 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
Row 24: 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
Row 26: Purple Purple 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 Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Red Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Black Yellow Green Yellow Black Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Red Yellow Black Yellow Red Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: 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>
| 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 Yellow Black Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow
Yellow Yellow Yellow Yellow Black Yellow Green Yellow Black Yellow
Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow
Yellow Yellow Yellow Yellow Red Yellow Black Yellow 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 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 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 |
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: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 3: 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
Row 5: 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
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Black 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
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Black Gray Gray Gray Gray Black Gray Gray Gray Black
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 Gray Gray
Row 18: 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
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: 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
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 7: Pink Pink Gray Gray Gray Gray Gray Gray Pink Pink Pink Gray
Row 8: Black Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink
Row 9: Pink Pink Gray Gray Gray Gray Gray Gray Pink Pink Pink Gray
Row 10: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Pink Pink Pink Pink Gray Gray Pink Pink Pink Gray Pink Pink
Row 13: Black Pink Black Pink Pink Pink Pink Black Pink Pink Pink Black
Row 14: Pink Pink Pink Pink Gray Gray Pink Pink Pink Gray Pink Pink
Row 15: Gray Gray Black Gray Gray Gray Gray Black Gray Gray Gray Black
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 Gray Gray
Row 18: 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
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Brown Yellow Blue Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Brown Yellow Blue Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 9: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Blue Yellow Yellow Yellow Yellow Blue Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Blue Blue Blue
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Brown Blue Brown Brown Blue Brown Blue
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Blue Blue Blue
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Blue Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Blue Brown Blue Yellow Yellow Yellow Blue Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Blue Blue Blue
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Brown Blue Brown Brown Blue Brown Blue
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Blue Blue Blue
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Blue Yellow Yellow Yellow Blue Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Blue Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Blue Brown Blue Yellow Yellow Yellow Blue Yellow
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
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
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: 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
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: 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
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: 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
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
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
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
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
Row 16: Black Black Black Black Black Orange 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
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
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: 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
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: 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 Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Black Black Black Black Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Orange 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: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 5: Blue Blue Red Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink 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>
| Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Red Red Red Red Pink Red Pink Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Pink Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink 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: 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
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 Pink Pink Pink Pink Pink Pink
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 Orange Orange
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: 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
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 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 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 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 Brown
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
Output:
Row 1: Yellow
Row 2: Pink
Row 3: Orange
Row 4: Purple
Row 5: Orange
Row 6: Brown
Row 7: 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: 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
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
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
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
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
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
Output:
Row 1: Pink
Row 2: Orange
Row 3: Black
Example 3
Input:
Row 1: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 2: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 3: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 4: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 5: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 6: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 7: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 8: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 9: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 10: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 11: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 12: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 13: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 14: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 15: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 16: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 17: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 18: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 19: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Row 20: Pink Pink Pink Gray Blue Red Red Red Red Orange Green Black Black Black Yellow Yellow Green Purple Purple Purple Yellow Gray
Output:
Row 1: Pink Gray Blue Red Orange Green Black Yellow Green Purple Yellow Gray
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 2: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 3: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 4: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 5: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 6: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 7: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 8: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 9: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 10: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 11: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 12: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 13: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 14: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 15: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 16: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 17: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 18: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 19: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 20: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Row 21: Gray Gray Gray Gray Purple Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Purple Gray Pink 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: Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue
Row 5: Blue Blue Green Purple
Row 6: Orange Blue Gray Purple
Row 7: Gray Green Blue Blue
Row 8: Blue Red Brown Green
Row 9: Blue Brown Gray Blue
Row 10: Brown Pink Pink Green
Row 11: Red Pink Green Red
Row 12: Blue Blue Black Brown
Row 13: Blue Purple Blue Green
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Green Purple Purple Green Blue Blue
Row 6: Orange Blue Gray Purple Purple Gray Blue Orange
Row 7: Gray Green Blue Blue Blue Blue Green Gray
Row 8: Blue Red Brown Green Green Brown Red Blue
Row 9: Blue Brown Gray Blue Blue Gray Brown Blue
Row 10: Brown Pink Pink Green Green Pink Pink Brown
Row 11: Red Pink Green Red Red Green Pink Red
Row 12: Blue Blue Black Brown Brown Black Blue Blue
Row 13: Blue Purple Blue Green Green Blue Purple Blue
Row 14: Blue Purple Blue Green Green Blue Purple Blue
Row 15: Blue Blue Black Brown Brown Black Blue Blue
Row 16: Red Pink Green Red Red Green Pink Red
Row 17: Brown Pink Pink Green Green Pink Pink Brown
Row 18: Blue Brown Gray Blue Blue Gray Brown Blue
Row 19: Blue Red Brown Green Green Brown Red Blue
Row 20: Gray Green Blue Blue Blue Blue Green Gray
Row 21: Orange Blue Gray Purple Purple Gray Blue Orange
Row 22: Blue Blue Green Purple Purple Green Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: 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
Row 3: 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
Row 5: 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
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Green Black Black Black Black Black Black Black Black Black Black
Row 9: 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
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
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
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 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
Row 8: Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green 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 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
Row 13: Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green 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: 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
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
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
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
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
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink
Row 6: Gray Pink Pink Pink Pink
Row 7: Pink Purple Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray
Row 7: Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink
Row 11: Gray Pink Pink Pink Pink Pink Pink Pink Pink Gray
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Yellow Green Blue Blue Green Gray Red Green Black
Row 2: Red Green Green Yellow Red Gray Gray Gray Red
Row 3: Blue Blue Red Yellow Blue Red Green Black Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Yellow Green Blue Blue Green Gray Red Green Black Black Green Red Gray Green Blue Blue Green Yellow
Red Green Green Yellow Red Gray Gray Gray Red Red Gray Gray Gray Red Yellow Green Green Red
Blue Blue Red Yellow Blue Red Green Black Gray Gray Black Green Red Blue Yellow Red Blue Blue
Blue Blue Red Yellow Blue Red Green Black Gray Gray Black Green Red Blue Yellow Red Blue Blue
Red Green Green Yellow Red Gray Gray Gray Red Red Gray Gray Gray Red Yellow Green Green Red
Yellow Green Blue Blue Green Gray Red Green Black Black Green Red Gray Green Blue Blue Green 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Row 2: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Row 3: Red Red Red Pink Pink Pink Pink Gray Pink Pink Pink Pink Red Red Pink Pink Pink Pink Gray Pink Pink Pink Pink Red
Row 4: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Row 5: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Row 6: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Pink Pink Pink Pink Pink
Row 10: Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Brown Yellow Brown Red Red Red Pink Pink Pink Pink Pink
Row 11: Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Brown Gray Yellow Yellow Red Red Pink Pink Pink Pink Pink
Row 12: Red Red Pink Pink Gray Pink Pink Pink Red Red Red Red Red Brown Brown Brown Red Red Red Pink Pink Pink Pink Pink
Row 13: Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Pink Pink Gray Pink Pink
Row 14: Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
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
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
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
Output:
Row 1: Red Red Red Pink Pink Pink Pink Yellow Pink Pink Pink Pink Red Red Pink Pink Pink Pink Yellow Pink Pink Pink Pink Red
Row 2: Red Red Red Pink Pink Pink Brown Yellow Brown Pink Pink Pink Red Red Pink Pink Pink Brown Yellow Brown Pink Pink Pink Red
Row 3: Red Red Red Pink Pink Pink Brown Gray Yellow Yellow Yellow Yellow Red Red Pink Pink Pink Brown Gray Yellow Yellow Yellow Yellow Red
Row 4: Red Red Red Pink Pink Pink Brown Brown Brown Pink Pink Pink Red Red Pink Pink Pink Brown Brown Brown Pink Pink Pink Red
Row 5: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Row 6: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Yellow Pink Pink
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Yellow Pink Pink
Row 10: Red Red Pink Pink Yellow Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Pink Pink Yellow Pink Pink
Row 11: Red Red Pink Brown Yellow Brown Pink Pink Red Red Red Red Red Red Red Red Red Red Red Pink Pink Yellow Pink Pink
Row 12: Red Red Pink Brown Gray Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Pink Brown Yellow Brown Pink
Row 13: Red Red Pink Brown Brown Brown Pink Pink Red Red Red Red Red Red Red Red Red Red Red Pink Brown Gray Yellow Yellow
Row 14: Red Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Pink Brown Brown Brown Pink
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink
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
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
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
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 Blue 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 Brown Blue Brown Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Gray Brown Black Blue Blue Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Gray Brown Brown Brown Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Black Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Black Orange Orange Gray
Row 13: Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Black Orange Orange Orange Gray
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray
Row 22: 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
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 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 Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Orange Orange 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 Orange Orange Blue Orange Orange 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 Orange Orange Blue Orange Orange 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 Orange Orange Blue Orange Orange 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 Orange Orange Blue Orange Orange Gray Gray Gray Orange Orange Orange Orange Blue Orange Orange Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Orange Orange Gray Gray Gray Orange Orange Orange Orange Blue Orange Orange Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Orange Orange Gray Gray Gray Orange Orange Orange Orange Blue Orange Orange Gray
Row 10: Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Gray Orange Brown Blue Brown Orange Gray Gray Gray Orange Orange Orange Orange Blue Orange Orange Gray
Row 11: Orange Orange Orange Blue Orange Orange Blue Orange Orange Orange Orange Gray Orange Brown Black Blue Blue Gray Gray Gray Orange Orange Orange Brown Blue Brown Orange Gray
Row 12: Orange Orange Orange Blue Orange Brown Blue Brown Orange Orange Orange Gray Orange Brown Brown Brown Orange Gray Gray Gray Orange Orange Orange Brown Black Blue Blue Gray
Row 13: Orange Orange Orange Blue Orange Brown Black Blue Blue Blue Blue Gray Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Brown Brown Brown Orange Gray
Row 14: Orange Orange Orange Blue Orange Brown Brown Brown Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray
Row 15: Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Orange Orange Brown Blue Brown Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Orange Orange Brown Black Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Blue Orange Orange Orange Gray
Row 18: Orange Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Brown Blue Brown Orange Orange Gray
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Brown Black Blue Blue Blue Gray
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Brown Brown Brown Orange Orange Gray
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray
Row 22: 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
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 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
Row 3: Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Pink Pink Pink Green Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Purple Yellow Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Purple Green Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Purple Yellow Purple 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 Yellow 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 Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Brown Brown Brown Brown Brown Pink Pink Pink Green Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Green Pink Pink Pink Pink Pink
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
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 Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Green Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink 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 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 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 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 Pink Pink Pink Yellow Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Pink Pink Purple Yellow Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Pink Pink Purple Green Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Pink Pink Purple Yellow Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Pink Pink Pink Yellow Pink Pink Pink 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
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 Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Pink Pink Pink Yellow Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Pink Pink Pink Yellow Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Pink Pink Purple Yellow Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Yellow Pink Pink Pink Pink Pink
Row 13: Brown Brown Brown Brown Brown Pink Pink Purple Green Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Yellow Pink Pink Pink Pink Pink
Row 14: Brown Brown Brown Brown Brown Pink Pink Purple Yellow Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Purple Yellow Purple Pink Pink Pink Pink
Row 15: Brown Brown Brown Brown Brown Pink Pink Pink Yellow Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Pink Pink Purple Green Yellow Yellow Yellow Yellow Yellow
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Purple Yellow Purple Pink Pink Pink Pink
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Yellow Pink Pink Pink Pink Pink
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 Pink Pink Yellow Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Pink Purple Yellow Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Pink Purple Green Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Pink Purple Yellow Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Yellow Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Yellow Pink Pink Pink 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 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 Brown Brown Brown Brown
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 Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
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 Orange
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 Orange
Row 11: 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
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Gray Pink Pink Pink Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Yellow Blue Yellow Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Blue Blue Gray Blue Blue Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Yellow Blue Yellow Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Blue 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 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 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 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 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 Orange Orange Orange Orange Orange Orange Orange
Row 30: 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
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 Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Yellow Blue Yellow Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Yellow Blue Yellow Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Yellow Blue Yellow Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Gray Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Yellow Blue Yellow Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Pink Pink Blue Pink Pink Pink 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 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 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: Green Green Green Red Yellow Red Black Gray Yellow Red Yellow Red
Row 2: Green Green Green Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 3: Green Green Green Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 4: Green Green Green Red Red Red Black Yellow Red Red Red Red
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Gray Yellow Yellow Gray Red Black Gray Yellow Yellow Gray Red
Row 7: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 8: Black Gray Gray Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 9: Black Red Yellow Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 10: Black Yellow Red Red Red Red Black Yellow Red Red Red Red
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Gray Yellow Yellow Gray Red Black Gray Yellow Yellow Gray Red
Row 13: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 14: Black Gray Gray Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 15: Black Red Yellow Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 16: Black Yellow Red Red Red Red Black Yellow Red Red Red Red
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Gray Yellow Yellow Gray Red Black Gray Yellow Yellow Gray Red
Row 19: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 20: Black Gray Gray Green Green Green Green Green Green Gray Yellow Gray
Row 21: Black Red Yellow Green Green Green Green Green Green Yellow Yellow Gray
Row 22: Black Yellow Red Green Green Green Green Green Green Red Red Red
Row 23: Black Black Black Green Green Green Green Green Green Black Black Black
Output:
Row 1: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 2: Black Gray Gray Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 3: Black Red Yellow Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 4: Black Yellow Red Red Red Red Black Yellow Red Red Red Red
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Gray Yellow Yellow Gray Red Black Gray Yellow Yellow Gray Red
Row 7: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 8: Black Gray Gray Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 9: Black Red Yellow Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 10: Black Yellow Red Red Red Red Black Yellow Red Red Red Red
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Gray Yellow Yellow Gray Red Black Gray Yellow Yellow Gray Red
Row 13: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 14: Black Gray Gray Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 15: Black Red Yellow Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 16: Black Yellow Red Red Red Red Black Yellow Red Red Red Red
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Gray Yellow Yellow Gray Red Black Gray Yellow Yellow Gray Red
Row 19: Black Gray Yellow Red Yellow Red Black Gray Yellow Red Yellow Red
Row 20: Black Gray Gray Gray Yellow Gray Black Gray Gray Gray Yellow Gray
Row 21: Black Red Yellow Yellow Yellow Gray Black Red Yellow Yellow Yellow Gray
Row 22: Black Yellow Red Red Red Red Black Yellow Red Red Red Red
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple
Row 2: Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Gray Gray Gray Gray Gray Gray Pink Purple
Row 3: Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Gray Gray Gray Gray Gray Gray Green Purple
Row 4: Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Gray Gray Gray Gray Gray Gray Orange Purple
Row 5: Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Gray Gray Gray Gray Gray Gray Pink Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Purple Purple Purple
Row 7: Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Gray Gray Gray Gray Gray Gray Pink Purple
Row 8: Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple Yellow Brown Green Gray Gray Green Purple
Row 9: Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple
Row 10: Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Gray Gray
Row 12: Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple Gray Gray Gray Yellow Pink Gray Gray
Row 13: Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple Gray Gray Gray Pink Yellow Green Purple
Row 14: Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple Gray Gray Gray Yellow Brown Orange Purple
Row 15: Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple
Row 3: Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple
Row 4: Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple
Row 5: Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple
Row 8: Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple
Row 9: Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple
Row 10: Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple Yellow Yellow Pink Yellow Pink Pink Purple
Row 13: Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple Yellow Brown Green Pink Yellow Green Purple
Row 14: Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple Purple Pink Brown Yellow Brown Orange Purple
Row 15: Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple Red Brown Yellow Orange Red Pink Purple
Example 3
Input:
Row 1: Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple
Row 2: Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple Brown Orange Orange Black Black Black Black Black Black Purple
Row 3: Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple Orange Green Pink Black Black Black Black Black Black Black
Row 4: Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple Green Green Pink Black Black Black Black Black Black Black
Row 5: Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Black Black Black Black Black Black Black Black Black Black Black
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Black Black Black Black
Row 7: Yellow Pink Purple Yellow Green Pink Orange Orange Yellow Pink Yellow Pink Black Black Black Black Black Black Black Black Black Black Purple
Row 8: Pink Pink Purple Orange Yellow Orange Green Orange Green Green Pink Pink Black Black Black Black Black Black Black Black Black Black Purple
Row 9: Yellow Black Black Orange Green Orange Yellow Green Pink Green Yellow Brown Black Black Black Black Black Green Pink Green Black Black Black
Row 10: Green Black Black Green Pink Pink Orange Brown Brown Yellow Green Green Black Black Black Black Black Brown Brown Yellow Black Black Black
Row 11: Green Black Black Green Brown Yellow Pink Green Brown Brown Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple
Row 12: Pink Black Black Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple
Row 13: Brown Black Black Orange Green Pink Green Green Pink Orange Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple
Row 14: Orange Black Black Green Green Pink Yellow Green Green Brown Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple
Row 15: Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Purple
Row 16: Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Yellow Pink Purple Yellow Green Pink Black Black Yellow Pink Yellow Pink Black Black Black Pink Orange Orange Yellow Pink Yellow Pink Purple
Row 18: Pink Black Black Orange Yellow Orange Black Black Green Green Pink Pink Black Black Black Orange Black Black Black Black Black Black Purple
Row 19: Yellow Black Black Orange Green Orange Black Black Pink Green Yellow Black Black Black Black Black Black Black Black Black Black Black Purple
Row 20: Green Black Black Green Pink Pink Black Black Brown Yellow Green Black Black Black Black Black Black Brown Brown Yellow Green Green Purple
Row 21: Green Black Black Green Brown Yellow Black Black Brown Brown Green Black Black Black Black Black Black Green Brown Brown Green Orange Purple
Row 22: Pink Black Black Brown Orange Orange Yellow Brown Green Pink Pink Black Black Black Black Black Black Brown Black Black Pink Brown Purple
Row 23: Brown Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Green Black Black Brown Brown Purple
Row 24: Orange Black Black Black Black Black Black Black Black Black Orange Pink Purple Green Green Pink Yellow Green Black Black Orange Pink Purple
Row 25: Orange Brown Black Black Black Black Black Black Black Black Orange Brown Purple Pink Yellow Green Pink Orange Black Black Orange Black Black
Row 26: Purple Purple Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Black Black
Output:
Row 1: Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple
Row 2: Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple
Row 3: Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple
Row 4: Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple
Row 5: Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown 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: Yellow Pink Purple Yellow Green Pink Orange Orange Yellow Pink Yellow Pink Purple Yellow Green Pink Orange Orange Yellow Pink Yellow Pink Purple
Row 8: Pink Pink Purple Orange Yellow Orange Green Orange Green Green Pink Pink Purple Orange Yellow Orange Green Orange Green Green Pink Pink Purple
Row 9: Yellow Brown Purple Orange Green Orange Yellow Green Pink Green Yellow Brown Purple Orange Green Orange Yellow Green Pink Green Yellow Brown Purple
Row 10: Green Green Purple Green Pink Pink Orange Brown Brown Yellow Green Green Purple Green Pink Pink Orange Brown Brown Yellow Green Green Purple
Row 11: Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple
Row 12: Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple
Row 13: Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple
Row 14: Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple
Row 15: Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown 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: Yellow Pink Purple Yellow Green Pink Orange Orange Yellow Pink Yellow Pink Purple Yellow Green Pink Orange Orange Yellow Pink Yellow Pink Purple
Row 18: Pink Pink Purple Orange Yellow Orange Green Orange Green Green Pink Pink Purple Orange Yellow Orange Green Orange Green Green Pink Pink Purple
Row 19: Yellow Brown Purple Orange Green Orange Yellow Green Pink Green Yellow Brown Purple Orange Green Orange Yellow Green Pink Green Yellow Brown Purple
Row 20: Green Green Purple Green Pink Pink Orange Brown Brown Yellow Green Green Purple Green Pink Pink Orange Brown Brown Yellow Green Green Purple
Row 21: Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple Green Brown Yellow Pink Green Brown Brown Green Orange Purple
Row 22: Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple Brown Orange Orange Yellow Brown Green Pink Pink Brown Purple
Row 23: Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple Orange Green Pink Green Green Pink Orange Brown Brown Purple
Row 24: Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple Green Green Pink Yellow Green Green Brown Orange Pink Purple
Row 25: Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Purple Pink Yellow Green Pink Orange Orange Pink Orange Brown Purple
Row 26: 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: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange
Row 2: Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Orange Orange Orange Orange Orange
Row 3: Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Orange Orange Orange Orange Orange
Row 4: Gray Gray Yellow Orange Orange Orange Orange Orange Orange Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Orange Orange Orange Orange Orange
Row 5: Gray Purple Brown Orange Orange Orange Orange Orange Orange Purple Brown Black Gray Purple Brown Black Gray Purple Brown Orange Orange Orange Orange Orange
Row 6: Gray Brown Gray Orange Orange Orange Orange Orange Orange Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Orange Orange Orange Orange Orange
Row 7: Gray Black Gray Orange Orange Orange Orange Orange Orange Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green
Row 8: Gray Yellow Yellow Orange Orange Orange Orange Orange Orange Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown
Row 9: Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple
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 Yellow Red Gray Gray Yellow Orange Orange Orange Orange Orange Orange Orange Orange Red Gray Gray Yellow Red Gray Gray Yellow Red
Row 12: Gray Blue Pink Brown Gray Blue Pink Orange Orange Orange Orange Orange Orange Orange Orange Brown Gray Blue Pink Brown Gray Blue Pink Brown
Row 13: Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Orange Orange Orange Brown Gray Gray Yellow Brown Gray Gray Yellow Brown
Row 14: Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Orange Orange Orange Black Gray Purple Brown Black Gray Purple Brown Black
Row 15: Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple
Row 16: Gray Black Gray Green Gray Black Gray Green Gray Black Gray Orange Orange Orange Gray Green Gray Black Gray Green Gray Black Gray Green
Row 17: Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Orange Orange Orange Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown
Row 18: Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Blue Brown Purple
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray
Row 20: Gray Gray Yellow Red Gray Gray Yellow Red Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Red
Row 21: Gray Blue Pink Brown Gray Blue Pink Brown Gray Orange Orange Orange Orange Orange Orange Brown Gray Orange Orange Orange Orange Orange Pink Brown
Row 22: Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Orange Orange Orange Orange Orange Orange Brown Gray Orange Orange Orange Orange Orange Yellow Brown
Row 23: Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Orange Orange Orange Orange Orange Brown Black
Row 24: Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Orange Orange Orange Orange Orange Gray Purple
Row 25: Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Orange Orange Orange Orange Orange Gray 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red
Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown
Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown
Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black
Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple
Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green
Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown
Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue 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 Gray
Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red
Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown
Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown
Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black
Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple
Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green
Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown Gray Yellow Yellow Brown
Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue Brown Purple Gray Blue 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 Gray
Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red Gray Gray Yellow Red
Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown Gray Blue Pink Brown
Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown Gray Gray Yellow Brown
Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black Gray Purple Brown Black
Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple Gray Brown Gray Purple
Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray Green Gray Black Gray 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 Brown Yellow Yellow Yellow Brown 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
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Purple Yellow Orange Yellow Purple Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Pink 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 Green Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Brown Brown Brown
Row 2: Brown Brown Brown
Row 3: Brown Brown Brown
Row 4: Brown Brown Brown
Row 5: Yellow Brown Brown
Row 6: Brown Brown Brown
Row 7: Brown Brown Brown
Row 8: Brown Brown Brown
Row 9: Brown Yellow Brown
Row 10: Brown Brown Brown
Row 11: Brown Brown Brown
Row 12: Brown Brown Brown
Row 13: Brown Brown Brown
Row 14: Brown Brown Yellow
Output:
Row 1: Brown Brown Brown
Row 2: Brown Brown Brown
Row 3: Brown Brown Brown
Row 4: Brown Pink Brown
Row 5: Brown Brown Brown
Row 6: Brown Orange Brown
Row 7: Brown Brown Brown
Row 8: Green Brown Pink
Row 9: Brown Brown Brown
Row 10: Purple Brown Orange
Row 11: Brown Brown Brown
Row 12: Brown Brown Brown
Row 13: Brown Green Brown
Row 14: Brown Brown Brown
Example 3
Input:
Row 1: Black Black Black Black Red 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 Red
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Red 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 Green Black
Row 2: Black Black Black Purple Black Orange Black Black Black Black Black Black Black Black Black
Row 3: Black Green Black Pink Black Black Black Black Black Black Black Black Black Purple Black
Row 4: 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: Red Red Red Red Black 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 2: Black Red Red Red Red Red Red Red Black Red Red Red Black Red Red Black Red Red Red Red Red Red Black 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 Black Red Red
Row 4: Red Red 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 Red
Row 5: Black Red Red Red Red Red Red Red Red Red Black 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 Black Red Red Red Black Red Red Black Red Red Red Red
Row 7: Red Red Red Red Red Red Red Black Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Black Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Red
Row 9: Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red Red Red Red Red Red Red Black 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 Black Red Red Red Red Red Red Black 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 Black Red Red Red Red Black Red Red Red Black Red Red Black Red Red Red Red Red Black 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 Black Red Red Red Red Red Red Red Black Red Red Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Pink Red Red Red Red Red Green Red Pink Red Green Red Pink Green Red Pink Red Red Red Red Green Red Pink Red Red Red Red Red
Red Red Red Purple Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Orange Red Red Red Red Green Red Pink Red
Red Orange Green Red Pink Red Red Purple Red Orange Red Purple Red Orange Purple Red Orange Red Red Red Red Purple Red Orange Red Red Red Red Red
Red Pink Red Red Red Red Red Red Red Green Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Orange Red
Red Red Purple Red Orange Red Red Red Red Red Red Red Red Red Red Red Green Red Pink Red Green Red Pink Green Red Pink Red Red Red
Red Orange Red Red Red Red Green Red Pink Purple Red Orange Red Green Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Red Pink Green Red Pink Red Red Red Red Red Red Red Red Red Red Purple Red Orange Red Purple Red Orange Purple Red Orange Green Red Pink
Red Red Red Red Red Red Purple Red Orange Green Red Pink Red Purple Red Orange Red Red Red Red Green Red Pink Red Red Red Red Red Red
Purple Red Orange Purple Red Orange Red Red Red Red Red Red Red Red Red Red Green Red Pink Red Red Red Red Green Red Pink Purple Red Orange
Red Red Red Red Red Red Red Red Red Purple Red Orange Red Red Red Red Red Red Red Red Purple Red Orange Red Red Red Red Red Red
Red Green Red Pink Red Red Green Red Pink Red Green Red Pink Green Red Pink Purple Red Orange Green Red Pink Red Purple Red Orange Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Red Pink Red Red Red Red Red Green Red Pink Green Red
Red Purple Red Orange Red Red Purple Red Orange Red Purple Red Orange Purple Red Orange Red Red Red Purple Red Orange 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 Pink Yellow Black Gray Black Blue Gray Red Pink Red Pink Black Blue Blue Blue Gray Brown Gray
Row 2: Brown Red Pink Gray Yellow Black Yellow Gray Brown Gray Gray Blue Yellow Black Gray Pink Blue Red Gray
Row 3: Pink Gray Brown Brown Red Black Yellow Black Gray Blue Brown Yellow Gray Black Yellow Blue Pink Yellow Pink
Row 4: Red Brown Yellow Red Yellow Brown Red Gray Blue Pink Yellow Gray Pink Brown Gray Black Gray Pink Pink
Row 5: Pink Gray Gray Blue Black Black Yellow Pink Red Brown Brown Blue Black Pink Red Blue Blue Black Blue
Row 6: Brown Red Blue Brown Yellow Pink Red Blue Gray Pink Blue Brown Red Red Red Yellow Black Brown Black
Row 7: Red Yellow Gray Brown Blue Red Red Black Yellow Gray Yellow Red Pink Gray Black Black Red Black Blue
Row 8: Pink Pink Pink Black Yellow Pink Red Black Red Black Pink Black Yellow Yellow Black Brown Brown Blue Red
Row 9: Gray Red Blue Brown Gray Red Black Yellow Brown Red Brown Red Pink Yellow Black Black Blue Gray Blue
Row 10: Brown Yellow Red Gray Yellow Yellow Blue Red Brown Blue Yellow Brown Brown Brown Brown Gray Brown Pink Black
Row 11: Red Red Brown Yellow Black Black Red Yellow Pink Gray Brown Blue Blue Blue Gray Black Yellow Gray Brown
Row 12: Pink Black Yellow Red Gray Red Brown Brown Black Brown Blue Black Yellow Yellow Pink Red Black Yellow Brown
Row 13: Yellow Pink Blue Brown Brown Gray Pink Yellow Gray Red Pink Blue Gray Red Red Red Yellow Pink Black
Row 14: Red Yellow Pink Yellow Black Brown Pink Pink Gray Yellow Yellow Gray Gray Gray Yellow Pink Pink Blue Pink
Row 15: Pink Yellow Red Red Yellow Blue Pink Pink Red Yellow Yellow Pink Red Pink Red Yellow Pink Black Yellow
Row 16: Gray Red Red Pink Brown Yellow Black Yellow Brown Yellow Gray Yellow Brown Yellow Gray Yellow Pink Pink Black
Row 17: Brown Brown Brown Blue Brown Pink Red Black Red Pink Gray Yellow Red Gray Gray Red Gray Pink Yellow
Row 18: Red Pink Blue Red Gray Yellow Black Blue Black Blue Blue Brown Pink Gray Pink Pink Gray Gray Red
Row 19: Blue Pink Brown Blue Blue Yellow Blue Gray Red Gray Gray Gray Black Red Red Gray Gray Yellow Gray
Row 20: Black Red Yellow Pink Brown Pink Brown Pink Pink Gray Pink Brown Brown Gray Blue Black Gray Blue Red
Row 21: Red Gray Gray Yellow Gray Black Black Red Brown Pink Red Red Brown Black Brown Brown Pink Blue Red
Row 22: Blue Brown Blue Blue Gray Black Black Gray Yellow Brown Brown Blue Red Pink Pink Black Blue Red Red
Row 23: Black Black Gray Yellow Yellow Blue Yellow Yellow Blue Brown Brown Black Brown Black Yellow Gray Red Brown Red
Row 24: Black Blue Blue Black Black Yellow Yellow Brown Blue Gray Yellow Brown Red Brown Red Black Pink Pink Blue
Row 25: Brown Yellow Red Gray Black Black Red Yellow Red Red Yellow Yellow Gray Brown Brown Brown Black Blue Yellow
Row 26: Blue Pink Black Red Red Black Brown Brown Gray Gray Brown Gray Yellow Brown Black Yellow Brown Blue Gray
Row 27: Red Yellow Pink Gray Brown Gray Black Pink Blue Yellow Red Yellow Pink Pink Gray Pink Pink Pink Yellow
Row 28: Pink Brown Black Black Pink Black Gray Yellow Red Brown Pink Blue Black Black Gray Yellow Yellow Red Brown
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Brown Red Pink Gray Yellow Black Yellow Gray Brown Gray Gray Blue Yellow Black Gray Pink Blue Red Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green
Row 4: Green Brown Yellow Red Yellow Brown Red Gray Blue Pink Yellow Gray Pink Brown Gray Black Green Pink Green
Row 5: Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Green Black Green
Row 6: Green Red Green Brown Yellow Pink Red Blue Gray Pink Blue Brown Red Red Green Yellow Green Brown Green
Row 7: Green Yellow Green Brown Green Green Green Green Green Green Green Green Green Gray Green Black Green Black Green
Row 8: Green Pink Green Black Green Pink Red Black Red Black Pink Black Green Yellow Green Brown Green Blue Green
Row 9: Green Red Green Brown Green Red Green Green Green Green Green Red Green Yellow Green Black Green Gray Green
Row 10: Green Yellow Green Gray Green Yellow Green Red Brown Blue Green Brown Green Brown Green Gray Green Pink Green
Row 11: Green Red Green Yellow Green Black Green Yellow Green Gray Green Blue Green Blue Green Black Green Gray Green
Row 12: Green Black Green Red Green Red Green Brown Green Brown Green Black Green Yellow Green Red Green Yellow Green
Row 13: Green Pink Green Brown Green Gray Green Yellow Green Red Green Blue Green Red Green Red Green Pink Green
Row 14: Green Yellow Green Yellow Green Brown Green Pink Green Yellow Green Gray Green Gray Green Pink Green Blue Green
Row 15: Green Yellow Green Red Green Blue Green Pink Green Yellow Green Pink Green Pink Green Yellow Green Black Green
Row 16: Green Red Green Pink Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Yellow Green Pink Green
Row 17: Green Brown Green Blue Green Pink Green Black Green Pink Green Yellow Green Gray Green Red Green Pink Green
Row 18: Green Pink Green Red Green Yellow Green Blue Green Blue Green Brown Green Gray Green Pink Green Gray Green
Row 19: Green Pink Green Blue Green Yellow Green Gray Green Gray Green Gray Green Red Green Gray Green Yellow Green
Row 20: Green Red Green Pink Green Pink Green Pink Green Green Green Brown Green Gray Green Black Green Blue Green
Row 21: Green Gray Green Yellow Green Black Green Red Brown Pink Red Red Green Black Green Brown Green Blue Green
Row 22: Green Brown Green Blue Green Black Green Green Green Green Green Green Green Pink Green Black Green Red Green
Row 23: Green Black Green Yellow Green Blue Yellow Yellow Blue Brown Brown Black Brown Black Green Gray Green Brown Green
Row 24: Green Blue Green Black Green Green Green Green Green Green Green Green Green Green Green Black Green Pink Green
Row 25: Green Yellow Green Gray Black Black Red Yellow Red Red Yellow Yellow Gray Brown Brown Brown Green Blue Green
Row 26: Green Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Green
Row 27: Green Yellow Pink Gray Brown Gray Black Pink Blue Yellow Red Yellow Pink Pink Gray Pink Pink Pink Green
Row 28: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Gray Yellow Gray Red Black Gray Orange Gray Orange Orange Blue Yellow Gray Orange Brown Yellow Brown Yellow Pink Pink Red
Row 2: Black Blue Yellow Blue Gray Blue Gray Gray Gray Pink Blue Red Orange Brown Red Gray Pink Yellow Brown Red Gray
Row 3: Orange Pink Blue Orange Orange Orange Orange Red Black Black Brown Yellow Blue Red Yellow Gray Black Orange Gray Orange Blue
Row 4: Brown Brown Yellow Brown Orange Red Black Black Brown Black Blue Pink Gray Pink Blue Red Pink Black Pink Yellow Orange
Row 5: Orange Yellow Brown Yellow Black Orange Pink Gray Black Pink Brown Red Red Brown Orange Black Black Yellow Yellow Gray Pink
Row 6: Yellow Black Yellow Blue Orange Black Yellow Blue Red Black Black Red Black Red Pink Red Yellow Brown Black Blue Gray
Row 7: Pink Red Gray Blue Blue Brown Black Brown Pink Black Pink Yellow Blue Blue Yellow Pink Red Blue Yellow Gray Red
Row 8: Blue Pink Brown Brown Pink Yellow Brown Black Pink Gray Brown Pink Red Pink Gray Yellow Gray Red Pink Gray Blue
Row 9: Orange Blue Pink Brown Brown Yellow Brown Orange Brown Gray Black Brown Yellow Black Brown Black Pink Blue Brown Pink Orange
Row 10: Blue Red Pink Gray Brown Red Blue Black Red Black Pink Black Blue Yellow Brown Pink Gray Blue Red Blue Blue
Row 11: Pink Gray Orange Brown Black Orange Pink Black Pink Red Pink Blue Red Red Blue Black Gray Brown Brown Pink Brown
Row 12: Yellow Blue Brown Gray Yellow Black Red Pink Red Gray Red Black Red Red Black Pink Yellow Yellow Red Black Orange
Row 13: Pink Gray Black Yellow Gray Gray Brown Red Pink Orange Black Yellow Brown Red Black Pink Pink Pink Red Orange Pink
Row 14: Black Brown Brown Yellow Brown Brown Blue Black Brown Pink Gray Yellow Black Red Gray Red Gray Blue Gray Orange Orange
Row 15: Yellow Gray Brown Pink Pink Yellow Gray Blue Pink Blue Brown Yellow Brown Pink Orange Brown Yellow Blue Red Gray Brown
Row 16: Brown Red Blue Brown Yellow Brown Red Red Brown Blue Pink Pink Pink Brown Yellow Black Orange Red Brown Orange Gray
Row 17: Black Gray Brown Blue Gray Orange Blue Orange Black Gray Blue Black Gray Gray Blue Brown Gray Yellow Red Orange Blue
Row 18: Black Pink Yellow Yellow Red Pink Blue Gray Pink Brown Blue Brown Gray Red Orange Red Pink Yellow Pink Pink Orange
Row 19: Black Blue Yellow Blue Black Orange Yellow Red Gray Brown Black Brown Blue Brown Red Orange Gray Brown Pink Black Black
Row 20: Blue Pink Blue Pink Brown Brown Black Yellow Red Pink Orange Pink Black Brown Gray Red Red Red Yellow Gray Gray
Row 21: Yellow Gray Gray Black Pink Pink Yellow Brown Yellow Brown Red Black Gray Pink Yellow Blue Orange Blue Orange Orange Yellow
Row 22: Orange Orange Blue Yellow Yellow Orange Yellow Yellow Brown Pink Blue Blue Brown Red Pink Brown Yellow Gray Black Brown Orange
Row 23: Yellow Pink Brown Gray Red Blue Red Yellow Gray Blue Yellow Blue Blue Black Blue Red Blue Brown Gray Blue Gray
Row 24: Pink Yellow Blue Blue Brown Brown Gray Yellow Black Orange Red Orange Black Yellow Gray Gray Brown Red Yellow Yellow Red
Row 25: Blue Red Red Black Blue Pink Red Yellow Blue Blue Gray Orange Yellow Yellow Black Brown Brown Brown Brown Pink Red
Row 26: Yellow Gray Brown Blue Orange Yellow Gray Red Black Yellow Red Gray Black Orange Blue Red Blue Red Yellow Brown Black
Row 27: Yellow Red Blue Pink Pink Yellow Orange Brown Brown Black Black Yellow Pink Pink Brown Gray Yellow Red Orange Black Pink
Output:
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: Black Blue Yellow Blue Gray Blue Gray Gray Gray Pink Blue Red Orange Brown Red Gray Pink Yellow Brown Red Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Green
Row 4: Green Brown Yellow Brown Orange Red Black Black Brown Black Blue Pink Gray Pink Blue Red Pink Black Green Yellow Green
Row 5: Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Gray Green
Row 6: Green Black Green Blue Orange Black Yellow Blue Red Black Black Red Black Red Pink Red Green Brown Green Blue Green
Row 7: Green Red Green Blue Green Green Green Green Green Green Green Green Green Green Green Pink Green Blue Green Gray Green
Row 8: Green Pink Green Brown Green Yellow Brown Black Pink Gray Brown Pink Red Pink Green Yellow Green Red Green Gray Green
Row 9: Green Blue Green Brown Green Yellow Green Green Green Green Green Green Green Black Green Black Green Blue Green Pink Green
Row 10: Green Red Green Gray Green Red Green Black Red Black Pink Black Green Yellow Green Pink Green Blue Green Blue Green
Row 11: Green Gray Green Brown Green Orange Green Black Green Green Green Blue Green Red Green Black Green Brown Green Pink Green
Row 12: Green Blue Green Gray Green Black Green Pink Green Gray Green Black Green Red Green Pink Green Yellow Green Black Green
Row 13: Green Gray Green Yellow Green Gray Green Red Green Orange Green Yellow Green Red Green Pink Green Pink Green Orange Green
Row 14: Green Brown Green Yellow Green Brown Green Black Green Pink Green Yellow Green Red Green Red Green Blue Green Orange Green
Row 15: Green Gray Green Pink Green Yellow Green Blue Green Blue Green Yellow Green Pink Green Brown Green Blue Green Gray Green
Row 16: Green Red Green Brown Green Brown Green Red Green Blue Green Pink Green Brown Green Black Green Red Green Orange Green
Row 17: Green Gray Green Blue Green Orange Green Orange Green Gray Green Black Green Gray Green Brown Green Yellow Green Orange Green
Row 18: Green Pink Green Yellow Green Pink Green Gray Green Brown Blue Brown Green Red Green Red Green Yellow Green Pink Green
Row 19: Green Blue Green Blue Green Orange Green Red Green Green Green Green Green Brown Green Orange Green Brown Green Black Green
Row 20: Green Pink Green Pink Green Brown Green Yellow Red Pink Orange Pink Black Brown Green Red Green Red Green Gray Green
Row 21: Green Gray Green Black Green Pink Green Green Green Green Green Green Green Green Green Blue Green Blue Green Orange Green
Row 22: Green Orange Green Yellow Green Orange Yellow Yellow Brown Pink Blue Blue Brown Red Pink Brown Green Gray Green Brown Green
Row 23: Green Pink Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green Blue Green
Row 24: Green Yellow Green Blue Brown Brown Gray Yellow Black Orange Red Orange Black Yellow Gray Gray Brown Red Green Yellow Green
Row 25: Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green
Row 26: Green Gray Brown Blue Orange Yellow Gray Red Black Yellow Red Gray Black Orange Blue Red Blue Red Yellow Brown Green
Row 27: 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: Yellow Orange Orange Gray Orange Yellow Orange Gray Orange Yellow Orange Yellow Gray Gray Gray Orange Yellow Gray Orange Orange Gray Gray Yellow Yellow Gray Gray Yellow Yellow
Row 2: Gray Orange Gray Orange Gray Orange Orange Yellow Gray Gray Gray Gray Yellow Yellow Yellow Gray Orange Gray Orange Orange Orange Gray Gray Orange Orange Gray Orange Yellow
Row 3: Yellow Orange Gray Orange Gray Orange Yellow Orange Gray Yellow Yellow Orange Gray Gray Orange Orange Orange Gray Yellow Orange Yellow Yellow Orange Yellow Gray Yellow Gray Orange
Row 4: Yellow Yellow Gray Orange Gray Orange Gray Yellow Gray Gray Orange Yellow Gray Orange Yellow Gray Yellow Gray Yellow Gray Yellow Yellow Orange Yellow Gray Yellow Yellow Yellow
Row 5: Gray Gray Gray Gray Yellow Gray Orange Yellow Gray Orange Yellow Orange Gray Gray Orange Orange Orange Gray Yellow Yellow Orange Orange Orange Orange Orange Orange Gray 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 Green Green
Row 2: Gray Orange Gray Orange Gray Orange Orange Yellow Gray Gray Gray Gray Yellow Yellow Yellow Gray Orange Gray Orange Orange Orange Gray Gray Orange Orange Gray Orange 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 Gray Green
Row 4: Green Yellow Gray Orange Gray Orange Gray Yellow Gray Gray Orange Yellow Gray Orange Yellow Gray Yellow Gray Yellow Gray Yellow Yellow Orange Yellow Gray Yellow Yellow 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
Here is the input grid for the test example:
Input:
Row 1: Black Gray Yellow Purple Pink Pink Black Yellow Black Pink Gray Pink Black Pink Yellow Pink Gray Purple Purple Pink
Row 2: Purple Brown Red Brown Gray Black Purple Red Gray Pink Yellow Yellow Brown Yellow Brown Purple Purple Purple Pink Purple
Row 3: Purple Red Red Gray Pink Black Gray Gray Red Yellow Yellow Yellow Pink Pink Gray Pink Purple Pink Pink Gray
Row 4: Red Pink Red Black Black Yellow Yellow Black Yellow Red Pink Black Pink Red Black Black Purple Gray Purple Yellow
Row 5: Yellow Black Yellow Purple Black Pink Yellow Gray Purple Pink Black Brown Pink Gray Pink Pink Black Yellow Yellow Yellow
Row 6: Yellow Purple Pink Purple Gray Yellow Brown Pink Purple Black Brown Red Pink Purple Yellow Brown Black Black Brown Pink
Row 7: Brown Brown Brown Pink Black Brown Pink Purple Yellow Purple Purple Yellow Brown Brown Gray Black Red Red Brown Purple
Row 8: Black Red Red Pink Pink Gray Yellow Brown Gray Yellow Purple Red Gray Red Black Brown Purple Red Red Gray
Row 9: Brown Red Purple Brown Pink Red Red Gray Black Pink Pink Pink Brown Purple Gray Brown Brown Purple Red Red
Row 10: Red Red Red Pink Pink Gray Pink Black Brown Gray Red Yellow Purple Yellow Gray Purple Yellow Brown Yellow Black
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
Purple Brown Red Brown Gray Black Purple Red Gray Pink Yellow Yellow Brown Yellow Brown Purple Purple Purple Pink Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Green
Green Pink Red Black Black Yellow Yellow Black Yellow Red Pink Black Pink Red Black Black Purple Green Purple Green
Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Yellow Green
Green Purple Green Purple Green Green Green Green Green Green Green Green Green Green Green Green Black Green Brown Green
Green Brown Green Pink Black Brown Pink Purple Yellow Purple Purple Yellow Brown Brown Gray Black Red Green Brown Green
Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green
Green Red Purple Brown Pink Red Red Gray Black Pink Pink Pink Brown Purple Gray Brown Brown Purple Red 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 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 Yellow Yellow Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Purple Purple Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Yellow Yellow Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Purple Yellow Yellow Purple Yellow Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow 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 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
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
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Purple Red Purple Purple Purple Purple Red Red Red Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Red Red Red Purple Red Red Red Purple Red Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Red Red Red Red Red Red Purple Purple Purple Red Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Red Red Red Red Red Red Purple Red Red Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Purple Purple Purple Red Red Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Red Purple Red Red Red Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Purple Red Red Purple Red Red Purple Red Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Red Red Red Red Red Red Red Purple Red Red Red Red Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Purple Red Red Red Purple Purple Purple Purple Red Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Purple Red Red Red Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Purple Red Red Red Red Red Red Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Red Red Purple Red Purple Red Red 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
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 Orange Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Orange Pink Orange Orange Pink Orange Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Pink Pink
Row 7: Pink Pink Pink Orange Pink Pink Orange Orange Orange Orange Pink Pink Pink Pink
Row 8: Pink Pink Pink Orange Pink Pink Orange Pink Orange Pink Orange Pink Orange Pink
Row 9: Pink Pink Pink Orange Orange Orange Orange Orange Orange Pink Pink Orange Orange Pink
Row 10: Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Orange Pink Pink Pink
Row 11: Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Pink
Row 12: Pink Pink Pink Pink Pink Orange Orange Orange Orange Pink Orange Pink Pink Pink
Row 13: Pink Pink Pink Pink Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Orange 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 Red Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Red Pink Red Red Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Red Pink Red Red Pink Red Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Red Red Pink Red Pink Red Red Pink Pink Pink Pink
Row 8: Pink Pink Pink Red Pink Pink Red Red Red Red Pink Pink Pink Pink
Row 9: Pink Pink Pink Red Pink Pink Red Pink Red Pink Red Pink Red Pink
Row 10: Pink Pink Pink Red Red Red Red Red Red Pink Pink Red Red Pink
Row 11: Pink Pink Pink Red Red Red Red Red Pink Pink Red Pink Pink Pink
Row 12: Pink Pink Pink Red Red Red Red Red Red Red Pink Red Pink Pink
Row 13: Pink Pink Pink Pink Pink Red Red Red Red Pink Red Pink Pink Pink
Row 14: Pink Pink Pink Pink Red Red Red Red Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Green Green Green Green Brown Green Green Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Green Green Green Green Green Green Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Green Green Green Green Green Green Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Green Green Brown Green Green Green Green Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Green Brown Green Green Green Green Green Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Green Green Green Green Green Green 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
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Red Red Red Red Brown Red Red Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Brown Red Red Red Red Red Red Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Brown Red Red Red Red Red Red Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Red Red Red Red Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Red Brown Red Red Red Red Red Brown Brown
Here is the input grid for the test example:
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 Brown Black Black
Row 5: Black Black Brown Brown Black Black Brown Black
Row 6: Black Black Brown Black Black Brown Black Black
Row 7: Black Brown Brown Brown Black Brown Black Black
Row 8: Black Black Black Black Brown Black Black Black
Row 9: Black Brown Brown Brown Brown Brown Black Black
Row 10: Black Brown Brown Brown Brown Brown Black Brown
Row 11: Black Brown Black Black Brown Brown Brown Black
Row 12: Black Black Brown Brown Brown Brown Brown Brown
Row 13: Black Black Brown Brown Brown Black Brown 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
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 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 Red Black Black
Black Black Red Red Black Black Red Black
Black Black Red Black Black Red Black Black
Black Red Red Red Black Red Black Black
Black Black Black Black Red Black Black Black
Black Red Red Red Red Red Black Black
Black Red Red Red Red Red Black Red
Black Red Black Black Red Red Red Black
Black Black Red Red Red Red Red Red
Black Black Red Red Red Black 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 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: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Red
Row 3: Blue Blue Blue Blue Red Red Blue Red Blue Blue Blue Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Red 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
Row 6: Blue Red 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 Red
Row 8: Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 3: Blue Blue Blue Blue Gray Gray Blue Gray Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Gray 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
Row 6: Blue Gray 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 Gray
Row 8: Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Example 2
Input:
Row 1: Yellow Black Yellow Yellow Orange Purple Yellow Brown Blue Brown Black Yellow Yellow Yellow
Row 2: Blue Yellow Yellow Yellow Yellow Yellow Orange Purple Yellow Purple Yellow Yellow Yellow Black
Row 3: Black Yellow Blue Yellow Brown Yellow Brown Yellow Orange Red Black Yellow Purple Yellow
Row 4: Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Red Black Orange Black Yellow Purple
Row 5: Yellow Blue Blue Blue Yellow Blue Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 6: Yellow Black Yellow Yellow Purple Yellow Yellow Yellow Blue Yellow Yellow Orange Yellow Orange
Row 7: Orange Yellow Yellow Yellow Brown Yellow Yellow Red Purple Purple Brown Brown Black Black
Row 8: Brown Red Purple Purple Yellow Red Black Purple Yellow Yellow Yellow Yellow Orange Yellow
Row 9: Yellow Orange Yellow Yellow Yellow Red Yellow Yellow Yellow Brown Yellow Orange Yellow Yellow
Row 10: Yellow Orange Yellow Brown Purple Yellow Brown Blue Yellow Yellow Yellow Yellow Purple Yellow
Row 11: Yellow Blue Yellow Orange Brown Yellow Purple Black Yellow Yellow Yellow Yellow Black Black
Row 12: Yellow Yellow Yellow Black Brown Blue Purple Yellow Brown Brown Orange Yellow Orange Brown
Row 13: Yellow Yellow Yellow Purple Black Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Blue Yellow Yellow Blue Yellow Yellow Red Yellow Orange Yellow Yellow Yellow
Row 15: Red Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow
Row 17: Orange Yellow Yellow Yellow Blue Yellow Purple Purple Orange Black Yellow Black Orange Yellow
Row 18: Yellow Brown Black Black Yellow Black Yellow Yellow Yellow Orange Blue Red Orange Blue
Row 19: Yellow Orange Blue Yellow Yellow Yellow Yellow Yellow Black Yellow Purple Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Blue Purple Yellow Yellow Yellow Black Yellow Red Yellow Red
Row 21: Brown Yellow Red Yellow Black Blue Blue Purple Purple Yellow Blue Purple Blue Red
Row 22: Brown Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow
Row 23: Red Black Yellow Orange Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 24: Yellow Brown Yellow Blue Yellow Yellow Yellow Blue Brown Yellow Blue Yellow Blue Yellow
Output:
Row 1: Yellow Gray Yellow Yellow Gray Gray Yellow Gray Gray Gray Gray Yellow Yellow Yellow
Row 2: Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Yellow Gray Yellow Yellow Yellow Gray
Row 3: Gray Yellow Gray Yellow Gray Yellow Gray Yellow Gray Gray Gray Yellow Gray Yellow
Row 4: Yellow Yellow Gray Yellow Gray Yellow Yellow Yellow Gray Gray Gray Gray Yellow Gray
Row 5: Yellow Gray Gray Gray Yellow Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 6: Yellow Gray Yellow Yellow Gray Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Gray
Row 7: Gray Yellow Yellow Yellow Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Yellow Gray Gray Gray Yellow Yellow Yellow Yellow Gray Yellow
Row 9: Yellow Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow Gray Yellow Gray Yellow Yellow
Row 10: Yellow Gray Yellow Gray Gray Yellow Gray Gray Yellow Yellow Yellow Yellow Gray Yellow
Row 11: Yellow Gray Yellow Gray Gray Yellow Gray Gray Yellow Yellow Yellow Yellow Gray Gray
Row 12: Yellow Yellow Yellow Gray Gray Gray Gray Yellow Gray Gray Gray Yellow Gray Gray
Row 13: Yellow Yellow Yellow Gray Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Gray Yellow Yellow Yellow
Row 15: Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow
Row 17: Gray Yellow Yellow Yellow Gray Yellow Gray Gray Gray Gray Yellow Gray Gray Yellow
Row 18: Yellow Gray Gray Gray Yellow Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 19: Yellow Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Yellow Gray Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Gray Gray Yellow Yellow Yellow Gray Yellow Gray Yellow Gray
Row 21: Gray Yellow Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray
Row 22: Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow
Row 23: Gray Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow
Row 24: Yellow Gray Yellow Gray Yellow Yellow Yellow Gray Gray Yellow Gray Yellow Gray Yellow
Example 3
Input:
Row 1: Blue Red Green Red Green Green Green Green Green Green Green Green Green Green
Row 2: Green Blue Orange Green Green Red Green Green Red Red Blue Green Green Green
Row 3: Green Green Green Red Green Red Red Orange Green Green Green Orange Green Orange
Row 4: Green Green Red Red Green Orange Blue Green Red Green Orange Green Red Blue
Row 5: Green Orange Green Blue Green Green Red Green Blue Green Green Orange Red Blue
Row 6: Blue Red Red Blue Orange Red Red Blue Red Green Orange Green Blue Green
Row 7: Blue Green Green Red Orange Red Green Green Blue Blue Green Green Red Red
Row 8: Blue Red Red Blue Blue Orange Green Blue Blue Orange Red Green Green Green
Row 9: Green Green Red Blue Green Green Red Orange Green Green Red Green Orange Green
Row 10: Orange Green Blue Green Green Green Green Green Green Orange Green Orange Blue Green
Row 11: Green Green Green Green Green Green Green Green Red Red Green Orange Orange Blue
Row 12: Green Blue Blue Blue Orange Green Green Blue Orange Green Green Blue Green Green
Row 13: Green Green Orange Green Blue Green Red Green Red Green Green Orange Green Green
Row 14: Red Green Red Blue Green Green Blue Blue Blue Green Green Orange Green Orange
Row 15: Green Orange Red Blue Orange Green Orange Orange Green Red Green Red Green Green
Row 16: Green Orange Blue Green Green Blue Blue Green Green Red Green Green Green Orange
Row 17: Blue Green Red Orange Green Blue Green Blue Red Blue Orange Orange Red Blue
Row 18: Green Blue Orange Red Red Red Blue Blue Orange Orange Green Green Green Red
Row 19: Red Orange Red Red Orange Green Blue Orange Green Green Orange Orange Green Orange
Row 20: Orange Red Red Red Red Red Orange Green Green Orange Blue Green Orange Green
Row 21: Green Blue Green Green Green Blue Orange Green Green Orange Green Green Orange Green
Row 22: Green Blue Orange Blue Green Green Red Green Blue Green Green Blue Green Green
Row 23: Blue Red Green Green Orange Blue Orange Green Orange Blue Green Orange Blue Red
Row 24: Red Blue Orange Green Red Green Red Red Green Blue Blue Green Green Orange
Row 25: Green Red Green Green Green Red Orange Green Blue Green Green Green Orange Orange
Row 26: Orange Red Red Green Orange Orange Orange Green Green Green Blue Green Orange Red
Row 27: Blue Green Orange Green Red Blue Blue Green Blue Red Orange Green Green Red
Row 28: Orange Red Red Green Orange Red Red Orange Orange Green Blue Orange Green Red
Row 29: Green Red Green Green Orange Orange Blue Blue Red Orange Green Green Green Green
Output:
Row 1: Gray Gray Green Gray Green Green Green Green Green Green Green Green Green Green
Row 2: Green Gray Gray Green Green Gray Green Green Gray Gray Gray Green Green Green
Row 3: Green Green Green Gray Green Gray Gray Gray Green Green Green Gray Green Gray
Row 4: Green Green Gray Gray Green Gray Gray Green Gray Green Gray Green Gray Gray
Row 5: Green Gray Green Gray Green Green Gray Green Gray Green Green Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Green Gray Green
Row 7: Gray Green Green Gray Gray Gray Green Green Gray Gray Green Green Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Green Green Green
Row 9: Green Green Gray Gray Green Green Gray Gray Green Green Gray Green Gray Green
Row 10: Gray Green Gray Green Green Green Green Green Green Gray Green Gray Gray Green
Row 11: Green Green Green Green Green Green Green Green Gray Gray Green Gray Gray Gray
Row 12: Green Gray Gray Gray Gray Green Green Gray Gray Green Green Gray Green Green
Row 13: Green Green Gray Green Gray Green Gray Green Gray Green Green Gray Green Green
Row 14: Gray Green Gray Gray Green Green Gray Gray Gray Green Green Gray Green Gray
Row 15: Green Gray Gray Gray Gray Green Gray Gray Green Gray Green Gray Green Green
Row 16: Green Gray Gray Green Green Gray Gray Green Green Gray Green Green Green Gray
Row 17: Gray Green Gray Gray Green Gray Green Gray Gray Gray Gray Gray Gray Gray
Row 18: Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray
Row 19: Gray Gray Gray Gray Gray Green Gray Gray Green Green Gray Gray Green Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Green Green Gray Gray Green Gray Green
Row 21: Green Gray Green Green Green Gray Gray Green Green Gray Green Green Gray Green
Row 22: Green Gray Gray Gray Green Green Gray Green Gray Green Green Gray Green Green
Row 23: Gray Gray Green Green Gray Gray Gray Green Gray Gray Green Gray Gray Gray
Row 24: Gray Gray Gray Green Gray Green Gray Gray Green Gray Gray Green Green Gray
Row 25: Green Gray Green Green Green Gray Gray Green Gray Green Green Green Gray Gray
Row 26: Gray Gray Gray Green Gray Gray Gray Green Green Green Gray Green Gray Gray
Row 27: Gray Green Gray Green Gray Gray Gray Green Gray Gray Gray Green Green Gray
Row 28: Gray Gray Gray Green Gray Gray Gray Gray Gray Green Gray Gray Green Gray
Row 29: Green Gray Green Green Gray Gray Gray Gray Gray Gray Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Blue Brown Brown Brown Green Brown Orange Black Brown Blue Brown Brown Brown Orange Black Brown Orange Orange Brown
Row 2: Black Yellow Brown Red Brown Brown Brown Brown Blue Blue Brown Red Brown Brown Brown Black Red Black Brown
Row 3: Green Orange Brown Blue Orange Blue Brown Brown Orange Green Black Red Brown Black Yellow Brown Red Red Orange
Row 4: Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Green Green Brown Red Green Black Orange Green Yellow
Row 5: Blue Black Black Brown Brown Black Black Brown Brown Brown Red Brown Orange Brown Brown Orange Brown Brown Brown
Row 6: Brown Brown Yellow Brown Brown Brown Orange Blue Brown Blue Brown Yellow Blue Brown Black Brown Black Brown Brown
Row 7: Orange Black Brown Black Blue Brown Blue Yellow Orange Red Brown Blue Brown Brown Red Brown Yellow Brown Brown
Row 8: Black Brown Black Yellow Brown Brown Blue Green Green Black Brown Brown Brown Brown Brown Black Orange Black Brown
Row 9: Orange Brown Blue Yellow Green Brown Yellow Brown Red Brown Brown Yellow Brown Brown Blue Brown Green Yellow Brown
Row 10: Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Blue Black Brown Red Brown
Row 11: Brown Brown Green Brown Brown Green Brown Green Brown Red Brown Brown Orange Yellow Orange Black Brown Orange Green
Row 12: Brown Brown Black Brown Blue Green Red Red Brown Blue Yellow Brown Brown Yellow Brown Orange Brown Brown Blue
Row 13: Brown Orange Blue Black Brown Brown Brown Brown Blue Brown Brown Brown Brown Yellow Brown Brown Green Green Brown
Row 14: Black Blue Green Brown Brown Green Brown Yellow Brown Brown Yellow Brown Brown Brown Black Red Brown Brown Yellow
Row 15: Orange Brown Brown Brown Black Brown Brown Brown Orange Brown Blue Yellow Brown Red Orange Black Brown Yellow Brown
Row 16: Brown Black Brown Orange Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Yellow Brown Blue Brown Brown
Row 17: Brown Red Black Blue Brown Green Brown Brown Brown Brown Blue Blue Brown Brown Brown Green Black Blue Blue
Row 18: Brown Brown Orange Brown Red Brown Black Brown Red Red Red Red Yellow Brown Blue Brown Brown Yellow Green
Row 19: Orange Brown Green Green Brown Brown Brown Brown Brown Blue Brown Brown Blue Yellow Brown Yellow Brown Brown Red
Row 20: Blue Yellow Yellow Orange Brown Brown Yellow Blue Brown Blue Black Yellow Brown Brown Brown Brown Blue Brown Brown
Row 21: Brown Brown Brown Blue Brown Brown Blue Brown Blue Brown Brown Brown Black Blue Brown Red Yellow Green Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Brown Brown Brown Gray Brown Gray Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray Gray Brown
Gray Gray Brown Gray Brown Brown Brown Brown Gray Gray Brown Gray Brown Brown Brown Gray Gray Gray Brown
Gray Gray Brown Gray Gray Gray Brown Brown Gray Gray Gray Gray Brown Gray Gray Brown Gray Gray Gray
Brown Gray Gray Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray Gray Gray Gray Gray Gray
Gray Gray Gray Brown Brown Gray Gray Brown Brown Brown Gray Brown Gray Brown Brown Gray Brown Brown Brown
Brown Brown Gray Brown Brown Brown Gray Gray Brown Gray Brown Gray Gray Brown Gray Brown Gray Brown Brown
Gray Gray Brown Gray Gray Brown Gray Gray Gray Gray Brown Gray Brown Brown Gray Brown Gray Brown Brown
Gray Brown Gray Gray Brown Brown Gray Gray Gray Gray Brown Brown Brown Brown Brown Gray Gray Gray Brown
Gray Brown Gray Gray Gray Brown Gray Brown Gray Brown Brown Gray Brown Brown Gray Brown Gray Gray Brown
Brown Gray Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Gray Gray Brown Gray Brown
Brown Brown Gray Brown Brown Gray Brown Gray Brown Gray Brown Brown Gray Gray Gray Gray Brown Gray Gray
Brown Brown Gray Brown Gray Gray Gray Gray Brown Gray Gray Brown Brown Gray Brown Gray Brown Brown Gray
Brown Gray Gray Gray Brown Brown Brown Brown Gray Brown Brown Brown Brown Gray Brown Brown Gray Gray Brown
Gray Gray Gray Brown Brown Gray Brown Gray Brown Brown Gray Brown Brown Brown Gray Gray Brown Brown Gray
Gray Brown Brown Brown Gray Brown Brown Brown Gray Brown Gray Gray Brown Gray Gray Gray Brown Gray Brown
Brown Gray Brown Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Gray Brown Gray Brown Brown
Brown Gray Gray Gray Brown Gray Brown Brown Brown Brown Gray Gray Brown Brown Brown Gray Gray Gray Gray
Brown Brown Gray Brown Gray Brown Gray Brown Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray Gray
Gray Brown Gray Gray Brown Brown Brown Brown Brown Gray Brown Brown Gray Gray Brown Gray Brown Brown Gray
Gray Gray Gray Gray Brown Brown Gray Gray Brown Gray Gray Gray Brown Brown Brown Brown Gray Brown Brown
Brown Brown Brown Gray Brown Brown Gray Brown Gray Brown Brown Brown Gray Gray Brown Gray Gray 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: Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Blue Blue Blue Blue Green
Row 2: Green Green Green Green Green Green Green Green Green Pink Green Green Green Green Green Green Green Green Green Green Green Blue Green
Row 3: Green Green Green Green Green Green Green Green Green Pink 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 Pink Pink Green Green Green Green
Row 5: Green Green Green Yellow Yellow Green Green Green Green Green Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green
Row 6: Green Green Green Yellow Yellow Green Green Green Green Green Green Green Brown Brown Brown Brown Green Green Brown Brown Brown Brown Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green Brown Green Green Brown Green Brown Brown Green
Row 8: Green Green Green Yellow Yellow Green Green Green Green Green Green Green Brown Brown Green Brown Green Green Brown Green Brown Brown Green
Row 9: Green Green Pink Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Green Green Brown Green Brown Brown Green
Row 10: Green Green Pink Green Green Green Green Green Gray Green Orange Orange Brown Brown Brown Brown Gray Green Brown Brown Brown Brown Green
Row 11: Green Green Green Green Green Green Green Green Gray Green Green Brown Brown Brown Brown Green Gray Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Gray Green Green Brown Green Brown Brown Green Gray Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Gray Green Green Brown Brown Brown Brown Green Gray Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Black 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 Blue Blue Blue Blue Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue 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
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink Green Green Green Green
Row 5: Green Green Green Yellow Yellow Green Green Green Green Green Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green
Row 6: Green Green Green Yellow Yellow Green Green Green Green Green Green Green Brown Brown Brown Brown Green Green Brown Brown Brown Brown Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Pink Brown Green Green Brown Pink Brown Brown Green
Row 8: Green Green Green Yellow Yellow Green Green Green Green Green Green Green Brown Brown Pink Brown Green Green Brown Pink Brown Brown Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Green Green Brown Pink Brown Brown Green
Row 10: Green Green Green Green Green Green Green Green Gray Green Orange Orange Brown Brown Brown Brown Gray Green Brown Brown Brown Brown Green
Row 11: Green Green Green Green Green Green Green Green Gray Green Green Brown Brown Brown Brown Green Gray Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Gray Green Green Brown Black Brown Brown Green Gray Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Gray Green Green Brown Brown Brown Brown Green Gray 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
Example 2
Input:
Row 1: Red Red Red Red Red Red Pink Pink Pink Red
Row 2: Red Blue Blue Blue Red Red Pink Pink Pink Red
Row 3: Red Red Red Red Red Red Pink Red Pink Red
Row 4: Red Gray Red Red Red Red Pink Red Pink Red
Row 5: Red Gray Red Red Red Red Pink Pink Pink Red
Row 6: Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Blue Red Red Red
Row 9: Red Red Red Red Red Red Blue Red Red Red
Row 10: Red Red Red Red Red Red Blue Red Red Red
Row 11: Red Red Red Pink Pink Pink Pink Red Red Red
Row 12: Red Red Red Pink Pink Pink Pink Orange Orange Red
Row 13: Red Red Red Pink Pink Red Pink Red Red Red
Row 14: Red Red Red Pink Pink Pink Pink Gray Red Red
Row 15: Red Red Red Pink Pink Pink Pink Red Red Red
Row 16: Red Green Green Pink Pink Pink Pink Red Red Red
Output:
Row 1: Red Red Red Red Red Red Pink Pink Pink Red
Row 2: Red Blue Blue Blue Red Red Pink Pink Pink Red
Row 3: Red Red Red Red Red Red Pink Gray Pink Red
Row 4: Red Red Red Red Red Red Pink Gray Pink Red
Row 5: Red Red Red Red Red Red Pink Pink Pink Red
Row 6: Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Blue Red Red Red
Row 9: Red Red Red Red Red Red Blue Red Red Red
Row 10: Red Red Red Red Red Red Blue Red Red Red
Row 11: Red Red Red Pink Pink Pink Pink Red Red Red
Row 12: Red Red Red Pink Pink Pink Pink Orange Orange Red
Row 13: Red Red Red Pink Pink Gray Pink Red Red Red
Row 14: Red Red Red Pink Pink Pink Pink Red Red Red
Row 15: Red Red Red Pink Pink Pink Pink Red Red Red
Row 16: Red Green Green Pink Pink Pink Pink Red Red Red
Example 3
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
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Red Red Red Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Red Red Red Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Red Red Red Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Red Red Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Red Gray Gray Yellow Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Red Gray Gray Yellow Yellow Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Red Gray Gray Yellow Yellow Yellow Yellow Yellow 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 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
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 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 Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown 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 Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Yellow Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Yellow Gray Yellow Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 24: 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 25: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Row 26: 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
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Pink Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Red Red Red Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Red Red Red Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Red Gray Gray Yellow Red Red Red Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Red Gray Gray Yellow Yellow Red Red Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Red Gray Gray Yellow Yellow Yellow Yellow Yellow 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 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
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 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 Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown 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 Gray Gray Gray Yellow Yellow Yellow 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 Yellow Yellow Yellow 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 Yellow Purple Yellow Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Yellow Purple Yellow Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 24: 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 25: 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 26: 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
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 Purple Purple Red Red
Row 2: Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Purple Red Red Red
Row 3: Red Purple Purple Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red
Row 4: Red Purple Purple Purple Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red
Row 5: Red Red Red Red Green Green Green 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
Row 7: 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
Row 9: 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
Row 11: Red Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Gray Red Red Gray Red Red Red Red Brown Red Red Red Red Red Red
Row 13: Red Red Gray Red Gray Gray Red Red Red Red Brown Brown Red Red Red Red Red
Row 14: Red Red Gray Gray Gray Gray 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
Row 16: Red Gray Gray Gray Gray Red Red Brown Red Red Red Red Red Red Red Red Red
Row 17: Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Gray Red Gray Gray Red Red Yellow Red Red Red Red Red Red Red Red Red
Row 19: Red Gray Red Red Gray Red Red Yellow Red Red Red Red Gray Gray Gray Gray Gray
Row 20: Red Gray Gray Gray Gray Red Red Yellow Red Red Red Red Gray Gray Gray Red Gray
Row 21: Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Red Red Red Red Red Red Gray Gray Red Red Gray Gray Orange Orange Red Red Red
Row 23: Red Red Red Red Red Red Gray Gray Red Red Red Gray Red Red Red Red Red
Row 24: Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Red Red Red Red Red
Row 25: 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 Red Red Red Red Red Red
Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red
Red Red Red Red Red Red Red Gray Orange Orange Gray Red Red Red Red Red Red
Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red Red
Red Red Red Red Green Green Green Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red 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 Red Red Red Red Red Red Red Red Red Red Red
Red Red Gray Purple Purple Gray Red Red Red Red Red Red Red Red Red Red Red
Red Red Gray Purple Gray Gray Red Red Red Red Red Red Red Red Red Red Red
Red Red Gray Gray Gray Gray Red Red Red Red Red Red 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 Red Red Red Red Red Red Red Red Red Red Red Red
Red Gray Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red Red
Red Gray Brown Gray Gray Red Red Yellow Red Red Red Red Red Red Red Red Red
Red Gray Brown Brown Gray Red Red Yellow Red Red Red Red Gray Gray Gray Gray Gray
Red Gray Gray Gray Gray Red Red Yellow Red Red Red Red Gray Gray Gray Brown Gray
Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Red Red Red Red Red Red Gray Gray Purple Purple Gray Gray Red Red Red Red Red
Red Red Red Red Red Red Gray Gray Purple Purple Purple Gray Red Red Red Red Red
Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray 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: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Brown Brown Brown Orange Orange Orange Orange Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 5: Brown Brown Brown Orange Orange Orange Orange Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 6: Brown Brown Brown Orange Orange Orange Orange Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 7: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Brown Brown Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 10: Brown Brown Brown Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 11: Brown Brown Brown Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black 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
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Brown Orange Brown Orange Orange Orange Orange Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 5: Brown Brown Brown Orange Orange Orange Orange Green Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange
Row 6: Brown Orange Brown Orange Orange Orange Orange Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange
Row 7: Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Brown Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Brown Brown Brown Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 10: Brown Orange Brown Orange Orange Orange Orange Orange Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 11: Brown Brown Brown Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Blue Orange Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Blue Orange Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Blue Orange Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Blue Orange Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Blue Orange Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Blue Orange Blue Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Blue Blue Blue Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black 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
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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 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 Purple Purple Purple 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 Purple Purple Purple 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 Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 17: Brown Gray Gray Gray Gray Gray Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 18: Brown Gray Gray Gray Gray Gray Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 19: Brown Gray Gray Gray Gray Gray Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Red Red Red Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Red Red Red Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Red Red Red Brown Brown Brown Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Red Red Red Brown Brown Brown Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Red Red Red 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 Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 29: Brown Brown Brown Brown Brown 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 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 Purple Purple Purple 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 Purple Brown Purple 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 Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Orange Brown Orange Brown Orange Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Orange Orange Orange Orange Orange Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 17: Brown Gray Gray Gray Gray Gray Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 18: Brown Gray Brown Gray Brown Gray Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 19: Brown Gray Gray Gray Gray Gray Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Red Red Red Pink Brown Pink Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Red Brown Red Pink Pink Pink Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Purple Brown Brown Red Red Red Brown Brown Brown Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Brown Brown Red Brown Red Brown Brown Brown Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Yellow Brown Yellow Red Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Red Red Red 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 Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 29: Brown Brown Brown Brown Brown 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 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 Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Brown Brown Brown Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Brown Brown Brown Orange Orange Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Brown Brown Brown Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Brown Brown Brown Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Brown Brown Brown Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Brown Brown Brown Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange
Row 9: Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange
Row 11: 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
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 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 Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Brown Brown Brown Orange Orange Orange Orange Orange Yellow Orange Yellow Orange Yellow Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Brown Orange Brown Orange Orange Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Brown Brown Brown Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Brown Orange Brown Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Brown Brown Brown Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Brown Orange Brown Orange Orange Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange
Row 9: Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange
Row 11: 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
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 Orange
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 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 Orange
Row 3: Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Green Green Green Green Green Green Green Orange Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black 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 Orange
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
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: 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 12: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
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
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
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
Row 18: 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 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
Row 20: Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange
Row 21: Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange
Row 22: Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange
Row 23: 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 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
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 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
Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Green Orange Green Orange Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Green Green Green Green Green Green Green Orange Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Black Orange Black Orange Black Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black 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 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Gray Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray 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 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 Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange
Orange Orange Orange Red Orange Red Orange Red Orange Red Orange Red Orange Red Orange Red Orange Red Orange Red Orange Red Orange Red Orange
Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red 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 |
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
Row 2: Purple Purple Purple
Row 3: Black Purple Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black
Row 3: Black Purple Black Black Purple Black Black Purple Black Black Purple Black Black Black Black
Row 4: 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
Row 6: 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
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 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
Row 12: 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
Row 14: 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
Example 2
Input:
Row 1: Black Black Black Black
Row 2: Black Orange 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 Black
Row 2: Black Orange 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 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 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 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 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 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 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 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 Black Black Black
Example 3
Input:
Row 1: Blue Black Black Black
Row 2: Blue Blue Blue Black
Row 3: Blue Black Blue Blue
Row 4: Blue Blue Black Blue
Output:
Row 1: Blue Black Black Black Blue Black Black Black Blue Black Black Black Blue Black Black Black Blue Black Black Black Blue Black Black Black
Row 2: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black
Row 3: Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue
Row 4: Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Row 5: Blue Black Black Black Blue Black Black Black Blue Black Black Black Blue Black Black Black Black Black Black Black Black Black Black Black
Row 6: Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Black Black Black Black Black Black Black Black
Row 7: Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Black Black Black Black Black Black Black Black
Row 8: Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue 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 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
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: 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
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
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
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
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
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 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
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
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Black Blue
Row 2: Blue Blue Black Blue
Row 3: Blue Blue Black Blue
Row 4: Black Black Blue Blue
Row 5: 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 Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue 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 Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue 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 Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue
Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue Black Black Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 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 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 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 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 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: 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 Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink 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 Orange Purple Purple Purple Purple Purple Purple Purple Purple Pink 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 Black 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 Purple Purple Purple Brown 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 Black Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Brown 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
Row 17: 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
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 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
Row 2: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Pink Pink 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 Black Black Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Brown Brown Brown 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
Row 17: 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
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 Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Red Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Red Blue Blue Blue Blue Blue Blue Gray Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Red Red Red Red Red Blue Blue Blue Blue
Row 3: Blue Red Red Red Red Red Gray Gray Gray Blue
Row 4: Blue Red Red Red Red Red Gray Gray Gray Blue
Row 5: Blue Red Red Red Red Red Gray Gray Gray Blue
Row 6: Blue Red Red Red Red Red Gray Gray Gray Blue
Row 7: Blue Red Red Red Red Red Gray Gray Gray Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray
Row 11: Gray Gray Gray Gray Gray Black Gray Gray Gray Green Gray Gray Gray
Row 12: 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
Row 14: Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 15: 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
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray
Row 19: 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
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: 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
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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Black Black Black Black Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Black Black Black Black Gray Gray Gray Green Green Gray Gray
Row 11: Gray Gray Black Black Black Black Gray Gray Gray Green Green Gray Gray
Row 12: 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
Row 14: Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray
Row 19: 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
Row 21: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
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: 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
Row 4: 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
Row 6: 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
Row 8: 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 Black 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
Row 11: 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 Black Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Yellow 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: Blue 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 Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Yellow 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 Blue
Row 21: 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue 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 Black Black Black Black Black Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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: Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Red Red Red Red Red Red Brown
Row 3: Brown Red Orange Orange Orange Orange Red Brown
Row 4: Brown Red Orange Blue Blue Orange Red Brown
Row 5: Brown Red Orange Blue Blue Orange Red Brown
Row 6: Brown Red Orange Blue Blue Orange Red Brown
Row 7: Brown Red Orange Blue Blue Orange Red Brown
Row 8: Brown Red Orange Blue Blue Orange Red Brown
Row 9: Brown Red Orange Blue Blue Orange Red Brown
Row 10: Brown Red Orange Orange Orange Orange Red Brown
Row 11: Brown Red Red Red Red Red Red Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Orange Orange Orange Orange Orange Orange Blue
Row 3: Blue Orange Red Red Red Red Orange Blue
Row 4: Blue Orange Red Brown Brown Red Orange Blue
Row 5: Blue Orange Red Brown Brown Red Orange Blue
Row 6: Blue Orange Red Brown Brown Red Orange Blue
Row 7: Blue Orange Red Brown Brown Red Orange Blue
Row 8: Blue Orange Red Brown Brown Red Orange Blue
Row 9: Blue Orange Red Brown Brown Red Orange Blue
Row 10: Blue Orange Red Red Red Red Orange Blue
Row 11: Blue Orange Orange Orange Orange Orange Orange Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue
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 Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 3: Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 4: Purple Green Green Red Red Red Red Red Red Red Red Red Red Red Red Green Green Purple
Row 5: Purple Green Green Red Red Red Red Red Red Red Red Red Red Red Red Green Green Purple
Row 6: Purple Green Green Red Red Green Green Green Green Green Green Green Green Red Red Green Green Purple
Row 7: Purple Green Green Red Red Green Purple Purple Purple Purple Purple Purple Green Red Red Green Green Purple
Row 8: Purple Green Green Red Red Green Purple Purple Purple Purple Purple Purple Green Red Red Green Green Purple
Row 9: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 10: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 11: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 12: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 13: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 14: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 15: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 16: Purple Green Green Red Red Green Purple Purple Red Red Purple Purple Green Red Red Green Green Purple
Row 17: Purple Green Green Red Red Green Purple Purple Purple Purple Purple Purple Green Red Red Green Green Purple
Row 18: Purple Green Green Red Red Green Purple Purple Purple Purple Purple Purple Green Red Red Green Green Purple
Row 19: Purple Green Green Red Red Green Green Green Green Green Green Green Green Red Red Green Green Purple
Row 20: Purple Green Green Red Red Red Red Red Red Red Red Red Red Red Red Green Green Purple
Row 21: Purple Green Green Red Red Red Red Red Red Red Red Red Red Red Red Green Green Purple
Row 22: Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 23: Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 24: 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
Row 2: Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 3: Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 4: Red Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Red
Row 5: Red Purple Purple Green Red Red Red Red Red Red Red Red Red Red Green Purple Purple Red
Row 6: Red Purple Purple Green Red Red Red Red Red Red Red Red Red Red Green Purple Purple Red
Row 7: Red Purple Purple Green Red Red Green Green Green Green Green Green Red Red Green Purple Purple Red
Row 8: Red Purple Purple Green Red Red Green Green Green Green Green Green Red Red Green Purple Purple Red
Row 9: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 10: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 11: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 12: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 13: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 14: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 15: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 16: Red Purple Purple Green Red Red Green Green Purple Purple Green Green Red Red Green Purple Purple Red
Row 17: Red Purple Purple Green Red Red Green Green Green Green Green Green Red Red Green Purple Purple Red
Row 18: Red Purple Purple Green Red Red Green Green Green Green Green Green Red Red Green Purple Purple Red
Row 19: Red Purple Purple Green Red Red Red Red Red Red Red Red Red Red Green Purple Purple Red
Row 20: Red Purple Purple Green Red Red Red Red Red Red Red Red Red Red Green Purple Purple Red
Row 21: Red Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Red
Row 22: Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 23: Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Green Green Green Green Green Green Gray
Row 3: Gray Green Blue Blue Blue Blue Green Gray
Row 4: Gray Green Blue Yellow Yellow Blue Green Gray
Row 5: Gray Green Blue Yellow Yellow Blue Green Gray
Row 6: Gray Green Blue Yellow Yellow Blue Green Gray
Row 7: Gray Green Blue Yellow Yellow Blue Green Gray
Row 8: Gray Green Blue Blue Blue Blue Green Gray
Row 9: Gray Green Green Green Green Green Green Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 3: Yellow Blue Green Green Green Green Blue Yellow
Row 4: Yellow Blue Green Gray Gray Green Blue Yellow
Row 5: Yellow Blue Green Gray Gray Green Blue Yellow
Row 6: Yellow Blue Green Gray Gray Green Blue Yellow
Row 7: Yellow Blue Green Gray Gray Green Blue Yellow
Row 8: Yellow Blue Green Green Green Green Blue Yellow
Row 9: Yellow Blue Blue Blue Blue Blue Blue Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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 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 Green Green
Row 3: Green 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 Gray Green Green
Row 4: Green Green Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Green Green
Row 5: Green Green Gray Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Gray Green Green
Row 6: Green Green Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Purple Gray Green Green
Row 7: Green Green Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Purple Gray Green Green
Row 8: Green Green Gray Purple Brown Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Brown Purple Gray Green Green
Row 9: Green Green Gray Purple Brown Gray Gray Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Gray Gray Brown Purple Gray Green Green
Row 10: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 11: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 12: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 13: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 14: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Black Black Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 15: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 16: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 17: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Black Black Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 18: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 19: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 20: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 21: Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Black Gray Gray Brown Purple Gray Green Green
Row 22: Green Green Gray Purple Brown Gray Gray Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Gray Gray Brown Purple Gray Green Green
Row 23: Green Green Gray Purple Brown Gray Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Gray Brown Purple Gray Green Green
Row 24: Green Green Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Purple Gray Green Green
Row 25: Green Green Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Purple Gray Green Green
Row 26: Green Green Gray Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Gray Green Green
Row 27: Green Green Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Green Green
Row 28: Green 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 Gray Green Green
Row 29: Green Green Green Green Green Green 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 30: Green Green Green Green Green Green Green Green Green Green Green Green Green 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>
| Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown 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 Brown
Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Brown
Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Gray Gray Gray Gray Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Green Green Green Green Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Gray Gray Gray Gray Gray Gray Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Black Brown
Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Brown
Brown Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Brown
Brown 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 Brown
Brown Brown Brown Brown Brown Brown 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: Orange Orange Orange Blue Black Orange Black
Row 2: Gray Gray Gray Blue Black Orange Black
Row 3: Gray Orange Orange Blue Orange Orange Black
Row 4: Orange Orange Orange Blue Black Orange Black
Row 5: Orange Orange Orange Blue Orange Black Black
Row 6: Orange Orange Orange Blue Black Black Black
Row 7: Orange Orange Orange Blue Black Black Orange
Row 8: Orange Gray Orange Blue Black Black Black
Row 9: Orange Orange Orange Blue Black Black Black
Row 10: Orange Orange Gray Blue Black Orange Black
Row 11: Gray Orange Orange Blue Black Black Black
Row 12: Orange Orange Orange Blue Black Black Black
Row 13: Orange Orange Orange Blue Black Black Black
Row 14: Orange Orange Orange Blue Black Black Black
Row 15: Orange Orange Orange Blue Orange Orange Black
Row 16: Orange Orange Orange Blue Black Black Black
Row 17: Gray Orange Orange Blue Orange Orange Black
Row 18: Gray Gray Orange Blue Orange Black Black
Row 19: Orange Gray Orange Blue Black Black Black
Row 20: Orange Gray Orange Blue Black Black Black
Row 21: Orange Orange Orange Blue Orange Orange Orange
Row 22: Gray Gray Orange Blue Black Black Black
Row 23: Gray Gray Orange Blue Black Black Black
Output:
Row 1: Orange Green Orange
Row 2: Orange Orange Orange
Row 3: Orange Green Orange
Row 4: Orange Green Orange
Row 5: Green Orange Orange
Row 6: Orange Orange Orange
Row 7: Orange Orange Green
Row 8: Orange Orange Orange
Row 9: Orange Orange Orange
Row 10: Orange Green Orange
Row 11: Orange Orange Orange
Row 12: Orange Orange Orange
Row 13: Orange Orange Orange
Row 14: Orange Orange Orange
Row 15: Green Green Orange
Row 16: Orange Orange Orange
Row 17: Orange Green Orange
Row 18: Orange Orange Orange
Row 19: Orange Orange Orange
Row 20: Orange Orange Orange
Row 21: Green Green Green
Row 22: Orange Orange Orange
Row 23: Orange Orange Orange
Example 2
Input:
Row 1: Orange Black Orange Black Gray Pink Pink Orange Orange
Row 2: Orange Black Orange Black Gray Pink Orange Orange Pink
Row 3: Black Black Orange Orange Gray Orange Pink Pink Orange
Row 4: Orange Orange Orange Black Gray Orange Orange Orange Pink
Row 5: Orange Orange Orange Black Gray Pink Pink Orange Orange
Row 6: Orange Orange Orange Orange Gray Orange Pink Pink Orange
Row 7: Orange Black Orange Orange Gray Orange Orange Orange Orange
Row 8: Orange Orange Orange Black Gray Orange Pink Orange Orange
Row 9: Black Orange Black Black Gray Pink Orange Orange Orange
Row 10: Black Orange Black Orange Gray Pink Orange Orange Orange
Row 11: Orange Orange Orange Black Gray Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Gray Pink Orange Pink Pink
Row 13: Orange Orange Orange Black Gray Orange Orange Orange Pink
Row 14: Orange Orange Black Orange Gray Pink Orange Pink Orange
Row 15: Orange Orange Orange Orange Gray Orange Orange Orange Orange
Row 16: Black Black Orange Orange Gray Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Gray Orange Pink Pink Orange
Row 18: Black Orange Black Orange Gray Pink Orange Orange Orange
Row 19: Orange Orange Orange Orange Gray Orange Orange Orange Orange
Row 20: Black Black Orange Orange Gray Orange Pink Orange Pink
Row 21: Orange Orange Orange Orange Gray Orange Orange Orange Pink
Row 22: Black Black Orange Orange Gray Orange Orange Orange Orange
Output:
Row 1: Orange Orange Green Orange
Row 2: Orange Orange Green Orange
Row 3: Orange Orange Orange Green
Row 4: Green Green Green Orange
Row 5: Orange Orange Green Orange
Row 6: Green Orange Orange Green
Row 7: Green Orange Green Green
Row 8: Green Orange Green Orange
Row 9: Orange Green Orange Orange
Row 10: Orange Green Orange Green
Row 11: Green Green Green Orange
Row 12: Orange Green Orange Orange
Row 13: Green Green Green Orange
Row 14: Orange Green Orange Green
Row 15: Green Green Green Green
Row 16: Orange Orange Green Green
Row 17: Green Orange Orange Green
Row 18: Orange Green Orange Green
Row 19: Green Green Green Green
Row 20: Orange Orange Green Orange
Row 21: Green Green Green Orange
Row 22: Orange Orange Green Green
Example 3
Input:
Row 1: Purple Purple Purple 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 2: Purple Purple Purple 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 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Pink 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 Pink 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 Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple
Row 6: Purple Purple Purple 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 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink 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 Pink 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 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 Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Gray 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 Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Red Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple
Row 15: Purple Purple Purple 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 16: Purple Purple Purple 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 17: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink 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 Pink 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 Pink 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 Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Pink 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 Pink 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 Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: 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
Row 3: Green Green Green Green Green Green Green Green Green Green Green Purple 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 Purple Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Purple 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 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
Row 11: Green Green Green Green Purple Green Green Green Green Green Green Green Green
Row 12: Green Green Green Purple Green Green Green Green Green Green Green Green Green
Row 13: Green Purple Green Green Purple Green Green Green Green Green Purple Green Green
Row 14: Green Green Green Green Green Green Green Purple Purple Green Green Purple Green
Row 15: 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
Row 17: Green Green Green Purple Green Green Green Green Green Green Green Green Green
Row 18: 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
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Purple Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Purple Green Green Green Green Green Green Green
Row 23: 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
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Yellow Yellow Red Yellow Yellow Red Yellow Red Red Yellow Red Red Yellow Yellow Yellow Red Yellow
Row 2: Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Yellow Red Yellow Red
Row 3: Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Red Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Red Red Yellow Yellow Yellow Red Red Red Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Yellow Yellow Yellow
Row 6: Yellow Yellow Red Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Pink Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Yellow Yellow Pink Pink Pink Pink
Row 9: Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Pink Yellow Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Yellow Yellow Yellow Pink Yellow Pink Pink Pink
Row 11: Pink Yellow Pink Pink Yellow Pink Pink Pink Pink Pink Pink Yellow Pink Pink Yellow Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Pink Pink Pink
Row 13: Yellow Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Yellow Pink Yellow 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>
| Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Green Green Yellow Green Yellow Yellow Yellow
Yellow Green Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Green Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow Green 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: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue
Row 3: Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Row 7: 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
Row 9: 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
Row 11: Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue
Row 14: 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
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: 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
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 2: Gray Gray Gray Gray Yellow Gray Yellow Gray Gray Gray Gray Gray Gray
Row 3: Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown
Row 4: Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple
Row 5: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 6: Gray Gray Gray Gray Yellow Gray Yellow Gray Gray Gray Gray Gray Gray
Row 7: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 11: Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple
Row 12: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 13: Gray Gray Gray Gray Yellow Gray Yellow Gray Gray Gray Gray Gray Gray
Row 14: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 17: Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown
Row 18: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 21: Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple
Row 22: Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown
Row 23: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 25: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Gray Blue Brown Blue Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Red Red Black Red Orange Red Red
Row 2: Red Red Black Red Orange Red Red
Row 3: Red Red Red Red Orange Red Red
Row 4: Red Red Red Red Orange Red Red
Row 5: Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red
Row 7: Pink Pink 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: Green Green Green Green Green Green Green
Row 16: Brown Brown Brown Brown Brown Brown Brown
Row 17: Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red
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
Output:
Row 1: Red Red Black Red Orange Red Red
Row 2: Red Red Black Red Orange Red Red
Row 3: Red Red Black Red Orange Red Red
Row 4: Red Red Black Red Orange Red Red
Row 5: Red Red Black Red Orange Red Red
Row 6: Red Red Black Red Orange Red Red
Row 7: Pink Pink Yellow Pink Yellow Pink Pink
Row 8: Red Red Black Red Orange Red Red
Row 9: Red Red Black Red Orange Red Red
Row 10: Red Red Black Red Orange Red Red
Row 11: Red Red Black Red Orange Red Red
Row 12: Red Red Black Red Orange Red Red
Row 13: Red Red Black Red Orange Red Red
Row 14: Red Red Black Red Orange Red Red
Row 15: Green Green Yellow Green Yellow Green Green
Row 16: Brown Brown Yellow Brown Yellow Brown Brown
Row 17: Red Red Black Red Orange Red Red
Row 18: Red Red Black Red Orange Red Red
Row 19: Red Red Black Red Orange Red Red
Row 20: Red Red Black Red Orange Red Red
Row 21: Red Red Black Red Orange Red Red
Row 22: Red Red Black Red Orange Red Red
Row 23: Red Red Black Red Orange Red Red
Row 24: Red Red Black Red Orange Red Red
Row 25: Red Red Black Red Orange Red Red
Row 26: Red Red Black Red Orange Red Red
Row 27: Red Red Black Red Orange Red Red
Row 28: Red Red Black Red Orange Red Red
Example 3
Input:
Row 1: Pink Gray Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Gray Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Gray Pink Pink Pink Gray Pink Pink Pink Pink Green Pink Pink Pink Pink Green Green
Row 4: Pink Gray Pink Pink Green Gray Pink Pink Pink Pink Green Pink Pink Gray Pink Pink Pink
Row 5: Pink Gray Pink Pink Green Gray Pink Pink Pink Pink Green Pink Pink Gray Pink Pink Pink
Output:
Row 1: Pink Gray Pink Pink Green Gray Pink Pink Pink Pink Green Pink Pink Gray Pink Pink Pink
Row 2: Pink Gray Pink Pink Green Gray Pink Pink Pink Pink Green Pink Pink Gray Pink Pink Pink
Row 3: Green Yellow Green Green Yellow Yellow Green Green Green Green Yellow Green Green Yellow Green Green Green
Row 4: Pink Gray Pink Pink Green Gray Pink Pink Pink Pink Green Pink Pink Gray Pink Pink Pink
Row 5: Pink Gray Pink Pink Green Gray Pink Pink Pink Pink Green Pink Pink Gray Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple
Row 4: Pink Pink Pink Pink Pink Pink Pink
Row 5: Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple
Row 7: Gray Gray Gray Gray Gray Gray Gray
Row 8: Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Pink Pink Pink
Row 12: Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Black Purple Purple
Row 17: Purple Purple Purple Purple Black 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 Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Pink Pink Pink Pink Yellow Pink Pink
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Gray Gray Gray Gray Yellow Gray Gray
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Pink Pink Pink Pink Yellow Pink Pink
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black Purple Purple
Purple Purple Purple Purple Black 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 Black Black Black Black
Row 2: 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
Row 4: 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
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Brown 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
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
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 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
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
Row 6: Black Black Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Black Black Black Purple Black Purple Black Black
Row 7: Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black
Row 8: Black Black Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Black Black Black Purple Black Purple 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
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 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
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 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
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 Black
Row 15: Black Black Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Black Black Black Purple Black Purple Black Black
Row 16: Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black
Row 17: Black Black Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Black Black Black Purple Black Purple 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
Example 2
Input:
Row 1: Orange Orange Orange
Row 2: Orange Yellow Orange
Row 3: Orange Orange Orange
Row 4: Orange Orange Orange
Output:
Row 1: Purple Orange Purple Purple Orange Purple
Row 2: Orange Yellow Orange Orange Yellow Orange
Row 3: Purple Orange Purple Purple Orange Purple
Row 4: Orange Orange Orange Orange Orange Orange
Row 5: Purple Orange Purple Purple Orange Purple
Row 6: Orange Yellow Orange Orange Yellow Orange
Row 7: Purple Orange Purple Purple Orange Purple
Row 8: Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Gray Red Red Red Red
Row 2: Red Red Green Red Gray Green Red Red Black Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Purple Red Purple Purple Purple Purple Gray Red Purple Red Red Red Purple Red Purple Purple Purple Purple Gray Red Purple Red Red
Row 2: Red Red Green Red Gray Green Purple Red Black Red Red Red Red Red Green Red Gray Green Purple Red Black Red Red Red
Row 3: Red Purple Red Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Red Purple Purple Purple Purple Purple Purple Purple Red Red
Row 4: Red Purple Red Purple Purple Purple Purple Gray Red Purple Red Red Red Purple Red Purple Purple Purple Purple Gray Red Purple Red Red
Row 5: Red Red Green Red Gray Green Purple Red Black Red Red Red Red Red Green Red Gray Green Purple Red Black Red Red Red
Row 6: Red Purple Red Purple Purple Purple Purple Purple Red Purple Red Red Red Purple Red Purple Purple Purple Purple Purple Red Purple Red Red
Here is the input grid for the test example:
Input:
Row 1: Red Orange Red Red Yellow
Row 2: Red Red Red Red Red
Row 3: Red Red Red Red Red
Row 4: Red Red Red Red Red
Row 5: Orange Orange Red Red Red
Row 6: Red Red Red Red Red
Row 7: Red Orange Red Red Red
Row 8: 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 Orange Red Red Yellow Red Orange Red Red Yellow
Purple Red Purple Purple Red Purple Red Purple Purple Red
Red Red Red Red Red Red Red Red Red Red
Purple Purple Purple Red Purple Purple Purple Purple Red Red
Orange Orange Red Red Red Orange Orange Red Red Red
Purple Purple Purple Red Purple Purple Purple Purple Red Red
Red Orange Red Red Red Red Orange Red Red Red
Purple Red Purple Purple Red Purple Red Purple Purple Red
Red Orange Red Red Yellow Red Orange Red Red Yellow
Purple Red Purple Purple Red Purple Red Purple Purple Red
Red Red Red Red Red Red Red Red Red Red
Purple Purple Purple Red Purple Purple Purple Purple Red Red
Orange Orange Red Red Red Orange Orange Red Red Red
Purple Purple Purple Red Purple Purple Purple Purple Red Red
Red Orange Red Red Red Red Orange Red Red Red
Purple Red Purple Red Red Purple Red Purple 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 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 Red Red Black Red Red
Row 4: Red Red Red Red Red Red Red Red Red Gray Black Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Blue Red Red
Row 7: 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
Row 9: 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
Row 11: 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
Row 13: 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
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 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
Row 19: 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
Row 21: 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
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: 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
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Black
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Black Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Black Red Red
Row 4: Red Red Red Red Red Red Red Red Red Gray Black Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Blue Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue
Row 9: 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
Row 11: 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
Row 13: 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
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 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
Row 19: 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
Row 21: 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
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: 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
Example 2
Input:
Row 1: 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 Brown Green Green Purple
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Purple Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Brown Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Brown
Row 6: 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
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green Green Purple
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Purple Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Brown Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Brown
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green Green
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
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 Orange 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 Gray Orange 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 Gray Pink 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 Gray 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 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 Orange
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 Orange 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 Orange 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 Orange 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 Orange 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 Orange 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 Orange 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 Gray Orange 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 Gray Pink 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 Gray Green Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
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 Orange Black Black Black Black
Row 4: Black Black Black Black Black Black Black Orange Purple Black Black
Row 5: Black Black Black Black Black Black Black Yellow Red Black Black
Row 6: Black Black Black Black Black Black Yellow Black Black Red 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
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 Orange Black Black Black Black Black Black
Black Black Black Black Black Orange Black Black Black Black Black
Black Black Black Black Black Black Orange Black Black Black Black
Black Black Black Black Black Black Black Orange Purple Black Black
Black Black Black Black Black Black Black Yellow Red Black Black
Black Black Black Black Black Black Yellow Black Black Red Black
Black Black Black Black Black Yellow Black Black Black Black Red
Black Black Black Black Yellow 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Orange Orange 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 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 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
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
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
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
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
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
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
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
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
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
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
Row 18: Pink 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 19: Pink 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 20: Pink 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 21: Pink 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 22: Pink 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 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink
Row 25: Pink Pink 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: Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange
Row 4: Orange Orange Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Brown Red 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
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
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
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
Row 27: Brown Brown Brown Brown Brown 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 Brown Brown Brown Brown Brown
Output:
Row 1: Red Black Black
Row 2: Black Black Black
Row 3: Black Black 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
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 Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Pink 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 Black Black Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Black Black Black Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black 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
Row 18: 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
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Pink Pink Pink Pink Pink Pink
Row 2: Black Black Pink Pink Pink Pink
Row 3: Black Black Black Pink Pink Pink
Row 4: Black Black Black Black Pink Pink
Row 5: Black Black Black Black Black Pink
Row 6: Black Black Black Black Black 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
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red 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
Row 10: 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
Row 12: 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
Row 14: 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
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Pink Gray Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray 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
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 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
Row 27: 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
Row 29: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 30: 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>
| Red Red Red Red Red Red Red
Red Red Red Red Red Red Red
Gray Gray Red Red Red Red Red
Gray Gray Gray Gray Red Red Red
Gray Gray Gray Gray Red Red Red
Gray Gray Gray Gray Red Gray Red
Gray Gray Gray Gray Gray 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: Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Yellow Purple Purple Purple
Row 2: Purple Purple Pink Purple Pink Pink Yellow Purple Purple Yellow Pink Pink Purple Pink
Row 3: Purple Pink Yellow Gray Purple Purple Yellow Gray Gray Yellow Purple Purple Gray Yellow
Row 4: Purple Purple Gray Yellow Pink Purple Pink Yellow Yellow Pink Purple Pink Yellow Gray
Row 5: Purple Pink Purple Pink Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Pink Purple
Row 6: Yellow Pink Purple Purple Yellow Yellow Pink Pink Pink Pink Yellow Yellow Purple Purple
Row 7: Purple Yellow Yellow Pink Yellow Pink Yellow Purple Purple Yellow Pink Yellow Pink Yellow
Row 8: Purple Purple Gray Blue Blue Pink Purple Gray Gray Purple Pink Purple Yellow Gray
Row 9: Purple Purple Gray Blue Blue Pink Purple Gray Gray Purple Pink Purple Yellow Gray
Row 10: Purple Yellow Yellow Pink Yellow Pink Yellow Purple Purple Yellow Pink Yellow Pink Yellow
Row 11: Yellow Pink Purple Purple Blue Blue Pink Pink Pink Pink Yellow Yellow Purple Purple
Row 12: Purple Pink Purple Pink Blue Blue Yellow Purple Purple Yellow Yellow Yellow Pink Purple
Row 13: Purple Purple Gray Yellow Blue Blue Pink Yellow Yellow Pink Purple Pink Yellow Gray
Row 14: Purple Pink Yellow Gray Purple Purple Yellow Gray Gray Yellow Purple Purple Gray Yellow
Output:
Row 1: Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Yellow Purple Purple Purple
Row 2: Purple Purple Pink Purple Pink Pink Yellow Purple Purple Yellow Pink Pink Purple Pink
Row 3: Purple Pink Yellow Gray Purple Purple Yellow Gray Gray Yellow Purple Purple Gray Yellow
Row 4: Purple Purple Gray Yellow Pink Purple Pink Yellow Yellow Pink Purple Pink Yellow Gray
Row 5: Purple Pink Purple Pink Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Pink Purple
Row 6: Yellow Pink Purple Purple Yellow Yellow Pink Pink Pink Pink Yellow Yellow Purple Purple
Row 7: Purple Yellow Yellow Pink Yellow Pink Yellow Purple Purple Yellow Pink Yellow Pink Yellow
Row 8: Purple Purple Gray Yellow Purple Pink Purple Gray Gray Purple Pink Purple Yellow Gray
Row 9: Purple Purple Gray Yellow Purple Pink Purple Gray Gray Purple Pink Purple Yellow Gray
Row 10: Purple Yellow Yellow Pink Yellow Pink Yellow Purple Purple Yellow Pink Yellow Pink Yellow
Row 11: Yellow Pink Purple Purple Yellow Yellow Pink Pink Pink Pink Yellow Yellow Purple Purple
Row 12: Purple Pink Purple Pink Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Pink Purple
Row 13: Purple Purple Gray Yellow Pink Purple Pink Yellow Yellow Pink Purple Pink Yellow Gray
Row 14: Purple Pink Yellow Gray Purple Purple Yellow Gray Gray Yellow Purple Purple Gray Yellow
Example 2
Input:
Row 1: Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Red Green Green Green Yellow Red Green Green Green Green Green Green Red Yellow Green Green Green Red
Row 3: Green Red Green Green Green Blue Pink Pink Pink Pink Pink Pink Green Green Green Green Blue Green Green Green
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Black Green Red Green Green
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Blue Green Green Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Green Green Blue Green Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Green Green Green Green Yellow Green Green Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Green Green Green Green Yellow Green Green Green Green Yellow Green
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Pink Pink Pink Pink Pink Pink Green Blue Green Green Yellow Yellow Green Green Blue Green Green Green Green Green
Row 15: Pink Pink Pink Pink Pink Pink Green Green Blue Green Green Green Green Blue Green Green Green Green Green Green
Row 16: Green Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 17: Green Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue
Row 18: Green Pink Pink Pink Pink Green Black Green Green Green Green Green Green Green Green Black Green Red Green Green
Row 19: Green Green Pink Pink Pink Green Green Green Green Green Yellow Yellow Green Green Green Green Green Green Green Green
Row 20: Green Red Green Green Green Blue Green Green Green Green Green Green Green Green Green Green Blue Green Green Green
Output:
Row 1: Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Red Green Green Green Yellow Red Green Green Green Green Green Green Red Yellow Green Green Green Red
Row 3: Green Red Green Green Green Blue Green Green Green Green Green Green Green Green Green Green Blue Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Yellow Yellow Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Red Green Black Green Green Green Green Green Green Green Green Black Green Red Green Green
Row 6: Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue
Row 7: Green Yellow Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 8: Green Red Green Green Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Blue Green Green Yellow Yellow Green Green Blue 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
Row 11: Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Yellow Green
Row 12: Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Yellow Green Green Green Green Yellow 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 Blue Green Green Yellow Yellow Green Green Blue Green Green Green Green Green
Row 15: Green Red Green Green Green Green Green Green Blue Green Green Green Green Blue Green Green Green Green Green Green
Row 16: Green Yellow Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 17: Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue
Row 18: Green Green Green Green Red Green Black Green Green Green Green Green Green Green Green Black Green Red Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Yellow Yellow Green Green Green Green Green Green Green Green
Row 20: Green Red Green Green Green Blue Green Green Green Green Green Green Green Green Green Green Blue Green Green Green
Example 3
Input:
Row 1: Orange Purple Yellow Blue Gray Black Purple Blue Blue Red Orange Yellow Gray Gray Yellow Orange Red Blue Blue Purple Black Gray Blue Yellow
Row 2: Purple Red Yellow Red Red Gray Black Orange Blue Blue Yellow Red Gray Gray Red Yellow Blue Blue Orange Black Gray Red Red Yellow
Row 3: Yellow Yellow Orange Gray Orange Purple Black Black Black Blue Yellow Black Black Black Black Yellow Brown Brown Black Black Purple Orange Gray Orange
Row 4: Blue Red Gray Blue Red Black Purple Blue Yellow Black Orange Gray Yellow Yellow Gray Orange Brown Brown Blue Purple Black Red Blue Gray
Row 5: Gray Red Orange Red Red Red Brown Brown Brown Purple Brown Brown Brown Brown Purple Red Brown Brown Red Orange Red Red Red Orange
Row 6: Black Gray Purple Black Red Blue Brown Brown Brown Orange Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Red Black Purple
Row 7: Purple Brown Brown Brown Brown Red Brown Brown Brown Purple Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Orange Purple Black
Row 8: Blue Brown Brown Brown Brown Blue Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Red Blue Black
Row 9: Blue Brown Brown Brown Brown Blue Brown Brown Brown Purple Brown Brown Brown Brown Purple Yellow Purple Gray Red Purple Blue Orange Yellow Black
Row 10: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Black Gray Purple Yellow Purple Orange Purple Black Blue
Row 11: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Black Yellow Brown Brown Brown Brown Brown Yellow
Row 12: Yellow Red Brown Brown Brown Brown Brown Yellow Purple Blue Blue Purple Yellow Yellow Purple Blue Blue Purple Brown Brown Brown Brown Brown Black
Row 13: Gray Gray Brown Brown Brown Brown Brown Yellow Gray Blue Orange Yellow Yellow Yellow Yellow Orange Brown Brown Brown Brown Brown Brown Brown Black
Row 14: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Orange Brown Brown Brown Brown Brown Brown Yellow Black
Row 15: Yellow Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Purple Blue Brown Brown Brown Brown Brown Purple Gray Black
Row 16: Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Blue Blue Brown Brown Brown Brown Brown Red Orange Yellow
Row 17: Red Blue Blue Brown Brown Orange Purple Brown Brown Brown Brown Brown Blue Blue Blue Black Gray Purple Yellow Purple Orange Purple Black Blue
Row 18: Blue Blue Black Yellow Orange Blue Purple Brown Brown Brown Brown Brown Gray Gray Purple Yellow Purple Gray Red Purple Blue Orange Yellow Black
Row 19: Blue Orange Black Blue Red Blue Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Purple Yellow Red Gray Yellow Blue Red Blue Black
Row 20: Purple Black Black Purple Orange Red Brown Brown Brown Brown Brown Brown Brown Blue Red Yellow Purple Purple Yellow Yellow Red Orange Purple Black
Row 21: Black Gray Purple Black Red Blue Red Brown Brown Brown Brown Brown Red Red Blue Red Orange Blue Blue Red Blue Red Black Purple
Row 22: Gray Red Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Purple Red Purple Orange Red Orange Red Red Red Orange
Row 23: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Orange Gray Yellow Yellow Gray Orange Black Yellow Blue Purple Black Red Blue Gray
Row 24: Brown Brown Orange Gray Orange Purple Black Black Black Blue Yellow Black Black Black Black Yellow Blue Black Black Black Purple Orange Gray Orange
Output:
Row 1: Orange Purple Yellow Blue Gray Black Purple Blue Blue Red Orange Yellow Gray Gray Yellow Orange Red Blue Blue Purple Black Gray Blue Yellow
Row 2: Purple Red Yellow Red Red Gray Black Orange Blue Blue Yellow Red Gray Gray Red Yellow Blue Blue Orange Black Gray Red Red Yellow
Row 3: Yellow Yellow Orange Gray Orange Purple Black Black Black Blue Yellow Black Black Black Black Yellow Blue Black Black Black Purple Orange Gray Orange
Row 4: Blue Red Gray Blue Red Black Purple Blue Yellow Black Orange Gray Yellow Yellow Gray Orange Black Yellow Blue Purple Black Red Blue Gray
Row 5: Gray Red Orange Red Red Red Orange Red Orange Purple Red Purple Black Black Purple Red Purple Orange Red Orange Red Red Red Orange
Row 6: Black Gray Purple Black Red Blue Red Blue Blue Orange Red Blue Red Red Blue Red Orange Blue Blue Red Blue Red Black Purple
Row 7: Purple Black Black Purple Orange Red Yellow Yellow Purple Purple Yellow Red Blue Blue Red Yellow Purple Purple Yellow Yellow Red Orange Purple Black
Row 8: Blue Orange Black Blue Red Blue Yellow Gray Red Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Red Gray Yellow Blue Red Blue Black
Row 9: Blue Blue Black Yellow Orange Blue Purple Red Gray Purple Yellow Purple Gray Gray Purple Yellow Purple Gray Red Purple Blue Orange Yellow Black
Row 10: Red Blue Blue Black Purple Orange Purple Yellow Purple Gray Black Blue Blue Blue Blue Black Gray Purple Yellow Purple Orange Purple Black Blue
Row 11: Orange Yellow Yellow Orange Red Red Yellow Purple Yellow Black Blue Blue Orange Orange Blue Blue Black Yellow Purple Yellow Red Red Orange Yellow
Row 12: Yellow Red Black Gray Purple Blue Red Yellow Purple Blue Blue Purple Yellow Yellow Purple Blue Blue Purple Yellow Red Blue Purple Gray Black
Row 13: Gray Gray Black Yellow Black Red Blue Yellow Gray Blue Orange Yellow Yellow Yellow Yellow Orange Blue Gray Yellow Blue Red Black Yellow Black
Row 14: Gray Gray Black Yellow Black Red Blue Yellow Gray Blue Orange Yellow Yellow Yellow Yellow Orange Blue Gray Yellow Blue Red Black Yellow Black
Row 15: Yellow Red Black Gray Purple Blue Red Yellow Purple Blue Blue Purple Yellow Yellow Purple Blue Blue Purple Yellow Red Blue Purple Gray Black
Row 16: Orange Yellow Yellow Orange Red Red Yellow Purple Yellow Black Blue Blue Orange Orange Blue Blue Black Yellow Purple Yellow Red Red Orange Yellow
Row 17: Red Blue Blue Black Purple Orange Purple Yellow Purple Gray Black Blue Blue Blue Blue Black Gray Purple Yellow Purple Orange Purple Black Blue
Row 18: Blue Blue Black Yellow Orange Blue Purple Red Gray Purple Yellow Purple Gray Gray Purple Yellow Purple Gray Red Purple Blue Orange Yellow Black
Row 19: Blue Orange Black Blue Red Blue Yellow Gray Red Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Red Gray Yellow Blue Red Blue Black
Row 20: Purple Black Black Purple Orange Red Yellow Yellow Purple Purple Yellow Red Blue Blue Red Yellow Purple Purple Yellow Yellow Red Orange Purple Black
Row 21: Black Gray Purple Black Red Blue Red Blue Blue Orange Red Blue Red Red Blue Red Orange Blue Blue Red Blue Red Black Purple
Row 22: Gray Red Orange Red Red Red Orange Red Orange Purple Red Purple Black Black Purple Red Purple Orange Red Orange Red Red Red Orange
Row 23: Blue Red Gray Blue Red Black Purple Blue Yellow Black Orange Gray Yellow Yellow Gray Orange Black Yellow Blue Purple Black Red Blue Gray
Row 24: Yellow Yellow Orange Gray Orange Purple Black Black Black Blue Yellow Black Black Black Black Yellow Blue Black Black Black Purple Orange Gray Orange
Here is the input grid for the test example:
Input:
Row 1: Black Red Purple Red Black Black Black Gray Black Black Gray Black Black Black Red Purple
Row 2: Red Black Gray Pink Yellow Yellow Yellow Orange Orange Orange Yellow Yellow Yellow Yellow Pink Gray
Row 3: Purple Gray Black Black Yellow Yellow Yellow Gray Brown Brown Yellow Yellow Yellow Yellow Yellow Black
Row 4: Red Pink Black Black Black Red Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 5: Black Orange Pink Black Black Gray Red Pink Purple Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 6: Black Black Purple Red Gray Orange Purple Purple Black Black Yellow Yellow Yellow Yellow Red Purple
Row 7: Black Orange Orange Black Red Purple Black Red Pink Pink Red Black Purple Red Black Orange
Row 8: Gray Orange Gray Black Pink Purple Red Purple Purple Purple Purple Red Purple Pink Black Gray
Row 9: Black Orange Brown Black Yellow Yellow Yellow Purple Blue Blue Purple Pink Yellow Yellow Yellow Brown
Row 10: Black Orange Brown Yellow Yellow Yellow Yellow Purple Blue Blue Purple Pink Yellow Yellow Yellow Brown
Row 11: Gray Orange Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 12: Black Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Orange
Row 13: Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Purple
Row 14: Black Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Pink
Row 15: Red Pink Black Black Yellow Yellow Yellow Yellow Yellow Black Black Black Red Black Black Black
Row 16: Purple Gray Black Black Yellow Yellow Yellow Yellow Yellow Brown Gray Orange Purple 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 Red Purple Red Black Black Black Gray Black Black Gray Black Black Black Red Purple
Red Black Gray Pink Orange Black Orange Orange Orange Orange Orange Orange Black Orange Pink Gray
Purple Gray Black Black Pink Purple Orange Gray Brown Brown Gray Orange Purple Pink Black Black
Red Pink Black Black Black Red Black Black Black Black Black Black Red Black Black Black
Black Orange Pink Black Black Gray Red Pink Purple Purple Pink Red Gray Black Black Pink
Black Black Purple Red Gray Orange Purple Purple Black Black Purple Purple Orange Gray Red Purple
Black Orange Orange Black Red Purple Black Red Pink Pink Red Black Purple Red Black Orange
Gray Orange Gray Black Pink Purple Red Purple Purple Purple Purple Red Purple Pink Black Gray
Black Orange Brown Black Purple Black Pink Purple Blue Blue Purple Pink Black Purple Black Brown
Black Orange Brown Black Purple Black Pink Purple Blue Blue Purple Pink Black Purple Black Brown
Gray Orange Gray Black Pink Purple Red Purple Purple Purple Purple Red Purple Pink Black Gray
Black Orange Orange Black Red Purple Black Red Pink Pink Red Black Purple Red Black Orange
Black Black Purple Red Gray Orange Purple Purple Black Black Purple Purple Orange Gray Red Purple
Black Orange Pink Black Black Gray Red Pink Purple Purple Pink Red Gray Black Black Pink
Red Pink Black Black Black Red Black Black Black Black Black Black Red Black Black Black
Purple Gray Black Black Pink Purple Orange Gray Brown Brown Gray Orange Purple Pink 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 Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Row 2: Orange Orange Orange Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Row 3: Orange Orange Orange Green Orange Orange Orange Red Orange Orange Orange Gray Orange Pink Orange Brown Orange Orange Yellow Purple Orange Orange Brown
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Row 2: Orange Orange Orange Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Row 3: Orange Orange Orange Green Orange Orange Orange Red Orange Orange Orange Gray Orange Pink Orange Brown Orange Orange Yellow Purple Orange Orange Brown
Row 4: Orange Orange Orange Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Row 5: Orange Orange Orange Green Orange Orange Orange Red Orange Orange Orange Gray Orange Pink Orange Brown Orange Orange Yellow Purple Orange Orange Brown
Row 6: Orange Orange Orange Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Row 7: Orange Orange Orange Green Orange Orange Orange Red Orange Orange Orange Gray Orange Pink Orange Brown Orange Orange Yellow Purple Orange Orange Brown
Row 8: Orange Orange Orange Pink Orange Orange Orange Black Orange Orange Orange Brown Orange Brown Orange Blue Orange Orange Black Pink Orange Orange Red
Example 2
Input:
Row 1: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Row 2: Yellow Blue Purple Yellow Yellow Gray Yellow Purple Yellow Red Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Gray Yellow Blue
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green 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 Purple Yellow Yellow Yellow Yellow 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 Purple 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 Yellow Yellow Yellow Yellow Green 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 Purple 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 Green 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 Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Row 2: Yellow Blue Purple Yellow Yellow Gray Yellow Purple Yellow Red Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Gray Yellow Blue
Row 3: Yellow Blue Purple Yellow Yellow Gray Yellow Purple Yellow Red Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Gray Yellow Blue
Row 4: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Row 5: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Row 6: Yellow Blue Purple Yellow Yellow Gray Yellow Purple Yellow Red Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Gray Yellow Blue
Row 7: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Row 8: Yellow Blue Purple Yellow Yellow Gray Yellow Purple Yellow Red Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Gray Yellow Blue
Row 9: Yellow Blue Purple Yellow Yellow Gray Yellow Purple Yellow Red Green Black Brown Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Brown Yellow Yellow Yellow Gray Yellow Blue
Row 10: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Row 11: Yellow Gray Red Yellow Yellow Black Yellow Black Yellow Green Purple Pink Gray Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Purple Yellow Brown
Example 3
Input:
Row 1: Pink Pink Pink Brown Green Pink Pink Purple Pink Pink
Row 2: Pink Pink Pink Brown Green Pink Pink Purple Pink Pink
Row 3: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 4: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Brown Green Pink Pink Purple Pink Pink
Row 2: Pink Pink Pink Brown Green Pink Pink Purple Pink Pink
Row 3: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 4: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 5: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 6: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 7: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 8: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 9: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 10: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 11: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 12: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 13: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 14: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 15: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 16: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 17: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 18: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 19: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 20: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 21: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 22: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 23: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 24: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 25: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 26: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Row 27: Pink Pink Pink Blue Black Pink Pink Yellow Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Gray Blue Blue Blue Blue Orange Blue Orange Pink Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 19: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 20: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 21: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 22: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 23: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 24: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 25: Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Blue Blue Blue Blue Orange Blue Orange Pink Blue Blue Blue Blue Blue Blue Blue Blue Purple
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Gray Blue Blue Blue Blue Orange Blue Orange Pink Blue Blue Blue Blue Blue Blue Blue Blue Purple
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Gray Blue Blue Blue Blue Orange Blue Orange Pink Blue Blue Blue Blue Blue Blue Blue Blue Purple
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Gray Blue Blue Blue Blue Orange Blue Orange Pink Blue Blue Blue Blue Blue Blue Blue Blue Purple
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Gray Blue Blue Blue Blue Orange Blue Orange Pink Blue Blue Blue Blue Blue Blue Blue Blue Purple
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Pink
Purple Blue Blue Blue Blue Black Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue 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: Black Black Black Red Black Black Blue Brown Black Black Black Brown Black Black Red
Row 2: Black Black Green Black Black Red Black Black Green Orange Black Black Black Black Black
Row 3: Black Black Black Black Black Black Brown Black Black Green Black Black Black Black Black
Row 4: Black Black Black Orange Green Black Black Brown Black Black Black Black Black Red Brown
Row 5: Black Black Black Green Black Black Black Green Black Black Green Black Black Green Black
Row 6: Red Black Black Black Black Black Black Black Black Black Black Black Black Black Orange
Row 7: Black Black Black Black Black Black Black Brown Black Orange Black Black Black Black Black
Row 8: Black Orange Red Black Black Black Black Orange Black Black Black Black Black Black Brown
Row 9: Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black
Row 10: Black Black Black Black Black Blue Black Black Brown Black Black Black Black Orange Black
Row 11: Black Blue Black Black Black Black Black Green Black Black Black Black Black Black Black
Row 12: Black Black Orange Black Black Black Black Green Black Green Black Black Black Black Black
Row 13: Brown Green Orange Black Black Black Green Black Black Green Black Black Black Black Black
Row 14: Black Red Black Green Orange Black Black Black Black Red Black Green Black Black Blue
Row 15: Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Orange Black Brown Black Green Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Green Black Black Black Black Blue
Row 18: Black Black Black Black Black Black Black Black Orange Blue Red Green Black Black Black
Row 19: Green Black Black Black Black Orange Red Black Black Black Black Black Red Black Black
Row 20: Orange Red Black Black Black Black Black Black Black Black Black Black Orange Black Black
Row 21: Black Orange Orange Green Black Green Blue Red Black Black Green Black Black Black Black
Row 22: Black Black Black Brown Green Red Black Black Black Black Black Black Black Black Black
Row 23: Black Black Green Green Blue Orange Black Black Black Green Black Black Black Black Black
Row 24: Orange Black Black Black Black Black Brown Black Red Red Black Black Black Red Black
Row 25: Black Orange Red Black Black Black Black Black Green Black Black Black Orange Black Black
Output:
Row 1: Black Orange Red Black Black Black Black Black Green Black Black Black Orange Black Black
Row 2: Orange Black Black Black Black Black Brown Black Red Red Black Black Black Red Black
Row 3: Black Black Green Green Blue Orange Black Black Black Green Black Black Black Black Black
Row 4: Black Black Black Brown Green Red Black Black Black Black Black Black Black Black Black
Row 5: Black Orange Orange Green Black Green Blue Red Black Black Green Black Black Black Black
Row 6: Orange Red Black Black Black Black Black Black Black Black Black Black Orange Black Black
Row 7: Green Black Black Black Black Orange Red Black Black Black Black Black Red Black Black
Row 8: Black Black Black Black Black Black Black Black Orange Blue Red Green Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Green Black Black Black Black Blue
Row 10: Black Black Black Black Black Orange Black Brown Black Green Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 12: Black Red Black Green Orange Black Black Black Black Red Black Green Black Black Blue
Row 13: Brown Green Orange Black Black Black Green Black Black Green Black Black Black Black Black
Row 14: Black Black Orange Black Black Black Black Green Black Green Black Black Black Black Black
Row 15: Black Blue Black Black Black Black Black Green Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Blue Black Black Brown Black Black Black Black Orange Black
Row 17: Black Black Black Black Black Black Black Black Black Orange Black Black Black Black Black
Row 18: Black Orange Red Black Black Black Black Orange Black Black Black Black Black Black Brown
Row 19: Black Black Black Black Black Black Black Brown Black Orange Black Black Black Black Black
Row 20: Red Black Black Black Black Black Black Black Black Black Black Black Black Black Orange
Row 21: Black Black Black Green Black Black Black Green Black Black Green Black Black Green Black
Row 22: Black Black Black Orange Green Black Black Brown Black Black Black Black Black Red Brown
Row 23: Black Black Black Black Black Black Brown Black Black Green Black Black Black Black Black
Row 24: Black Black Green Black Black Red Black Black Green Orange Black Black Black Black Black
Row 25: Black Black Black Red Black Black Blue Brown Black Black Black Brown Black Black Red
Example 2
Input:
Row 1: Purple Orange Pink Red Orange Orange Red Orange Red Pink Orange Orange Red Orange Orange Pink Orange Purple Red Red Red Orange Pink Orange Red Orange Orange
Row 2: Pink Orange Orange Purple Orange Purple Purple Orange Orange Pink Purple Red Red Orange Purple Purple Orange Orange Red Orange Purple Orange Red Orange Orange Orange Red
Row 3: Orange Purple Red Pink Purple Orange Red Pink Orange Red Orange Orange Orange Orange Red Orange Orange Orange Purple Pink Orange Orange Orange Orange Orange Red Orange
Row 4: Red Purple Orange Orange Orange Orange Purple Orange Orange Pink Orange Pink Orange Red Purple Purple Pink Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange
Output:
Row 1: Red Purple Orange Orange Orange Orange Purple Orange Orange Pink Orange Pink Orange Red Purple Purple Pink Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange
Row 2: Orange Purple Red Pink Purple Orange Red Pink Orange Red Orange Orange Orange Orange Red Orange Orange Orange Purple Pink Orange Orange Orange Orange Orange Red Orange
Row 3: Pink Orange Orange Purple Orange Purple Purple Orange Orange Pink Purple Red Red Orange Purple Purple Orange Orange Red Orange Purple Orange Red Orange Orange Orange Red
Row 4: Purple Orange Pink Red Orange Orange Red Orange Red Pink Orange Orange Red Orange Orange Pink Orange Purple Red Red Red Orange Pink Orange Red Orange Orange
Example 3
Input:
Row 1: Red Black Black Black Black Purple Pink Black Orange Orange Black Black Black Pink
Row 2: Yellow Gray Black Black Red Black Black Black Red Yellow Orange Yellow Black Black
Row 3: Black Yellow Black Red Orange Black Black Yellow Gray Gray Purple Black Purple Brown
Output:
Row 1: Black Yellow Black Red Orange Black Black Yellow Gray Gray Purple Black Purple Brown
Row 2: Yellow Gray Black Black Red Black Black Black Red Yellow Orange Yellow Black Black
Row 3: Red Black Black Black Black Purple Pink Black Orange Orange Black Black Black Pink
Here is the input grid for the test example:
Input:
Row 1: Orange Red Orange Red Red Red Orange Red Red Red Red Gray Yellow Blue Red Red Red Red Red Purple Red
Row 2: Red Brown Red Red Red Red Purple Purple Red Blue Red Red Brown Red Brown Red Blue Brown Purple Red Gray
Row 3: Red Red Red Brown Red Red Red Brown Red Red Red Red Red Purple Red Orange Red Brown Red Red Pink
Row 4: Red Orange Red Red Yellow Red Purple Red Brown Red Red Red Red Pink Red Red Red Red Red Red Orange
Row 5: Pink Red Red Brown Red Red Red Red Red Red Orange Red Brown Yellow Red Green Orange Yellow Red Red Green
Row 6: Orange Red Orange Red Red Red Red Brown Pink Purple Brown Red Red Red Red Red Yellow Red Red Red Red
Row 7: Red Orange Purple Purple Pink Brown Red Red Purple Red Red Red Red Red Red Red Brown Red Purple Orange Orange
Row 8: Red Blue Red Yellow Orange Gray Yellow Red Purple Red Red Red Red Red Red Yellow Purple Red Red Purple Red
Row 9: Brown Red Brown Red Red Brown Red Yellow Brown Purple Purple Red Red Orange Red Red Pink Pink Purple Yellow Red
Row 10: Brown Red Orange Purple Red Pink Red Red Purple Red Brown Red Orange Brown Red Red Red Purple Red Brown Pink
Row 11: Red Pink Purple Yellow Red Red Red Pink Purple Purple Purple Red Red Red Orange Yellow Red Red Red Yellow Red
Row 12: Purple Red Red Pink Brown Purple Brown Red Red Blue Red Red Purple Red Purple Red Brown Red Orange Red Purple
Row 13: Red Red Orange Red Red Red Red Brown Brown Red Pink Red Red Red Red Red Orange Brown Red Orange Brown
Row 14: Purple Red Purple Red Red Red Yellow Gray Orange Brown Pink Orange Yellow Red Red Red Red Orange Red Brown Red
Row 15: Red Red Pink Pink Red Red Red Orange Pink Red Purple Purple Red Red Brown Brown Red Red Orange Blue Green
Row 16: Red Pink Red Red Red Pink Purple Purple Purple Red Yellow Pink Blue Red Orange Red Red Red Pink Red Red
Row 17: Red Red Red Yellow Red Brown Red Red Brown Red Brown Red Orange Red Red Orange Red Yellow Brown Blue Red
Row 18: Brown Red Brown Red Red Blue Red Red Red Yellow Red Red Red Red Brown Red Red Red Red Red Red
Row 19: Brown Pink Red Yellow Red Red Pink Purple Red Red Gray Red Red Red Purple Red Brown Red Red Red Red
Row 20: Red Purple Red Red Red Blue Red Red Blue Pink Brown Red Red Purple Red Yellow Red Red Red Brown Red
Row 21: Yellow Red Red Yellow Brown Pink Purple Red Red Purple Yellow Purple Blue Red Red Red Pink Red Red Red Purple
Row 22: Red Red Gray Red Pink Red Orange Red Red Purple Red Red Orange Blue Pink Red Red Brown Orange Orange Red
Row 23: Red Yellow Red Red Red Green Red Red Orange Purple Red Brown Red Red Gray Purple 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 Yellow Red Red Red Green Red Red Orange Purple Red Brown Red Red Gray Purple Red Red Red Red Red
Red Red Gray Red Pink Red Orange Red Red Purple Red Red Orange Blue Pink Red Red Brown Orange Orange Red
Yellow Red Red Yellow Brown Pink Purple Red Red Purple Yellow Purple Blue Red Red Red Pink Red Red Red Purple
Red Purple Red Red Red Blue Red Red Blue Pink Brown Red Red Purple Red Yellow Red Red Red Brown Red
Brown Pink Red Yellow Red Red Pink Purple Red Red Gray Red Red Red Purple Red Brown Red Red Red Red
Brown Red Brown Red Red Blue Red Red Red Yellow Red Red Red Red Brown Red Red Red Red Red Red
Red Red Red Yellow Red Brown Red Red Brown Red Brown Red Orange Red Red Orange Red Yellow Brown Blue Red
Red Pink Red Red Red Pink Purple Purple Purple Red Yellow Pink Blue Red Orange Red Red Red Pink Red Red
Red Red Pink Pink Red Red Red Orange Pink Red Purple Purple Red Red Brown Brown Red Red Orange Blue Green
Purple Red Purple Red Red Red Yellow Gray Orange Brown Pink Orange Yellow Red Red Red Red Orange Red Brown Red
Red Red Orange Red Red Red Red Brown Brown Red Pink Red Red Red Red Red Orange Brown Red Orange Brown
Purple Red Red Pink Brown Purple Brown Red Red Blue Red Red Purple Red Purple Red Brown Red Orange Red Purple
Red Pink Purple Yellow Red Red Red Pink Purple Purple Purple Red Red Red Orange Yellow Red Red Red Yellow Red
Brown Red Orange Purple Red Pink Red Red Purple Red Brown Red Orange Brown Red Red Red Purple Red Brown Pink
Brown Red Brown Red Red Brown Red Yellow Brown Purple Purple Red Red Orange Red Red Pink Pink Purple Yellow Red
Red Blue Red Yellow Orange Gray Yellow Red Purple Red Red Red Red Red Red Yellow Purple Red Red Purple Red
Red Orange Purple Purple Pink Brown Red Red Purple Red Red Red Red Red Red Red Brown Red Purple Orange Orange
Orange Red Orange Red Red Red Red Brown Pink Purple Brown Red Red Red Red Red Yellow Red Red Red Red
Pink Red Red Brown Red Red Red Red Red Red Orange Red Brown Yellow Red Green Orange Yellow Red Red Green
Red Orange Red Red Yellow Red Purple Red Brown Red Red Red Red Pink Red Red Red Red Red Red Orange
Red Red Red Brown Red Red Red Brown Red Red Red Red Red Purple Red Orange Red Brown Red Red Pink
Red Brown Red Red Red Red Purple Purple Red Blue Red Red Brown Red Brown Red Blue Brown Purple Red Gray
Orange Red Orange Red Red Red Orange Red Red Red Red Gray Yellow Blue Red Red Red Red Red Purple 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: Green Green Green Red Red Green Green Green Green Green Green Green Green Green Green Red Red Green Green Green Green Green Green
Row 2: Green Green Green Orange Red Green Green Green Green Green Green Green Green Green Green Orange Orange Green Green Red Red Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Orange 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
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
Row 6: Green Green Green Green Green Green Green Green Green Green Green Orange Red Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Orange Red Green Red Red Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red Orange Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Orange Red Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Orange Orange Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Red Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Orange Red 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 Orange Orange Green Green Green
Row 14: Green Green Green Green Green Green Green Red Orange Green Green Green Green Green Green Green Green Green Red Red Green Green Green
Row 15: Green Green Green Green Green Green Green Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Orange Red Green Green Green Green Green Green Green Green Orange Orange Green Green Green Green Green Green Green Green Green
Row 17: Green Green Orange Red Green Green Green Green Green Green Green Green Red Red 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
Row 19: Green Green Green Green Green Green Green Red Orange Green Green Green Red Orange Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Red Red Green Green Green Orange Red Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Orange Orange Orange Orange Green Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Green Green Green Orange Orange Orange Green Green Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Green
Row 3: Green Green Green Green Orange Orange Orange Green Green Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Green Green
Row 4: Orange Green Green Green Green Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green
Row 5: Orange Orange Green Green Green Green Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green
Row 6: Orange Orange Orange Green Green Green Green Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green
Row 7: Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green
Row 8: Orange Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green
Row 9: Green Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green
Row 10: Green Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green
Row 11: Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green
Row 12: Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Green Green Green Green
Row 13: Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange Orange Orange Green Green Green
Row 14: Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Green Green
Row 15: Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Orange Orange Orange Orange Orange Orange Green
Row 16: Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange
Row 18: Green Green Green Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange Orange
Row 19: Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange Orange
Row 20: Green Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Red Purple Pink Pink Pink
Row 4: Pink Red Purple Pink Purple Red Pink Pink Pink
Row 5: Pink Purple Red Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Purple Purple Purple Pink Pink Pink Pink Pink
Row 2: Purple Pink Purple Purple Purple Pink Pink Pink Pink
Row 3: Purple Purple Pink Purple Purple Purple Pink Pink Pink
Row 4: Purple Purple Purple Pink Purple Purple Purple Pink Pink
Row 5: Pink Purple Purple Purple Pink Purple Purple Purple Pink
Row 6: Pink Pink Purple Purple Purple Pink Purple Purple Purple
Row 7: Pink Pink Pink Purple Purple Purple Pink Purple Purple
Row 8: Pink Pink Pink Pink Purple Purple Purple Pink Purple
Row 9: Pink Pink Pink Pink Pink Purple Purple Purple Pink
Row 10: Pink Pink Pink Pink Pink Pink Purple Purple Purple
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Red Red Yellow
Row 3: Yellow Yellow Yellow Yellow Gray Red Yellow
Row 4: Gray Gray Yellow Yellow Yellow Yellow Yellow
Row 5: Gray Red Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Red Gray Yellow
Row 12: Yellow Yellow Yellow Yellow Gray Red Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Gray Gray Yellow Yellow
Row 15: Yellow Yellow Yellow Red Red Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Gray Gray Gray Gray Gray
Row 2: Yellow Yellow Yellow Gray Gray Gray Gray
Row 3: Yellow Yellow Yellow Yellow Gray Gray Gray
Row 4: Gray Gray Yellow Yellow Yellow Gray Gray
Row 5: Gray Gray Gray Yellow Yellow Yellow Gray
Row 6: Gray Gray Gray Gray Yellow Yellow Yellow
Row 7: Gray Gray Gray Gray Gray Yellow Yellow
Row 8: Gray Gray Gray Gray Gray Gray Yellow
Row 9: Yellow Gray Gray Gray Gray Gray Gray
Row 10: Yellow Yellow Gray Gray Gray Gray Gray
Row 11: Yellow Yellow Yellow Gray Gray Gray Gray
Row 12: Yellow Yellow Yellow Yellow Gray Gray Gray
Row 13: Yellow Yellow Yellow Yellow Yellow Gray Gray
Row 14: Yellow Yellow Yellow Gray Gray Yellow Gray
Row 15: Yellow Yellow Gray Gray Gray Gray Yellow
Row 16: Yellow Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Yellow Yellow Gray Gray
Row 18: Gray Gray Yellow Yellow Yellow Yellow Gray
Row 19: Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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
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 Yellow Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Yellow Yellow Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Red Red Gray Gray Gray Gray Gray Red Yellow 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
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 Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Yellow Yellow Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Yellow Yellow Yellow Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow 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 Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Green Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Purple Purple Purple Purple Green Green
Row 3: Purple Purple Purple Purple Purple Green Purple Purple Purple Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Green Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Green Purple Green Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Green Green Purple Purple Green Green Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Green Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Green Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Green Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Green Purple Purple Green Purple Purple Green
Row 13: Green Purple Green Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
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: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Green Purple Green Green Purple Purple
Row 16: Purple Purple Purple Green Purple Green Purple Purple Purple Green Green Green Purple Purple Green Purple Purple Green Green Purple Purple
Row 17: Purple Purple Purple Purple Purple Green Purple Purple Purple Green Green Green Purple Purple Purple Green Purple Purple Purple Green Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Green Green Purple Green Purple Green
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Green Purple Purple Purple Green
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Green Purple Purple Green Purple Green Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Green Purple Purple Purple Green Green Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Green Green Purple Green Purple Purple Purple Green
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple Green Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Green Purple Green Green Green Purple Purple Purple Purple Purple Green Purple Green Green
Row 26: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Green Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Green
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: Purple Purple Purple Purple Purple Purple 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 Purple Purple
Row 6: Purple Purple Purple Purple 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 Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Example 2
Input:
Row 1: Red Blue Red Blue Blue Blue Blue Blue Red Red Red Red Blue Blue Blue Red Red Red Red Blue Red Red Blue Red Red Red Red
Row 2: Red Blue Blue Blue Blue Blue Red Red Blue Blue Blue Red Blue Blue Blue Red Blue Red Red Red Red Red Blue Red Red Red Red
Row 3: Blue Red Red Blue Red Blue Red Blue Red Blue Red Blue Blue Blue Blue Red Red Red Red Red Red Red Red Blue Red Red Red
Row 4: Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Red Red Red Red Red Red Red Red Red Red
Row 5: Red Blue Red Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Blue Red Blue Red
Row 6: Red Blue Blue Blue Red Red Blue Red Blue Red Blue Blue Blue Blue Blue Red Blue Blue Red Red Red Red Red Red Red Blue Red
Row 7: Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Red Blue Red Red Red Red Red Red Blue Red
Row 8: Blue Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Red Red Blue Red Blue Red
Row 9: Blue Red Blue Red Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Red Blue Red Red Red Blue Red Red Red Blue Red Red
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
Row 11: Blue Red Red Blue Blue Blue Red Blue Red Blue Red Blue Blue Blue Blue Blue Red Red Blue Red Red Red Blue Blue Blue Blue Blue
Row 12: Blue Red Blue Blue Red Red Red Red Blue Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Red Blue Red Red Red Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Red Red Blue Red Blue Blue Red Red Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Red Blue Blue
Row 15: Red Red Red Blue Blue Red Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Red Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Red Red Red Blue Red Red Blue Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue
Row 17: Blue Red Red Red Blue Red Blue Blue Red Red Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Red Red Red Blue Red Blue Red Blue Blue Blue Red Blue Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Red Red Red Red Blue Red Blue Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Blue Blue Blue Blue Blue
Output:
Row 1: Red Red Red Red Red Blue Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Blue Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Blue 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
Row 6: Red Red Red Red Red Red Red Red Red Red Red Blue Red
Row 7: Blue Red Red Red Blue Red Red Red Red Red Red Red Red
Row 8: Blue Red Red Red Red Red Blue Red Red Red Red Blue Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Blue Blue Red Red Red Red Red Red Blue Red Red Blue Blue
Example 3
Input:
Row 1: Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green 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
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green 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
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange
Row 7: Orange Orange Green 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 Green Orange Orange Orange Orange Orange Orange Orange Green
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange 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 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 Orange Orange Orange
Row 13: Orange Green Green Orange Green Green Orange Orange Green Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange
Row 14: Green Green Orange Green Orange Green Green Orange Orange Orange Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange
Row 15: Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Green Green
Row 16: Orange Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange
Row 17: Green Orange Orange Orange Green Orange Green Orange Green Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Green Orange
Row 18: Orange Orange Green Green Green Orange Orange Orange Green Orange Orange Orange Green Green Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 20: Orange Green Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 21: Orange Orange Green Orange Green Green Orange Orange Green Orange Orange Orange Green Green Orange Green Orange Green Orange Orange Orange
Row 22: Orange Green Orange Orange Orange Green Green Green Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange
Row 23: Orange Green Orange Orange Green Orange Green Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Green Orange Orange Green Orange Orange Orange Orange
Row 2: Orange Green Green Orange Green Green Orange Orange Green Orange
Row 3: Green Green Green Green Orange Green Green Orange Orange Orange
Row 4: Green Orange Green Green Orange Orange Orange Orange Green Green
Row 5: Orange Green Orange Green Green Green Orange Orange Orange Orange
Row 6: Green Green Orange Orange Green Green Green Orange Green Orange
Row 7: Orange Green Green Green Green Orange Orange Orange Green Orange
Row 8: Orange Green Orange Orange Orange Orange Orange Orange Green Green
Row 9: Orange Green Orange Orange Green Green Orange Orange Green Orange
Row 10: Orange Green Green Orange Green Green Green Orange Green Orange
Row 11: Orange Green Orange Orange Green Green Green Green Orange Orange
Row 12: Orange Green Orange Orange Green Orange Green Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Gray Blue Blue Blue Blue Blue Blue Blue Gray Blue Gray Gray Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Gray
Row 3: Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Gray Blue Gray Gray Gray Blue Blue Blue Gray Blue Blue Blue Blue
Row 6: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Gray Blue Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Blue Gray Gray Blue
Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Blue
Gray Gray Gray Gray Gray 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray 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 Blue Gray Gray 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 Blue Gray Gray 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Pink
Row 18: Pink Pink Pink 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 19: Pink Pink Pink 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 20: Pink Pink Pink 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 21: Pink Pink Pink 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 22: Pink Pink Pink 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 23: Pink Pink Pink 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 24: Pink Pink Pink Pink 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: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Gray Green Green Gray 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 Gray Gray Gray Gray 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 Gray Gray Gray Gray 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
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 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
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
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
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
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
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
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 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 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
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: Green Green Green 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 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
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
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
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
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 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 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 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 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 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 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 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 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 Gray Gray Gray Gray
Row 10: Brown Brown Brown Brown Brown Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Red Red Red Red Gray Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Red Red Red Red Red Red Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Red Red Red Red Gray Gray Red 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 Red 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
Row 17: Red Gray Red 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
Row 18: Gray 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
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 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 Green
Row 4: Red 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 5: Red 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 6: Red Red Red Red Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Red Red Red Red Red Red Green Red 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 Green Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Red Red Red Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Red Red Red Red Green Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Red Red Red Red Red Red Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Red Red Red Red Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Red 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 17: Red 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 18: 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 Green
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 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 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 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 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 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 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 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 Orange
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
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: 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 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
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
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: 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
Row 16: 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
Row 17: 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
Row 18: 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
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange
Row 20: 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
Row 21: 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
Row 22: 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
Row 23: 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
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
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
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
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
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
Row 6: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 11: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 20: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Green Green Green Green Green Green Green Green Green Green 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: 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
Row 3: 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
Row 5: 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
Row 7: 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
Row 9: Orange Orange 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 Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Purple Purple Orange Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Purple Orange Orange Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Purple Purple Purple Orange Purple Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Purple Purple Purple Orange Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Purple Orange Purple Purple Purple Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Purple Purple Orange Orange Purple Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Purple Orange Orange Orange Orange Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Purple Purple Purple Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange 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
Row 23: 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
Row 25: 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
Row 27: 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>
| Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
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 Green Purple Purple Green Purple Purple Green Green Green Green Green Green Green Green
Green Green Purple Green Green Purple Purple Green Green Purple Purple Green Green Purple Green Green Green Green Green Green
Green Green Purple Purple Purple Green Purple Purple Purple Purple Green Purple Purple Purple Green Green Green Green Green Green
Green Green Green Purple Purple Purple Green Purple Purple Green Purple Purple Purple Green Green Green Green Green Green Green
Green Green Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Green Green Green Green Green Green
Green Green Purple Purple Green Green Purple Purple Purple Purple Green Green Purple Purple Green Green Green Green Green Green
Green Green Purple Green Green Green Green Purple Purple Green Green Green Green Purple Green Green Green Green Green Green
Green Green Green Green Purple Purple Purple Green Green Purple Purple Purple Green Green Green Green Green Green Green Green
Green Green Green Green Green 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 Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange
Row 2: Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Red Orange 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red 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 Red Orange Orange Orange Orange Orange Red Orange Orange Orange
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 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 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 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 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 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 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 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 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 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 Gray Gray Gray
Row 18: 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
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 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 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: 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
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red 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 Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange
Row 26: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 27: Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Red 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 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 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 Gray 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 Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange
Row 5: Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange
Row 6: Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange
Row 7: Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Orange Orange Orange
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 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 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 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 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 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 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 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 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 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 Gray Gray Gray
Row 18: 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
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 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 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 22: 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
Row 23: Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Gray Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Gray Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray 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 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 Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Purple Pink Pink Pink Pink Purple Pink Purple
Row 3: Pink Purple Pink Pink Pink Pink Purple Pink Purple
Row 4: Pink Purple Pink Pink Pink Pink Purple Pink Purple
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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Pink Purple Purple Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Purple Pink
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Yellow Pink Pink Pink Pink Yellow Pink Yellow
Row 3: Pink Yellow Pink Pink Pink Pink Yellow Pink Yellow
Row 4: Pink Yellow Pink Pink Pink Pink Yellow Pink 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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Pink Yellow Yellow Pink Pink Pink Yellow Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 3
Input:
Row 1: Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Black Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Black Brown Brown Brown Brown Brown Brown Brown
Row 6: Black Brown Brown Brown Brown Brown Brown Brown Brown
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
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 18: Brown Black Brown Black Black Brown Brown Brown Brown
Row 19: Brown Black Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Black Black Black Black Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Blue Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Blue Blue Brown Brown Brown Brown Brown Brown Brown
Row 6: Blue Blue Brown Brown Brown Brown Brown Brown Brown
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
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Brown Blue Blue Blue Blue Brown Brown Brown Brown
Row 18: Brown Blue Brown Blue Blue Brown Brown Brown Brown
Row 19: Brown Blue Brown Blue Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Orange Orange Gray
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: Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Orange Gray Gray Gray Gray Gray Gray Gray
Row 8: Orange Gray Gray Gray Gray Gray Orange 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 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 Gray Gray Gray Gray Gray Black Gray
Black 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: Blue Blue Blue Green Blue Blue Blue Yellow Gray Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Gray Blue
Row 5: Blue Blue Blue Blue Blue Blue Green Green Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Yellow Blue Blue Blue Blue Blue Green Blue
Row 9: Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Orange Blue Blue Blue Gray Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 12: Green Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue
Row 13: Orange Blue Blue Blue Orange Blue Blue Gray Blue Blue Blue
Row 14: Blue Blue Blue Green Blue Yellow Orange Blue Blue Blue Blue
Row 15: Yellow Blue Blue Orange Blue Blue Blue Blue Blue Gray Blue
Row 16: Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Orange
Row 17: Orange Blue Green Blue Gray Blue Blue Blue Yellow Blue Blue
Row 18: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Gray Blue Green Blue Blue Yellow
Row 21: Gray Blue Blue Blue Blue Green Blue Green Blue Blue Blue
Row 22: Blue Blue Gray Gray Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Orange Green Blue Blue Blue Blue Blue Blue Blue
Row 25: Orange Orange Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 26: Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue
Row 27: Orange Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue
Row 28: Blue Yellow Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 3: Purple Blue Blue Blue Blue Blue Orange Blue Blue Blue Purple
Row 4: Purple Blue Blue Blue Blue Blue Blue Blue Yellow Gray Purple
Row 5: Purple Blue Blue Blue Blue Blue Green Green Blue Blue Purple
Row 6: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 7: Purple Blue Blue Blue Blue Green Blue Blue Blue Blue Purple
Row 8: Purple Blue Blue Yellow Blue Blue Blue Blue Blue Green Purple
Row 9: Purple Blue Blue Blue Yellow Blue Blue Blue Blue Blue Purple
Row 10: Purple Blue Orange Blue Blue Blue Gray Blue Blue Blue Purple
Row 11: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 12: Purple Blue Blue Orange Blue Blue Blue Blue Blue Blue Purple
Row 13: Purple Blue Blue Blue Orange Blue Blue Gray Blue Blue Purple
Row 14: Purple Blue Blue Green Blue Yellow Orange Blue Blue Blue Purple
Row 15: Purple Blue Blue Orange Blue Blue Blue Blue Blue Gray Purple
Row 16: Purple Blue Blue Blue Blue Orange Blue Blue Blue Blue Purple
Row 17: Purple Blue Green Blue Gray Blue Blue Blue Yellow Blue Purple
Row 18: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 19: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 20: Purple Blue Blue Blue Blue Gray Blue Green Blue Blue Purple
Row 21: Purple Blue Blue Blue Blue Green Blue Green Blue Blue Purple
Row 22: Purple Blue Gray Gray Blue Blue Blue Blue Blue Blue Purple
Row 23: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 24: Purple Blue Orange Green Blue Blue Blue Blue Blue Blue Purple
Row 25: Purple Orange Blue Gray Blue Blue Blue Blue Blue Blue Purple
Row 26: Purple Blue Blue Blue Blue Blue Blue Orange Blue Blue Purple
Row 27: Purple Blue Blue Blue Yellow Blue Blue Blue Blue Blue Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Black Black Gray Black Black Red Blue Black Black Black Black Black Black Red Black Black
Row 2: Black Black Black Black Black Black Yellow Black Black Black Black Black Black Brown Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Blue Red Black Black Black Blue Black Yellow Blue Black Black Black
Row 5: Yellow Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black
Row 6: Yellow Black Black Green Pink Pink Black Red Black Black Black Black Black Gray Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Black
Row 9: Black Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 10: Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow
Row 11: Black Gray Black Black Red Black Black Black Blue Black Gray Black Black Black Black Black
Row 12: Black Black Red Black Black Brown Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black
Row 14: Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Yellow Black Black Black Black Black Black Brown Black Yellow Yellow Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Brown Black Black Pink 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 Blue Green Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Brown Black Black Black Green Black Yellow Black Black Black
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Black Black Black Black Black Yellow Black Black Black Black Black Black Brown Black Purple
Row 3: Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Row 4: Purple Black Black Black Blue Red Black Black Black Blue Black Yellow Blue Black Black Purple
Row 5: Purple Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Purple
Row 6: Purple Black Black Green Pink Pink Black Red Black Black Black Black Black Gray Black Purple
Row 7: Purple Black Black Black Black Black Black Black Black Black Black Black Black Gray Black Purple
Row 8: Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Gray Purple
Row 9: Purple Black Gray Black Black Black Black Gray Black Black Black Black Black Black Black Purple
Row 10: Purple Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Row 11: Purple Gray Black Black Red Black Black Black Blue Black Gray Black Black Black Black Purple
Row 12: Purple Black Red Black Black Brown Black Black Black Black Black Black Black Black Black Purple
Row 13: Purple Black Black Black Black Black Black Black Black Black Black Green Black Black Black Purple
Row 14: Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Row 15: Purple Black Black Black Black Black Black Brown Black Yellow Yellow Black Black Black Black Purple
Row 16: Purple Black Black Black Black Black Black Black Brown Black Black Pink Black Black Black Purple
Row 17: Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple
Row 18: Purple Black Black Black Black Black Black Blue Green Black Black Black Black Black Black Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Orange Brown Brown Red Red Red Orange Orange Orange Green Blue Green
Row 2: Orange Gray Brown Gray Red Brown Red Orange Gray Orange Orange Orange
Row 3: Orange Gray Orange Red Red Orange Orange Orange Orange Green Gray Blue
Row 4: Red Green Orange Orange Orange Orange Orange Brown Orange Green Green Red
Row 5: Orange Brown Gray Orange Brown Orange Orange Orange Orange Blue Orange Orange
Row 6: Orange Brown Green Gray Orange Orange Orange Orange Gray Orange Blue Orange
Row 7: Orange Blue Orange Orange Orange Orange Blue Brown Orange Orange Orange Gray
Row 8: Orange Orange Orange Red Orange Orange Orange Orange Orange Brown Brown Orange
Row 9: Brown Green Orange Orange Orange Brown Orange Green Gray Gray Blue Orange
Row 10: Gray Blue Orange Gray Orange Orange Gray Orange Orange Orange Orange Gray
Row 11: Orange Orange Brown Orange Orange Green Green Red Blue Orange Red Gray
Row 12: Orange Blue Orange Brown Green Orange Brown Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Blue Orange Orange Orange Orange Red Orange Green Orange
Row 14: Blue Gray Blue Orange Orange Orange Orange Orange Brown Red Gray Orange
Row 15: Green Orange Red Orange Blue Orange Orange Orange Blue Orange Green Orange
Row 16: Orange Orange Brown Brown Orange Orange Orange Orange Orange Blue Orange Blue
Row 17: Orange Blue Gray Red Orange Orange Orange Gray Orange Gray Gray Gray
Row 18: Orange Orange Orange Orange Gray Orange Orange Orange Orange Brown Green Orange
Row 19: Brown Gray Orange Orange Orange Brown Green Red Orange Orange Orange Red
Row 20: Orange Orange Orange Blue Red Red Green Orange Blue Gray Red Gray
Row 21: Red Red Brown Orange Orange Green Orange Brown Orange Orange Orange Blue
Row 22: Orange Orange Brown Orange Brown Orange Orange Orange Red Gray Blue Green
Row 23: Blue Orange Brown Orange Red Orange Blue Red Orange Red Brown Blue
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Gray Brown Gray Red Brown Red Orange Gray Orange Orange Purple
Row 3: Purple Gray Orange Red Red Orange Orange Orange Orange Green Gray Purple
Row 4: Purple Green Orange Orange Orange Orange Orange Brown Orange Green Green Purple
Row 5: Purple Brown Gray Orange Brown Orange Orange Orange Orange Blue Orange Purple
Row 6: Purple Brown Green Gray Orange Orange Orange Orange Gray Orange Blue Purple
Row 7: Purple Blue Orange Orange Orange Orange Blue Brown Orange Orange Orange Purple
Row 8: Purple Orange Orange Red Orange Orange Orange Orange Orange Brown Brown Purple
Row 9: Purple Green Orange Orange Orange Brown Orange Green Gray Gray Blue Purple
Row 10: Purple Blue Orange Gray Orange Orange Gray Orange Orange Orange Orange Purple
Row 11: Purple Orange Brown Orange Orange Green Green Red Blue Orange Red Purple
Row 12: Purple Blue Orange Brown Green Orange Brown Orange Orange Orange Orange Purple
Row 13: Purple Orange Orange Blue Orange Orange Orange Orange Red Orange Green Purple
Row 14: Purple Gray Blue Orange Orange Orange Orange Orange Brown Red Gray Purple
Row 15: Purple Orange Red Orange Blue Orange Orange Orange Blue Orange Green Purple
Row 16: Purple Orange Brown Brown Orange Orange Orange Orange Orange Blue Orange Purple
Row 17: Purple Blue Gray Red Orange Orange Orange Gray Orange Gray Gray Purple
Row 18: Purple Orange Orange Orange Gray Orange Orange Orange Orange Brown Green Purple
Row 19: Purple Gray Orange Orange Orange Brown Green Red Orange Orange Orange Purple
Row 20: Purple Orange Orange Blue Red Red Green Orange Blue Gray Red Purple
Row 21: Purple Red Brown Orange Orange Green Orange Brown Orange Orange Orange Purple
Row 22: Purple Orange Brown Orange Brown Orange Orange Orange Red Gray Blue Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Pink Brown Red Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink
Row 2: Pink Brown Pink Pink Pink Brown Pink Brown Pink Pink Brown Red Pink Pink Brown Pink
Row 3: Pink Red Pink Pink Red Brown Pink Red Pink Pink Red Pink Brown Pink Pink Pink
Row 4: Pink Red Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink
Row 5: Red Pink Pink Pink Brown Brown Red Red Pink Pink Pink Pink Pink Brown Brown Brown
Row 6: Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Brown Red Pink Pink
Row 7: Pink Brown Red Brown Pink Pink Pink Pink Pink Pink Brown Pink Red Pink Brown Red
Row 8: Brown Red Pink Pink Pink Red Red Pink Brown Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink
Row 10: Pink Red Pink Pink Brown 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>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Brown Pink Pink Pink Brown Pink Brown Pink Pink Brown Red Pink Pink Brown Purple
Purple Red Pink Pink Red Brown Pink Red Pink Pink Red Pink Brown Pink Pink Purple
Purple Red Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Purple
Purple Pink Pink Pink Brown Brown Red Red Pink Pink Pink Pink Pink Brown Brown Purple
Purple Brown Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Brown Red Pink Purple
Purple Brown Red Brown Pink Pink Pink Pink Pink Pink Brown Pink Red Pink Brown Purple
Purple Red Pink Pink Pink Red Red Pink Brown Pink Pink Pink Pink Pink Pink Purple
Purple Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink 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: 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
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Red Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Red Red Red Red Red Red 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
Row 11: 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
Row 13: 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
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 25: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 26: Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Gray Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Blue Gray Gray
Row 2: Gray Gray Gray
Row 3: Gray Gray 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
Row 2: 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 Gray Gray
Row 4: 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
Row 6: 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
Row 8: 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
Row 10: Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Red Red Red Red Red
Row 11: Black Black Black Black Black Black Brown Brown Black Red Red Red Black Black Red Red Red Red Red
Row 12: Black Black Black Black Black Black Brown Brown Black Red Red Red Black Black Red Red Red Red Red
Row 13: Black Black Black Black Black Black Brown Brown Black Red Red Red Black Black Red Red Red Red Red
Row 14: Black Black Black Black Black Black Brown Brown Black Red Red Red Black Black Red Red Red Red Red
Row 15: Black Black Black Black Black Black Brown Brown Black Red Red Red Black Black Red Red Red Red Red
Row 16: Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Red Red Red Red Red
Row 17: Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Red Red Red Red Red
Row 18: Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Brown Brown Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Brown Brown 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
Output:
Row 1: Blue Black Blue
Row 2: Black Black Black
Row 3: Black Black Black
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Orange
Row 2: Orange Red Red Red Red Orange Red Red Orange Red Red Red Red Red Orange Orange Orange Orange Orange Orange
Row 3: Orange Red Red Red Red Orange Red Red Orange Red Red Red Red Red Orange Orange Yellow Yellow Orange Orange
Row 4: Orange Red Red Red Red Orange Red Red Orange Red Red Red Red Red Orange Orange Yellow Yellow Orange Orange
Row 5: Orange Red Red Red Red Orange Orange Orange Orange Red Red Red Red Red Orange Orange Orange Orange Orange Orange
Row 6: Orange Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Red Red Red Red Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Purple 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 Orange Orange
Row 10: Orange Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Red Red Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Orange Red Red Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Orange Red Red Orange Orange Orange Orange Orange
Output:
Row 1: Blue Orange Blue
Row 2: Orange Blue Orange
Row 3: Blue Orange 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
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: 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 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: 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Red Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Red Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Red Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown 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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red 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 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: Orange Orange Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 2: Black Orange Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 3: Orange Orange Orange Black Black Red Yellow Black Yellow Yellow Yellow
Row 4: Black Orange Black Black Black Red Yellow Yellow Black Yellow Yellow
Row 5: Orange Orange Orange Orange Orange Red Yellow Yellow Black Black Yellow
Row 6: Black Orange Orange Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 7: Black Black Black Orange Orange Red Yellow Yellow Yellow Yellow Yellow
Row 8: Black Black Black Orange Orange Red Yellow Yellow Yellow Yellow Yellow
Row 9: Orange Black Orange Orange Black Red Yellow Yellow Yellow Yellow Yellow
Row 10: Black Orange Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 11: Black Black Black Orange Black Red Yellow Yellow Yellow Yellow Yellow
Row 12: Black Black Black Black Black Red Yellow Yellow Black Yellow Yellow
Row 13: Black Orange Orange Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 14: Black Black Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 15: Black Black Black Black Black Red Yellow Yellow Yellow Black Yellow
Row 16: Black Black Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 17: Black Black Orange Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 18: Orange Black Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 19: Black Black Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 20: Black Orange Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 21: Black Black Black Black Black Red Yellow Yellow Yellow Yellow Yellow
Row 22: Black Black Black Orange Orange Red Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Black Black Green Green Green
Row 2: Green Black Green Green Green
Row 3: Black Green Black Green Green
Row 4: Green Black Black Green Green
Row 5: Black Black Green Green Black
Row 6: Green Black Black Green Green
Row 7: Green Green Green Black Black
Row 8: Green Green Green Black Black
Row 9: Black Green Black Black Green
Row 10: Green Black Green Green Green
Row 11: Green Green Green Black Green
Row 12: Green Green Black Green Green
Row 13: Green Black Black Green Green
Row 14: Green Green Green Green Green
Row 15: Green Green Green Black Green
Row 16: Green Green Green Green Green
Row 17: Green Green Black Green Green
Row 18: Black Green Green Green Green
Row 19: Green Green Green Green Green
Row 20: Green Black Green Green Green
Row 21: Green Green Green Green Green
Row 22: Green Green Green Black Black
Example 2
Input:
Row 1: Black Yellow Black Purple Black Red Black
Row 2: Black Yellow Yellow Purple Red Red Red
Row 3: Black Black Black Purple Black Black Black
Row 4: Black Yellow Yellow Purple Red Red Red
Row 5: Yellow Black Yellow Purple Red Black Black
Row 6: Yellow Yellow Black Purple Black Black Black
Row 7: Yellow Yellow Black Purple Red Red Red
Row 8: Yellow Yellow Black Purple Red Red Black
Row 9: Black Black Yellow Purple Red Red Black
Row 10: Black Black Black Purple Red Black Black
Row 11: Yellow Yellow Yellow Purple Black Red Black
Row 12: Yellow Yellow Black Purple Black Red Black
Row 13: Yellow Yellow Yellow Purple Red Black Red
Row 14: Black Yellow Black Purple Red Red Red
Row 15: Black Black Yellow Purple Red Black Red
Row 16: Black Yellow Yellow Purple Black Red Red
Row 17: Black Black Black Purple Red Red Black
Row 18: Yellow Yellow Yellow Purple Black Red Black
Row 19: Yellow Black Yellow Purple Red Black Black
Row 20: Black Yellow Black Purple Black Red Red
Row 21: Black Black Black Purple Red Red Red
Row 22: Black Black Yellow Purple Black Black Red
Row 23: Black Yellow Black Purple Black Black Red
Row 24: Black Yellow Black Purple Black Black Black
Row 25: Black Black Black Purple Black Red Black
Row 26: Yellow Yellow Black Purple Black Black Black
Row 27: Yellow Yellow Black Purple Black Red Black
Row 28: Black Black Yellow Purple Black Red Black
Row 29: Yellow Yellow Yellow Purple Black Red Red
Row 30: Yellow Yellow Yellow Purple Black Black Black
Output:
Row 1: Black Black Black
Row 2: Green Black Black
Row 3: Black Black Black
Row 4: Green Black Black
Row 5: Black Black Green
Row 6: Green Green Black
Row 7: Black Black Green
Row 8: Black Black Black
Row 9: Green Green Green
Row 10: Green Black Black
Row 11: Green Black Green
Row 12: Green Black Black
Row 13: Black Green Black
Row 14: Green Black Green
Row 15: Green Black Black
Row 16: Black Black Black
Row 17: Green Green Black
Row 18: Green Black Green
Row 19: Black Black Green
Row 20: Black Black Green
Row 21: Green Green Green
Row 22: Black Black Black
Row 23: Black Green Green
Row 24: Black Green Black
Row 25: Black Green Black
Row 26: Green Green Black
Row 27: Green Black Black
Row 28: Black Green Green
Row 29: Green Black Black
Row 30: Green Green Green
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue
Row 3: Blue Black Blue Black Black Blue Black Blue Blue Blue Blue Blue Black Blue Black Black Blue Blue Blue Black Blue Black Blue Black Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Black Blue Blue Blue Black Blue Blue Black Blue Blue Blue Blue Black Black
Row 5: Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Black Blue Blue Blue Black Blue Blue Blue Blue Blue Black
Row 6: Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black Black
Row 7: Blue Blue Blue Blue Blue Blue Black Black Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Black Blue Black Black Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue
Row 10: Black Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black Black Blue Black Black Blue Blue Blue Blue Blue Blue Blue
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: Black Yellow Yellow Yellow Black Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Black Yellow Black Yellow Yellow
Row 13: Black Yellow Yellow Black Yellow Black Yellow Black Black Black Yellow Black Yellow Black Black Yellow Black Black Yellow Yellow Yellow Black Yellow Yellow Yellow Black
Row 14: Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Black Black Black Yellow Yellow Black Yellow Yellow
Row 15: Black Black Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Black
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Black Yellow Black Yellow Yellow Yellow Yellow Black Yellow Black Black Yellow Yellow Yellow Black Yellow
Row 17: Black Black Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Black
Row 18: Yellow Black Black Black Yellow Black Yellow Yellow Yellow Black Yellow Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Yellow Yellow Yellow
Row 19: Black Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 20: Yellow Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Yellow Black Yellow Yellow Black Yellow Black Yellow Black Yellow Yellow Yellow Black
Row 21: Yellow Black Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Black Black Yellow Black Yellow Yellow Yellow Black Yellow Black Yellow
Output:
Row 1: Green Black Black Black Green Black Black Black Black Black Black Black Green Black Black Green Black Green Black Black Black Black Black Green Black Black
Row 2: Green Black Black Green Black Green Black Green Green Green Black Green Black Green Black Black Green Green Black Green Black Green Black Black Black Green
Row 3: Black Green Black Green Black Black Green Green Black Green Black Black Green Black Black Green Black Black Green Black Green Green Black Black Black Black
Row 4: Green Green Black Green Black Black Black Black Green Green Black Green Green Green Black Black Green Black Black Black Black Green Black Black Green Black
Row 5: Black Black Black Green Black Black Black Green Black Green Green Black Black Black Black Green Black Green Black Black Green Black Black Black Green Green
Row 6: Green Green Black Green Black Black Black Green Black Black Green Black Black Green Green Black Green Black Black Green Black Black Black Black Black Black
Row 7: Black Green Green Green Black Green Green Green Black Green Black Black Green Black Black Black Black Black Black Green Green Green Black Black Black Black
Row 8: Black Black Green Green Green Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black Green Green Black Black Black Green
Row 9: Black Green Green Black Black Black Black Green Black Black Green Green Green Black Green Black Black Green Green Green Black Green Black Black Black Green
Row 10: Green Green Black Green Black Black Black Black Black Black Black Green Black Black Green Black Green Green Black Black Black Black Green Black Green Black
Here is the input grid for the test example:
Input:
Row 1: Blue Black Blue Black Blue Black Black Black Black Blue Blue Blue Black
Row 2: Blue Black Black Black Black Black Black Black Blue Black Black Black Blue
Row 3: Black Black Black Black Black Black Black Black Black Blue Black Black Black
Row 4: Black Black Black Blue Black Blue Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Blue Black Black Black Black Black Black
Row 6: Black Black Blue Black Black Black Black Black Black Black Blue Black Blue
Row 7: Black Black Blue Blue Blue Black Black Black Black Black Blue Black Black
Row 8: Black Black Blue Black Black Blue Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Blue
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Black Black Black Pink Black Black Black Black Black Black Black Black Black
Row 12: Black Pink Black Pink Pink Black Black Black Black Black Black Black Pink
Row 13: Black Black Black Black Black Pink Pink Black Black Pink Black Pink Black
Row 14: Black Pink Black Black Black Black Black Pink Pink Black Pink Black Pink
Row 15: Pink Black Pink Pink Black Black Pink Black Black Black Black Black Black
Row 16: Pink Pink Black Black Pink Pink Black Black Black Black Black Pink Black
Row 17: Black Black Black Black Black Black Black Black Pink Black Pink Black Black
Row 18: Pink Black Black Black Pink Black Pink Black Pink Black Black Pink Black
Row 19: Black Pink Pink Black Pink Black Black Black Pink Black 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>
| Green Black Green Green Green Black Black Black Black Green Green Green Black
Green Green Black Green Green Black Black Black Green Black Black Black Black
Black Black Black Black Black Green Green Black Black Black Black Green Black
Black Green Black Green Black Green Black Green Green Black Green Black Green
Green Black Green Green Black Black Black Black Black Black Black Black Black
Green Green Green Black Green Green Black Black Black Black Green Green Green
Black Black Green Green Green Black Black Black Green Black Black Black Black
Green Black Green Black Green Green Green Black Green Black Black Green Black
Black Green Green Black Green Black Black Black Green Black 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: Purple Green Purple Purple Purple Green Purple Purple Purple Purple Green Blue Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple Green Purple Purple Green Blue Green Purple Purple Green Purple
Row 3: Green Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Purple Purple Green
Row 4: Purple Green Purple Green Green Green Green Green Purple Purple Purple Purple Purple Green Green Purple Green Purple Green Green Green
Row 5: Green Purple Purple Purple Green Purple Purple Green Purple Green Purple Green Purple Green Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple Purple Purple Green Green Purple Purple Green
Row 7: Green Purple Purple Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Green Green Purple Purple Green Purple Purple
Row 8: Green Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Green
Row 9: Purple Purple Purple Purple Green Green Purple Green Purple Green Green Green Green Purple Purple Purple Purple Purple Purple Green Green
Row 10: Purple Green Purple Green Purple Green Green Green Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Green Purple
Row 11: Purple Green Purple Green Green Green Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Green Purple Purple Green Purple
Row 12: Green Purple Purple Green Purple Green Green Green Purple Purple Green Purple Purple Purple Green Purple Purple Purple Purple Green Purple
Row 13: Purple Purple Purple Green Green Green Purple Purple Purple Purple Green Purple Green Purple Purple Purple Purple Green Green Purple Purple
Row 14: Green Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple
Row 15: Purple Green Purple Green Green Purple Purple Purple Green Purple Purple Green Purple Purple Purple Purple Purple Green Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Green Purple Purple Purple
Row 17: Green Green Green Purple Purple Purple Purple Green Green Green Green Green Green Purple Purple Purple Green Purple Purple Green Green
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Purple Green Purple Purple Purple
Row 19: Purple Green Green Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Green Green Purple Green Green Green Purple Purple
Output:
Row 1: Red Red Red
Row 2: Purple Purple Purple
Row 3: Purple Purple Purple
Example 2
Input:
Row 1: Green Orange Green Green Green Green
Row 2: Green Green Green Green Green Green
Row 3: Green Gray Green Green Green Green
Row 4: Blue Green Gray Gray Purple Green
Row 5: Green Blue Green Green Green Pink
Row 6: Green Green Green Blue Green Green
Row 7: Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green
Row 9: Green Green Black Green Green Green
Row 10: Yellow Green Green Green Green Orange
Row 11: Green Green Green Green Green Green
Output:
Row 1: Red Red Red
Row 2: Green Green Green
Row 3: Green Green Green
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray
Row 2: Pink Gray Gray Gray Gray Gray
Row 3: Brown Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray
Row 8: Gray Orange Gray Gray Gray Gray
Row 9: Gray Gray Orange Orange Gray Gray
Row 10: Gray Brown Gray Orange Gray Gray
Row 11: Gray Gray Gray Orange Brown Gray
Row 12: Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Orange Blue
Row 14: Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Orange Gray Pink Yellow
Row 16: Brown Gray Gray Gray Gray Gray
Row 17: Gray Pink Brown Gray Gray Gray
Row 18: Gray Gray Brown Gray Gray Pink
Row 19: Brown Brown Gray Blue Gray Gray
Row 20: Gray Gray Gray Gray Purple Gray
Row 21: Gray Gray Gray Gray Orange Gray
Output:
Row 1: Red Red Gray
Row 2: Gray Gray Gray
Row 3: Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Black Purple Black Gray Gray Black Blue Gray Gray Orange Gray Gray Gray Purple
Row 2: Gray Purple Gray Gray Gray Gray Purple Gray Gray Purple Gray Gray Purple Gray
Row 3: Black Black Purple Gray Orange Gray Black Purple Gray Gray Gray Purple Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Blue Gray Purple
Row 5: Gray Gray Gray Blue Gray Orange Gray Orange Orange Gray Orange Purple Gray Gray
Row 6: Purple Gray Black Gray Gray Gray Gray Gray Orange Gray Black Orange Gray 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
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: 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 Purple Purple Purple Purple Purple Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Purple Red Red Blue Purple Red Red Red
Row 4: Blue Blue Blue Blue Blue Red Red Red Red Red Purple Red Red Red Purple Red Red Red
Row 5: Blue Red Red Brown Blue Red Red Red Red Red Purple Purple Red Purple Purple Red Red Red
Row 6: Blue Blue Red Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Purple Purple Purple Purple Purple Red Red Red Red Red
Row 8: Red Green Green Green Green Green Red Red Purple Red Red Red Purple Red Red Red Red Red
Row 9: Red Green Red Red Red Green Red Red Purple Yellow Red Red Purple Red Red Red Red Red
Row 10: Red Green Green Pink Green Green Red Red Purple Purple Red Purple Purple 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
Row 12: 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
Row 14: Red Red Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Yellow Red Red Red Yellow Red Red Red Red Green Green Green Green Green Red Red
Row 16: Red Red Yellow Red Red Red Yellow Red Red Red Red Green Red Brown Red Green Red Red
Row 17: Red Red Yellow Red Red Red Yellow Red Red Red Red Green Red Red Red Green Red Red
Row 18: Red Red Yellow Yellow Purple Yellow Yellow Red Red Red Red Green Green Red Green Green Red Red
Row 19: 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
Row 21: Red Red Red Red Red Red Red Red Red Blue Blue Red Blue Blue Red Red Red Red
Row 22: Brown Brown Brown Brown Brown Red Red Red Red Blue Purple Red Red Blue Red Red Red Red
Row 23: Brown Blue Red Red Brown Red Red Red Red Blue Red Red Red Blue Red Red Red Red
Row 24: Brown Brown Red Brown Brown Red Red Red Red Blue Blue Blue Blue Blue Red Red Red Red
Row 25: 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
Output:
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 Purple Purple Purple Purple Purple Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Purple Blue Blue Blue Purple Red Red Red
Row 4: Blue Blue Blue Blue Blue Red Red Red Red Red Purple Blue Blue Blue Purple Red Red Red
Row 5: Blue Brown Brown Brown Blue Red Red Red Red Red Purple Purple Blue Purple Purple Red Red Red
Row 6: Blue Blue Brown Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Red Red Red
Row 7: Brown Brown Brown Brown Brown Red Red Red Purple Purple Purple Purple Purple Red Red Red Red Red
Row 8: Red Green Green Green Green Green Red Red Purple Yellow Yellow Yellow Purple Red Red Red Red Red
Row 9: Red Green Pink Pink Pink Green Red Red Purple Yellow Yellow Yellow Purple Red Red Red Red Red
Row 10: Red Green Green Pink Green Green Red Red Purple Purple Yellow Purple Purple Red Red Red Red Red
Row 11: Red Pink Pink Pink Pink Pink Red Red Yellow Yellow Yellow Yellow Yellow 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
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Yellow Purple Purple Purple Yellow Red Red Red Red Green Green Green Green Green Red Red
Row 16: Red Red Yellow Purple Purple Purple Yellow Red Red Red Red Green Brown Brown Brown Green Red Red
Row 17: Red Red Yellow Purple Purple Purple Yellow Red Red Red Red Green Brown Brown Brown Green Red Red
Row 18: Red Red Yellow Yellow Purple Yellow Yellow Red Red Red Red Green Green Brown Green Green Red Red
Row 19: Red Red Purple Purple Purple Purple Purple Red Red Red Red Brown Brown Brown Brown Brown Red Red
Row 20: Red Red Red Red Red Red Red Red Red Purple Purple Purple Purple Purple Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Blue Blue Purple Blue Blue Red Red Red Red
Row 22: Brown Brown Brown Brown Brown Red Red Red Red Blue Purple Purple Purple Blue Red Red Red Red
Row 23: Brown Blue Blue Blue Brown Red Red Red Red Blue Purple Purple Purple Blue Red Red Red Red
Row 24: Brown Brown Blue Brown Brown Red Red Red Red Blue Blue Blue Blue Blue Red Red Red Red
Row 25: Blue Blue Blue Blue Blue 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
Example 2
Input:
Row 1: Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Yellow Green Pink Green Yellow Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Yellow Yellow Green Yellow Yellow 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
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Green Green
Row 6: Green Green Green Green Green Green Pink Pink Pink Pink Pink Green Pink Green Green Green Pink Green Green
Row 7: Gray Gray Green Gray Gray Green Pink Gray Green Green Pink Green Pink Green Green Green Pink Green Green
Row 8: Gray Yellow Green Green Gray Green Pink Green Green Green Pink Green Pink Blue Green Green Pink Green Green
Row 9: Gray Green Green Green Gray Green Pink Pink Green Pink Pink Green Pink Pink Green Pink Pink Green Green
Row 10: Gray Gray Gray Gray Gray 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
Row 12: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Green Green Green Green Green
Row 13: Green Gray Gray Gray Gray Gray Green Green Green Blue Green Green Pink Blue Green Green Green Green Green
Row 14: Green Gray Green Yellow Green Gray Green Green Green Blue Green Green Green Blue Green Green Green Green Green
Row 15: Green Gray Gray Green Gray Gray Green Green Green Blue Blue Green Blue Blue 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
Row 17: 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 Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Yellow Pink Pink Pink Yellow Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Yellow Yellow Pink Yellow Yellow Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Pink Pink Pink Pink Pink Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Green Green
Row 6: Yellow Yellow Yellow Yellow Yellow Green Pink Pink Pink Pink Pink Green Pink Blue Blue Blue Pink Green Green
Row 7: Gray Gray Yellow Gray Gray Green Pink Gray Gray Gray Pink Green Pink Blue Blue Blue Pink Green Green
Row 8: Gray Yellow Yellow Yellow Gray Green Pink Gray Gray Gray Pink Green Pink Blue Blue Blue Pink Green Green
Row 9: Gray Yellow Yellow Yellow Gray Green Pink Pink Gray Pink Pink Green Pink Pink Blue Pink Pink Green Green
Row 10: Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Green Blue Blue Blue Blue Blue Green Green
Row 11: 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 Blue Blue Blue Blue Blue Green Green Green Green Green
Row 13: Green Gray Gray Gray Gray Gray Green Green Green Blue Pink Pink Pink Blue Green Green Green Green Green
Row 14: Green Gray Yellow Yellow Yellow Gray Green Green Green Blue Pink Pink Pink Blue Green Green Green Green Green
Row 15: Green Gray Gray Yellow Gray Gray Green Green Green Blue Blue Pink Blue Blue Green Green Green Green Green
Row 16: Green Yellow Yellow Yellow Yellow Yellow Green Green Green Pink Pink Pink Pink Pink 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
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 Brown Brown Blue Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Brown Orange Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Brown Brown Brown Brown Brown 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 Brown Brown Blue Brown Brown
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Pink Blue Blue Brown
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Brown Orange Orange Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange 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 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 Green Green Green Green Green Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Gray Blue Blue Green Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Green Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Blue Green Green Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue 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 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
Row 2: Blue Brown Brown Orange Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Brown Orange Orange Orange Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Brown Orange Orange Orange Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Brown Orange Orange Orange Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Pink Brown Brown
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Pink Pink Pink Brown
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Pink Pink Pink Brown
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Blue Brown Pink Pink Pink Brown
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Brown Orange Orange Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange 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 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 Green Green Green Green Green Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Gray Gray Gray Green Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Gray Gray Gray Green Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Gray Gray Gray Green Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Gray Green Green Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Yellow
Row 2: Yellow Black Black Yellow Black Black Yellow Green Yellow Yellow Gray Green Yellow Yellow Yellow
Row 3: Yellow Black Gray Yellow Yellow Black Yellow Green Green Yellow Green Green Yellow Yellow Yellow
Row 4: Yellow Black Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Green Green Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Gray Yellow Green Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Gray Gray Green Gray Gray Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow 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 Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow Green Green Green Green Green
Row 18: Yellow Yellow Yellow Green Black Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Green
Row 19: Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Green Green Gray Green Green
Row 20: Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Green Green Yellow Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Green Green
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Pink Green
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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>
| Yellow Gray Gray Gray Gray Gray Yellow Green Green Green Green Green Yellow Yellow Yellow
Yellow Black Black Gray Black Black Yellow Green Gray Gray Gray Green Yellow Yellow Yellow
Yellow Black Gray Gray Gray Black Yellow Green Green Gray Green Green Yellow Yellow Yellow
Yellow Black Gray Gray Gray Black Yellow Gray Gray Gray Gray Gray Yellow Yellow Yellow
Yellow Black Black Black Black Black Yellow Yellow Gray Gray Gray Gray Gray Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Gray Green Green Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Gray Gray Gray Green Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Yellow Yellow
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 Yellow
Yellow Yellow Yellow Yellow Yellow Gray Gray Green Gray Gray Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Gray Green Green Green Gray Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray 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 Green Green Green Green Green Yellow Yellow Green Green Green Green Green
Yellow Yellow Yellow Green Black Black Black Green Yellow Yellow Green Gray Gray Gray Green
Yellow Yellow Yellow Green Black Black Black Green Yellow Yellow Green Green Gray Green Green
Yellow Yellow Yellow Green Black Black Black Green Yellow Yellow Gray Gray Gray Gray Gray
Yellow Yellow Yellow Green Green Black Green Green Yellow Yellow Pink Pink Pink Pink Pink
Yellow Yellow Yellow Black Black Black Black Black Yellow Yellow Green Green Pink Green Green
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Pink Pink Pink Green
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Orange Purple Orange Pink Purple Purple Purple Red
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: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: Purple Orange Purple Orange Pink Purple Purple Purple Red
Output:
Row 1: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 2: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 3: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 4: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 5: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 6: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 7: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 8: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 9: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 10: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 11: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 12: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 13: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 14: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 15: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 16: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 17: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 18: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 19: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 20: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 21: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 22: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 23: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 24: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 25: Purple Orange Purple Orange Pink Purple Purple Purple Red
Row 26: Purple Orange Purple Orange Pink Purple Purple Purple Red
Example 2
Input:
Row 1: Yellow Pink Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple 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
Row 3: Yellow Yellow Yellow Yellow 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 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
Row 6: Yellow Yellow Yellow Yellow 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 Yellow Yellow 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
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 11: Yellow Yellow Yellow Yellow 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 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 Yellow Yellow 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
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow 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 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Row 23: Yellow Black Red Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Pink Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Black Red Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
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 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 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 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 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 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 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 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 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 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 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 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 Gray Gray Gray Gray
Row 14: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Output:
Row 1: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 2: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 3: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 4: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 5: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 6: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 7: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 8: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 9: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 10: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 11: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 12: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 13: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Row 14: Gray Orange Pink Gray Green Pink Gray Gray Orange Green Red Gray Blue Gray Gray Yellow Purple Gray Gray Orange Brown Gray Yellow Gray Red Gray Gray Green
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple
Row 8: Yellow Brown 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>
| Yellow Yellow Purple Purple Purple
Yellow Purple Purple Purple Purple
Yellow Purple Purple Purple Purple
Yellow Purple Purple Purple Purple
Yellow Purple Purple Purple Purple
Yellow Purple Purple Purple Purple
Yellow Purple Purple Purple Purple
Yellow Brown 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 Yellow Green Green Green Yellow
Row 2: Green Green Green Green Green Green Green Green Green Green Green Blue
Row 3: Green Green Gray Green Green Green Green Green Gray Green Green Pink
Row 4: Red Green Green Green Green Green Green Green Gray Green Green Orange
Row 5: 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
Row 7: Green Green Yellow Green Green Green Green Green Green Green Brown Green
Row 8: Green Pink Green Green Green Green Green Green Green Green Green Green
Row 9: Blue Green Green Green Green Green Green Green Green Gray Green Black
Row 10: Green Green Blue Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Gray Green Pink Green Green Green Green Green Green Green Green Green
Row 13: Purple Green Yellow Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Yellow Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Yellow Green Green Blue Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Gray Green Green Green Green Green Gray Yellow Green Pink Blue Yellow Green Green Green Green Green Green Green Green Green Green
Row 4: Red Green Green Gray Green Green Green Green Gray Gray Yellow Orange Pink Blue Yellow Green Green Green Green Green Green Green Green Green
Row 5: Green Red Green Green Gray Green Green Green Green Gray Gray Yellow Orange Pink Blue Yellow Green Green Green Green Green Green Green Green
Row 6: Green Green Red Green Green Gray Green Gray Green Green Gray Gray Yellow Orange Pink Blue Yellow Green Green Green Green Green Green Green
Row 7: Green Green Yellow Red Green Green Gray Green Gray Green Brown Gray Gray Yellow Orange Pink Blue Yellow Green Green Green Green Green Green
Row 8: Green Pink Green Yellow Red Green Green Gray Green Gray Green Brown Gray Gray Yellow Orange Pink Blue Yellow Green Green Green Green Green
Row 9: Blue Green Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink Blue Yellow Green Green Green Green
Row 10: Green Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink Blue Yellow Green Green Green
Row 11: Green Green Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink Blue Yellow Green Green
Row 12: Gray Green Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink Blue Yellow Green
Row 13: Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink Blue Yellow
Row 14: Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink Blue
Row 15: Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange Pink
Row 16: Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow Orange
Row 17: Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray Yellow
Row 18: Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray Gray
Row 19: Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown Gray
Row 20: Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black Brown
Row 21: Green Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray Black
Row 22: Green Green Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray Gray
Row 23: Green Green Green Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray Gray
Row 24: Green Green Green Green Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green Gray
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Gray Yellow Pink Blue Blue Pink Green Yellow Red Green
Example 2
Input:
Row 1: Brown Brown Yellow Yellow Brown
Row 2: Brown Red Purple Brown Brown
Row 3: Brown Brown Brown Brown Brown
Row 4: Blue Brown Purple Brown Brown
Output:
Row 1: Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown
Row 2: Brown Red Purple Yellow Yellow Brown Brown Brown Brown Brown
Row 3: Brown Brown Red Purple Yellow Yellow Brown Brown Brown Brown
Row 4: Blue Brown Purple Red Purple Yellow Yellow Brown Brown Brown
Row 5: Brown Blue Brown Purple Red Purple Yellow Yellow Brown Brown
Row 6: Brown Brown Blue Brown Purple Red Purple Yellow Yellow Brown
Row 7: Brown Brown Brown Blue Brown Purple Red Purple Yellow Yellow
Row 8: Brown Brown Brown Brown Blue Brown Purple Red Purple Yellow
Example 3
Input:
Row 1: Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple
Row 3: Purple Green Purple Purple
Row 4: Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple
Row 7: Purple Purple Green Purple
Row 8: Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Green Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Green Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Green Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Green Purple Purple Purple
Row 7: Purple Purple Green Purple Purple Green Purple Purple
Row 8: Purple Purple Purple Green Purple Purple Green Purple
Row 9: Purple Purple Purple Purple Green Purple Purple Green
Row 10: Purple Purple Purple Purple Purple Green Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Green Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Green
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Gray Blue Gray Gray Gray Gray Purple Gray Gray Gray Gray Purple Brown
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Blue Blue
Row 5: Gray Gray Brown Brown Gray Gray Gray Gray Gray Green Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Black Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 9: Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Brown Gray Green 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 Blue Gray Gray Gray Gray Purple Gray Gray Gray Gray Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Blue Gray Gray Gray Gray Purple Gray Gray Gray Brown Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Blue Gray Gray Gray Gray Purple Gray Gray Gray Brown Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Blue Gray Brown Gray Gray Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Brown Brown Gray Blue Gray Brown Gray Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Brown Brown Gray Blue Gray Brown Gray Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray Gray Gray Gray Gray
Gray Purple Brown Gray Brown Brown Gray Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray Gray Gray Gray
Gray Gray Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray Gray Gray
Gray Gray Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray Gray
Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray Gray
Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray Gray Gray
Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray Gray
Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown Gray
Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple Brown
Gray Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown Purple
Gray Gray Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue Brown
Gray Gray Gray Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue Blue
Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray Blue
Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green Purple Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Green Blue Purple Brown Gray Brown Brown Purple Blue Gray Brown Black Green 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: Red Red Red Green Green Red Green Red Green Black Green Black Black Red Black Black Red Green Green Red Red Black Black Black
Row 2: Green Green Red Black Black Black Red Green Green Green Red Green Black Red Red Red Red Black Black Green Red Black Green Black
Row 3: Red Black Red Green Black Red Black Green Green Red Green Green Red Green Green Green Green Red Red Green Black Black Black Green
Row 4: Black Black Black Green Green Green Green Green Green Green Red Green Black Green Black Red Black Red Black Green Black Black Green Black
Row 5: Green Black Green Green Green Black Green Red Black Red Black Black Black Green Green Green Black Green Red Red Black Black Red Black
Output:
Row 1: Red Red Red Green Green Red Green Red Green Black Green Black Black Red Black Black Red Green Green Red Red Black Black Black
Row 2: Green Green Red Black Black Black Red Green Green Green Red Green Black Red Red Red Red Black Black Green Red Black Green Black
Row 3: Red Black Red Green Black Red Black Green Green Red Green Green Red Green Green Green Green Red Red Green Black Black Black Green
Row 4: Black Black Black Green Green Green Green Green Green Green Red Green Black Green Black Red Black Red Black Green Black Black Green Black
Row 5: Green Black Green Green Green Black Green Red Black Red Black Black Black Green Green Green Black Green Red Red Black Black Red Black
Row 6: Black Black Black Green Green Green Green Green Green Green Red Green Black Green Black Red Black Red Black Green Black Black Green Black
Row 7: Red Black Red Green Black Red Black Green Green Red Green Green Red Green Green Green Green Red Red Green Black Black Black Green
Row 8: Green Green Red Black Black Black Red Green Green Green Red Green Black Red Red Red Red Black Black Green Red Black Green Black
Row 9: Red Red Red Green Green Red Green Red Green Black Green Black Black Red Black Black Red Green Green Red Red Black Black Black
Row 10: Green Green Red Black Black Black Red Green Green Green Red Green Black Red Red Red Red Black Black Green Red Black Green Black
Row 11: Red Black Red Green Black Red Black Green Green Red Green Green Red Green Green Green Green Red Red Green Black Black Black Green
Row 12: Black Black Black Green Green Green Green Green Green Green Red Green Black Green Black Red Black Red Black Green Black Black Green Black
Row 13: Green Black Green Green Green Black Green Red Black Red Black Black Black Green Green Green Black Green Red Red Black Black Red Black
Row 14: Black Black Black Green Green Green Green Green Green Green Red Green Black Green Black Red Black Red Black Green Black Black Green Black
Row 15: Red Black Red Green Black Red Black Green Green Red Green Green Red Green Green Green Green Red Red Green Black Black Black Green
Row 16: Green Green Red Black Black Black Red Green Green Green Red Green Black Red Red Red Red Black Black Green Red Black Green Black
Row 17: Red Red Red Green Green Red Green Red Green Black Green Black Black Red Black Black Red Green Green Red Red Black Black Black
Example 2
Input:
Row 1: Gray Gray Gray Gray
Row 2: Pink Gray Gray Pink
Row 3: Pink Pink Gray Gray
Row 4: Gray Gray Gray Gray
Row 5: Gray Gray Gray Pink
Row 6: Brown Gray Brown Gray
Row 7: Gray Pink Gray Gray
Row 8: Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray
Row 2: Pink Gray Gray Pink
Row 3: Pink Pink Gray Gray
Row 4: Gray Gray Gray Gray
Row 5: Gray Gray Gray Pink
Row 6: Brown Gray Brown Gray
Row 7: Gray Pink Gray Gray
Row 8: Gray Gray Gray Gray
Row 9: Gray Pink Gray Gray
Row 10: Brown Gray Brown Gray
Row 11: Gray Gray Gray Pink
Row 12: Gray Gray Gray Gray
Row 13: Pink Pink Gray Gray
Row 14: Pink Gray Gray Pink
Row 15: Gray Gray Gray Gray
Row 16: Pink Gray Gray Pink
Row 17: Pink Pink Gray Gray
Row 18: Gray Gray Gray Gray
Row 19: Gray Gray Gray Pink
Row 20: Brown Gray Brown Gray
Row 21: Gray Pink Gray Gray
Row 22: Gray Gray Gray Gray
Row 23: Gray Pink Gray Gray
Row 24: Brown Gray Brown Gray
Row 25: Gray Gray Gray Pink
Row 26: Gray Gray Gray Gray
Row 27: Pink Pink Gray Gray
Row 28: Pink Gray Gray Pink
Row 29: Gray Gray Gray Gray
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Yellow Pink Pink
Row 2: Pink Pink Pink Pink Gray Pink Pink Yellow
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Pink Pink Pink Pink Pink Yellow Pink Pink
Row 2: Pink Pink Pink Pink Gray Pink Pink Yellow
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Gray Pink Pink Yellow
Row 13: Pink Pink Pink Pink Pink Yellow Pink Pink
Row 14: Pink Pink Pink Pink Gray Pink Pink Yellow
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Gray Pink Pink Yellow
Row 25: Pink Pink Pink Pink Pink Yellow Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Pink Red Purple Gray Gray Pink Purple Purple Green
Row 2: Red Purple Green Purple Green Pink Purple Green Red
Row 3: Gray Green Green Green Gray Pink Pink Pink Green
Row 4: Purple Pink Gray Purple Purple Green Green Gray Red
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Red Purple Gray Gray Pink Purple Purple Green
Red Purple Green Purple Green Pink Purple Green Red
Gray Green Green Green Gray Pink Pink Pink Green
Purple Pink Gray Purple Purple Green Green Gray Red
Gray Green Green Green Gray Pink Pink Pink Green
Red Purple Green Purple Green Pink Purple Green Red
Pink Red Purple Gray Gray Pink Purple Purple Green
Red Purple Green Purple Green Pink Purple Green Red
Gray Green Green Green Gray Pink Pink Pink Green
Purple Pink Gray Purple Purple Green Green Gray Red
Gray Green Green Green Gray Pink Pink Pink Green
Red Purple Green Purple Green Pink Purple Green Red
Pink Red Purple Gray Gray Pink Purple Purple 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: Orange Orange
Row 2: Brown Brown
Row 3: Orange Brown
Row 4: Brown Orange
Row 5: Brown Orange
Row 6: Orange Orange
Row 7: Orange Orange
Row 8: Orange Orange
Row 9: Brown Brown
Row 10: Orange Orange
Row 11: Orange Orange
Row 12: Orange Brown
Row 13: Orange Orange
Output:
Row 1: Orange Brown
Row 2: Orange Brown
Row 3: Orange Brown
Row 4: Orange Brown
Row 5: Orange Brown
Row 6: Orange Brown
Row 7: Orange Brown
Row 8: Orange Brown
Row 9: Orange Black
Row 10: Orange Black
Row 11: Orange Black
Row 12: Orange Black
Row 13: Orange Black
Row 14: Orange Black
Row 15: Orange Black
Row 16: Orange Black
Row 17: Orange Black
Row 18: Orange Black
Example 2
Input:
Row 1: Gray Gray Pink Blue Blue Brown Blue Pink
Row 2: Blue Blue Pink Brown Pink Pink Gray Pink
Row 3: Red Yellow Pink Yellow Blue Yellow Red Yellow
Row 4: Brown Gray Pink Yellow Gray Brown Brown Yellow
Row 5: Yellow Blue Gray Green Brown Blue Yellow Gray
Row 6: Pink Gray Pink Blue Brown Yellow Blue Blue
Row 7: Yellow Yellow Pink Gray Yellow Pink Yellow Pink
Row 8: Gray Blue Pink Blue Orange Yellow Yellow Gray
Row 9: Green Blue Pink Gray Red Brown Pink Brown
Output:
Row 1: Pink Yellow Blue Gray Brown Red Green Orange
Row 2: Pink Yellow Blue Gray Brown Red Green Black
Row 3: Pink Yellow Blue Gray Brown Red Black Black
Row 4: Pink Yellow Blue Gray Brown Black Black Black
Row 5: Pink Yellow Blue Gray Brown Black Black Black
Row 6: Pink Yellow Blue Gray Brown Black Black Black
Row 7: Pink Yellow Blue Gray Brown Black Black Black
Row 8: Pink Yellow Blue Gray Brown Black Black Black
Row 9: Pink Yellow Blue Gray Brown Black Black Black
Row 10: Pink Yellow Blue Gray Black Black Black Black
Row 11: Pink Yellow Blue Gray Black Black Black Black
Row 12: Pink Yellow Blue Gray Black Black Black Black
Row 13: Pink Yellow Blue Black Black Black Black Black
Row 14: Pink Yellow Blue Black Black Black Black Black
Row 15: Pink Yellow Black Black Black Black Black Black
Row 16: Pink Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Yellow Pink Yellow Yellow Pink Blue Gray
Row 2: Yellow Orange Brown Gray Gray Yellow Brown
Row 3: Pink Brown Gray Purple Purple Pink Gray
Row 4: Blue Pink Yellow Brown Brown Purple Yellow
Row 5: Yellow Blue Purple Brown Orange Yellow Gray
Row 6: Brown Yellow Pink Purple Yellow Yellow Blue
Row 7: Gray Blue Purple Brown Orange Yellow Yellow
Row 8: Orange Orange Pink Brown Pink Pink Gray
Row 9: Purple Orange Gray Brown Gray Pink Brown
Row 10: Purple Orange Yellow Gray Brown Pink Pink
Row 11: Brown Orange Brown Brown Gray Yellow Orange
Row 12: Purple Blue Orange Yellow Yellow Pink Purple
Row 13: Pink Pink Brown Brown Pink Purple Pink
Row 14: Orange Orange Pink Gray Blue Pink Gray
Row 15: Orange Gray Orange Gray Orange Gray Purple
Row 16: Pink Orange Gray Yellow Orange Purple Purple
Row 17: Gray Pink Purple Brown Yellow Yellow Pink
Row 18: Blue Gray Gray Purple Purple Yellow Gray
Row 19: Brown Brown Purple Blue Yellow Purple Gray
Row 20: Gray Yellow Orange Blue Yellow Purple Pink
Row 21: Gray Yellow Brown Pink Pink Purple Brown
Row 22: Brown Yellow Orange Pink Blue Yellow Brown
Output:
Row 1: Yellow Pink Gray Brown Purple Orange Blue
Row 2: Yellow Pink Gray Brown Purple Orange Blue
Row 3: Yellow Pink Gray Brown Purple Orange Blue
Row 4: Yellow Pink Gray Brown Purple Orange Blue
Row 5: Yellow Pink Gray Brown Purple Orange Blue
Row 6: Yellow Pink Gray Brown Purple Orange Blue
Row 7: Yellow Pink Gray Brown Purple Orange Blue
Row 8: Yellow Pink Gray Brown Purple Orange Blue
Row 9: Yellow Pink Gray Brown Purple Orange Blue
Row 10: Yellow Pink Gray Brown Purple Orange Blue
Row 11: Yellow Pink Gray Brown Purple Orange Blue
Row 12: Yellow Pink Gray Brown Purple Orange Black
Row 13: Yellow Pink Gray Brown Purple Orange Black
Row 14: Yellow Pink Gray Brown Purple Orange Black
Row 15: Yellow Pink Gray Brown Purple Orange Black
Row 16: Yellow Pink Gray Brown Purple Orange Black
Row 17: Yellow Pink Gray Brown Purple Orange Black
Row 18: Yellow Pink Gray Brown Purple Orange Black
Row 19: Yellow Pink Gray Brown Purple Orange Black
Row 20: Yellow Pink Gray Brown Purple Black Black
Row 21: Yellow Pink Gray Brown Purple Black Black
Row 22: Yellow Pink Gray Brown Black Black Black
Row 23: Yellow Pink Gray Brown Black Black Black
Row 24: Yellow Pink Gray Brown Black Black Black
Row 25: Yellow Pink Gray Black Black Black Black
Row 26: Yellow Pink Black Black Black Black Black
Row 27: Yellow Black Black Black Black Black Black
Row 28: Yellow Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Brown Pink Gray Brown Red Pink Gray Pink Orange
Row 2: Pink Gray Red Red Pink Red Orange Red Brown Orange Pink
Row 3: Pink Brown Pink Red Pink Gray Orange Red Pink Pink Brown
Row 4: Red Gray Red Pink Pink Orange Gray Red Brown Brown Brown
Row 5: Brown Brown Orange Brown Red Gray Brown Gray Pink Gray Pink
Row 6: Red Gray Red Brown Gray Pink Red Red Pink Gray Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Red Gray Brown Orange
Pink Red Gray Brown Orange
Pink Red Gray Brown Orange
Pink Red Gray Brown Orange
Pink Red Gray Brown Orange
Pink Red Gray Brown Orange
Pink Red Gray Brown Orange
Pink Red Gray Brown Black
Pink Red Gray Brown Black
Pink Red Gray Brown Black
Pink Red Gray Brown Black
Pink Red Gray Brown Black
Pink Red Gray Brown Black
Pink Red Gray Black Black
Pink Red Black Black Black
Pink Black Black Black Black
Pink 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: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Red Purple Red Red Gray
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Purple Brown Red Purple Red
Row 3: Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Gray Brown Red Purple Gray
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Red Brown Gray Gray Gray
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Gray Purple Gray Red Brown
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 8: Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Output:
Row 1: Red Purple Red Red Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Red Purple Red Red Gray
Row 2: Purple Brown Red Purple Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Purple Brown Red Purple Red
Row 3: Gray Brown Red Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Gray Brown Red Purple Gray
Row 4: Red Brown Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Red Brown Gray Gray Gray
Row 5: Gray Purple Gray Red Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Gray Purple Gray Red Brown
Row 6: Red Purple Red Red Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 7: Purple Brown Red Purple Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 8: Gray Brown Red Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 9: Red Brown Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 10: Gray Purple Gray Red Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 8: Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Purple Brown Brown Black Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Pink Purple Pink Purple Purple
Row 27: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Pink Purple Pink Purple Pink
Row 28: Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Black Purple Pink Purple Purple Purple
Row 29: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Purple Purple Purple Pink Pink
Row 30: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Purple Purple Pink Purple Pink
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 6: Pink Purple Pink Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 7: Pink Purple Pink Purple Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 8: Purple Pink Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 9: Purple Purple Purple Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 10: Purple Purple Pink Purple Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Pink Purple Pink Purple Purple Pink Purple Pink Purple Purple Black Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Pink Purple Pink Purple Pink Pink Purple Pink Purple Pink Black Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Black Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Purple Purple Purple Pink Pink Purple Purple Purple Pink Pink Black Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Purple Purple Pink Purple Pink Purple Purple Pink Purple Pink Black Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Pink Purple Pink Purple Purple Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Pink Purple Pink Purple Pink Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Purple Pink Purple Purple Purple Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Purple Purple Purple Pink Pink Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Purple Purple Pink Purple Pink Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Pink Purple Pink Purple Purple Brown Brown Brown Brown Brown Black Pink Purple Pink Purple Purple
Row 27: Brown Brown Brown Brown Brown Pink Purple Pink Purple Pink Brown Brown Brown Brown Brown Black Pink Purple Pink Purple Pink
Row 28: Brown Brown Brown Brown Brown Purple Pink Purple Purple Purple Brown Brown Brown Brown Brown Black Purple Pink Purple Purple Purple
Row 29: Brown Brown Brown Brown Brown Purple Purple Purple Pink Pink Brown Brown Brown Brown Brown Black Purple Purple Purple Pink Pink
Row 30: Brown Brown Brown Brown Brown Purple Purple Pink Purple Pink Brown Brown Brown Brown Brown Black Purple Purple Pink Purple Pink
Example 3
Input:
Row 1: Pink Red Brown Brown Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Blue Brown Black Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Orange Brown Black Pink Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue 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 Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue 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 Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue 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 Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue 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 Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple
Row 19: 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
Row 21: Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue 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 Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue 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 Blue Purple Purple Purple Purple Blue Purple Purple Purple Purple Blue Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Pink Red Brown Brown Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Blue Brown Black Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Orange Brown Black Pink Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 6: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 7: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Row 8: Pink Red Brown Brown Blue Purple Purple Purple Purple Purple Pink Red Brown Brown Blue
Row 9: Blue Brown Black Orange Red Purple Purple Purple Purple Purple Blue Brown Black Orange Red
Row 10: Orange Brown Black Pink Red Purple Purple Purple Purple Purple Orange Brown Black Pink Red
Row 11: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 12: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 13: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Row 14: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 15: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 16: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Row 17: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 18: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 19: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Row 20: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 21: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 22: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Row 23: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 24: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 25: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Row 26: Pink Red Brown Brown Blue Pink Red Brown Brown Blue Pink Red Brown Brown Blue
Row 27: Blue Brown Black Orange Red Blue Brown Black Orange Red Blue Brown Black Orange Red
Row 28: Orange Brown Black Pink Red Orange Brown Black Pink Red Orange Brown Black Pink Red
Here is the input grid for the test example:
Input:
Row 1: Black Purple Purple Black Orange Black Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Black Orange Black Black Black Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Purple Orange Black Purple Black Black Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Black Orange Purple Purple Black Purple Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Black Orange Purple Orange Orange Black Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: 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
Row 9: Red Red Red Purple 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
Row 11: 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
Row 13: 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
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
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple 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
Row 21: 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>
| Black Purple Purple Black Orange Black Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Black Orange Black Black Black Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Purple Orange Black Purple Black Black Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Black Orange Purple Purple Black Purple Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Black Orange Purple Orange Orange Black Purple Red Red Red Red Red Red Red Red Red Red 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
Black Purple Purple Black Orange Black Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Black Orange Black Black Black Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Purple Orange Black Purple Black Black Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Black Orange Purple Purple Black Purple Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Black Orange Purple Orange Orange Black Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Purple Purple Black Orange Black Purple
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Orange Black Black Black Black Black
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Orange Black Purple Black Black Orange
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Orange Purple Purple Black Purple Purple
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Black Orange Purple Orange Orange Black 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 Black Yellow Green Green Green Black Green Green Yellow Green Black Green Green Green Green
Row 2: Green Green Green Green Black Green Green Yellow Green Black Green Green Green Green Black Green Yellow Green Green
Row 3: Yellow Green Green Green Black Green Green Green Green Black Green Yellow Green Green Black Green Green Green Green
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Green Green Green Green Black Green Green Green Yellow Black Green Green Green Green Black Green Green Yellow Green
Row 6: Green Green Green Yellow Black Green Green Green Green Black Green Green Yellow Green Black Green Green Green Green
Row 7: Green Green Green Green Black Yellow Green Green Green Black Green Green Green Green Black Green Green Green Green
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Green Yellow Green Green Black Green Green Green Green Black Green Green Green Green Black Green Green Green Green
Row 10: Green Green Green Green Black Green Green Green Green Black Green Green Green Yellow Black Yellow Green Yellow Green
Row 11: Green Green Green Green Black Green Green Green Yellow Black Green Green Green Green Black Green Green Green Green
Output:
Row 1: Green Blue Blue Green
Row 2: Green Blue Green Green
Row 3: Green Green Green Blue
Example 2
Input:
Row 1: Purple Pink Purple Purple Purple Green Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Green Pink Purple Purple Purple Purple
Row 3: Green Green Green Green Green Green Green Green Green Green Green
Row 4: Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple
Row 5: Purple Pink Purple Purple Purple Green Purple Pink Pink Purple Purple
Row 6: Green Green Green Green Green Green Green Green Green Green Green
Row 7: Purple Purple Purple Pink Purple Green Purple Purple Purple Pink Purple
Row 8: Purple Purple Pink Purple Purple Green Purple Purple Purple Purple Purple
Row 9: Green Green Green Green Green Green Green Green Green Green Green
Row 10: Purple Purple Purple Purple Pink Green Purple Purple Pink Purple Purple
Row 11: Pink Purple Purple Purple Purple Green Purple Purple Purple Purple Purple
Row 12: Green Green Green Green Green Green Green Green Green Green Green
Row 13: Purple Purple Pink Purple Purple Green Pink Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple
Row 2: Purple Blue
Row 3: Blue Purple
Row 4: Blue Purple
Row 5: Purple Purple
Example 3
Input:
Row 1: Green Green Green Pink Purple Green Green Pink Green Green Green Pink Green Purple Green
Row 2: Green Purple Green Pink Green Green Green Pink Green Green Green Pink Green Green Green
Row 3: Green Green Green Pink Green Green Green Pink Green Purple Green Pink Green Green Green
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Purple Green Green Pink Green Green Green Pink Green Green Purple Pink Green Purple Green
Row 6: Green Green Green Pink Purple Green Purple Pink Green Green Green Pink Green Green Green
Row 7: Green Green Green Pink Green Green Green Pink Green Green Green Pink Green Green Green
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Purple Green Green Pink Purple Green Green Pink Green Green Green Pink Green Green Green
Row 10: Green Green Green Pink Green Green Green Pink Green Purple Green Pink Green Green Purple
Row 11: Green Green Green Pink Green Green Green Pink Green Green Green Pink Green Green Green
Output:
Row 1: Green Green Green Green
Row 2: Green Blue Green Green
Row 3: Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Orange Brown Brown Green Brown Orange Brown Brown Brown Green Brown Brown Brown Orange Brown Green Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Orange Green Brown Orange Brown Brown Brown Green Orange Brown Brown Brown Brown
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
Row 5: Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Orange Brown Brown Green Brown Orange Brown Brown Brown
Row 6: Brown Orange Brown Brown Brown Green Brown Brown Brown Orange Brown Green Brown Brown Brown Brown Brown Green Orange Brown Brown Brown Brown
Row 7: Brown Orange Brown Brown Brown Green Brown Brown Orange Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown
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
Row 9: Brown Brown Brown Orange Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 10: Brown Brown Orange Brown Brown Green Brown Orange Brown Brown Orange Green Brown Orange Brown Brown Orange Green Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Orange Brown Brown Brown
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
Row 13: Brown Brown Brown Brown Brown Green Brown Brown Orange Brown Brown Green Brown Orange Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 14: Brown Brown Orange Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Green Brown Brown Brown Orange Brown Green Brown Brown Orange 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 Blue Blue Brown
Blue Blue Brown Blue
Blue Blue Blue Brown
Brown 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: Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Orange Orange Orange Purple
Row 2: Purple Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple
Row 3: Purple Orange Purple Purple Orange Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple
Row 4: Purple Orange Purple Purple Orange Purple Purple Blue Purple Purple Pink Pink Pink Pink Purple Orange Purple Orange Purple
Row 5: Purple Orange Purple Purple Orange Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple
Row 6: Purple Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Orange Purple Orange Purple
Row 7: Purple Orange Purple Purple Orange Purple Purple Black Black Black Purple Purple Gray Gray Purple Orange Orange Orange Purple
Row 8: Purple Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Black Black Black 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
Output:
Row 1: 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 Green Purple Purple
Row 3: Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple
Row 4: Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple
Row 5: Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple
Row 6: Purple Purple Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple
Row 7: Purple Purple Green Green 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
Row 9: 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
Example 2
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 Gray Red Red Red Red Red Red Gray Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray 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 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
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 Pink Pink Pink Pink Pink Pink Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Pink Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink 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
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
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 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
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 Red Red Green Green Green Green 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
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Blue Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Blue Red Red Red Red Red Blue Red Gray Gray Gray Gray Gray Gray Gray Red Black Red
Row 4: Purple Purple Purple Purple Purple Red Red Blue Red Red Red Red Red Blue Red Gray Red Red Red Red Red Gray Red Black Red
Row 5: Purple Red Red Red Purple Red Red Blue Red Red Red Red Red Blue Red Gray Red Red Red Red Red Gray Red Red Red
Row 6: Purple Red Red Red Purple Red Red Blue Blue Blue Blue Blue Blue Blue Red Gray Gray Gray Gray Gray Gray Gray Red Red Red
Row 7: Purple Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Purple Red Red Red Purple Red Red Red Red Red Red Pink Red Red Red Red Gray Gray Gray Gray Red Red Red Black Red
Row 9: Purple Purple Purple Purple Purple Red Red Red Red Red Red Pink Red Red Red Red Gray Red Red Gray Red Red Red Black Red
Row 10: Red Red Red Red Red Red Red Red Yellow Red Red Pink Red Red Red Red Gray Red Red Gray Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Yellow Red Red Pink Red Red Red Red Gray Red Red Gray Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Gray Gray Gray Gray Red Red Red Red Red
Row 13: Orange Orange Orange Orange Orange Orange Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Orange Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Brown Brown Brown Red Red Red Red Red Brown Red
Row 15: Orange Red Red Red Red Orange Red Gray Gray Gray Gray Gray Gray Red Red Brown Brown Brown Red Red Red Red Red Brown Red
Row 16: Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Gray Red Brown Red
Row 17: 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
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
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
Row 2: Red Red Red Red Red Red Red Red Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Green Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Green Green Green Green Green Red Red Red Green Green Green Green Green Red Red Red Red
Row 5: Red Green Green Green Red Red Red Red Green Green Green Green Green Red Red Red Green Green Green Green Green Red Red Red Red
Row 6: Red Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Green Green Green 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 Green Green 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 Green Green 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 Green Green 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
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
Row 14: Red Green Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Green Green Green Green 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
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
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
Here is the input grid for the test example:
Input:
Row 1: Black Black Blue Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black
Row 2: Black Black Blue Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black
Row 3: 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
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 Blue Blue 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 Blue Blue Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black
Row 8: Black Black Blue Blue Black Black Black Black Black Black Black Pink Black Black Black Black Pink Black Black Black Black Black Black Black Black
Row 9: Black Black Blue Blue Black Black Black Black Black Black Black Pink Black Black Black Black Pink Black Black Black Black Black Black Black Black
Row 10: Black Black Blue Blue Black Black Black Black Black Black Black Pink Black Black Black Black Pink Black Black Black Black Black Black Black Black
Row 11: Black Black Blue Blue Black Black Black Black Black Black Black Pink Black Black Black Black Pink Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Pink Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Pink Pink Pink Pink Pink Pink 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
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 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 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 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 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
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 Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Green Green Green Green 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 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 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 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: 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 Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Gray Purple Purple Purple Gray Purple Green Green Green Green Green Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Gray Purple Purple Purple Gray Purple Green Purple Yellow Purple Green Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Gray Purple Purple Purple Gray Purple Green Purple Purple Purple Green Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Gray Gray Black Gray Gray Purple Green Green Purple Green Green 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 Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Pink Purple Orange Orange Purple Orange Orange
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Blue Pink Purple Orange Purple Gray Purple Orange
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Pink Purple Orange Purple Purple Purple Orange
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Purple Pink Pink Purple Orange Purple Purple Purple Orange
Row 16: Purple Purple Blue Blue Yellow Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange
Row 17: Purple Purple Blue Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Blue Blue Blue Blue Blue 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
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 Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Gray Black Black Black Gray Purple Green Green Green Green Green Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Gray Black Black Black Gray Purple Green Yellow Yellow Yellow Green Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Gray Black Black Black Gray Purple Green Yellow Yellow Yellow Green Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Gray Gray Black Gray Gray Purple Green Green Yellow Green Green Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Black Black Black Black Black Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Purple Gray Gray Gray Gray Gray
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Blue Blue Blue Pink Purple Orange Orange Gray Orange Orange
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Blue Blue Blue Pink Purple Orange Gray Gray Gray Orange
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Blue Blue Blue Pink Purple Orange Gray Gray Gray Orange
Row 15: Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Pink Pink Blue Pink Pink Purple Orange Gray Gray Gray Orange
Row 16: Purple Purple Blue Blue Yellow Blue Blue Purple Purple Blue Blue Blue Blue Blue Purple Orange Orange Orange Orange Orange
Row 17: Purple Purple Blue Yellow Yellow Yellow Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Blue Blue Blue Blue Blue 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 Pink Pink Pink Pink Pink
Row 2: Pink Pink Yellow Yellow Orange Yellow Yellow 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 Yellow Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Pink Orange Orange Pink Pink Blue Blue Pink Blue Blue
Row 4: Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Blue Orange Pink Pink Blue Orange Pink Pink Blue
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Blue Blue Blue Blue Blue
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue 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 Blue Black Pink Pink Blue 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 Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Black Black Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Black Pink Pink
Row 10: Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Brown Brown Pink Pink Black Black Yellow Black Black Pink Pink
Row 11: Pink Yellow Pink Pink Black Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Black Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Yellow Yellow Pink Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown 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 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 Pink Pink
Output:
Row 1: Pink Pink Orange Orange Orange Orange Orange 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 Yellow Yellow Orange Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Orange Orange Orange Orange Orange
Row 3: Pink Pink Yellow Orange Orange Orange Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Blue Orange Orange Pink Pink Blue Blue Orange Blue Blue
Row 4: Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Blue Blue Blue Orange Pink Pink Blue Orange Orange Orange Blue
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Pink Pink Blue Blue Blue Blue Blue
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue 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 Blue Black Black Black Blue 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 Blue Black Black Black Blue Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Black Black Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Black Blue Blue Pink Black Black Black Black Black Pink Pink Black Yellow Yellow Yellow Black Pink Pink
Row 10: Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Black Black Black Black Black Pink Brown Brown Black Brown Brown Pink Pink Black Black Yellow Black Black Pink Pink
Row 11: Pink Yellow Black Black Black Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Black Black Black Brown Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink
Row 12: Pink Yellow Yellow Black Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Black Black Black Black Black 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 Pink Pink
Example 3
Input:
Row 1: 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
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green
Row 5: Blue Pink Pink Pink Pink Pink Blue Green Blue Orange Blue Green
Row 6: Blue Pink Blue Blue Blue Pink Blue Green Blue Blue Blue Green
Row 7: Blue Pink Yellow Blue Blue Pink Blue Green Green Blue Green Green
Row 8: Blue Pink Pink Blue Pink Pink Blue Blue Blue Blue Blue Blue
Row 9: 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
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: Yellow Yellow Blue Yellow Yellow Blue Blue Red Red Blue Red Red
Row 14: Yellow Blue Blue Blue Yellow Blue Blue Red Blue Yellow Blue Red
Row 15: Yellow Blue Orange Blue Yellow Blue Blue Red Red Red Red Red
Row 16: Yellow Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue
Row 17: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Gray Gray Blue Gray Gray
Row 20: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray
Row 21: Blue Blue Blue Blue Blue Blue Blue Gray Blue Yellow Blue Gray
Row 22: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray
Row 23: Pink Pink Pink Pink Pink Blue Blue Gray Gray Gray Gray Gray
Row 24: Pink Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue
Row 25: Pink Blue Blue Blue Pink Blue Green Green Blue Green Green Blue
Row 26: Pink Pink Black Pink Pink Blue Green Blue Blue Blue Green Blue
Row 27: Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Green Blue
Row 28: Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue
Output:
Row 1: 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
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green
Row 5: Blue Pink Pink Pink Pink Pink Blue Green Orange Orange Orange Green
Row 6: Blue Pink Yellow Yellow Yellow Pink Blue Green Orange Orange Orange Green
Row 7: Blue Pink Yellow Yellow Yellow Pink Blue Green Green Orange Green Green
Row 8: Blue Pink Pink Yellow Pink Pink Blue Orange Orange Orange Orange Orange
Row 9: Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 10: 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
Row 12: Orange Orange Orange Orange Orange Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Orange Yellow Yellow Blue Blue Red Red Yellow Red Red
Row 14: Yellow Orange Orange Orange Yellow Blue Blue Red Yellow Yellow Yellow Red
Row 15: Yellow Orange Orange Orange Yellow Blue Blue Red Red Red Red Red
Row 16: Yellow Orange Orange Orange Yellow Blue Blue Blue Blue Blue Blue Blue
Row 17: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow
Row 19: Blue Blue Blue Blue Blue Blue Blue Gray Gray Yellow Gray Gray
Row 20: Blue Blue Blue Blue Blue Blue Blue Gray Yellow Yellow Yellow Gray
Row 21: Blue Blue Blue Blue Blue Blue Blue Gray Yellow Yellow Yellow Gray
Row 22: Blue Blue Blue Blue Blue Blue Blue Gray Yellow Yellow Yellow Gray
Row 23: Pink Pink Pink Pink Pink Blue Blue Gray Gray Gray Gray Gray
Row 24: Pink Black Black Black Pink Blue Pink Pink Pink Pink Pink Blue
Row 25: Pink Black Black Black Pink Blue Green Green Pink Green Green Blue
Row 26: Pink Pink Black Pink Pink Blue Green Pink Pink Pink Green Blue
Row 27: Black Black Black Black Black Blue Green Pink Pink Pink Green Blue
Row 28: Blue Blue Blue Blue Blue Blue Green Green Green Green Green Blue
Here is the input grid for the test example:
Input:
Row 1: 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
Row 3: 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
Row 5: Brown Brown Pink Brown Brown Pink Pink Brown Brown Pink Brown Brown
Row 6: Brown Pink Pink Pink Brown Pink Pink Brown Purple Pink Pink Brown
Row 7: Brown Pink Pink Purple Brown Pink Pink Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Purple Purple Pink Purple Purple Pink Pink Pink Pink Pink Pink Pink
Row 11: Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 12: Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 13: Purple Pink Brown Pink Purple Pink Brown Brown Brown Brown Brown Pink
Row 14: Purple Purple Purple Purple Purple Pink Brown Purple Pink Pink Brown Pink
Row 15: Pink Pink Pink Pink Pink Pink Brown Brown Pink Brown Brown 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
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
Purple Purple Purple Purple Purple Pink Pink Purple Purple Purple Purple Purple
Brown Brown Purple Brown Brown Pink Pink Brown Brown Purple Brown Brown
Brown Purple Purple Purple Brown Pink Pink Brown Purple Purple Purple Brown
Brown Purple Purple Purple Brown Pink Pink Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink
Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink
Purple Purple Brown Purple Purple Pink Pink Pink Pink Pink Pink Pink
Purple Brown Brown Brown Purple Pink Pink Pink Pink Pink Pink Pink
Purple Brown Brown Brown Purple Pink Pink Pink Pink Pink Pink Pink
Purple Brown Brown Brown Purple Pink Brown Brown Brown Brown Brown Pink
Purple Purple Purple Purple Purple Pink Brown Purple Purple Purple Brown Pink
Pink Pink Pink Pink Pink Pink Brown Brown Purple Brown Brown Pink
Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Pink
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: Green Green Green Green Green Green Green Green Green Green Green Green Green Black Red 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 Red Green Green Green Green Green Yellow Yellow 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 Red Yellow Yellow 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 Yellow 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 Yellow Yellow 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 Yellow 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 Yellow Green Green
Row 8: Green Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green
Row 9: Orange Orange Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Row 29: Green 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
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 Yellow Yellow Green Green
Row 7: Green Green Green Black Black Yellow Yellow Yellow Green
Row 8: Green Green Orange Black Green Green Green Yellow Green
Row 9: Orange Orange Orange Green Green Green Green Yellow Yellow
Row 10: Green Green Green Green Green Green Green Green Yellow
Row 11: Green Green Green Green Green Green Green Green Yellow
Row 12: Green Green Green Green Green Green Green Green Yellow
Row 13: Green Green Green Green Green Green Green Green Yellow
Row 14: Green Green Green Green Green Green Green Green Yellow
Row 15: Green Green Green Green Green Green Green Green Yellow
Row 16: Green Green Green Green Green Green Green Green Yellow
Row 17: Green Green Green Green Green Green Green Green Yellow
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 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
Row 28: Green Green Green Green Green Green Green Green Green
Row 29: Green Green Green Green Green Green Green Green Green
Example 2
Input:
Row 1: Gray Gray Orange Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Yellow Yellow Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Yellow Yellow Yellow Brown
Row 4: Brown Brown Brown Brown Orange Gray Orange Brown Black Brown Brown Yellow Brown Yellow Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Orange Brown Yellow Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Yellow Yellow
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Yellow
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Gray Gray Gray Gray Gray Gray Black Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Black Brown Yellow Yellow Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Black Black Yellow Yellow Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Black Yellow Yellow Yellow Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Black Yellow Brown Yellow Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Black Yellow Brown Yellow Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow
Example 3
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: Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Purple Green Green
Row 11: Green Green Green Green Green Green Green Green Purple Green Green
Row 12: Green Green Green Green Green Green Green Green Purple Green Green
Row 13: Green Green Green Green Green Green Green Green Purple Green Green
Row 14: Green Green Green Green Green Green Green Green Purple Green Green
Row 15: Green Green Green Green Green Green Green Purple Purple Green Green
Row 16: Red Red Green Blue Green Green Green Purple Green Green Green
Row 17: Red Red Red Red Green Green Green Purple Green Green Green
Row 18: Green Green Green Green Green Green Purple Purple Green Green Green
Row 19: Green Green Green Green Green Green Purple Green Green Green Green
Row 20: Green Green Green Green Green Green Purple Green Green Green Green
Row 21: Green Green Green Green Green Blue Purple Green Green Green Green
Row 22: Green Green Green Green Green Purple Purple Green Green Green Green
Row 23: Green Green Green Green Green Purple Purple Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Purple
Row 6: Green Green Green Green Green Green Green Purple
Row 7: Green Green Green Green Green Green Green Purple
Row 8: Green Green Green Green Green Green Green Purple
Row 9: Green Green Green Green Green Green Green Purple
Row 10: Green Green Green Green Green Green Purple Purple
Row 11: Green Green Green Green Green Green Purple Green
Row 12: Green Green Green Green Green Green Purple Green
Row 13: Green Green Green Green Green Purple Purple Green
Row 14: Green Green Green Green Green Purple Green Green
Row 15: Green Green Green Green Green Purple Green Green
Row 16: Red Red Green Red Purple Purple Green Green
Row 17: Red Red Red Red Purple Purple Green Green
Row 18: Green Green Green Green Purple Purple Green Green
Row 19: Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Yellow Green Green Green Purple 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green Brown Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green Brown Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown 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 Brown Brown 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
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
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
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
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
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 Green Green Brown
Yellow Green Green Green Yellow Brown Green Brown
Green Green Green Green Green Brown Green Brown
Green Green Green Green Green Brown Brown Brown
Green Green Green Green Green Green Brown Brown
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green
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: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Brown Orange Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Orange Orange Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Orange Orange Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Orange Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Orange Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Orange Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Orange
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Yellow 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 Green Green Green Green Green Green Green Green Green
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Orange Orange Orange Orange Yellow Orange Gray Orange Orange
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Black Black Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Orange Black Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Orange Pink Black Black Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Black
Row 11: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Black
Row 12: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 24: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 25: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink
Row 27: Pink Pink Pink Pink Pink Pink Pink Orange 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>
| Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange 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: Black Black Black Green Black Black
Row 2: Black Black Black Green Black Black
Row 3: Black Black Black Green Black Black
Row 4: Black Black Black Green Black Black
Row 5: Black Black Black Green Black Black
Row 6: Black Black Black Green Black Black
Row 7: Black Green Black Green Black Black
Row 8: Black Green Black Green Black Green
Row 9: Black Green Black Green Black Green
Row 10: Black Green Black Green Black Green
Row 11: Black Green Black Green Black Green
Row 12: Black Green Black Green Black Green
Row 13: Black Green Black Green Black Green
Row 14: Black Green Black Green Black Green
Row 15: Black Green Black Green Black Green
Row 16: Black Green Black Green Black Green
Row 17: Black Green Black Green Black Green
Row 18: Black Green Black Green Black Green
Row 19: Black Green Black Green Black Green
Row 20: Black Green Black Green Black Green
Row 21: Black Green Black Green Black Green
Row 22: Black Green Black Green Black Green
Output:
Row 1: Black Black Black Blue Black Black
Row 2: Black Black Black Blue Black Black
Row 3: Black Black Black Blue Black Black
Row 4: Black Black Black Blue Black Black
Row 5: Black Black Black Blue Black Black
Row 6: Black Black Black Blue Black Black
Row 7: Black Black Black Blue Black Black
Row 8: Black Black Black Blue Black Red
Row 9: Black Black Black Blue Black Red
Row 10: Black Black Black Blue Black Red
Row 11: Black Black Black Blue Black Red
Row 12: Black Black Black Blue Black Red
Row 13: Black Black Black Blue Black Red
Row 14: Black Black Black Blue Black Red
Row 15: Black Black Black Blue Black Red
Row 16: Black Black Black Blue Black Red
Row 17: Black Black Black Blue Black Red
Row 18: Black Black Black Blue Black Red
Row 19: Black Black Black Blue Black Red
Row 20: Black Black Black Blue Black Red
Row 21: Black Black Black Blue Black Red
Row 22: Black Black Black Blue Black Red
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
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
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
Row 4: Brown 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 5: Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 8: Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 9: Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 10: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 11: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 12: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 13: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 14: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 15: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 16: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 17: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 18: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 19: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 20: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 21: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 22: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 23: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Row 24: Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow
Output:
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
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
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
Row 4: Blue 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 5: Blue 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 6: Blue 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 7: Blue 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 8: Blue 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 9: Blue 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 10: Blue 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 11: Blue 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 12: Blue 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 13: Blue 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 14: Blue 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 15: Blue 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 16: Blue 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 17: Blue 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 18: Blue 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 19: Blue 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 20: Blue 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 21: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow
Row 2: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow
Row 3: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow
Row 4: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 5: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 6: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 7: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 8: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 9: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Yellow Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 12: Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Red Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Red Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Red Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 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 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 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 Black Black Black
Row 5: Black Black Black 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 Brown Brown
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 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 Black Black
Row 8: Black Brown Brown Brown Brown Brown 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: 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
Row 10: Black Black Black Black Black 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 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 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 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 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 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 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 Black Black
Row 17: Black 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 Brown Brown Brown Brown
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 Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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 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 Black Black Black Black
Row 22: Black Black Black Black 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 Brown
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 Black Black Black Black
Row 24: Black Black Black Brown Brown Brown 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: 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
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 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 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 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 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
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 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 Blue Blue Blue Blue 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 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 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 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 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 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 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 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 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 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 Black Red Red Red Red Red Red Red Red Red Red Red 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 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 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 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 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 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: Black Gray Gray Black Black Black Gray Gray Black
Row 2: Black Gray Black Black Black Black Black Black Gray
Row 3: Gray Black Black Black Gray Black Black Black Gray
Row 4: Gray Black Black Gray Gray Black Black Black Gray
Row 5: Black Black Black Black Black Black Black Black Gray
Row 6: Black Black Gray Black Black Gray Gray Gray Black
Row 7: Black Black Gray Black Black Black Black Black Gray
Row 8: Black Black Black Black Black Black Black Black Gray
Row 9: Black Black Black Gray Black Gray Gray Black Gray
Row 10: Black Black Black Gray Gray Black Gray Black Black
Row 11: Gray Gray Black Black Black Black Black Gray Gray
Row 12: Black Gray Black Black Black Gray Gray Black Gray
Row 13: Black Black Black Black Gray Black Black Black Black
Row 14: Gray Gray Gray Black Gray Black Black Gray Black
Row 15: Black Black Black Black Gray Black Black Gray Black
Row 16: Black Gray Gray Gray Black Black Gray Gray Black
Output:
Row 1: Black Red Red Black Black Black Green Green Black
Row 2: Black Red Black Black Black Black Black Black Blue
Row 3: Green Black Black Black Red Black Black Black Blue
Row 4: Green Black Black Red Red Black Black Black Blue
Row 5: Black Black Black Black Black Black Black Black Blue
Row 6: Black Black Green Black Black Red Red Red Black
Row 7: Black Black Green Black Black Black Black Black Red
Row 8: Black Black Black Black Black Black Black Black Red
Row 9: Black Black Black Red Black Red Red Black Red
Row 10: Black Black Black Red Red Black Red Black Black
Row 11: Red Red Black Black Black Black Black Red Red
Row 12: Black Red Black Black Black Green Green Black Red
Row 13: Black Black Black Black Red Black Black Black Black
Row 14: Red Red Red Black Red Black Black Blue Black
Row 15: Black Black Black Black Red Black Black Blue Black
Row 16: Black Red Red Red Black Black Blue Blue Black
Example 2
Input:
Row 1: Brown Gray Gray Gray Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Gray Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 4: Brown Brown Gray Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown
Row 8: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 9: Brown Brown Gray Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Brown Gray Brown
Row 10: Brown Brown Brown Brown Brown Gray Brown Gray Brown Gray Gray Brown Brown Gray Brown Brown Gray Gray Brown Brown Brown
Row 11: Brown Brown Gray Brown Gray Gray Brown Brown Brown Brown Gray Brown Gray Gray Brown Brown Brown Brown Gray Brown Brown
Row 12: Brown Brown Gray Brown Brown Brown Gray Gray Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Gray Brown Brown
Row 13: Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown
Row 14: Brown Brown Gray Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Gray Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Gray Brown Gray Gray Brown Brown Brown Gray Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Gray Gray Brown Brown Gray Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown
Row 18: Brown Gray Gray Brown Brown Gray Gray Brown Gray Gray Gray Brown Gray Gray Brown Brown Gray Gray Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown
Row 20: Brown Gray Gray 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 Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Gray Gray Brown Gray Brown Brown Brown Gray Brown Gray Brown Gray Gray Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Gray Brown Gray Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Gray Brown Brown Gray Gray Brown Brown Gray Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Gray Brown Brown Brown Gray Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Gray Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Blue Blue Blue Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Blue Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red
Row 4: Brown Brown Red Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Red Red Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 8: Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 9: Brown Brown Green Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Brown Blue Brown
Row 10: Brown Brown Brown Brown Brown Red Brown Green Brown Red Red Brown Brown Blue Brown Brown Blue Blue Brown Brown Brown
Row 11: Brown Brown Blue Brown Red Red Brown Brown Brown Brown Red Brown Blue Blue Brown Brown Brown Brown Green Brown Brown
Row 12: Brown Brown Blue Brown Brown Brown Green Green Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Green Brown Brown
Row 13: Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown
Row 14: Brown Brown Blue Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Red Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Red Brown Blue Blue Brown Brown Brown Red Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red Red Brown Brown Blue Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown
Row 18: Brown Green Green Brown Brown Blue Blue Brown Blue Blue Blue Brown Green Green Brown Brown Blue Blue Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown
Row 20: Brown Green Green 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 Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Green Green Brown Blue Brown Brown Brown Red Brown Green Brown Green Green Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Red Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Red Brown Brown Blue Blue Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Red Brown Brown Brown Blue Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 26: Brown Red Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Gray Pink Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink
Row 2: Pink Pink Gray Gray Gray Pink Pink Gray Gray Gray Pink Pink Gray Pink Pink Gray Pink
Row 3: Pink Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray Pink Pink
Row 5: Gray Pink Gray Pink Pink Pink Gray Gray Pink Pink Gray Gray Pink Gray Gray Pink Gray
Row 6: Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Pink Gray Gray Pink
Row 7: Gray Gray Pink Pink Gray Gray Pink Gray Gray Gray Gray Gray Gray Pink Gray Pink Pink
Row 8: Pink Pink Gray Gray Gray Gray Pink Gray Gray Pink Gray Pink Gray Pink Gray Pink Gray
Row 9: Gray Pink Pink Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray
Output:
Row 1: Gray Blue Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green
Row 2: Blue Blue Gray Gray Gray Red Red Gray Gray Gray Green Green Gray Green Green Gray Green
Row 3: Blue Gray Gray Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Gray Red Red
Row 5: Gray Green Gray Red Red Red Gray Gray Red Red Gray Gray Red Gray Gray Red Gray
Row 6: Gray Gray Gray Gray Gray Gray Red Gray Red Gray Gray Gray Gray Red Gray Gray Blue
Row 7: Gray Gray Green Green Gray Gray Red Gray Gray Gray Gray Gray Gray Red Gray Blue Blue
Row 8: Blue Blue Gray Gray Gray Gray Red Gray Gray Green Gray Green Gray Red Gray Blue Gray
Row 9: Gray Blue Blue Gray Gray Gray Gray Gray Gray Green Gray Green Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Orange Orange Orange Gray Gray Gray Orange Orange Orange
Row 2: Gray Orange Gray Gray Orange Orange Orange Orange Orange Gray Gray
Row 3: Orange Orange Orange Gray Orange Orange Orange Orange Orange Gray Orange
Row 4: Gray Orange Orange Gray Orange Gray Gray Orange Orange Gray Orange
Row 5: Gray Orange Orange Orange Gray Orange Gray Gray Orange Orange Gray
Row 6: Gray Gray Orange Orange Gray Orange Orange Orange Orange Orange Gray
Row 7: Orange Orange Orange Orange Gray Orange Orange Orange Gray Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Orange
Row 9: Gray Orange Gray Orange Orange Orange Orange Orange Orange Gray Orange
Row 10: Gray Orange Gray Gray Gray Orange Orange Orange Orange Gray Orange
Row 11: Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Gray
Row 12: Gray Gray Orange Orange Orange Orange Gray Orange Orange Orange Gray
Row 13: Gray Gray Orange Orange Gray Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Gray Gray Orange Gray Gray Gray Orange
Row 15: Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Gray Orange Orange Orange Orange Gray Gray Orange
Row 17: Orange Gray Gray Orange Orange Orange Orange Orange Gray Orange Orange
Row 18: Orange Orange Gray Gray Orange Orange Gray Orange Orange Gray Orange
Row 19: Orange Orange Orange Orange Orange Orange Gray Orange Orange 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 Red Orange Orange Orange Red Red Red Orange Orange Orange
Red Orange Blue Blue Orange Orange Orange Orange Orange Blue Blue
Orange Orange Orange Blue Orange Orange Orange Orange Orange Blue Orange
Blue Orange Orange Blue Orange Blue Blue Orange Orange Blue Orange
Blue Orange Orange Orange Red Orange Blue Blue Orange Orange Green
Blue Blue Orange Orange Red Orange Orange Orange Orange Orange Green
Orange Orange Orange Orange Red Orange Orange Orange Green Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange
Green Orange Blue Orange Orange Orange Orange Orange Orange Green Orange
Green Orange Blue Blue Blue Orange Orange Orange Orange Green Orange
Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange Green
Blue Blue Orange Orange Orange Orange Blue Orange Orange Orange Green
Blue Blue Orange Orange Red Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Red Red Orange Red Red Red Orange
Orange Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Blue Orange Orange Orange Orange Red Red Orange
Orange Blue Blue Orange Orange Orange Orange Orange Red Orange Orange
Orange Orange Blue Blue Orange Orange Green Orange Orange Green Orange
Orange Orange Orange Orange Orange Orange Green Orange Orange Green 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 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 Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: 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
Row 5: 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: Purple Purple Purple Purple Purple Brown 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 Brown 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 Brown 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 Purple Purple
Row 5: 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 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Brown 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
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: 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: 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 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
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink 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 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 Orange 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 Orange
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange 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 Orange Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
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
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
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: Red Red Red Red Red 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: Orange Orange Brown Orange Orange Orange
Row 2: Orange Orange Orange Orange Brown Orange
Row 3: Brown Orange Orange Orange Orange Orange
Row 4: Orange Brown Orange Orange Orange Orange
Row 5: Orange Brown Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Brown Orange
Row 7: Orange Orange Orange Orange Orange Brown
Row 8: Orange Orange Brown Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Brown
Row 10: Orange Orange Orange Orange Brown Orange
Row 11: Orange Orange Brown Orange Orange Orange
Row 12: Orange Orange Orange Brown Orange Orange
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
Green Green Green Green Green Green
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 Green Green Green Green
Yellow Yellow Yellow Yellow Yellow Yellow
Green Green Green Green Green Green
Green Green Green Green Green Green
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: Black Black Orange Black Black Gray Green Green Purple Black Purple Black Orange Orange Black Green Orange Yellow Yellow Black Black Gray Green Yellow Gray Green Black Orange
Row 2: Green Black Black Yellow Black Orange Black Gray Black Black Yellow Yellow Orange Black Green Gray Green Black Black Gray Black Purple Black Green Black Yellow Gray Orange
Row 3: Purple Black Black Yellow Gray Gray Black Yellow Yellow Black Gray Gray Black Black Gray Black Black Black Black Gray Black Black Black Black Black Yellow Black Green
Row 4: Orange Orange Orange Orange Black Gray Yellow Green Black Yellow Orange Black Black Black Purple Black Black Black Yellow Yellow Black Black Black Black Green Black Black Black
Row 5: Black Orange Gray Black Purple Black Purple Black Green Black Gray Orange Green Purple Black Gray Black Black Purple Orange Black Orange Black Gray Black Black Black Yellow
Row 6: Green Orange Yellow Gray Purple Black Orange Black Black Black Black Gray Gray Black Black Yellow Gray Gray Black Purple Gray Black Black Black Orange Black Purple Green
Row 7: Black Green Orange Black Gray Black Black Yellow Orange Black Purple Black Orange Black Purple Purple Black Black Black Black Black Black Black Green Black Black Black Green
Row 8: Black Green Black Black Black Black Orange Green Black Yellow Black Black Purple Black Orange Black Yellow Black Black Black Black Black Yellow Orange Black Black Black Purple
Output:
Row 1: Black Black Orange Black Black Gray Pink Green Purple Black Purple Black Pink Orange Black Pink Orange Yellow Pink Black Black Pink Green Yellow Pink Green Black Pink
Row 2: Pink Black Black Pink Black Orange Black Gray Black Black Yellow Yellow Pink Black Green Pink Green Black Black Gray Black Pink Black Green Black Yellow Gray Pink
Row 3: Pink Black Black Pink Gray Gray Black Yellow Yellow Black Gray Gray Black Black Gray Black Black Black Black Gray Black Black Black Black Black Yellow Black Pink
Row 4: Pink Orange Orange Pink Black Gray Pink Green Black Pink Orange Black Black Black Purple Black Black Black Pink Yellow Black Black Black Black Pink Black Black Black
Row 5: Black Orange Gray Black Purple Black Pink Black Green Black Gray Orange Pink Purple Black Pink Black Black Pink Orange Black Pink Black Gray Black Black Black Pink
Row 6: Pink Orange Yellow Pink Purple Black Pink Black Black Black Black Gray Pink Black Black Pink Gray Gray Black Purple Gray Black Black Black Pink Black Purple Pink
Row 7: Black Green Orange Black Gray Black Black Yellow Orange Black Purple Black Pink Black Purple Pink Black Black Black Black Black Black Black Green Black Black Black Pink
Row 8: Black Green Black Black Black Black Pink Green Black Pink Black Black Pink Black Orange Black Yellow Black Black Black Black Black Yellow Orange Black Black Black Pink
Example 2
Input:
Row 1: Brown Black Green Gray Black Brown Gray Brown Black Purple Black Green Purple Black Black Black Green
Row 2: Purple Black Purple Black Black Brown Black Green Purple Purple Black Black Green Black Black Green Brown
Row 3: Black Black Brown Black Black Green Gray Brown Purple Purple Green Purple Brown Purple Black Brown Purple
Row 4: Gray Black Green Green Black Purple Brown Green Gray Black Black Black Purple Black Purple Black Black
Row 5: Green Black Purple Black Black Purple Green Black Brown Gray Black Black Green Black Gray Green Green
Row 6: Brown Black Green Purple Black Gray Black Black Green Black Purple Black Green Black Brown Green Brown
Row 7: Gray Black Purple Black Black Black Black Black Green Black Black Black Black Gray Brown Brown Green
Row 8: Brown Black Green Brown Black Purple Gray Black Green Purple Black Black Green Black Gray Green Black
Row 9: Green Black Green Gray Black Brown Purple Black Black Gray Black Black Purple Black Gray Purple Green
Row 10: Black Black Brown Black Black Brown Black Black Green Black Black Purple Black Black Black Black Black
Row 11: Green Brown Brown Brown Black Purple Brown Black Brown Black Gray Gray Gray Black Black Brown Green
Row 12: Brown Brown Black Green Green Purple Gray Black Gray Brown Black Black Green Black Green Brown Black
Row 13: Green Black Brown Black Black Purple Brown Purple Gray Black Black Brown Black Black Gray Black Black
Row 14: Green Black Brown Purple Black Black Purple Black Brown Black Green Purple Black Green Gray Black Black
Row 15: Green Black Brown Black Green Purple Purple Black Purple Black Black Purple Gray Black Gray Purple Black
Row 16: Gray Black Green Gray Black Green Black Gray Green Green Green Gray Black Black Brown Brown Black
Row 17: Gray Black Purple Black Black Green Green Brown Gray Black Black Brown Purple Black Green Brown Purple
Row 18: Purple Black Gray Black Black Gray Green Gray Brown Black Brown Green Purple Black Green Black Black
Row 19: Purple Black Gray Black Black Brown Green Black Gray Black Black Black Black Black Brown Black Black
Row 20: Gray Black Black Gray Black Brown Green Gray Gray Gray Black Green Green Black Brown Gray Black
Row 21: Purple Black Gray Black Black Black Gray Gray Green Gray Black Purple Black Purple Brown Brown Black
Row 22: Brown Black Gray Green Green Brown Brown Black Purple Brown Black Black Brown Black Brown Gray Black
Row 23: Gray Purple Gray Gray Black Black Gray Black Green Black Black Black Black Black Brown Brown Black
Row 24: Brown Black Brown Black Black Purple Purple Black Brown Brown Brown Black Gray Brown Black Black Gray
Row 25: Brown Black Purple Black Black Green Purple Black Purple Green Black Black Black Black Gray Black Gray
Output:
Row 1: Pink Black Green Pink Black Brown Pink Brown Black Pink Black Green Pink Black Black Black Green
Row 2: Pink Black Purple Black Black Brown Black Green Purple Pink Black Black Pink Black Black Pink Brown
Row 3: Black Black Brown Black Black Green Pink Brown Purple Pink Green Purple Pink Purple Black Pink Purple
Row 4: Pink Black Green Pink Black Purple Pink Green Gray Black Black Black Pink Black Purple Black Black
Row 5: Pink Black Purple Black Black Purple Pink Black Brown Pink Black Black Pink Black Gray Pink Green
Row 6: Pink Black Green Pink Black Gray Black Black Green Black Purple Black Pink Black Brown Pink Brown
Row 7: Pink Black Purple Black Black Black Black Black Green Black Black Black Black Gray Brown Pink Green
Row 8: Pink Black Green Pink Black Purple Pink Black Green Pink Black Black Pink Black Gray Pink Black
Row 9: Pink Black Green Pink Black Brown Pink Black Black Pink Black Black Pink Black Gray Pink Green
Row 10: Black Black Brown Black Black Brown Black Black Green Black Black Purple Black Black Black Black Black
Row 11: Pink Brown Brown Pink Black Purple Pink Black Brown Black Gray Gray Pink Black Black Pink Green
Row 12: Pink Brown Black Pink Green Purple Pink Black Gray Pink Black Black Pink Black Green Pink Black
Row 13: Pink Black Brown Black Black Purple Pink Purple Gray Black Black Brown Black Black Gray Black Black
Row 14: Pink Black Brown Pink Black Black Pink Black Brown Black Green Purple Black Green Gray Black Black
Row 15: Pink Black Brown Black Green Purple Pink Black Purple Black Black Purple Pink Black Gray Pink Black
Row 16: Pink Black Green Pink Black Green Black Gray Green Pink Green Gray Black Black Brown Pink Black
Row 17: Pink Black Purple Black Black Green Pink Brown Gray Black Black Brown Pink Black Green Pink Purple
Row 18: Pink Black Gray Black Black Gray Pink Gray Brown Black Brown Green Pink Black Green Black Black
Row 19: Pink Black Gray Black Black Brown Pink Black Gray Black Black Black Black Black Brown Black Black
Row 20: Pink Black Black Pink Black Brown Pink Gray Gray Pink Black Green Pink Black Brown Pink Black
Row 21: Pink Black Gray Black Black Black Pink Gray Green Pink Black Purple Black Purple Brown Pink Black
Row 22: Pink Black Gray Pink Green Brown Pink Black Purple Pink Black Black Pink Black Brown Pink Black
Row 23: Pink Purple Gray Pink Black Black Pink Black Green Black Black Black Black Black Brown Pink Black
Row 24: Pink Black Brown Black Black Purple Pink Black Brown Pink Brown Black Pink Brown Black Black Gray
Row 25: Pink Black Purple Black Black Green Pink Black Purple Pink Black Black Black Black Gray Black Gray
Example 3
Input:
Row 1: Black Black Black Red Brown Black Green Orange Orange Green Orange Black Red Orange Black
Row 2: Black Black Orange Black Green Black Black Orange Green Brown Orange Brown Black Black Black
Row 3: Black Black Black Red Orange Orange Orange Black Black Green Orange Brown Black Green Black
Row 4: Black Black Black Black Black Black Black Orange Brown Orange Brown Red Black Brown Black
Row 5: Black Black Black Green Black Black Red Black Black Black Green Black Orange Brown Black
Row 6: Black Black Black Black Black Black Brown Black Orange Orange Red Black Brown Black Black
Row 7: Green Black Black Black Orange Green Green Black Red Brown Black Black Red Black Green
Row 8: Black Brown Black Black Black Black Brown Black Red Red Brown Black Orange Black Black
Row 9: Black Black Black Orange Red Black Black Black Black Black Brown Brown Brown Black Black
Row 10: Black Black Black Black Green Brown Brown Black Black Black Green Red Black Green Black
Row 11: Black Black Green Orange Green Orange Green Brown Brown Brown Brown Black Brown Black Red
Row 12: Black Brown Brown Black Black Black Green Red Black Black Black Black Orange Brown Black
Output:
Row 1: Black Black Black Pink Brown Black Pink Orange Orange Pink Orange Black Pink Orange Black
Row 2: Black Black Orange Black Green Black Black Orange Green Pink Orange Brown Black Black Black
Row 3: Black Black Black Pink Orange Orange Pink Black Black Pink Orange Brown Black Green Black
Row 4: Black Black Black Black Black Black Black Orange Brown Pink Brown Red Black Brown Black
Row 5: Black Black Black Pink Black Black Pink Black Black Black Green Black Pink Brown Black
Row 6: Black Black Black Black Black Black Pink Black Orange Pink Red Black Pink Black Black
Row 7: Pink Black Black Black Orange Green Pink Black Red Pink Black Black Pink Black Green
Row 8: Black Brown Black Black Black Black Pink Black Red Pink Brown Black Pink Black Black
Row 9: Black Black Black Pink Red Black Black Black Black Black Brown Brown Pink Black Black
Row 10: Black Black Black Black Green Brown Pink Black Black Black Green Red Black Green Black
Row 11: Black Black Green Pink Green Orange Pink Brown Brown Pink Brown Black Pink Black Red
Row 12: Black Brown Brown Black Black Black Pink Red Black Black Black Black Pink Brown Black
Here is the input grid for the test example:
Input:
Row 1: Orange Black Green Green Black Orange Black Green Black Green Black Black Black Black Orange Black Yellow Green Orange Black Black
Row 2: Black Black Black Black Black Yellow Black Orange Orange Black Orange Black Black Black Yellow Green Yellow Yellow Black Green Green
Row 3: Yellow Orange Green Yellow Green Orange Black Orange Black Yellow Black Black Black Green Black Green Green Green Black Black Black
Row 4: Black Black Yellow Black Green Orange Black Yellow Green Black Black Black Black Orange Yellow Black Green Black Black Yellow Yellow
Row 5: Black Black Black Orange Orange Orange Black Orange Black Yellow Green Black Black Orange Orange Green Orange Black Black Green Black
Row 6: Black Black Black Orange Orange Green Yellow Black Black Green Black Black Black Orange Orange Green Black Black Black Green Black
Row 7: Black Orange Yellow Yellow Green Yellow Orange Orange Yellow Yellow Yellow Black Black Green Orange Black Orange Green Black Orange Black
Row 8: Black Yellow Yellow Orange Orange Orange Black Orange Black Orange Green Black Black Green Green Black Yellow Black Black Black Yellow
Row 9: Yellow Orange Black Black Orange Orange Yellow Black Yellow Green Black Black Green Black Yellow Green Green Black Black Black Green
Row 10: Green Green Black Black Orange Yellow Black Orange Black Orange Black Black Black Black Black Orange Black Black Black Black Black
Row 11: Black Black Yellow Yellow Yellow Orange Black Orange Black Yellow Black Black Black Green Black Yellow Orange Black Black Yellow Black
Row 12: Black Black Yellow Black Black Orange Black Green Yellow Orange Yellow Black Black Black Black Black Green Black Black Orange Black
Row 13: Black Yellow Black Black Yellow Yellow Black Black Orange Orange Black Black Green Black Black Black Orange Yellow Black Black Black
Row 14: Black Black Yellow Yellow Orange Yellow Black Green Black Yellow Yellow Black Black Yellow Orange Yellow Green Green Black Black Black
Row 15: Black Black Yellow Orange Green Black Black Black Black Black Green Orange Black Yellow Black Orange Green Green Black Black Black
Row 16: Black Orange Yellow Orange Orange Orange Yellow Green Black Green Black Green Black Black Black Yellow Yellow Yellow Black Black Black
Row 17: Black Black Yellow Yellow Yellow Yellow Black Black Black Black Yellow Black Black Yellow Black Green Green Yellow Black Black Green
Row 18: Black Green Black Orange Green Black Black Green Green Black Black Black Black Orange Black Yellow Orange Yellow Black Orange Yellow
Row 19: Green Orange Yellow Yellow Green Yellow Black Orange Black Black Green Black Black Black Black Green Green Orange 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>
| Pink Black Green Pink Black Orange Black Green Black Pink Black Black Black Black Orange Black Yellow Green Pink Black Black
Black Black Black Black Black Yellow Black Orange Orange Black Orange Black Black Black Yellow Pink Yellow Yellow Black Green Green
Pink Orange Green Pink Green Orange Black Orange Black Pink Black Black Black Green Black Pink Green Green Black Black Black
Black Black Yellow Black Green Orange Black Yellow Green Black Black Black Black Orange Yellow Black Green Black Black Yellow Yellow
Black Black Black Pink Orange Orange Black Orange Black Pink Green Black Black Orange Orange Pink Orange Black Black Green Black
Black Black Black Pink Orange Green Pink Black Black Pink Black Black Black Orange Orange Pink Black Black Black Green Black
Black Orange Yellow Pink Green Yellow Pink Orange Yellow Pink Yellow Black Black Green Orange Black Orange Green Black Orange Black
Black Yellow Yellow Pink Orange Orange Black Orange Black Pink Green Black Black Green Green Black Yellow Black Black Black Yellow
Pink Orange Black Black Orange Orange Pink Black Yellow Pink Black Black Pink Black Yellow Pink Green Black Black Black Green
Pink Green Black Black Orange Yellow Black Orange Black Pink Black Black Black Black Black Pink Black Black Black Black Black
Black Black Yellow Pink Yellow Orange Black Orange Black Pink Black Black Black Green Black Pink Orange Black Black Yellow Black
Black Black Yellow Black Black Orange Black Green Yellow Pink Yellow Black Black Black Black Black Green Black Black Orange Black
Black Yellow Black Black Yellow Yellow Black Black Orange Pink Black Black Pink Black Black Black Orange Yellow Black Black Black
Black Black Yellow Pink Orange Yellow Black Green Black Pink Yellow Black Black Yellow Orange Pink Green Green Black Black Black
Black Black Yellow Pink Green Black Black Black Black Black Green Orange Black Yellow Black Pink Green Green Black Black Black
Black Orange Yellow Pink Orange Orange Pink Green Black Pink Black Green Black Black Black Pink Yellow Yellow Black Black Black
Black Black Yellow Pink Yellow Yellow Black Black Black Black Yellow Black Black Yellow Black Pink Green Yellow Black Black Green
Black Green Black Pink Green Black Black Green Green Black Black Black Black Orange Black Pink Orange Yellow Black Orange Yellow
Pink Orange Yellow Pink Green Yellow Black Orange Black Black Green Black Black Black Black Pink Green Orange 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 Yellow Orange Yellow Yellow Yellow Yellow Red Purple Yellow Orange Yellow Red Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Yellow Red Purple Yellow Orange Yellow Red Yellow
Row 2: Yellow Yellow Yellow Orange Yellow Yellow Purple Yellow Orange Yellow Yellow Orange Yellow Orange Yellow Yellow Yellow Yellow Orange Yellow Yellow Purple Yellow Orange Yellow Yellow Orange Yellow Orange
Row 3: Black Orange Purple Black Orange Yellow Yellow Orange Yellow Red Black Yellow Yellow Yellow Yellow Black Orange Purple Black Orange Yellow Yellow Orange Yellow Red Black Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Red Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Red Orange Yellow Yellow Yellow Yellow
Row 5: Orange Yellow Yellow Purple Orange Yellow Orange Yellow Yellow Yellow Orange Yellow Orange Yellow Yellow Orange Yellow Yellow Purple Orange Yellow Orange Yellow Yellow Yellow Orange Yellow Orange 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 Yellow Yellow
Row 7: Orange Yellow Yellow Yellow Yellow Yellow Black Red Orange Yellow Orange Yellow Black Red Yellow Orange Yellow Orange Yellow Yellow Yellow Yellow Red Purple Yellow Orange Yellow Red Yellow
Row 8: Orange Yellow Yellow Orange Yellow Red Orange Yellow Yellow Orange Yellow Yellow Purple Purple Yellow Yellow Yellow Yellow Orange Yellow Yellow Purple Yellow Orange Yellow Yellow Orange Yellow Orange
Row 9: Black Orange Purple Black Yellow Yellow Orange Orange Purple Red Black Yellow Yellow Yellow Yellow Black Orange Purple Black Orange Yellow Yellow Orange Yellow Red Black Yellow Yellow Yellow
Row 10: Yellow Yellow Red Yellow Purple Yellow Yellow Orange Orange Red Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Red Orange Yellow Yellow Yellow Yellow
Row 11: Orange Orange Yellow Red Orange Yellow Orange Purple Purple Purple Black Yellow Purple Black Yellow Orange Yellow Yellow Purple Orange Yellow Orange Yellow Yellow Yellow Orange Yellow Orange Yellow
Output:
Row 1: Orange Yellow Yellow Yellow Yellow Yellow Black Red Orange Yellow Orange Yellow Black Red
Row 2: Orange Yellow Yellow Orange Yellow Red Orange Yellow Yellow Orange Yellow Yellow Purple Purple
Row 3: Black Orange Purple Black Yellow Yellow Orange Orange Purple Red Black Yellow Yellow Yellow
Row 4: Yellow Yellow Red Yellow Purple Yellow Yellow Orange Orange Red Orange Yellow Yellow Yellow
Row 5: Orange Orange Yellow Red Orange Yellow Orange Purple Purple Purple Black Yellow Purple Black
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange
Row 2: Purple Orange Orange Purple Orange
Row 3: Orange Orange Orange Orange Orange
Row 4: Orange Purple Orange Orange Purple
Row 5: Orange Purple Orange Orange Purple
Row 6: Purple Purple Orange Purple Purple
Row 7: Orange Orange Orange Orange Orange
Row 8: Orange Purple Orange Orange Orange
Row 9: Purple Orange Orange Purple Orange
Row 10: Purple Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Purple
Row 12: Purple Purple Orange Orange Purple
Row 13: Orange Orange Orange Purple Purple
Output:
Row 1: Orange Purple
Row 2: Purple Orange
Row 3: Purple Orange
Row 4: Orange Orange
Row 5: Purple Purple
Row 6: Orange Orange
Example 3
Input:
Row 1: Pink Purple Red Gray Blue Green Brown Black Orange Pink Purple Red Gray Blue Green Brown Black
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Pink Purple Red Gray Blue Green Brown Black Orange Pink Purple Purple Gray Blue Blue Brown Black
Output:
Row 1: Pink Purple Purple Gray Blue Blue Brown Black
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Gray Brown Pink Brown Brown Brown Brown Brown Brown Black Gray Brown Black Brown Yellow Red Pink Pink Black Red Brown Pink Brown Red Black Gray
Row 2: Brown Red Brown Brown Purple Yellow Brown Gray Brown Purple Brown Green Brown Brown Brown Brown Red Brown Black Green Green Brown Gray Brown Purple Green Green Brown Yellow
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 Gray Brown Pink Brown Brown Brown Brown Brown Brown Black Gray Brown Brown Brown Brown Gray Brown Pink Brown Brown Brown Brown Brown Brown Black Gray
Row 5: Brown Red Brown Brown Purple Yellow Brown Gray Brown Purple Brown Green Brown Brown Brown Brown Red Brown Brown Purple Yellow Brown Gray Brown Purple Brown Green Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Brown Yellow Red Pink Pink Black Red Brown Pink Brown Red Black Gray
Brown Red Brown Black Green Green Brown Gray Brown Purple Green Green Brown 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: Pink Purple Purple Purple Purple Purple Purple Pink Purple Purple Pink
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple
Row 3: Purple Pink Purple Pink Purple Pink Purple Pink Purple Purple Pink
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple
Row 5: Purple Purple Purple Pink Pink Pink Pink Pink Purple Pink Purple
Row 6: Pink Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 7: Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Purple
Row 8: Pink Pink Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 9: Pink Pink Pink Purple Pink Pink Pink Pink Pink Purple Pink
Row 10: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Pink Pink Purple Purple Purple Purple Purple Purple Pink Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 6: Purple Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 7: Pink Pink Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 8: Pink Pink Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 9: Pink Pink Purple Purple Pink Pink Pink Pink Purple Purple Purple
Row 10: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Blue Black Blue Black Blue Black Blue Black Blue Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue Blue
Row 2: Black Blue Blue Blue Black Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Blue Black
Row 3: Blue Blue Black Black Blue Black Black Black Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue Blue
Row 4: Black Blue Black Black Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue
Row 5: Blue Blue Black Black Blue Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Black
Row 6: Blue Blue Black Black Blue Blue Black Black Black Blue Blue Black Blue Black Blue Black Blue Black Blue Blue Blue Blue Black Blue
Row 7: Blue Black Black Black Blue Blue Black Black Black Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 8: Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Black Blue Blue Blue Black Black Black Black Blue
Row 9: Blue Black Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Black Black Black Black
Row 10: Blue Blue Blue Blue Blue Blue Black Blue Blue Black Blue Blue Blue Blue Black Blue Black Blue Black Blue Black Black Black Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue Blue
Row 3: Blue Blue Black Black Blue Blue Black Black Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue Blue
Row 4: Blue Blue Black Black Blue Blue Black Black Black Blue Black Black Black Black Black Blue Black Black Black Black Black Black Blue Blue
Row 5: Blue Blue Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Black Black Blue Blue Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue
Example 3
Input:
Row 1: Green Green Black Black Black Black Green Black Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Black Black Black Green Black Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green
Row 3: Black Green Black Black Black Green Green Green Green Green Green Green Black Green Green Green Green Green Green Black Green Green Black Green Green Green Green
Row 4: Green Black Black Black Black Black Green Black Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Black Green
Row 5: Green Green Green Green Green Green Black Green Green Green Green Green Black Green Green Green Black Black Black Green Green Green Green Green Green Green Green
Row 6: Black Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Black Black Black Green Green Green Green Black Green Green Green
Row 7: Green Green Green Black Green Black Green Green Green Green Green Green Black Green Green Green Black Black Black Green Green Green Black Green Green Black Green
Row 8: Green Green Green Green Green Green Green Black Green Green Green Green Green Green Black Green Green Green Black Green Green Green Green Green Green Green Green
Row 9: Green Green Black Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green
Row 10: Green Black Green Green Black Green Green Green Green Green Green Green Green Black Green Green Green Green Green Black Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Black Black Green Green Green Green Black Black Black Black Green Green Black Black Black Black Black Green Green Green Green
Row 12: Green Green Green Green Black Green Black Black Green Green Green Black Black Black Black Black Green Green Black Black Black Black Black Green Green Green Green
Row 13: Green Green Green Green Green Green Black Black Green Black Green Green Green Green Green Green Green Black Black Black Black Black Black Green Green Green Green
Row 14: Black Green Green Green Green Black Black Black Green Green Green Green Green Black Green Black Green Green Black Black Black Black Black Green Green Black Green
Row 15: Green Green Black Green Green Green Black Black Black Green Green Black Green Green Green Green Green Green Black Black Black Black Black Green Green Green Green
Row 16: Black Green Green Green Green Green Black Green Green Green Black Green Green Black Green Green Green Green Black Black Black Black Black Green Green Green Black
Row 17: Green Green Green Green Black Green Green Green Black Green Green Green Green Green Black Green Green Green Green Green Green Black Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Black Green Green Green Green Green Black Green Green Green Green Green Green Black Green Black Green Black Green Green
Row 19: Green Black Green Green Black Black Black Black Black Black Green Black Green Green Black Green Green Green Green Green Green Green Black Black Black Black Black
Row 20: Green Green Green Green Black Black Black Black Black Black Green Green Green Green Green Green Black Green Green Black Green Green Black Black Black Black Black
Row 21: Green Green Black Green Black Black Black Black Black Black Green Green Black Green Green Green Green Green Green Green Green Green Black Black Black Black Black
Row 22: Green Black Green Green Green Black Green Green Black Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 23: Green Green Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Black Green Green Green Green Green Green Black
Output:
Row 1: Green Green Black Black Black 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 Black Black Black 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 Black Black Black 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 Black Black Black 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 Black Black Black 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 Black Black Black 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 Black Black Black 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
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
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
Row 11: Green Green Green Green Green Green Black Black Green Green Green Green Black Black Black Black Green Green Black Black Black Black Black Green Green Green Green
Row 12: Green Green Green Green Green Green Black Black Green Green Green Green Black Black Black Black Green Green Black Black Black Black Black Green Green Green Green
Row 13: Green Green Green Green Green Green Black Black Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black Green Green Green Green
Row 14: Green Green Green Green Green Green Black Black Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black Green Green Green Green
Row 15: Green Green Green Green Green Green Black Black Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black 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
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: Green Green Green Green Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black
Row 20: Green Green Green Green Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black
Row 21: Green Green Green Green Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Black Black Black Black Black
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
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
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Purple Gray Purple Gray Gray Purple Gray Gray Gray Purple
Row 2: Purple Gray Gray Gray Gray Purple Gray Purple Gray Purple Gray Purple Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Purple Gray Purple Gray Purple Gray
Row 3: Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Purple Gray Purple Gray Gray Purple Gray Gray Gray Gray Gray Purple Gray Purple Gray Gray Gray Gray Gray Gray Purple Gray Gray Purple Gray Gray Gray Gray Purple
Row 5: Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Purple Purple Purple Gray Gray Purple Gray Gray Gray Gray
Row 6: Purple Purple Purple Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Purple Gray Purple Gray Purple Gray Purple Purple Purple Gray Purple Gray Gray Gray Gray Gray
Row 7: Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Gray Gray Purple Gray Gray Gray
Row 8: Purple Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Gray Gray Purple Gray Gray Gray Purple
Row 9: Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Gray Purple Gray Gray Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Gray
Row 10: Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Purple Gray Purple Purple Purple Gray Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray
Row 12: Purple Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Purple Gray Gray
Row 13: Gray Gray Gray Purple Gray Purple Gray Gray Purple Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Purple Gray Gray Gray Gray Purple Gray Purple Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Purple Gray Gray Purple Gray Purple Gray Gray Gray
Row 15: Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray Gray
Row 16: Gray Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Purple Gray Purple Gray Gray Gray
Row 17: Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray Purple Gray Gray Purple Gray
Row 18: Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 19: Gray Purple Purple Purple Purple Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Gray Purple Gray Gray Purple Gray
Row 20: Gray Gray Purple Purple Purple Purple Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray Gray Gray Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray
Row 21: Gray Purple Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Gray Purple Purple Purple Purple Gray Gray Purple Gray Gray Purple
Row 22: Purple Gray Gray Purple Gray Gray Purple Gray Gray Gray Purple Gray Gray Purple Gray Purple Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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
Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Purple Purple Purple Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray
Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Purple Purple Purple Purple Purple 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 Purple Purple Purple Purple Purple 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 Purple Purple Purple Purple Purple 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 Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Gray Gray Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Purple Purple Purple 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 Purple Purple Purple 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 Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray
Gray Gray Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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: 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
Row 2: Orange Orange Blue Blue 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 Blue Green 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 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 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 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 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 Orange Orange Orange
Row 9: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Output:
Row 1: 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
Row 3: 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
Row 5: 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
Row 7: 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
Row 9: Blue Blue Blue Green 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
Row 11: 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
Example 2
Input:
Row 1: Orange Orange Orange Black Black Black 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 Red Black Black 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 Red Black Black 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 Black Black Black 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 Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Black Black 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
Row 7: Orange Orange Black 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
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 Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Black Black Black Black Black Black Black Black Orange Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Black Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Black Black Black Black Black Black Black Black Orange Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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 Orange Orange Orange
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 Orange Orange Orange
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 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
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 Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 8: Black Yellow Black Black Black Black Black Black Red 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
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: 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
Row 3: 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
Row 5: Blue Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Blue Pink Pink Blue Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Blue Pink Blue Blue 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
Row 10: Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Pink Purple Pink Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Pink Pink Pink 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
Row 14: 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
Row 16: Red Pink Pink Pink Pink Red Red Pink Pink Red Red Red Red Red Red Red
Row 17: Red Pink Pink Pink Pink Red Red Red Pink Red Red Red Red Red Red Red
Row 18: Red Pink Pink Pink Pink Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Pink Pink Pink Pink Pink Red Pink Pink Red Red Red Red Red Red Red
Row 20: Red Pink Pink Pink Red Red Red Pink Pink Red Red Red Red Red Red Red
Row 21: Red Pink Pink Pink Red Pink Red Pink Pink Red Red Red Red Red Red Red
Row 22: Red Pink Pink Pink Red Red Red Pink Pink Red Red Red Red Red Red Red
Row 23: Red Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red
Output:
Row 1: Pink Pink Pink Pink Pink Pink Blue Blue
Row 2: Pink Pink Pink Pink Pink Pink Pink Blue
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Blue Pink Blue Blue
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Purple Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink
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
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 Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Orange Blue Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Orange Blue Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Orange Orange Orange 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 Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange 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
Row 25: 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 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>
| 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 Blue Blue 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: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Brown Orange Green Green Orange Brown Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Green Orange Orange Green Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Brown Orange Green Green Orange Brown Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Brown Orange Orange Brown Orange Orange Orange Orange Orange
Row 11: 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
Row 13: 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
Output:
Row 1: Orange Orange
Row 2: Orange Orange
Row 3: Orange Orange
Example 2
Input:
Row 1: Pink Green Pink Pink Green Pink
Row 2: Green Pink Blue Blue Pink Green
Row 3: Pink Blue Pink Pink Blue Pink
Row 4: Pink Blue Pink Pink Blue Pink
Row 5: Green Pink Blue Blue Pink Green
Row 6: Black Black Pink Pink Green Pink
Output:
Row 1: Pink Green
Example 3
Input:
Row 1: Gray Red Yellow Yellow Green Green Yellow Green Pink Green Gray Red Red Gray Green Pink Green Yellow Green Green Yellow Yellow Red Gray
Row 2: Red Yellow Pink Brown Red Brown Brown Gray Gray Brown Gray Green Green Gray Brown Gray Gray Brown Brown Red Brown Pink Yellow Red
Row 3: Yellow Pink Gray Yellow Red Yellow Gray Gray Brown Red Yellow Pink Pink Yellow Red Brown Gray Gray Yellow Red Yellow Gray Pink Yellow
Row 4: Yellow Brown Yellow Yellow Yellow Pink Gray Green Brown Gray Green Gray Gray Green Gray Brown Green Gray Pink Yellow Yellow Yellow Brown Yellow
Row 5: Green Red Red Yellow Red Green Gray Yellow Brown Red Pink Gray Gray Pink Red Brown Yellow Gray Green Red Yellow Red Red Green
Row 6: Green Brown Yellow Pink Green Yellow Gray Brown Green Green Red Gray Gray Red Green Green Brown Gray Yellow Green Pink Yellow Brown Green
Row 7: Yellow Brown Gray Gray Gray Gray Green Red Yellow Pink Green Gray Gray Green Pink Yellow Red Green Gray Gray Gray Gray Brown Yellow
Row 8: Green Gray Gray Green Yellow Brown Red Gray Brown Yellow Green Red Red Green Yellow Brown Gray Red Brown Yellow Green Gray Gray Green
Row 9: Pink Gray Brown Brown Brown Green Yellow Brown Red Green Gray Gray Gray Gray Green Red Brown Yellow Green Brown Brown Brown Gray Pink
Row 10: Green Brown Red Gray Red Green Pink Yellow Green Red Yellow Pink Pink Yellow Red Green Yellow Pink Green Red Gray Red Brown Green
Row 11: Gray Gray Yellow Green Pink Red Green Green Gray Yellow Pink Yellow Yellow Pink Yellow Gray Green Green Red Pink Green Yellow Gray Gray
Row 12: Red Green Pink Gray Gray Gray Gray Red Gray Pink Yellow Gray Gray Yellow Pink Gray Red Gray Gray Gray Gray Pink Green Red
Row 13: Red Green Pink Gray Black Black Black Black Black Pink Yellow Gray Gray Yellow Pink Gray Red Gray Gray Gray Gray Pink Green Red
Row 14: Gray Gray Yellow Green Black Black Black Black Black Yellow Pink Yellow Yellow Pink Yellow Gray Green Green Red Pink Green Yellow Gray Gray
Row 15: Green Brown Red Gray Black Black Black Black Black Red Yellow Pink Pink Yellow Red Green Yellow Pink Green Red Gray Red Brown Green
Row 16: Pink Gray Brown Brown Black Black Black Black Black Green Gray Gray Gray Gray Green Red Brown Yellow Green Brown Brown Brown Gray Pink
Row 17: Green Gray Gray Green Black Black Black Black Black Yellow Green Red Red Green Yellow Brown Gray Red Brown Yellow Green Gray Gray Green
Row 18: Yellow Brown Gray Gray Black Black Black Black Black Pink Green Gray Gray Green Pink Yellow Red Green Gray Gray Gray Gray Brown Yellow
Row 19: Green Brown Yellow Pink Black Black Black Black Black Green Red Gray Gray Red Green Green Brown Gray Yellow Green Pink Yellow Brown Green
Row 20: Green Red Red Yellow Black Black Black Black Black Red Pink Gray Gray Pink Red Brown Yellow Gray Green Red Yellow Red Red Green
Row 21: Yellow Brown Yellow Yellow Black Black Black Black Black Gray Green Gray Gray Green Gray Brown Green Gray Pink Yellow Yellow Yellow Brown Yellow
Row 22: Yellow Pink Gray Yellow Black Black Black Black Black Red Yellow Pink Pink Yellow Red Brown Gray Gray Yellow Red Yellow Gray Pink Yellow
Row 23: Red Yellow Pink Brown Red Brown Brown Gray Gray Brown Gray Green Green Gray Brown Gray Gray Brown Brown Red Brown Pink Yellow Red
Row 24: Gray Red Yellow Yellow Green Green Yellow Green Pink Green Gray Red Red Gray Green Pink Green Yellow Green Green Yellow Yellow Red Gray
Output:
Row 1: Gray Gray Gray Red Gray
Row 2: Pink Red Green Green Gray
Row 3: Red Green Pink Yellow Green
Row 4: Brown Green Yellow Brown Red
Row 5: Yellow Brown Red Gray Brown
Row 6: Gray Gray Green Red Yellow
Row 7: Green Yellow Gray Brown Green
Row 8: Red Green Gray Yellow Brown
Row 9: Yellow Pink Gray Green Brown
Row 10: Red Yellow Gray Gray Brown
Here is the input grid for the test example:
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 Black Black Black Black Black Black Black Brown
Row 9: Brown Brown Brown Brown Black Black Black Black Black Black Black Brown
Row 10: Brown Brown Brown Brown Black Black Black Black Black Black Black Brown
Row 11: Brown Brown Brown Brown Black Black Black Black Black Black Black Brown
Row 12: 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 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: Red Red Red Red Red Red Red Blue Red Red Green Red Brown Red Red Red Red Brown Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Brown
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Blue Red Brown Red
Row 4: Red Red Blue Red Brown Red Red Red Red Red Red Red Red Green Red Red Red Brown Blue Red Red Red Red Red Red Red Red
Row 5: Red Red Red Blue Red Red Red Red Green Red Red Red Red Red Red Red Red Green Blue Red Red Red Red Red Red Red Brown
Row 6: Green Red Green Red Red Red Green Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red
Row 8: Red Red Red Red Red Brown Red Red Red Red Red Red Red Green Red Green Red Red Red Red Red Red Green Red Red Red Blue
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Blue Red Red Red
Row 10: Red Red Brown Red Red Brown 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 Yellow Yellow Yellow Yellow Yellow Red Blue Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red
Row 12: Red Red Brown Red Yellow Yellow Yellow Yellow Yellow Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Brown Red Brown Red Red Brown Red Brown Red Red Red Red Red
Row 15: Red Red Green Red Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Green Red Red Red Red Green Red Red Red Green Red Red Green
Row 16: Green Red Red Red Yellow Yellow Yellow Yellow Yellow Blue Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Blue Red Red Green Red Brown Red Red Red Red Brown Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Blue Red Red Red Brown Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Brown
Row 3: Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Blue Red Brown Red
Row 4: Red Red Blue Red Brown Red Red Blue Red Red Red Red Red Green Red Red Red Brown Blue Red Red Red Red Red Red Red Red
Row 5: Red Red Red Blue Brown Red Red Blue Green Red Red Red Red Red Red Red Red Green Blue Red Red Red Red Red Red Red Brown
Row 6: Green Red Green Red Brown Red Green Blue Green Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Brown Red Green Blue Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red
Row 8: Red Red Red Red Brown Brown Green Blue Green Red Red Red Red Green Red Green Red Red Red Red Red Red Green Red Red Red Blue
Row 9: Red Red Red Red Brown Brown Green Blue Green Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Blue Red Red Red
Row 10: Red Red Brown Red Brown Brown Green Blue Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Red
Row 12: Red Red Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red
Row 15: Red Red Green Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Yellow 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 Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Brown Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black
Row 5: Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Purple Black Black Black Black Black Black Black Black Gray Black Black Black Black Black Black Yellow Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black
Row 8: 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
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange 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 Yellow Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Brown Black Yellow Black Black Black Black
Row 12: Green Black Red Red Red Red Red Red Red Red Red Red Red Black Black Black Yellow Black Black Black Black Black Black Black Black
Row 13: Purple Black Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Pink Black Orange 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 Brown Black Black Black Black Black Black Orange Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Black Black Black Black
Row 18: Pink Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Orange Black Black Black Black Black Black Brown Black Black Black Yellow Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Green Black Black Brown Black Black Gray Black Black Black Black Black Black Black Black Black
Row 21: Black Brown Black Orange Black Black Black Black Black Black Pink 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 Orange Black Black Black Black Black Black Black
Row 23: Black Black Black Black Brown Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black Black Black
Row 24: Black Black Black Black Black Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Brown Black Black Black Black Green Pink Black Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Black Black Black Black Black Black Gray Black Black Black Yellow Brown Black Black Black Black Black Brown Black Black
Row 27: Black Black Black Black Black Orange Black Black Black Black Black Gray Black Black Pink Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Brown 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 Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Brown Black Black Black Black Black Black Brown Yellow Black Black Black Black Black Black Black Black Black Black Black Pink Black Black Black
Row 5: Black Black Black Black Black Black Orange Black Brown Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Purple Black Orange Black Brown Yellow Black Black Black Gray Black Black Black Black Black Black Yellow Black Black Black Black
Row 7: Black Black Black Black Purple Black Orange Black Brown Yellow Black Black Black Black Black Black Black Black Black Pink Black Black Black Black Black
Row 8: Black Black Black Black Purple Black Orange Black Brown Yellow Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Purple Black Orange Black Brown Yellow Black Black Black Black Black Orange Gray Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Purple Black Orange Black Brown Yellow Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Purple Black Orange Black Brown Yellow Black Black Black Black Black Black Black Black Brown Black Yellow Black Black Black Black
Row 12: Green Green Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Black
Row 13: Purple Purple Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Red Red Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Orange Brown Orange Pink Black Orange Green Pink Gray Brown Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Orange Brown Orange Pink Black Black Green Pink Gray Brown Black Brown Black Black Black Black Black Black Orange Black Black Black
Row 17: Black Black Black Orange Brown Orange Pink Black Black Green Pink Gray Brown Black Black Black Purple Black Black Black Black Black Black Black Black
Row 18: Pink Black Black Orange Brown Orange Pink Black Black Green Pink Gray Brown Black Black Black Black Yellow Black Black Black Black Black Black Black
Row 19: Black Black Black Orange Brown Orange Pink Black Black Green Pink Gray Brown Black Black Black Yellow Black Black Black Black Black Black Black Black
Row 20: Black Black Black Orange Brown Orange Pink Black Black Green Pink Gray Brown Black Black Gray Black Black Black Black Black Black Black Black Black
Row 21: Black Brown Black Orange Brown Orange Pink Black Black Green Pink Gray Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Brown Orange Pink Black Black Green Pink Gray Black Black Black Black Black Orange Black Black Black Black Black Black Black
Row 23: Black Black Black Black Brown Orange Pink Black Black Green Pink Gray Black Black Black Black Black Black Black Black Black Orange Black Black Black
Row 24: Black Black Black Black Brown Orange Pink Black Black Green Pink Gray Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Brown Orange Black Black Black Green Pink Gray Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Orange Black Black Black Black Black Gray Black Black Black Yellow Brown Black Black Black Black Black Brown Black Black
Row 27: Black Black Black Black Black Orange Black Black Black Black Black Gray Black Black Pink Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Pink Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Purple Gray Gray Gray Gray Purple
Row 4: Pink Gray Gray Gray Pink Pink Gray Yellow Yellow Gray Gray Gray Gray Brown Gray Gray Gray
Row 5: Gray Gray Blue Gray Gray Gray Gray Yellow Yellow Purple Gray Gray Gray Gray Purple Gray Gray
Row 6: Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Green Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Orange Gray Gray Gray Gray Red Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Pink Green Gray Red Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Red Purple Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Brown Brown Brown Brown Brown Gray Gray Gray
Row 5: Gray Gray Blue Blue Blue Blue Blue Yellow Yellow Purple Purple Purple Purple Purple Purple Gray Gray
Row 6: Gray Gray Gray Orange Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Green Gray Gray Gray Red Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Orange Gray Gray Gray Gray Red Gray Purple Gray Gray Green Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Orange Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Pink Green Gray Red Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Red Purple Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray 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 Pink
Row 2: Red Red Red Blue Red Red Red Red Blue Red Gray
Row 3: Red Green Orange Blue Red Red Pink Red Red Red Red
Row 4: Red Red Red Red Red Red Pink Red Blue Red Red
Row 5: Green Red Green Blue Red Red Red Red Red Red Red
Row 6: Pink Gray Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Blue Pink Red Red Red Gray Red Red
Row 8: Red Red Red Blue Red Blue Red Red Red Red Red
Row 9: Red Orange Red Blue Red Red Red Red Blue Red Red
Row 10: Red Red Red Black Black Black Black Gray Red Red Red
Row 11: Red Red Red Black Black Black Black Red Red Red Red
Row 12: Red Red Pink Black Black Black Black Red Blue Red Blue
Row 13: Gray Red Red Black Black Black Black Gray Red Red Gray
Row 14: Red Red Gray Black Black Black Black Brown Brown Red Red
Row 15: Red Red Red Black Black Black Black Red Blue Red Red
Row 16: Red Purple Red Black Black Black Black Red Blue Red Red
Row 17: Red Red Brown Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Blue Pink Orange Red Red Red
Row 19: Blue Red Red Red Red Red Red Gray Red Red Red
Row 20: Pink Red Red Red Red Red Red Red Blue Red Red
Row 21: Red Brown Red Red Blue Red Red Red Red Red Red
Row 22: Red Red Red Orange Red Red Red Red Blue Red Red
Row 23: Red Red Red Red Red Red Red Red Red Purple 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 Pink
Red Red Red Blue Red Red Red Red Blue Red Gray
Red Green Orange Blue Red Red Pink Red Red Red Red
Red Red Red Blue Red Red Pink Red Blue Red Red
Green Red Green Blue Red Red Pink Red Red Red Red
Pink Gray Red Blue Red Red Pink Red Red Red Red
Red Red Red Blue Pink Red Pink Red Gray Red Red
Red Red Red Blue Pink Blue Pink Red Red Red Red
Red Orange Red Blue Pink Blue Pink Red Blue Red Red
Red Red Red Black Black Black Black Gray Red Red Red
Red Red Red Black Black Black Black Red Red Red Red
Red Red Pink Black Black Black Black Blue Blue Blue Blue
Gray Gray Gray Black Black Black Black Gray Gray Gray Gray
Red Red Gray Black Black Black Black Brown Brown Red Red
Red Red Red Black Black Black Black Blue Blue Red Red
Red Purple Purple Black Black Black Black Blue Blue Red Red
Red Red Brown Orange Blue Blue Pink Red Red Red Red
Red Red Red Orange Blue Blue Pink Orange Red Red Red
Blue Red Red Orange Blue Red Red Gray Red Red Red
Pink Red Red Orange Blue Red Red Red Blue Red Red
Red Brown Red Orange Blue Red Red Red Red Red Red
Red Red Red Orange Red Red Red Red Blue Red Red
Red Red Red Red Red Red Red Red Red Purple 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: Green 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 Brown
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 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 Yellow Orange
Output:
Row 1: Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Yellow Brown
Row 2: Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Yellow Yellow
Row 3: Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Orange Yellow Brown Yellow Orange
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Green Orange
Row 2: Brown Brown Brown Brown Brown Brown Brown Green Pink
Row 3: Brown Brown Brown Brown Brown Brown Brown Green Blue
Row 4: Brown Brown Brown Brown Brown Brown Brown Green Gray
Row 5: Brown Brown Brown Brown Brown Brown Brown Green Green
Row 6: Brown Brown Brown Brown Brown Brown Brown Green Purple
Row 7: Brown Brown Brown Brown Brown Brown Brown Green Red
Row 8: Brown Brown Brown Brown Brown Brown Brown Green Yellow
Output:
Row 1: Red Purple Green Gray Blue Pink Orange Green Orange
Row 2: Red Purple Green Gray Blue Pink Orange Green Pink
Row 3: Red Purple Green Gray Blue Pink Orange Green Blue
Row 4: Red Purple Green Gray Blue Pink Orange Green Gray
Row 5: Red Purple Green Gray Blue Pink Orange Green Green
Row 6: Red Purple Green Gray Blue Pink Orange Green Purple
Row 7: Red Purple Green Gray Blue Pink Orange Green Red
Row 8: Red Purple Green Gray Blue Pink Orange Green Yellow
Example 3
Input:
Row 1: Gray Yellow Orange Red Green Purple
Row 2: Blue Blue Blue Blue Blue Blue
Row 3: Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink
Output:
Row 1: Gray Yellow Orange Red Green Purple
Row 2: Blue Blue Blue Blue Blue Blue
Row 3: Gray Gray Gray Gray Gray Gray
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Orange Orange Orange Orange Orange Orange
Row 6: Red Red Red Red Red Red
Row 7: Green Green Green Green Green Green
Row 8: Purple Purple Purple Purple Purple Purple
Row 9: Gray Gray Gray Gray Gray Gray
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Brown Gray Red Red Red Red Red Red Red Red Red
Row 2: Orange Gray Red Red Red Red Red Red Red Red Red
Row 3: Blue Gray Red Red Red Red Red Red Red Red Red
Row 4: Purple Gray Red Red Red Red Red Red Red Red Red
Row 5: Gray Gray Red Red Red Red Red Red Red Red Red
Row 6: Pink Gray 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>
| Brown Gray Pink Gray Purple Blue Orange Brown Pink Gray Purple
Orange Gray Pink Gray Purple Blue Orange Brown Pink Gray Purple
Blue Gray Pink Gray Purple Blue Orange Brown Pink Gray Purple
Purple Gray Pink Gray Purple Blue Orange Brown Pink Gray Purple
Gray Gray Pink Gray Purple Blue Orange Brown Pink Gray Purple
Pink Gray Pink Gray Purple Blue Orange Brown Pink 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: 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 Yellow Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Black Black Black Yellow 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 Black Black Black Gray Gray Gray 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 Gray Gray 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 Black Yellow 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
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 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
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 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 Black Black Black Black Black Purple Purple Purple Black Yellow Yellow Yellow Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Purple Purple Black Black Yellow Yellow 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 Black Black Black Gray Gray Gray 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 Gray Gray 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 Yellow Yellow Yellow 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 Yellow Yellow 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 Black Black
Row 11: Black Black Black Black Black Black Yellow Yellow Yellow 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 Yellow Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: 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
Row 3: 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
Row 5: 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
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 Yellow Yellow Black Black Black Black
Row 10: Black Black Black Black Black Black Black Yellow Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Yellow Yellow 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 Purple Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Purple Black Black
Row 16: 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
Output:
Row 1: 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
Row 3: 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
Row 5: 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
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 Yellow Yellow Black Black Black Black
Row 10: Black Black Black Black Black Black Black Yellow Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Yellow Yellow 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 Purple Purple Black
Row 14: Black Black Black Black Black Black Black Black Black Black Purple Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Purple Purple Black
Row 16: 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
Example 3
Input:
Row 1: 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
Row 3: 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
Row 5: 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
Row 7: Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Black Black Green Green Green
Row 8: 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 Pink Green Pink Pink Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Pink Pink Pink 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
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Yellow Green Green Green
Row 13: 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
Output:
Row 1: Green Green Green Green Green Green Green Green Yellow Yellow Yellow 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
Row 3: Green Green Green Green Green Green Green Yellow Green Yellow Yellow Green Green Green Green Green Green Black Green
Row 4: Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green Green Green Green Green Black
Row 5: 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 Yellow Green Yellow Yellow Green Black Green Black Black Green Green Green
Row 7: Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Black Black Black Green Green Green
Row 8: 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 Pink Green Pink Pink Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Pink Pink Pink 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
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Yellow Yellow Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Green Green
Row 14: 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: 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 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
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Green Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray
Row 13: Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Pink Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Pink Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Gray 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 Gray
Row 27: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 28: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 29: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 30: 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
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
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
Gray Gray Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Black 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 Gray Gray Black Black Gray Gray Gray Gray Green Green
Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Green Gray
Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Pink Pink
Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray Pink Gray
Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Pink Pink
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray 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 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 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 |
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 Black Black Purple Purple Black Purple Purple Black Purple Purple Purple Purple Black Black Black Black Black Purple Purple Black Black Purple Purple Black Black Purple
Row 2: Purple Purple Purple Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Black Purple Black Purple Purple Purple Purple
Row 3: Black Black Black Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple
Row 4: Black Black Purple Purple Purple Purple Black Purple Purple Purple Black Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Purple
Row 5: Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Purple Purple Black Black Purple Black Purple
Row 6: Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Black Black Purple Purple Purple Purple
Row 7: Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Black Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Purple Black Purple Purple Purple Black
Row 10: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Black Purple Black Purple Purple
Row 11: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Purple Purple Purple Purple Purple Black Purple Purple Black Purple Purple Purple Purple Purple Purple Black Purple
Row 12: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Black Purple Purple
Row 13: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple Purple Purple Black Purple Purple
Row 14: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Black Purple Black Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Black
Row 15: Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Black Black Purple Purple Purple Purple Purple Purple Black Purple Black Black Purple Purple Purple Purple Black Purple Purple
Row 16: Purple Purple Black Purple Purple Purple Orange Orange Orange Orange Orange Purple Purple Black Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Black Purple
Row 17: Black Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Purple Black
Row 18: Purple Purple Purple Purple Black Purple Orange Orange Orange Orange Orange Purple Black Purple Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Purple Black Purple Black Purple
Row 19: Purple Purple Purple Black Purple Purple Orange Orange Orange Orange Orange Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Purple Black Purple Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Black Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Black Purple Black Purple Purple Black Purple Black Purple Black Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Black Purple Purple Purple Black
Row 23: Black Black Black Black Purple Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple
Row 24: Black Purple Purple Purple Purple Black Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Black Black Purple
Row 25: Purple Orange Orange Orange Orange Orange Purple Purple Purple Black Purple Purple Black Purple Black Purple Purple Purple Purple Purple Black Orange Orange Orange Orange Orange Purple Black Purple Black
Row 26: Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Black Purple Purple Purple
Row 27: Purple Orange Orange Orange Orange Orange Purple Black Purple Black Purple Black Purple Purple Purple Purple Black Purple Purple Black Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple
Row 28: Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Black Purple Black Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Purple Black Black Purple
Row 29: Purple Orange Orange Orange Orange Orange Black Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Black Purple Purple Orange Orange Orange Orange Orange Purple Purple Black Purple
Row 30: Black Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Black
Output:
Row 1: Purple Purple Black Black Purple
Row 2: Black Black Purple Purple Purple
Row 3: Purple Black Purple Purple Purple
Row 4: Purple Black Purple Purple Purple
Row 5: Black Purple Purple Purple Black
Example 2
Input:
Row 1: 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 Orange Orange Blue Blue Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Orange Orange Blue Blue Orange Orange 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
Row 5: 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 Orange Orange Orange Orange Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Orange Orange Blue Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Orange Orange Blue Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red
Row 10: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Orange Orange Orange Orange Blue Blue Blue Blue Red 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 Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue 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 Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Red Blue Red Blue
Row 2: Blue Blue Blue Blue
Row 3: Red Red Blue Blue
Row 4: Red Blue Blue Red
Row 5: Blue Red Red Blue
Row 6: Blue Red Red Blue
Example 3
Input:
Row 1: Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple
Row 3: Purple Pink Purple Purple Purple Pink Purple Pink Purple Purple Purple Brown Brown Brown Brown Brown Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Brown Brown Brown Brown Brown Pink
Row 5: Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple
Row 7: Purple Pink Purple Purple Purple Pink Purple Purple Purple Purple Pink Purple Purple Purple Pink 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 Pink Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Pink Purple Purple Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Purple
Row 13: Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Pink
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Purple Purple
Row 15: Purple Purple Purple Purple Pink Purple Purple Purple Purple Pink Pink Purple Purple Purple Purple Purple Pink
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 Pink Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Pink Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Pink Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Pink
Row 21: Purple Purple Pink Purple Pink Purple Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink
Row 24: Purple Purple Purple Pink 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 Pink Purple Purple Purple Purple Purple Purple
Row 26: Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple
Row 27: Purple Purple Pink Purple Purple Purple Purple Purple Pink Purple Purple Pink Pink Purple Purple Pink Pink
Row 28: Purple Purple Purple Pink Purple Purple Purple Purple Purple Pink Purple Pink Purple Purple Purple Purple Purple
Output:
Row 1: Purple Pink
Row 2: Purple Purple
Row 3: Purple Purple
Row 4: Pink Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Orange
Row 3: Orange Orange Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow
Row 4: Orange Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Orange Yellow
Row 6: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow
Row 10: Orange Yellow Yellow Orange Yellow Yellow Purple Purple Yellow Yellow
Row 11: Yellow Yellow Orange Yellow Yellow Yellow Purple Purple Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange
Yellow Yellow
Yellow 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: Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Black Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Black Green
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black
Row 2: Black Black Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black
Row 3: Black Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black
Row 2: Black Black Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black
Row 3: Black Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black
Row 4: Black Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black
Row 5: Black Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black Black
Row 6: Black Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black Black Black
Row 7: Black Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black Black Black Black
Row 8: Black Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black Black Black Black Black
Row 9: Black Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black Black Black Black Black Black
Row 10: Black Purple Black Black Yellow Green Orange Orange Purple Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Gray Pink Red Pink Orange Red Gray Gray Red Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Gray Pink Red Pink Orange Red Gray Gray Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Pink Red Gray Pink Red Pink Orange Red Gray Gray Red 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 Pink Red Gray Pink Red Pink Orange Red Gray Gray Red Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Pink Red Gray Pink Red Pink Orange Red Gray Gray Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Pink Red Gray Pink Red Pink Orange Red Gray Gray Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Gray Pink Red Pink Orange Red Gray Gray Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Red Gray Gray 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 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
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
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 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 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Red Green Pink Pink Pink
Row 2: Pink Pink Pink Pink Red Green Pink Pink Pink
Row 3: Pink Pink Pink Pink Red Green Pink Pink Pink
Row 4: Pink Pink Pink Pink Red Green Pink Pink Pink
Row 5: Pink Pink Pink Pink Red Green 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 Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green Pink Pink Pink
Pink Pink Pink Pink Red Green 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: Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple
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: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Purple Purple Purple Purple
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Red Red Red Red
Row 8: Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Brown
Row 9: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Yellow Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: 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
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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: 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 Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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: 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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Green Green Brown Brown Brown Green
Row 8: Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Orange
Row 9: Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow
Row 10: Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple
Row 11: Green Green Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown
Row 12: Orange Orange Brown Brown Orange Orange Orange Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 14: Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Yellow Yellow Yellow Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Purple Purple Purple Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Green Green Green Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 2: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 3: Brown Yellow Green Brown Yellow Green Black Black Black Black Yellow Green Brown Yellow Green Brown Yellow
Row 4: Green Brown Yellow Green Brown Yellow Black Black Black Black Brown Yellow Green Brown Yellow Green Brown
Row 5: Yellow Green Brown Yellow Green Brown Black Black Black Black Black Brown Yellow Green Brown Yellow Green
Row 6: Brown Yellow Green Brown Yellow Green Black Black Black Black Black Green Brown Yellow Green Brown Yellow
Row 7: Green Brown Yellow Green Brown Yellow Green Brown Black Black Black Yellow Green Brown Yellow Green Brown
Row 8: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 9: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Row 10: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 11: Yellow Green Brown Black Black Black Black Black Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 12: Brown Yellow Green Black Black Black Black Black Green Brown Yellow Green Brown Yellow Green Brown Yellow
Row 13: Green Brown Yellow Black Black Black Black Black Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 14: Yellow Green Brown Black Black Black Black Black Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 15: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Output:
Row 1: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 2: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 3: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Row 4: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 5: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 6: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Row 7: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 8: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 9: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Row 10: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 11: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 12: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Row 13: Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown
Row 14: Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green
Row 15: Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow Green Brown Yellow
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Row 2: Green Green Green Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Row 3: Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Row 4: Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Row 5: Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Row 6: Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Row 7: Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Row 8: Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Row 9: Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Row 10: Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Green Green Green Green Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Row 11: Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Green Green Green Green Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Row 12: Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Green Green Green Green Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink
Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue
Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown
Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue Pink Brown Blue 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: Green Pink Orange Gray
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Pink
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Green Pink Orange
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Green Pink Orange Gray
Row 5: Black Black Black Black Black Black Black Black Black Black Black Green Pink Orange Gray Black
Row 6: Black Black Black Black Black Black Black Black Black Black Green Pink Orange Gray Black Black
Row 7: Black Black Black Black Black Black Black Black Black Green Pink Orange Gray Black Black Black
Row 8: Black Black Black Black Black Black Black Black Green Pink Orange Gray Black Black Black Black
Row 9: Black Black Black Black Black Black Black Green Pink Orange Gray Black Black Black Black Black
Row 10: Black Black Black Black Black Black Green Pink Orange Gray Black Black Black Black Black Black
Row 11: Black Black Black Black Black Green Pink Orange Gray Black Black Black Black Black Black Black
Row 12: Black Black Black Black Green Pink Orange Gray Black Black Black Black Black Black Black Black
Row 13: Black Black Black Green Pink Orange Gray Black Black Black Black Black Black Black Black Black
Row 14: Black Black Green Pink Orange Gray Black Black Black Black Black Black Black Black Black Black
Row 15: Black Green Pink Orange Gray Black Black Black Black Black Black Black Black Black Black Black
Row 16: Green Pink Orange Gray Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Black Red Pink Gray Green
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 Red
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Pink
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Red Pink Gray Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Orange Black Green
Output:
Row 1: Black Black Black Black Black Orange
Row 2: Black Black Black Black Orange Black
Row 3: Black Black Black Orange Black Green
Row 4: Black Black Orange Black Green Black
Row 5: Black Orange Black Green Black Black
Row 6: Orange Black Green Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Brown Red Purple
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 Brown
Black Black Black Black Black Black Black Brown Red
Black Black Black Black Black Black Brown Red Purple
Black Black Black Black Black Brown Red Purple Black
Black Black Black Black Brown Red Purple Black Black
Black Black Black Brown Red Purple Black Black Black
Black Black Brown Red Purple Black Black Black Black
Black Brown Red Purple Black Black Black Black Black
Brown Red Purple 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 Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange Orange Orange Green
Row 7: Orange Orange Orange Orange Orange Red Red Red Green Orange
Row 8: Orange Orange Orange Orange Orange Red Red Green Red Orange
Row 9: Orange Orange Orange Orange Orange Red Green Red Red Orange
Row 10: Orange Orange Orange Orange Orange Green Red Red Red Orange
Row 11: Orange Orange Orange Orange Green Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Green
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Green Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Green Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Green Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Green Orange Orange Orange Orange Green
Row 7: Orange Orange Orange Green Orange Orange Orange Orange Green Orange
Row 8: Orange Orange Green Orange Orange Orange Orange Green Orange Orange
Row 9: Orange Green Orange Orange Orange Orange Green Orange Orange Orange
Row 10: Green Orange Orange Orange Orange Green Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Green Orange Orange Orange Orange Green
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Pink Pink Pink Pink Pink Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Pink Pink Pink Pink Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Pink Pink Pink Red Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Pink Pink Red Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Pink Red Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Red Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Red 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
Row 11: 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
Row 13: 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
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Red Red Red Green Brown Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Black Black Black Red Red Green Brown Brown Black Black Black Black
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Red Green Brown Brown Brown Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Green Brown Brown Brown Brown Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Red Black Black Black Black Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black
Row 2: Red Black Black Black Black Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Red Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green
Row 11: Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black
Row 12: Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black
Row 13: Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black
Row 14: Black Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black
Row 15: Red Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black Black
Row 21: Black Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black Black Green
Row 22: Black Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black Black Green Black
Row 23: Black Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black Black Green Black Black
Row 24: Black Black Black Black Black Black Green Black Black Black Black Green Black Black Black Black Black Green Black Black Black
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray
Row 3: Gray Orange Orange Orange Orange Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Orange Orange Orange Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Orange Orange Purple Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Orange Purple Yellow Yellow Gray Gray Gray Gray Gray Gray Brown Brown Brown Brown Yellow Pink Gray Gray Gray Gray Gray Gray Gray Gray Brown
Row 7: Gray Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Yellow Pink Pink Gray Gray Gray Gray Gray Gray Gray Brown Gray
Row 8: Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Brown Yellow Pink Pink Pink Gray Gray Gray Gray Gray Gray Brown Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Yellow Pink Pink Pink Pink Gray Gray Gray Gray Gray Brown Black Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Black Black Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Black Black Black Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Black Black Black Black Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Black Black Black Black Black Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray
Row 2: Purple Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow
Row 3: Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray
Row 4: Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray
Row 5: Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray
Row 6: Gray Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown
Row 7: Gray Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray
Row 8: Purple Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray
Row 9: Gray Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray
Row 10: Gray Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray
Row 11: Gray Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray Gray
Row 12: Purple Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Brown
Row 14: Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Brown Gray
Row 15: Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Brown Gray Gray
Row 16: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Yellow Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Brown Gray Gray 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 Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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 Yellow Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Yellow Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Yellow Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Yellow 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 Blue Yellow Pink 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 Yellow Pink Pink Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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 Yellow 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 Yellow 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 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 Yellow 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 Yellow 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 Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Black Pink Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Black Pink Pink Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black 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 Black 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 Black 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 Yellow Orange Orange Orange Orange Orange Yellow Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black
Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange
Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange
Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange
Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black
Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange
Orange Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange
Orange Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange
Orange Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black
Yellow Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange
Orange Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange
Orange Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange
Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange
Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Orange
Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Yellow Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Yellow Orange Orange Orange Orange Orange Black Orange Orange Orange Black Orange Orange Orange Black 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: Blue Blue Blue Blue 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 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 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
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
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
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 Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Green Green Green Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Green Green Green Blue Blue
Row 13: Blue Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Green Green Green Blue Blue
Row 14: Blue Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue
Row 15: Blue Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange 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 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 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 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 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 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
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
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
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 Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Red Red Red Red Red Yellow Blue Blue Blue Blue Blue Blue Blue Blue Green Red Green Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue Green Red Green Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Green Red Green Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Red Red Red Red Brown Blue Blue Blue Green Red Green Blue Blue
Row 13: Blue Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue Green Red Green Blue Blue
Row 14: Blue Black Red Red Red Black Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue
Row 15: Blue Black Black Black Black Black Orange Red Red Red Red Red Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange 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 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
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
Row 2: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Black Black Black Black Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Black Black Black Black Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Black Black Black Black Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray 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 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 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 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 Orange Orange
Row 2: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Yellow Red Red Red Red Yellow Orange Orange Orange Black Red Red Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Yellow Red Red Red Red Yellow Orange Orange Orange Black Red Red Black Orange Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Yellow Red Red Red Red Yellow Orange Orange Orange Black Red Red Black Orange Gray Red Red Gray Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Yellow Red Red Red Red Yellow Orange Orange Orange Black Black Black Black Orange Gray Red Red Gray Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Gray Red Red Gray Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray 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 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 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Green Green Green Green Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Green Green Green Green Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Purple Green Green Green Green Purple
Row 4: Purple Purple Gray Gray Gray Gray Gray Gray Purple Yellow Yellow Yellow Purple Purple Green Green Green Green Purple
Row 5: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Black Black Black Purple Green Green Green Green Purple
Row 6: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Black Black Black Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Black Black Black Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Black Black Black Brown Brown Brown Purple Purple Purple
Row 9: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple
Row 11: 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 Yellow Yellow Yellow Purple Purple Green Green Green Green Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Red Yellow Purple Purple Green Red Red Green Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Red Yellow Purple Purple Green Red Red Green Purple
Row 4: Purple Purple Gray Gray Gray Gray Gray Gray Purple Yellow Yellow Yellow Purple Purple Green Red Red Green Purple
Row 5: Purple Purple Gray Red Red Red Red Gray Purple Purple Black Black Black Purple Green Green Green Green Purple
Row 6: Purple Purple Gray Red Red Red Red Gray Purple Purple Black Red Black Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Gray Red Red Red Red Gray Purple Purple Black Red Black Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Gray Red Red Red Red Gray Purple Purple Black Black Black Brown Brown Brown Purple Purple Purple
Row 9: Purple Purple Gray Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Brown Red Brown Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple
Row 11: 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: Orange Orange Orange 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: Orange Orange Orange 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: Orange Orange Orange 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: Orange Orange Orange 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: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Purple Purple Purple Black Black Black Black Black Purple Purple
Row 6: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Purple Purple Purple Black Black Black Black Black Purple Purple
Row 7: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Purple Purple Purple Black Black Black Black Black Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Black Black Black Black Black Purple Purple
Row 9: 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
Row 10: 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
Row 11: 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
Row 12: 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
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
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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Orange Red Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Orange Red Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Orange Red Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Orange Red Orange Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Purple Purple Purple Black Black Black Black Black Purple Purple
Orange Red Orange Purple Purple Purple Purple Purple Purple Purple Green Red Red Red Green Purple Purple Purple Purple Black Red Red Red Black Purple Purple
Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green Purple Purple Purple Purple Black Red Red Red Black Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Black Black Black Black Black Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Red Red Red Red Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Red Red Red Red Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Red Red Red Red Blue 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 Purple 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: 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 Brown Brown Brown Brown Brown Brown Purple Purple
Row 4: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown
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
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 Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 24: Pink 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 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
Output:
Row 1: Purple Purple Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: 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
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Green Green Gray Gray Gray Gray Gray Gray
Row 5: Black Black Black Black Black Black Black Green Green Gray Gray Gray Gray Green Gray
Row 6: Black Black Black Black Black Black Black Green Green Gray Gray Gray Gray Gray Gray
Row 7: Black Black Black Black Black Black Black Green Green Green Gray Gray Gray Gray Gray
Row 8: Black Black Black Black Black Black Black Green Green Green Gray Green Gray Green Green
Row 9: Black Black Black Black Black Black Black Green Green Green Gray Gray Green Green Green
Row 10: Black Black Black Black Black Black Black Green Green Green Green Gray Green Green Green
Row 11: Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green
Row 12: 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
Output:
Row 1: Gray Gray Gray Gray Gray Gray Green Green
Row 2: Gray Green Gray Gray Gray Gray Green Green
Row 3: Gray Gray Gray Gray Gray Gray Green Green
Row 4: Gray Gray Gray Gray Gray Green Green Green
Row 5: Green Green Gray Green Gray Green Green Green
Row 6: Green Green Green Gray Gray Green Green Green
Row 7: Green Green Green Gray Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green
Example 3
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 Gray Gray Gray Black Black Black Black Orange Orange Orange Orange Orange
Row 12: Orange Gray Gray Gray Black Gray Gray Black Orange Orange Orange Orange Orange
Row 13: Orange Gray Gray Gray Gray Black Black Black Orange Orange Orange Orange Orange
Row 14: Orange Gray Gray Black Black Black Black Black Orange Orange Orange Orange Orange
Row 15: Orange Gray Gray Gray Gray Black Gray Black Orange Orange Orange Orange Orange
Row 16: Orange Gray Gray Gray Black Black Gray Gray 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 Orange 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 Orange 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
Output:
Row 1: Black Black Black Black Gray Gray Gray
Row 2: Black Gray Gray Black Gray Gray Gray
Row 3: Black Black Black Gray Gray Gray Gray
Row 4: Black Black Black Black Black Gray Gray
Row 5: Black Gray Black Gray Gray Gray Gray
Row 6: Gray Gray Black Black Gray Gray Gray
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 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 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 Orange Orange Orange Orange Orange Black Black Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Orange Orange Orange Orange Orange Orange Orange 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
Row 29: 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>
| Black Black 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: Blue Black Black Black Black Black Black Blue Black
Row 2: Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Red Orange Black Red Red Black
Row 4: Black Black Black Brown Red Brown Black Black Red
Row 5: Blue Black Black Black Red Red Black Blue 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
Output:
Row 1: Blue Black Black Black Black Black Black Blue Black
Row 2: Black Red Orange Black Red Red Black Black Black
Row 3: Black Brown Red Brown Black Black Red Black Black
Row 4: Black Black Red Red Black Black Black Black Black
Row 5: Blue Black Black Black Black Black Black Blue 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
Example 2
Input:
Row 1: Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange
Row 2: Yellow Yellow Yellow Yellow Blue Red Red Blue Blue Black Red Red Pink Black Blue Black Pink Red Yellow Blue Blue Black Red
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Black Black Blue Pink Black Pink Red Red Blue Pink Blue Red Red Red Yellow Red Black
Row 4: Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange
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
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
Output:
Row 1: Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange
Row 2: Yellow Yellow Yellow Blue Red Red Blue Blue Black Red Red Pink Black Blue Black Pink Red Yellow Blue Blue Black Red Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Black Black Blue Pink Black Pink Red Red Blue Pink Blue Red Red Red Yellow Red Black Yellow
Row 4: Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange
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
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
Example 3
Input:
Row 1: Green Green Blue Brown Red Green Green Green Green Brown Green Green Green Green Green Blue Green
Row 2: Green Green Green Green Gray Green Green Green Orange Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Orange Gray Gray Red Brown Orange Black Red Green Green Green Green Green
Row 4: Green Green Green Green Gray Green Orange Red Brown Green Orange Green Black Gray Green Green Green
Row 5: Green Green Green Green Green Green Orange Gray Red Gray Brown Green Green Green Red Green Green
Row 6: Green Green Green Green Green Green Brown Gray Black Black Orange Green Green Orange Orange Green Green
Row 7: Green Green Green Green Green Green Green Black Black Brown Brown Brown Black Brown Black Green Green
Row 8: Green Green Green Green Green Green Brown Orange Orange Orange Orange Red Gray Red Gray Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Blue Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Blue Green
Row 2: Green Green Green Brown Red Green Green Green Green Brown Green Green Green Green Green Green Green
Row 3: Green Green Green Green Gray Green Green Green Orange Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Orange Gray Gray Red Brown Orange Black Red Green Green Green Green Green
Row 5: Green Green Green Green Gray Green Orange Red Brown Green Orange Green Black Gray Green Green Green
Row 6: Green Green Green Green Green Green Orange Gray Red Gray Brown Green Green Green Red Green Green
Row 7: Green Green Green Green Green Green Brown Gray Black Black Orange Green Green Orange Orange Green Green
Row 8: Green Green Green Green Green Green Green Black Black Brown Brown Brown Black Brown Black Green Green
Row 9: Green Green Green Green Green Green Brown Orange Orange Orange Orange Red Gray Red Gray Green Green
Row 10: Green Green Blue Green Green Green Green Green Green Green Green Green Green Green Green Blue Green
Row 11: 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 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 Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Red Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Gray Blue Blue Blue Yellow Yellow Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Black Blue Blue Blue Pink Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Yellow Blue Blue Yellow Pink Purple Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Black Pink Blue Green Blue Black Green Purple Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Yellow Yellow Green Gray Black Gray Gray Purple Black Pink Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Pink Pink Yellow Gray Green Yellow Yellow Black Purple Green Yellow Blue Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Yellow Blue Blue Green Gray Gray Blue Yellow Green Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Gray Purple Pink Black Yellow Green Gray Gray Gray Pink Pink Black Gray Black Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Pink Gray Yellow Black Black Yellow Black Yellow Black Green Blue Yellow Purple Blue Black Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Green Pink Green Gray Purple Pink Pink Black Pink Gray Yellow Purple Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Gray Black Blue Pink Green Blue Green Yellow Yellow Yellow Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Pink Purple Green Black Blue Blue Purple Blue Purple Yellow Gray Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Yellow Pink Gray Purple Black 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 Gray Blue Pink Gray Yellow Blue Blue Blue 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 Green Black Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Gray Purple 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue
Row 25: Blue Blue Blue Blue 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 26: Blue Blue Blue Blue 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 27: Blue Blue Blue Blue 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 28: Blue Blue Blue Blue 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 Red Blue 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 Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Green 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 Blue Blue Pink Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Green Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Gray Blue Blue Blue Yellow Yellow Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Black Blue Blue Blue Pink Blue Blue Purple Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Yellow Blue Blue Yellow Pink Purple Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Black Pink Blue Green Blue Black Green Purple Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Yellow Yellow Green Gray Black Gray Gray Purple Black Pink Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Yellow Gray Green Yellow Yellow Black Purple Green Yellow Blue Black Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Yellow Blue Blue Green Gray Gray Blue Yellow Green Blue Purple Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Purple Pink Black Yellow Green Gray Gray Gray Pink Pink Black Gray Black Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Gray Yellow Black Black Yellow Black Yellow Black Green Blue Yellow Purple Blue Black Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Green Pink Green Gray Purple Pink Pink Black Pink Gray Yellow Purple Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Black Blue Pink Green Blue Green Yellow Yellow Yellow Blue Gray Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Pink Purple Green Black Blue Blue Purple Blue Purple Yellow Gray Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Yellow Pink Gray Purple 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 Gray Blue Pink Gray Yellow Blue Blue 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 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 Purple Gray Purple 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 Red Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
Subsets and Splits