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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: Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Orange Purple Orange Orange Purple Purple Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Orange
Row 3: Purple Purple Purple Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Orange Orange Purple Orange Purple Purple Purple Purple Purple Purple
Row 4: Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Purple Orange Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Purple Purple
Row 6: Purple Purple Orange Purple Purple Orange Purple Purple Purple Orange Orange Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Orange Purple Purple Orange Orange Purple Purple Orange Purple Purple Purple Orange
Row 9: Purple Purple Purple Purple Purple Orange Purple Orange Purple Purple Purple Purple Purple Purple Orange Orange Purple Orange Orange Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Black Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Black Black Black Orange Black Black Black Orange Black Black Black Black Black Black Black Orange Purple Purple Orange Purple Orange Orange Orange Purple Orange Purple Purple Purple Purple Purple
Row 14: Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Orange Purple Purple Orange Purple Orange Orange Orange Purple Purple Purple Purple Orange Purple Purple
Row 15: Black Black Black Black Black Black Black Orange Black Black Black Black Black Orange Black Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Row 16: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Purple Orange Purple Purple Purple Purple Orange Purple Purple Orange Purple Purple Purple Purple
Row 17: Black Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Orange Purple Orange Purple Orange Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Orange Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Orange Purple Purple Purple
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple
Row 20: Orange Black Black Black Black Black Orange Black Black Black Orange Black Black Black Black Orange Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple
Row 21: Black Black Black Black Black Black Black Orange Black Black Black Black Black Orange Black Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple
Row 22: Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple
Output:
Row 1: Purple Purple
Row 2: Black Purple
Example 2
Input:
Row 1: Orange Orange Orange Red Black Black Red Yellow Yellow Red Yellow Yellow Yellow
Row 2: Orange Orange Orange Red Black Black Red Red Red Red Yellow Yellow Red
Row 3: Orange Orange Orange Red Black Black Red Yellow Yellow Red Yellow Yellow Yellow
Row 4: Red Orange Orange Red Black Black Red Yellow Red Red Yellow Yellow Yellow
Row 5: Red Orange Orange Red Red Red Red Yellow Red Red Red Yellow Yellow
Row 6: Orange Orange Red Red Black Red Red Yellow Red Red Yellow Yellow Yellow
Row 7: Orange Orange Orange Red Red Black Red Yellow Yellow Red Yellow Yellow Yellow
Row 8: Orange Red Orange Red Black Black Red Yellow Yellow Red Yellow Yellow Yellow
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Yellow Red Yellow Red Red Black Red Red Orange Red Black Black Black
Row 11: Yellow Yellow Yellow Red Black Red Red Orange Orange Red Red Black Black
Row 12: Yellow Yellow Yellow Red Black Black Red Red Orange Red Red Black Black
Row 13: Yellow Yellow Yellow Red Red Black Red Orange Red Red Black Red Black
Row 14: Yellow Yellow Yellow Red Red Black Red Red Orange Red Black Black Black
Row 15: Yellow Red Yellow Red Red Black Red Orange Orange Red Black Red Black
Row 16: Yellow Yellow Yellow Red Red Black Red Orange Orange Red Black Black Red
Row 17: Yellow Yellow Red Red Black Black Red Orange Red Red Black Red Black
Row 18: Yellow Red Yellow Red Black Red Red Red Red Red Black Black Black
Row 19: Yellow Yellow Yellow Red Red Red Red Orange Orange Red Black Black Black
Row 20: Red Red Yellow Red Red Red Red Orange Orange Red Black Black Black
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Orange Orange Orange Red Orange Red Red Red Black Red Yellow Yellow Yellow
Row 23: Orange Orange Orange Red Orange Orange Red Black Black Red Yellow Yellow Yellow
Row 24: Red Orange Orange Red Red Red Red Black Black Red Yellow Yellow Yellow
Row 25: Orange Red Orange Red Orange Red Red Red Black Red Yellow Yellow Yellow
Row 26: Orange Orange Orange Red Red Orange Red Red Red Red Yellow Yellow Red
Row 27: Red Orange Red Red Orange Orange Red Black Black Red Red Yellow Red
Row 28: Orange Orange Orange Red Orange Orange Red Red Black Red Red Yellow Yellow
Row 29: Red Red Orange Red Red Orange Red Red Black Red Yellow Yellow Yellow
Output:
Row 1: Orange Black Yellow Yellow
Row 2: Yellow Black Orange Black
Row 3: Orange Orange Black Yellow
Example 3
Input:
Row 1: Orange Green Green Black Black Green Green Red Red Green Purple Purple Purple Green Black Green
Row 2: Green Orange Green Black Black Green Green Red Red Green Purple Green Green Green Black Black
Row 3: Green Orange Green Green Green Green Red Red Green Green Green Purple Green Green Black Black
Row 4: Orange Orange Green Green Black Green Green Red Red Green Purple Purple Green Green Black Black
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Blue Green Green Green Red Green Green Yellow Yellow Green Gray Gray Gray Green Purple Purple
Row 7: Green Blue Green Red Green Green Green Green Yellow Green Green Gray Gray Green Green Purple
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Pink Green Brown Brown Green Orange Green Orange Green Green Green Pink Green Orange Green
Row 10: Green Pink Green Green Green Green Green Orange Green Green Pink Pink Pink Green Green Orange
Row 11: Pink Pink Green Brown Brown Green Orange Green Orange Green Pink Pink Green Green Orange Green
Row 12: Green Pink Green Green Brown Green Orange Orange Orange Green Pink Green Pink Green Orange Orange
Row 13: Pink Green Green Brown Green Green Orange Orange Green Green Pink Green Pink Green Orange Orange
Row 14: Pink Pink Green Brown Brown Green Orange Orange Green Green Pink Pink Pink Green Orange Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Orange Orange Green Green Green Green Brown Brown Brown Green Green Green Red Green Green Gray
Row 17: Orange Orange Green Green Green Green Brown Brown Brown Green Green Green Red Green Green Gray
Row 18: Orange Green Green Yellow Yellow Green Brown Brown Green Green Red Red Green Green Gray Gray
Row 19: Orange Orange Green Yellow Yellow Green Brown Brown Brown Green Red Red Red Green Green Gray
Row 20: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Gray Gray Green Blue Green Green Purple Purple Green Green Brown Brown Brown Green Yellow Yellow
Row 22: Gray Green Green Blue Green Green Purple Purple Purple Green Brown Brown Green Green Green Green
Row 23: Gray Green Green Blue Blue Green Green Purple Green Green Brown Brown Brown Green Yellow Yellow
Row 24: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Pink Green Blue Blue Green Black Black Black Green Yellow Yellow Yellow Green Yellow Yellow
Row 26: Green Green Green Green Blue Green Black Black Green Green Green Yellow Yellow Green Yellow Yellow
Row 27: Pink Pink Green Blue Green Green Black Black Black Green Yellow Yellow Yellow Green Yellow Green
Output:
Row 1: Orange Black Red Purple Black
Row 2: Blue Red Yellow Gray Purple
Row 3: Pink Brown Orange Pink Orange
Row 4: Orange Yellow Brown Red Gray
Row 5: Gray Blue Purple Brown Yellow
Row 6: Pink Blue Black Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Black Black Brown Brown Blue Blue Blue Blue Brown Blue Blue Brown Brown Brown Blue Blue Brown Blue Blue Brown Brown Blue Blue Blue Blue
Row 2: Black Black Black Brown Blue Brown Blue Blue Brown Brown Blue Brown Brown Brown Blue Blue Blue Blue Blue Brown Blue Brown Blue Blue Blue
Row 3: Brown Brown Black Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Brown Brown Blue Blue Brown Brown Brown Blue Brown Blue Blue Blue
Row 4: Black Black Black Brown Blue Blue Blue Blue Brown Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Brown Brown Blue Blue Blue
Row 5: Black Brown Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown Brown Blue Blue Blue Blue Brown Blue Brown Blue Blue Blue
Row 6: Black Black Brown Brown Brown Blue Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Black Black Brown Black Black Black Black Brown Blue Blue Blue Blue Brown Black Brown Black Brown Black Brown Blue Brown Blue Blue Brown
Row 9: Black Brown Black Brown Brown Brown Black Black Brown Blue Blue Brown Brown Brown Black Black Brown Brown Black Brown Brown Brown Blue Brown Blue
Row 10: Black Black Black Brown Black Black Black Brown Brown Blue Brown Blue Blue Brown Black Black Brown Black Black Brown Blue Blue Brown Blue Blue
Row 11: Black Black Black Brown Brown Black Brown Black Brown Blue Brown Brown Blue Brown Black Brown Brown Brown Black Brown Blue Blue Blue Blue Brown
Row 12: Black Black Brown Brown Black Brown Brown Black Brown Blue Brown Blue Blue Brown Black Black Black Black Brown Brown Blue Blue Blue Brown Blue
Row 13: Black Black Black Brown Black Black Black Black Brown Blue Brown Blue Brown Brown Black Brown Black Black Black Brown Brown Blue Blue Brown Blue
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Yellow Yellow Brown Brown Blue Blue Blue Brown Brown Black Brown Black Brown Yellow Yellow Yellow Yellow Yellow Brown Black Black Black Black Black
Row 16: Yellow Yellow Brown Brown Blue Blue Blue Blue Brown Black Black Black Black Brown Yellow Yellow Yellow Yellow Yellow Brown Black Black Brown Black Black
Row 17: Yellow Yellow Yellow Brown Brown Brown Brown Blue Brown Black Black Black Black Brown Yellow Yellow Yellow Brown Yellow Brown Brown Black Black Black Black
Row 18: Yellow Yellow Yellow Brown Brown Brown Blue Blue Brown Black Black Black Brown Brown Brown Yellow Yellow Brown Yellow Brown Brown Black Black Brown Black
Row 19: Yellow Yellow Yellow Brown Blue Brown Blue Brown Brown Black Black Black Black Brown Yellow Yellow Yellow Yellow Yellow Brown Black Brown Black Black Black
Row 20: Yellow Yellow Yellow Brown Blue Brown Brown Brown Brown Black Brown Brown Black Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Black Black Black Black
Row 21: Yellow Yellow Yellow Brown Blue Blue Blue Blue Brown Brown Black Black Black Brown Yellow Brown Yellow Brown Yellow Brown Black Black Black Black Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Pink Brown Black Black Brown Black Brown Brown Yellow Yellow Yellow Brown Black Black Black Black Brown Brown Blue Blue Blue Blue Blue
Row 24: Pink Brown Pink Brown Black Black Black Brown Brown Yellow Yellow Yellow Yellow Brown Black Black Brown Black Brown Brown Brown Brown Brown Blue Blue
Row 25: Pink Pink Pink Brown Black Black Black Black Brown Yellow Yellow Yellow Yellow Brown Black Brown Black Black Brown Brown Blue Blue Brown Blue Brown
Row 26: Pink Pink Brown Brown Black Black Black Black Brown Yellow Yellow Yellow Yellow Brown Black Brown Black Brown Black Brown Brown Brown Blue Blue Blue
Row 27: Pink Pink Brown Brown Black Black Black Black Brown Yellow Yellow Yellow Brown Brown Black Brown Black Black Black Brown Brown Blue Brown Blue Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Blue Blue Blue Blue
Black Black Blue Black Blue
Yellow Blue Black Yellow Black
Pink Black Yellow 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: Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Green Green Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Green Green Green Green 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
Row 6: 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
Row 8: 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 Gray Gray Orange Gray Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray 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 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
Row 16: 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
Row 18: 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
Row 20: 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
Row 22: 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: Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green
Row 3: Green Green Green Gray Gray Green Gray
Row 4: Green Green Green Green Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Purple Pink Pink Purple Purple Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Purple Pink Pink Purple Purple Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple 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
Row 12: 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
Row 14: 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
Row 16: 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
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Orange Orange Orange Orange Purple
Row 2: Orange Orange Orange Orange Purple
Row 3: Purple Orange Orange Purple Purple
Row 4: Purple Orange Orange Purple Purple
Row 5: Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink 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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown 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
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Output:
Row 1: Brown Brown Brown
Row 2: Blue Brown Brown
Row 3: Blue 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
Row 2: 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
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Black Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Black Black Orange Orange Yellow Yellow Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: 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>
| Yellow Yellow Yellow Black
Yellow Yellow Black Black
Yellow Yellow Yellow Black
Yellow Yellow 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 Orange Orange Orange Orange
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: 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
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Red Red Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Red Red Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Red Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange
Row 20: 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
Row 22: 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
Row 24: 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
Row 26: 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
Row 28: 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
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Red Red Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Red Red Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Red Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Orange Orange Orange
Row 20: 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
Row 22: 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
Row 24: 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
Row 26: 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
Row 28: 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
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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: Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 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 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 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 Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
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
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
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 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: Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red 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 Red Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
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
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
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple
Row 10: Green Purple Purple Purple Purple Purple
Row 11: Green Purple Purple Purple Yellow Purple
Row 12: Green Purple Purple Purple Yellow Yellow
Row 13: Green Purple Purple Yellow Yellow Purple
Row 14: Green Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple
Row 10: Green Purple Purple Purple Purple Purple
Row 11: Green Purple Purple Purple Yellow Purple
Row 12: Green Purple Purple Purple Yellow Yellow
Row 13: Green Purple Purple Yellow Yellow Purple
Row 14: Green Purple Purple Purple Purple Purple
Row 15: Green Purple Purple Purple Purple Purple
Row 16: Green Purple Purple Purple Purple Purple
Row 17: Green Purple Purple Purple Purple Purple
Row 18: Green Purple Purple Purple Purple Purple
Row 19: Green Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Brown Yellow Yellow Green Green
Row 15: Brown Brown Yellow Yellow Green Yellow
Row 16: Yellow Brown Brown Yellow Green Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow
Row 29: 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 Brown Yellow Yellow Green Green
Brown Brown Yellow Yellow Green Yellow
Yellow Brown Brown Yellow Green Yellow
Yellow Yellow Yellow Yellow Green Yellow
Yellow Yellow Yellow Yellow Green Yellow
Yellow Yellow Yellow Yellow Green 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 |
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 Black Black Brown
Row 2: Black Black Black Black
Row 3: Black Black Black Black
Row 4: Black Black Black Black
Row 5: Black Black Black Black
Row 6: Black Black Black Black
Row 7: Black Black Black Black
Row 8: Black Black Black Black
Row 9: Black Black Black Black
Row 10: Black Black Black Black
Row 11: Black Black Black Black
Row 12: Black Black Black Black
Row 13: Black Black Black Black
Row 14: Black Black Black Black
Row 15: Black Black Black Black
Row 16: Black Black Black Black
Row 17: Black Black Black Black
Row 18: Black Black Black Black
Row 19: Black Black Black Black
Row 20: Brown Black Black Brown
Output:
Row 1: Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown
Row 3: Black Brown Brown Black
Row 4: Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown
Row 6: Black Brown Brown Black
Row 7: Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown
Row 9: Black Brown Brown Black
Row 10: Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown
Row 12: Black Brown Brown Black
Row 13: Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown
Row 15: Black Brown Brown Black
Row 16: Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown
Row 18: Black Brown Brown Black
Row 19: Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Brown
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Brown Pink Pink Pink Pink Pink Pink Pink Brown
Output:
Row 1: Pink Pink Brown Pink Pink Pink Brown Pink Brown
Row 2: Pink Brown Pink Brown Pink Brown Pink Brown Pink
Row 3: Brown Pink Pink Pink Brown Pink Brown Pink Brown
Row 4: Pink Pink Pink Brown Pink Brown Pink Pink Pink
Row 5: Brown Pink Brown Pink Brown Pink Brown Pink Pink
Row 6: Pink Brown Pink Brown Pink Pink Pink Brown Pink
Row 7: Brown Pink Brown Pink Pink Pink Pink Pink Brown
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange
Row 3: Purple Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Purple Orange Orange Orange
Row 2: Orange Purple Orange Purple Orange Purple
Row 3: Purple Orange Orange Orange Purple Orange
Here is the input grid for the test example:
Input:
Row 1: Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Purple Purple Purple Purple Purple Purple Purple
Purple Purple Green Purple Purple Purple Purple Purple Purple
Purple Purple Purple Green Purple Purple Purple Purple Purple
Purple Purple Purple Purple Green Purple Purple Purple Purple
Purple Purple Purple Purple Purple Green Purple Purple Purple
Purple Purple Purple Purple Purple Purple Green Purple Purple
Purple Purple Purple Purple Purple Purple Purple Green Purple
Purple Purple Purple Purple Purple Purple Purple Purple Green
Purple Purple Purple Purple Purple Purple Purple Green Purple
Purple Purple Purple Purple Purple Purple Green Purple Purple
Purple Purple Purple Purple Purple Green Purple Purple Purple
Purple Purple Purple Purple Green Purple Purple Purple Purple
Purple Purple Purple Green Purple Purple Purple Purple Purple
Purple Purple Green Purple Purple Purple Purple Purple Purple
Purple Green Purple Purple Purple Purple Purple Purple Purple
Green Purple Purple Purple Purple Purple Purple Purple Purple
Purple Green Purple Purple Purple Purple Purple Purple Purple
Purple Purple Green Purple Purple Purple Purple Purple Purple
Purple Purple Purple Green Purple Purple Purple Purple Purple
Purple Purple Purple Purple Green Purple Purple Purple Purple
Purple Purple Purple Purple Purple Green Purple Purple Purple
Purple Purple Purple Purple Purple Purple Green Purple Purple
Purple Purple Purple Purple Purple Purple Purple 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: Blue Blue 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 Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Black Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink 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 Pink 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 Pink 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 Pink Blue Brown Brown Brown Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Purple Pink Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Black Brown Brown Brown Blue Blue Gray Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown 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 Brown Brown Brown 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 Brown Brown Brown 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 Brown Brown Brown 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
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 Black Purple 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 Black Purple Blue Blue Blue Blue Blue Red Red Red Blue Purple Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Red Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Purple Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Red Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Purple Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Purple Pink Blue Brown Brown Brown Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue Blue Purple Pink Blue Gray Gray Gray Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Black Black Black Brown Brown Brown Blue Blue Gray Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Black Black Black Brown Brown Brown Blue Blue Gray Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Black Black Black Brown Brown Brown Blue Blue Gray Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Black Black Black Brown Brown Brown Blue Blue Gray Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Black Black Black Brown Brown Brown Blue Gray Blue Blue Brown 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
Example 2
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 Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Pink Pink Pink Pink Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Pink Pink Pink Pink 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: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Yellow Red Red Blue Blue Blue Green Brown Blue Blue
Row 14: Blue Blue Blue Blue Red Blue Red Blue Yellow Yellow Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow 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
Output:
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 Black Black Black Black Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Black Black Black Black Blue Blue Blue Blue Blue
Row 6: Pink Pink Pink Pink Red Red Red Red Blue Blue Blue Blue Blue
Row 7: Pink Pink Pink Pink Red Red Red Red 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: Blue Blue Blue Blue Green Blue Green Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Green Green Blue Blue Green Green Brown Brown Blue
Row 13: Blue Blue Yellow Yellow Red Red Blue Blue Green Green Brown Brown Blue
Row 14: Blue Yellow Blue Yellow Red Blue Red Blue Yellow Yellow Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow 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
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Red Red Gray Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Red Red Red Red Red Green Red Red Black Black Green Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Black Red Red Red Red Red Red Green Green Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red Red Red Red Red Green Green Red Red Red Red Red Red
Row 6: Red Red Red Red Orange Brown Red Red Red Red Red Pink Pink Red Red Red Red Red Red Red Purple Brown Red Red Red Pink Red Red Red
Row 7: Red Red Red Red Red Green Green Red Red Red Red Pink Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red
Row 8: Red Red Red Red Red Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red
Row 9: Blue Blue Red Red Red Green Green 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 Blue Yellow Red Red Green Green 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 Gray Pink Red Red Red Red Red Red Black Black Green 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 Black Red Black Red Red Red Red Red Red Gray Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Yellow Red Red Red Red Black Black Black Red Red Red Red Red Red Red Orange Orange Orange Red Red Red Pink Red Red Red Red
Row 15: Red Red Red Yellow Red Red Red Red Red Black Red Red Red Red Red Red Red Red Orange Red Orange Orange Red Purple Purple Yellow Red Red Red
Row 16: Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Red Red Purple Purple Red Red Red Red
Row 17: Red Red Yellow Yellow Red Red Red Red Red Red Pink Pink Pink Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Black Yellow Yellow Red Red Red Red Black Red Red Red Purple Red Red Red Red Orange Orange Red Red Red Red Red Red Red Red Red Red
Row 19: Red Pink Red Red Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Orange Orange Orange Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Yellow Yellow Yellow Red Red Red Red Red Red Red Red Orange Orange Orange Red Red Red Red Red Yellow Yellow Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Red Red Red Red Yellow Yellow Yellow Pink Red Red
Row 22: Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Orange Red Orange Gray Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Pink Pink Red Red Red Gray Red Red Red Red Red Red Red Green Pink Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Pink Red Red Red Red Red Green Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Orange Pink Pink Pink Pink Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 26: Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Pink Red
Row 28: Red Red Red Red Red Red Red Yellow Green Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red
Row 29: Red Red Red Red Red Red Red Red Gray Red Red Red Gray Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 30: Red Red Red Red Red Red Red Red Gray Red Red Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Green Red Gray Gray Red Red Red
Row 3: Red Red Red Orange Orange Brown Brown Red Red Red Red Red Red Red Purple Purple Red Red Red Red Red Green Red Red Black Black Green Green Red
Row 4: Red Red Red Orange Orange Brown Brown Red Red Brown Brown Red Pink Pink Black Black Red Red Red Red Red Green Green Red Red Red Red Red Red
Row 5: Red Red Red Orange Orange Brown Brown Red Red Brown Brown Red Red Red Red Red Red Red Red Red Red Green Green Red Red Pink Red Red Red
Row 6: Red Red Red Orange Orange Brown Brown Red Red Red Red Pink Pink Red Red Red Red Red Red Purple Purple Brown Brown Red Red Pink Red Red Red
Row 7: Red Red Red Red Red Green Green Red Red Red Red Pink Pink Red Red Red Red Red Red Purple Purple Brown Brown Red Red Red Orange Red Red
Row 8: Red Red Red Red Red Green Green Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Brown Red Red Red Red Orange Red Red
Row 9: Blue Blue Yellow Yellow Red Green Green Red Red Red Red Red Red Red Red Gray Gray Red Red Purple Purple Brown Brown Red Red Red Red Red Red
Row 10: Red Blue Yellow Red Red Green Green Red Red Red Red Red Red Red Gray Gray Red Gray Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Gray Pink Red Red Red Red Red Red Black Black Green Green Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red Red
Row 12: Gray Gray Pink Pink Red Red Red Red Black Red Black Green Red Green Red Red Red Gray Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Black Black Green Green Red Red Red Red Red Orange Red Red Red Red Pink Pink Red Red Red Red
Row 14: Black Red Red Yellow Red Red Red Red Black Black Black Green Green Green Red Red Red Red Orange Orange Orange Red Red Pink Pink Red Red Red Red
Row 15: Black Red Red Yellow Red Red Red Red Red Black Red Red Green Red Red Red Red Red Orange Red Orange Orange Red Purple Purple Yellow Yellow Red Red
Row 16: Black Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Red Red Purple Purple Yellow Yellow Red Red
Row 17: Black Black Yellow Yellow Red Black Black Black Red Red Pink Pink Pink Blue Blue Blue Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Black Black Yellow Yellow Red Black Red Black Black Red Purple Purple Purple Red Red Red Red Orange Orange Gray Gray Red Red Red Red Red Red Red Red
Row 19: Pink Pink Red Red Red Yellow Red Yellow Yellow Red Red Red Red Red Red Red Orange Orange Orange Gray Gray Gray Red Red Red Red Red Red Red
Row 20: Pink Pink Red Red Red Yellow Yellow Yellow Red Red Red Red Red Red Red Red Orange Orange Orange Gray Gray Gray Red Red Yellow Yellow Pink Pink Red
Row 21: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Gray Gray Gray Red Yellow Yellow Yellow Pink Pink Pink
Row 22: Pink Red Red Red Orange Pink Red Red Red Red Gray Red Red Red Red Red Orange Red Orange Gray Red Gray Red Red Red Red Red Red Red
Row 23: Pink Red Red Orange Orange Pink Pink Red Gray Gray Gray Red Red Red Red Red Green Red Green Pink Red Pink Red Red Red Red Red Red Red
Row 24: Red Red Red Red Orange Pink Red Red Red Red Red Green Green Green Red Red Green Green Green Pink Pink Pink Red Red Red Red Red Red Red
Row 25: Red Orange Orange Orange Orange Pink Pink Pink Pink Red Red Green Red Red Red Red Green Green Green Pink Pink Pink Red Red Red Red Red Red Red
Row 26: Red Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Green Green Green Pink Pink Pink Red Red Red Red Red Red Red
Row 27: Red Red Red Red Yellow Red Red Yellow Green Red Red Red Red Red Yellow Red Red Green Green Pink Pink Red Red Red Red Red Blue Pink Red
Row 28: Red Red Red Yellow Yellow Red Red Yellow Green Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Blue Blue Pink Pink
Row 29: Red Red Red Red Yellow Red Red Red Gray Red Red Red Gray Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 30: Red Red Red Red Red Red Red Red Gray Red Red Gray Red Red Black 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: Pink Green Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Pink Pink
Row 3: Pink Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Red Red Pink Pink
Row 4: Pink Pink Green Green Blue Pink Pink Pink Pink Pink Pink Pink Purple Red Red Pink Pink Pink Pink
Row 5: Pink Pink Pink Yellow Purple 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
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Black Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Orange Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Orange Blue Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Black Pink Pink Pink Gray Orange Pink Pink Pink Pink Pink Brown Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink
Row 15: 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 Green Pink Green Blue Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Green Green Pink Pink Blue Blue Pink Pink Purple Pink Pink Purple Red Pink Pink Red Pink Pink
Pink Pink Green Green Blue Blue Pink Pink Pink Purple Purple Pink Purple Red Pink Red Red Pink Pink
Pink Pink Green Green Blue Blue Pink Pink Pink Pink Pink Purple Purple Red Red Pink Pink Pink Pink
Pink Pink Yellow Yellow Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Yellow Yellow Purple Purple Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink
Pink Yellow Yellow Pink Pink Purple Purple Pink Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink
Pink Yellow Pink Yellow Purple Pink Purple Pink Pink Pink Pink Black Black Black Black Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink
Pink Pink Pink Orange Orange Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Orange Blue Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Orange Blue Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Black Pink Pink Pink Gray Orange Pink Pink Pink Pink Brown Brown Pink Pink Pink
Pink Pink Pink Pink Black Pink Pink Pink Gray Orange Pink Pink Pink Pink Red Red Pink Pink Pink
Pink Pink Pink Black Black 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 Pink Blue Red Black Gray Orange Blue Gray Red Gray Gray Red Gray Blue Orange Gray Black Red Blue Pink Brown
Row 2: Pink Orange Orange Pink Brown Blue Gray Blue Brown Blue Pink Pink Blue Brown Blue Gray Blue Brown Pink Orange Orange Pink
Row 3: Blue Orange Gray Pink Pink Red Gray Gray Purple Orange Gray Gray Orange Purple Gray Gray Red Pink Pink Gray Orange Blue
Row 4: Red Pink Pink Purple Red Gray Red Purple Blue Red Purple Purple Red Blue Purple Red Gray Red Purple Pink Pink Red
Row 5: Black Brown Pink Red Gray Pink Red Black Red Black Black Black Black Red Black Red Pink Gray Red Pink Brown Black
Row 6: Gray Blue Red Gray Pink Blue Black Gray Red Purple Gray Gray Purple Red Gray Black Blue Pink Gray Red Blue Gray
Row 7: Orange Gray Gray Red Red Black Purple Brown Pink Red Red Red Red Pink Brown Purple Black Red Red Gray Gray Orange
Row 8: Yellow Yellow Yellow Yellow Black Gray Brown Purple Orange Gray Red Red Gray Orange Purple Brown Gray Black Purple Gray Blue Blue
Row 9: Yellow Yellow Yellow Yellow Red Red Pink Orange Gray Blue Gray Gray Blue Gray Orange Pink Red Red Blue Purple Brown Gray
Row 10: Yellow Yellow Yellow Yellow Black Purple Red Gray Blue Gray Gray Gray Gray Blue Gray Red Purple Black Red Orange Blue Red
Row 11: Gray Pink Gray Purple Black Gray Red Red Gray Gray Gray Gray Gray Gray Red Red Gray Black Purple Gray Pink Gray
Row 12: Gray Pink Gray Purple Black Gray Red Red Gray Gray Gray Gray Gray Gray Red Red Gray Black Purple Gray Pink Gray
Row 13: Red Blue Orange Red Black Purple Red Gray Blue Gray Gray Gray Gray Blue Gray Red Purple Black Red Orange Blue Red
Row 14: Gray Brown Purple Blue Red Red Pink Orange Gray Blue Gray Gray Blue Gray Orange Pink Red Red Blue Purple Brown Gray
Row 15: Blue Blue Gray Purple Black Gray Brown Yellow Yellow Yellow Yellow Red Gray Orange Purple Brown Gray Black Purple Gray Blue Blue
Row 16: Orange Gray Gray Red Red Black Purple Brown Pink Red Red Red Red Pink Brown Purple Black Red Red Gray Gray Orange
Row 17: Gray Blue Red Gray Pink Blue Black Gray Red Purple Gray Gray Purple Red Gray Black Blue Pink Gray Red Blue Gray
Row 18: Black Brown Pink Red Gray Pink Red Black Red Black Black Black Black Red Black Red Pink Gray Red Pink Brown Black
Row 19: Red Pink Pink Purple Red Gray Red Purple Blue Red Purple Purple Red Blue Purple Red Gray Red Purple Pink Pink Red
Row 20: Blue Orange Gray Pink Pink Red Gray Gray Purple Orange Gray Gray Orange Purple Gray Gray Red Pink Pink Gray Orange Blue
Row 21: Pink Orange Orange Pink Brown Blue Gray Blue Brown Blue Pink Pink Blue Brown Blue Gray Blue Brown Pink Orange Orange Pink
Row 22: Brown Pink Blue Red Black Gray Orange Blue Gray Red Gray Gray Red Gray Blue Orange Gray Black Red Blue Pink Brown
Output:
Row 1: Brown Pink Blue Red Black Gray Orange Blue Gray Red Gray Gray Red Gray Blue Orange Gray Black Red Blue Pink Brown
Row 2: Pink Orange Orange Pink Brown Blue Gray Blue Brown Blue Pink Pink Blue Brown Blue Gray Blue Brown Pink Orange Orange Pink
Row 3: Blue Orange Gray Pink Pink Red Gray Gray Purple Orange Gray Gray Orange Purple Gray Gray Red Pink Pink Gray Orange Blue
Row 4: Red Pink Pink Purple Red Gray Red Purple Blue Red Purple Purple Red Blue Purple Red Gray Red Purple Pink Pink Red
Row 5: Black Brown Pink Red Gray Pink Red Black Red Black Black Black Black Red Black Red Pink Gray Red Pink Brown Black
Row 6: Gray Blue Red Gray Pink Blue Black Gray Red Purple Gray Gray Purple Red Gray Black Blue Pink Gray Red Blue Gray
Row 7: Orange Gray Gray Red Red Black Purple Brown Pink Red Red Red Red Pink Brown Purple Black Red Red Gray Gray Orange
Row 8: Blue Blue Gray Purple Black Gray Brown Purple Orange Gray Red Red Gray Orange Purple Brown Gray Black Purple Gray Blue Blue
Row 9: Gray Brown Purple Blue Red Red Pink Orange Gray Blue Gray Gray Blue Gray Orange Pink Red Red Blue Purple Brown Gray
Row 10: Red Blue Orange Red Black Purple Red Gray Blue Gray Gray Gray Gray Blue Gray Red Purple Black Red Orange Blue Red
Row 11: Gray Pink Gray Purple Black Gray Red Red Gray Gray Gray Gray Gray Gray Red Red Gray Black Purple Gray Pink Gray
Row 12: Gray Pink Gray Purple Black Gray Red Red Gray Gray Gray Gray Gray Gray Red Red Gray Black Purple Gray Pink Gray
Row 13: Red Blue Orange Red Black Purple Red Gray Blue Gray Gray Gray Gray Blue Gray Red Purple Black Red Orange Blue Red
Row 14: Gray Brown Purple Blue Red Red Pink Orange Gray Blue Gray Gray Blue Gray Orange Pink Red Red Blue Purple Brown Gray
Row 15: Blue Blue Gray Purple Black Gray Brown Purple Orange Gray Red Red Gray Orange Purple Brown Gray Black Purple Gray Blue Blue
Row 16: Orange Gray Gray Red Red Black Purple Brown Pink Red Red Red Red Pink Brown Purple Black Red Red Gray Gray Orange
Row 17: Gray Blue Red Gray Pink Blue Black Gray Red Purple Gray Gray Purple Red Gray Black Blue Pink Gray Red Blue Gray
Row 18: Black Brown Pink Red Gray Pink Red Black Red Black Black Black Black Red Black Red Pink Gray Red Pink Brown Black
Row 19: Red Pink Pink Purple Red Gray Red Purple Blue Red Purple Purple Red Blue Purple Red Gray Red Purple Pink Pink Red
Row 20: Blue Orange Gray Pink Pink Red Gray Gray Purple Orange Gray Gray Orange Purple Gray Gray Red Pink Pink Gray Orange Blue
Row 21: Pink Orange Orange Pink Brown Blue Gray Blue Brown Blue Pink Pink Blue Brown Blue Gray Blue Brown Pink Orange Orange Pink
Row 22: Brown Pink Blue Red Black Gray Orange Blue Gray Red Gray Gray Red Gray Blue Orange Gray Black Red Blue Pink Brown
Example 2
Input:
Row 1: Blue Pink Blue Green Red Brown Pink Pink Red Red Red Red Red Red Red Red Red Red Pink Pink Brown Red Green Blue Pink Blue
Row 2: Pink Gray Brown Pink Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Brown Gray Pink
Row 3: Blue Brown Red Orange Green Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Green Orange Red Brown Blue
Row 4: Green Pink Orange Purple Orange Brown Orange Blue Red Red Red Red Red Red Red Red Red Red Blue Orange Brown Orange Purple Orange Pink Green
Row 5: Red Orange Green Orange Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Orange Green Orange Red
Row 6: Brown Red Orange Brown Brown Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Brown Brown Orange Red Brown
Row 7: Pink Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Pink
Row 8: Pink Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Pink
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Pink Red Red Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Pink
Row 20: Pink Red Red Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Pink
Row 21: Brown Red Orange Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red Red Red Red Pink Brown Brown Orange Red Brown
Row 22: Red Orange Green Orange Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Orange Green Orange Red
Row 23: Green Pink Orange Purple Orange Brown Orange Blue Red Red Red Red Red Red Red Red Red Red Blue Orange Brown Orange Purple Orange Pink Green
Row 24: Blue Brown Red Orange Green Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Green Orange Red Brown Blue
Row 25: Pink Gray Brown Pink Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Brown Gray Pink
Row 26: Blue Pink Blue Green Red Brown Pink Pink Red Red Red Red Red Red Red Red Red Red Pink Pink Brown Red Green Blue Pink Blue
Output:
Row 1: Blue Pink Blue Green Red Brown Pink Pink Red Red Red Red Red Red Red Red Red Red Pink Pink Brown Red Green Blue Pink Blue
Row 2: Pink Gray Brown Pink Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Brown Gray Pink
Row 3: Blue Brown Red Orange Green Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Green Orange Red Brown Blue
Row 4: Green Pink Orange Purple Orange Brown Orange Blue Red Red Red Red Red Red Red Red Red Red Blue Orange Brown Orange Purple Orange Pink Green
Row 5: Red Orange Green Orange Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Orange Green Orange Red
Row 6: Brown Red Orange Brown Brown Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Brown Brown Orange Red Brown
Row 7: Pink Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Pink
Row 8: Pink Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Pink
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Pink Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Pink
Row 20: Pink Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Pink
Row 21: Brown Red Orange Brown Brown Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink Brown Brown Orange Red Brown
Row 22: Red Orange Green Orange Red Brown Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Orange Green Orange Red
Row 23: Green Pink Orange Purple Orange Brown Orange Blue Red Red Red Red Red Red Red Red Red Red Blue Orange Brown Orange Purple Orange Pink Green
Row 24: Blue Brown Red Orange Green Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Green Orange Red Brown Blue
Row 25: Pink Gray Brown Pink Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink Brown Gray Pink
Row 26: Blue Pink Blue Green Red Brown Pink Pink Red Red Red Red Red Red Red Red Red Red Pink Pink Brown Red Green Blue Pink Blue
Example 3
Input:
Row 1: Red Gray Gray Black Blue Black Gray Gray Black Blue Black Gray Gray Red
Row 2: Yellow Red Black Red Green Gray Gray Gray Gray Green Red Black Red Gray
Row 3: Yellow Black Brown Brown Gray Purple Gray Gray Purple Gray Brown Brown Black Gray
Row 4: Yellow Red Brown Brown Gray Gray Gray Gray Gray Gray Brown Brown Red Black
Row 5: Yellow Green Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Green Blue
Row 6: Yellow Gray Purple Gray Gray Red Green Green Red Gray Gray Purple Gray Black
Row 7: Yellow Gray Gray Gray Gray Green Gray Gray Green Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Green Gray Gray Green Gray Gray Gray Gray Gray
Row 9: Black Gray Purple Gray Gray Red Yellow Green Red Gray Gray Purple Gray Black
Row 10: Blue Green Gray Gray Purple Gray Yellow Gray Gray Purple Gray Gray Green Blue
Row 11: Black Red Brown Brown Gray Gray Gray Gray Gray Gray Brown Brown Red Black
Row 12: Gray Black Brown Brown Gray Purple Gray Gray Purple Gray Brown Brown Black Gray
Row 13: Gray Red Black Red Green Gray Gray Gray Gray Green Red Black Red Gray
Row 14: Red Gray Gray Black Blue Black Gray Gray Black Blue Black Gray Gray Red
Output:
Row 1: Red Gray Gray Black Blue Black Gray Gray Black Blue Black Gray Gray Red
Row 2: Gray Red Black Red Green Gray Gray Gray Gray Green Red Black Red Gray
Row 3: Gray Black Brown Brown Gray Purple Gray Gray Purple Gray Brown Brown Black Gray
Row 4: Black Red Brown Brown Gray Gray Gray Gray Gray Gray Brown Brown Red Black
Row 5: Blue Green Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Green Blue
Row 6: Black Gray Purple Gray Gray Red Green Green Red Gray Gray Purple Gray Black
Row 7: Gray Gray Gray Gray Gray Green Gray Gray Green Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Green Gray Gray Green Gray Gray Gray Gray Gray
Row 9: Black Gray Purple Gray Gray Red Green Green Red Gray Gray Purple Gray Black
Row 10: Blue Green Gray Gray Purple Gray Gray Gray Gray Purple Gray Gray Green Blue
Row 11: Black Red Brown Brown Gray Gray Gray Gray Gray Gray Brown Brown Red Black
Row 12: Gray Black Brown Brown Gray Purple Gray Gray Purple Gray Brown Brown Black Gray
Row 13: Gray Red Black Red Green Gray Gray Gray Gray Green Red Black Red Gray
Row 14: Red Gray Gray Black Blue Black Gray Gray Black Blue Black Gray Gray Red
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
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
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
Row 4: Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Brown Green Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Brown Gray Brown Green Pink Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Brown Gray Gray Gray
Row 8: Gray Gray Gray Gray Green Green Pink Gray Pink Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Row 19: Gray Gray Gray Gray Green Green Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Green Green Gray Gray Gray Gray
Row 20: Gray Gray Gray Brown Gray Brown Green Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Green Brown Gray Brown Gray Gray Gray
Row 21: Gray Gray Gray Gray Gray Gray Brown Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Brown Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown 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 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Brown Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Brown Gray Gray Gray Gray Gray Gray
Gray Gray Gray Brown Gray Brown Green Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Green Brown Gray Brown Gray Gray Gray
Gray Gray Gray Gray Green Green Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Green Green Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Green Green Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Pink Green Green Gray Gray Gray Gray
Gray Gray Gray Brown Gray Brown Green Pink Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Green Brown Gray Brown Gray Gray Gray
Gray Gray Gray Gray Gray Gray Brown Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Brown Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray 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: 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
Row 3: 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
Row 5: 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
Row 7: 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
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Black Brown Black Black Orange Brown Black Black Brown Brown Brown Orange Orange Brown Brown Orange Brown Brown Black
Row 12: Black Black Orange Brown Black Black Brown Brown Black Black Brown Brown Brown Brown Black Black Brown Brown Black
Row 13: Black Brown Orange Brown Orange Orange Black Black Black Brown Brown Black Brown Orange Black Orange Black Black Brown
Row 14: Black Black Brown Black Orange Black Orange Black Black Brown Orange Orange Black Orange Orange Orange Brown Black Black
Row 15: Brown Black Brown Black Black Brown Brown Black Orange Brown Orange Orange Brown Brown Black Orange Orange Brown Orange
Row 16: Brown Brown Black Brown Black Orange Black Brown Brown Black Black Orange Orange Brown Black Brown Orange Black Black
Row 17: Brown Orange Brown Black Brown Brown Orange Black Black Orange Orange Orange Brown Orange Brown Brown Brown Brown Brown
Row 18: Orange Black Black Brown Black Black Black Brown Orange Brown Orange Black Brown Black Orange Orange Brown Orange Orange
Row 19: Orange Orange Brown Black Brown Brown Black Black Orange Brown Brown Orange Orange Brown Black Brown Black Black Brown
Output:
Row 1: Orange Orange Brown Black Brown Brown Black Black Orange Brown Brown Orange Orange Brown Black Brown Black Black Brown
Row 2: Orange Black Black Brown Black Black Black Brown Orange Brown Orange Black Brown Black Orange Orange Brown Orange Orange
Row 3: Brown Orange Brown Black Brown Brown Orange Black Black Orange Orange Orange Brown Orange Brown Brown Brown Brown Brown
Row 4: Brown Brown Black Brown Black Orange Black Brown Brown Black Black Orange Orange Brown Black Brown Orange Black Black
Row 5: Brown Black Brown Black Black Brown Brown Black Orange Brown Orange Orange Brown Brown Black Orange Orange Brown Orange
Row 6: Black Black Brown Black Orange Black Orange Black Black Brown Orange Orange Black Orange Orange Orange Brown Black Black
Row 7: Black Brown Orange Brown Orange Orange Black Black Black Brown Brown Black Brown Orange Black Orange Black Black Brown
Row 8: Black Black Orange Brown Black Black Brown Brown Black Black Brown Brown Brown Brown Black Black Brown Brown Black
Row 9: Black Brown Black Black Orange Brown Black Black Brown Brown Brown Orange Orange Brown Brown Orange Brown Brown Black
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: 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
Row 13: 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 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 Orange
Row 16: 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
Row 18: 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
Example 2
Input:
Row 1: Gray Brown Purple Orange Orange Gray Purple Orange Orange Gray Orange Orange Brown Brown Gray Brown Orange Gray Black Brown Black Orange Gray
Row 2: Brown Orange Brown Brown Brown Gray Gray Orange Gray Black Brown Gray Orange Brown Orange Black Purple Orange Gray Gray Brown Black Orange
Row 3: Orange Gray Purple Orange Orange Gray Orange Orange Purple Orange Orange Purple Orange Gray Gray Orange Purple Purple Brown Brown Gray Brown Purple
Row 4: Brown Brown Gray Orange Black Orange Orange Brown Purple Black Orange Purple Gray Orange Orange Orange Orange Orange Black Purple Brown Purple Gray
Row 5: Brown Black Orange Orange Purple Purple Brown Gray Brown Orange Gray Black Brown Black Gray Orange Purple Purple Orange Orange Black Brown Black
Row 6: Purple Orange Purple Orange Orange Black Orange Brown Gray Orange Orange Orange Gray Brown Orange Purple Orange Gray Purple Orange Black Black Black
Row 7: Orange Brown Orange Orange Orange Brown Orange Orange Purple Gray Orange Gray Brown Purple Purple Black Orange Orange Gray Black Brown Gray Gray
Row 8: Purple Orange Orange Gray Orange Black Gray Black Gray Orange Brown Orange Orange Brown Gray Gray Orange Orange Purple Gray Black Black Orange
Row 9: Orange Orange Orange Brown Gray Black Black Orange Orange Brown Brown Orange Orange Orange Brown Orange Purple Orange Orange Orange Purple Gray Orange
Row 10: Orange Gray Orange Gray Orange Orange Orange Brown Gray Black Orange Purple Purple Orange Gray Purple Black Orange Orange Orange Orange Purple Brown
Row 11: Gray Black Orange Brown Black Orange Orange Purple Gray Gray Orange Brown Orange Purple Brown Orange Gray Black Orange Orange Orange Orange Orange
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: 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 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 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
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
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
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
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
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
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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
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
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
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
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
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: 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
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
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: Gray Black Orange Brown Black Orange Orange Purple Gray Gray Orange Brown Orange Purple Brown Orange Gray Black Orange Orange Orange Orange Orange
Row 14: Orange Gray Orange Gray Orange Orange Orange Brown Gray Black Orange Purple Purple Orange Gray Purple Black Orange Orange Orange Orange Purple Brown
Row 15: Orange Orange Orange Brown Gray Black Black Orange Orange Brown Brown Orange Orange Orange Brown Orange Purple Orange Orange Orange Purple Gray Orange
Row 16: Purple Orange Orange Gray Orange Black Gray Black Gray Orange Brown Orange Orange Brown Gray Gray Orange Orange Purple Gray Black Black Orange
Row 17: Orange Brown Orange Orange Orange Brown Orange Orange Purple Gray Orange Gray Brown Purple Purple Black Orange Orange Gray Black Brown Gray Gray
Row 18: Purple Orange Purple Orange Orange Black Orange Brown Gray Orange Orange Orange Gray Brown Orange Purple Orange Gray Purple Orange Black Black Black
Row 19: Brown Black Orange Orange Purple Purple Brown Gray Brown Orange Gray Black Brown Black Gray Orange Purple Purple Orange Orange Black Brown Black
Row 20: Brown Brown Gray Orange Black Orange Orange Brown Purple Black Orange Purple Gray Orange Orange Orange Orange Orange Black Purple Brown Purple Gray
Row 21: Orange Gray Purple Orange Orange Gray Orange Orange Purple Orange Orange Purple Orange Gray Gray Orange Purple Purple Brown Brown Gray Brown Purple
Row 22: Brown Orange Brown Brown Brown Gray Gray Orange Gray Black Brown Gray Orange Brown Orange Black Purple Orange Gray Gray Brown Black Orange
Row 23: Gray Brown Purple Orange Orange Gray Purple Orange Orange Gray Orange Orange Brown Brown Gray Brown Orange Gray Black Brown Black Orange Gray
Example 3
Input:
Row 1: 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
Row 2: Brown Red 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: Orange Orange Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Purple Purple Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Brown Black Gray Pink Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Orange Gray Brown Black Orange Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Orange Purple Yellow Black Black Blue Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Orange Gray Purple Orange Brown Black Orange Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Pink Gray Orange Black Pink Black Purple Pink Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Brown Gray Purple Orange Brown Brown Yellow Gray Brown Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Gray Gray Orange Black Orange Black Pink Brown Black Brown Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Pink Brown Purple Gray Purple Purple Blue Black Black Pink Black Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Pink Black Black Orange Pink Purple Pink Purple Black Pink Brown Gray Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Orange Yellow Black Purple Yellow Brown Pink Black Brown Brown Orange Gray Pink Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Gray Purple Orange Purple Gray Purple Brown Pink Pink Brown Blue Gray Brown Black Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Blue Black Gray Purple Blue Blue Brown Pink Purple Orange Brown Purple Pink Black Pink Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Gray Pink Black Orange Pink Blue Purple Purple Orange Pink Blue Orange Pink Pink Orange Pink Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Gray Blue Orange Orange Brown Gray Gray Black Pink Purple Gray Pink Brown Gray Brown Brown Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Gray Black Pink Pink Black Orange Yellow Purple Blue Gray Orange Brown Gray Black Orange Brown Pink Orange Red Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Brown Purple Gray Pink Brown Gray Brown Black Brown Black Blue Purple Pink Black Yellow Purple Blue Purple Black Red Yellow Yellow Yellow Yellow Yellow
Row 21: Black Gray Brown Orange Brown Pink Blue Blue Black Black Blue Gray Orange Brown Blue Pink Pink Orange Pink Blue Red Yellow Yellow Yellow Yellow
Row 22: Gray Gray Black Brown Black Blue Black Purple Purple Black Gray Pink Purple Black Brown Pink Pink Pink Purple Gray Purple Red Yellow Yellow Yellow
Row 23: Orange Brown Brown Pink Orange Brown Orange Gray Brown Purple Gray Brown Orange Black Black Brown Pink Black Pink Blue Yellow Gray Red Yellow Yellow
Row 24: Pink Pink Pink Brown Pink Gray Brown Pink Blue Brown Gray Orange Black Brown Orange Blue Orange Black Blue Orange Pink Black Orange Red Yellow
Row 25: Gray Yellow Orange Gray Pink Gray Gray Pink Purple Blue Black Gray Orange Blue Purple Yellow Pink Purple Brown Pink Purple Pink Brown Gray Red
Output:
Row 1: Red Brown Orange Purple Brown Orange Orange Orange Pink Brown Gray Pink Pink Orange Gray Blue Gray Yellow Gray Brown Black Gray Orange Pink Gray
Row 2: Yellow Red Orange Purple Black Gray Purple Gray Gray Gray Gray Brown Black Yellow Purple Black Pink Gray Black Purple Gray Gray Brown Pink Yellow
Row 3: Yellow Yellow Red Blue Gray Brown Yellow Purple Orange Purple Orange Purple Black Black Orange Gray Black Blue Pink Gray Brown Black Brown Pink Orange
Row 4: Yellow Yellow Yellow Red Pink Black Black Orange Black Orange Black Gray Orange Purple Purple Purple Orange Orange Pink Pink Orange Brown Pink Brown Gray
Row 5: Yellow Yellow Yellow Yellow Red Orange Black Brown Pink Brown Orange Purple Pink Yellow Gray Blue Pink Orange Black Brown Brown Black Orange Pink Pink
Row 6: Yellow Yellow Yellow Yellow Yellow Red Blue Black Black Brown Black Purple Purple Brown Purple Blue Blue Brown Orange Gray Pink Blue Brown Gray Gray
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Red Orange Purple Yellow Pink Blue Pink Pink Brown Brown Purple Gray Yellow Brown Blue Black Orange Brown Gray
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Pink Gray Brown Black Purple Black Pink Pink Purple Gray Purple Black Blue Purple Gray Pink Pink
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Black Black Black Brown Pink Purple Orange Black Blue Brown Black Purple Brown Blue Purple
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Pink Pink Brown Brown Orange Pink Pink Gray Black Black Black Purple Brown Blue
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black Brown Orange Blue Brown Blue Purple Orange Blue Blue Gray Gray Gray Black
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Gray Gray Gray Purple Orange Gray Brown Purple Gray Pink Brown Orange Gray
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Pink Brown Pink Pink Pink Gray Pink Orange Purple Orange Black Orange
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black Black Pink Brown Black Black Brown Black Black Brown Blue
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Pink Orange Gray Orange Yellow Blue Brown Black Orange Purple
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Pink Brown Brown Purple Pink Pink Brown Blue Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Brown Pink Blue Pink Pink Pink Orange Pink
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Orange Purple Orange Pink Black Black Purple
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Black Pink Purple Pink Blue Brown
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Blue Gray Blue Orange Pink
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Purple Yellow Pink Purple
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Gray Black Pink
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Orange Brown
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 Red 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 Red
Here is the input grid for the test example:
Input:
Row 1: Blue Yellow Black Black Blue Yellow Blue Gray Black Blue Gray Yellow Black Gray Gray Blue Gray Yellow Black Yellow Yellow
Row 2: Blue Blue Gray Blue Yellow Blue Black Gray Blue Blue Black Black Yellow Black Yellow Black Yellow Blue Blue Blue Black
Row 3: Gray Blue Blue Yellow Black Blue Blue Blue Black Blue Yellow Black Gray Black Blue Blue Blue Black Gray Black Black
Row 4: Yellow Yellow Yellow Gray Black Gray Blue Blue Gray Gray Blue Gray Blue Black Black Blue Gray Blue Yellow Gray Black
Row 5: Yellow Gray Black Blue Yellow Black Yellow Blue Blue Gray Black Gray Gray Black Yellow Blue Blue Black Gray Black Yellow
Row 6: Blue Black Blue Blue Black Blue Blue Gray Gray Blue Blue Yellow Gray Black Blue Blue Blue Black Blue Black Blue
Row 7: Blue Blue Yellow Black Blue Blue Blue Black Black Blue Blue Blue Black Blue Blue Yellow Black Yellow Blue Gray Yellow
Row 8: Yellow Black Yellow Gray Yellow Blue Blue Blue Blue Blue Yellow Blue Blue Black Gray Yellow Blue Yellow Black Blue Blue
Row 9: Black Blue Blue Blue Blue Black Gray Blue Blue Blue Blue Blue Black Blue Gray Black Gray Gray Gray Black Blue
Row 10: Gray Black Blue Yellow Blue Yellow Gray Gray Blue Black Blue Gray Blue Yellow Blue Blue Blue Yellow Gray 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
Row 12: 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
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
Row 18: 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
Row 20: 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
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
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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 Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Gray Black Blue Yellow Blue Yellow Gray Gray Blue Black Blue Gray Blue Yellow Blue Blue Blue Yellow Gray Blue Blue
Black Blue Blue Blue Blue Black Gray Blue Blue Blue Blue Blue Black Blue Gray Black Gray Gray Gray Black Blue
Yellow Black Yellow Gray Yellow Blue Blue Blue Blue Blue Yellow Blue Blue Black Gray Yellow Blue Yellow Black Blue Blue
Blue Blue Yellow Black Blue Blue Blue Black Black Blue Blue Blue Black Blue Blue Yellow Black Yellow Blue Gray Yellow
Blue Black Blue Blue Black Blue Blue Gray Gray Blue Blue Yellow Gray Black Blue Blue Blue Black Blue Black Blue
Yellow Gray Black Blue Yellow Black Yellow Blue Blue Gray Black Gray Gray Black Yellow Blue Blue Black Gray Black Yellow
Yellow Yellow Yellow Gray Black Gray Blue Blue Gray Gray Blue Gray Blue Black Black Blue Gray Blue Yellow Gray Black
Gray Blue Blue Yellow Black Blue Blue Blue Black Blue Yellow Black Gray Black Blue Blue Blue Black Gray Black Black
Blue Blue Gray Blue Yellow Blue Black Gray Blue Blue Black Black Yellow Black Yellow Black Yellow Blue Blue Blue Black
Blue Yellow Black Black Blue Yellow Blue Gray Black Blue Gray Yellow Black Gray Gray Blue Gray Yellow Black 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: Pink Brown Pink Pink Orange Pink
Row 2: Pink Pink Pink Pink Pink Pink
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
Row 11: Pink Brown Pink Pink Orange Pink
Output:
Row 1: Pink Brown Pink Pink Orange Pink
Row 2: Pink Brown Pink Pink Orange Pink
Row 3: Pink Brown Pink Pink Orange Pink
Row 4: Pink Brown Pink Pink Orange Pink
Row 5: Pink Brown Pink Pink Orange Pink
Row 6: Pink Gray Pink Pink Gray Pink
Row 7: Pink Brown Pink Pink Orange Pink
Row 8: Pink Brown Pink Pink Orange Pink
Row 9: Pink Brown Pink Pink Orange Pink
Row 10: Pink Brown Pink Pink Orange Pink
Row 11: Pink Brown Pink Pink Orange Pink
Example 2
Input:
Row 1: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Row 8: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Red
Row 11: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 12: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Red Red Red Red Red Gray Orange Orange Orange Orange Orange
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Brown Brown Brown Brown Brown Gray Black Black Black Black Black
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Black Black Black Black Black Gray Green Green Green Green Green
Row 8: Orange Orange Orange Orange Orange Gray Black Black Black Black Black
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Purple Purple Purple Purple Purple Gray Red Red Red Red Red
Row 11: Orange Orange Orange Orange Orange Gray Black Black Black Black Black
Row 12: Pink Pink Pink Pink Pink Gray Purple Purple Purple Purple Purple
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: 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
Row 3: 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
Row 5: Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 6: 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
Row 8: 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
Row 10: Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 11: Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 16: Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Output:
Row 1: 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
Row 3: 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
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Blue Blue Blue Blue Blue Blue Blue
Row 6: 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
Row 8: 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
Row 10: Blue Blue Blue Blue Blue Blue Blue Gray Red Red Red Red Red Red Red
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Black Black Black Black Black Black Black
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Red Red Red Red Red Red Red Gray Blue Blue Blue Blue Blue Blue Blue
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Black Black Black Black Black Black Black Gray Red Red Red Red Red Red Red
Row 16: Blue Blue Blue Blue Blue Blue Blue Gray Black Black Black Black Black Black Black
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green 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 Green Green Green Green Green Green Green Green Green
Row 12: 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
Row 14: 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
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Blue Green Orange Blue Green Green Pink Black Green Orange Green Green Yellow
Gray Green Gray Gray Green Green Gray Gray Green Gray Green Green Gray
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green Pink
Red Green Black Pink Green Green Brown Red Green Blue Green Green 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 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
Row 16: 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
Output:
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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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 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
Row 16: 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
Example 2
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 Yellow Yellow Yellow Yellow
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue
Row 16: 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
Row 18: 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
Row 20: 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
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 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
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue
Row 16: 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
Row 18: 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
Row 20: 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
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Blue Blue Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Blue Blue Blue Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Blue Blue Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Blue Blue Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray 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
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
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Blue Blue Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Blue Blue Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Blue Blue Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Blue Blue Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Blue Blue Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Gray Gray Gray Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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 Red Red Red
Row 4: 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
Row 6: 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 Gray Gray Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Gray Gray Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Gray Gray Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Gray Gray Red Purple Purple
Row 11: Red Red Red Red Red Red Red Red Red Gray Gray Red Purple Purple
Row 12: Red Red Red Red Red Red Red Red Red Gray Gray Purple Purple Purple
Row 13: Red Red Red Red Red Red Red Red Red Gray Gray Red Purple Purple
Row 14: Red Red Red Red Red Red Red Red Red Gray Gray Red Purple Purple
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple
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
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 Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red 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 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 Gray Gray Red Red Red
Red Red Red Red Red Red Red Red Red Gray Gray Purple Purple Red
Red Red Red Red Red Red Red Red Red Gray Gray Purple Purple Red
Red Red Red Red Red Red Red Red Red Gray Gray Purple Purple Red
Red Red Red Red Red Red Red Red Red Gray Gray Purple Purple Red
Red Red Red Red Red Red Red Red Red Gray Gray Purple Purple Red
Red Red Red Red Red Red Red Red Red Red Red Purple 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 |
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 Brown
Row 2: Brown Brown
Row 3: Brown Brown
Row 4: Green Green
Output:
Row 1: Green Brown Brown Green
Row 2: Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown
Row 4: Green Green Green Green
Row 5: Green Green Green Green
Row 6: Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown
Row 8: Green Brown Brown Green
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Purple Black Black Black Red
Row 3: Black Black Black Black Blue Black Purple Yellow Brown
Row 4: Black Black Black Black Black Pink Pink Gray Black
Row 5: Black Black Black Black Black Purple Yellow Yellow Purple
Row 6: Black Black Black Black Black Black Black Pink 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: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Purple Black Black Black Red Red Black Black Black Purple Black Black Black Black
Row 3: Black Black Black Black Blue Black Purple Yellow Brown Brown Yellow Purple Black Blue Black Black Black Black
Row 4: Black Black Black Black Black Pink Pink Gray Black Black Gray Pink Pink Black Black Black Black Black
Row 5: Black Black Black Black Black Purple Yellow Yellow Purple Purple Yellow Yellow Purple Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Pink Black Black Pink Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Pink Black Black Pink Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Purple Yellow Yellow Purple Purple Yellow Yellow Purple Black Black Black Black Black
Row 17: Black Black Black Black Black Pink Pink Gray Black Black Gray Pink Pink Black Black Black Black Black
Row 18: Black Black Black Black Blue Black Purple Yellow Brown Brown Yellow Purple Black Blue Black Black Black Black
Row 19: Black Black Black Black Purple Black Black Black Red Red Black Black Black Purple Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Brown Orange Purple Orange Gray Orange Blue Yellow Black Gray Orange Black Blue
Row 2: Blue Orange Yellow Black Blue Orange Orange Brown Orange Gray Red Brown Black
Row 3: Green Orange Brown Green Blue Orange Brown Purple Green Blue Green Orange Orange
Row 4: Blue Yellow Orange Purple Green Brown Red Purple Gray Yellow Red Brown Brown
Row 5: Yellow Brown Black Black Red Black Gray Purple Red Brown Orange Blue Brown
Row 6: Gray Blue Gray Blue Black Orange Black Blue Green Red Gray Blue Gray
Row 7: Green Brown Brown Orange Yellow Gray Red Red Blue Yellow Red Purple Green
Row 8: Blue Yellow Black Orange Blue Purple Green Blue Red Green Yellow Green Green
Row 9: Red Red Brown Blue Green Blue Green Yellow Black Gray Blue Brown Black
Row 10: Red Gray Purple Gray Purple Black Yellow Gray Blue Blue Gray Orange Brown
Row 11: Brown Orange Green Gray Orange Red Yellow Blue Orange Brown Blue Blue Gray
Output:
Row 1: Brown Orange Purple Orange Gray Orange Blue Yellow Black Gray Orange Black Blue Blue Black Orange Gray Black Yellow Blue Orange Gray Orange Purple Orange Brown
Row 2: Blue Orange Yellow Black Blue Orange Orange Brown Orange Gray Red Brown Black Black Brown Red Gray Orange Brown Orange Orange Blue Black Yellow Orange Blue
Row 3: Green Orange Brown Green Blue Orange Brown Purple Green Blue Green Orange Orange Orange Orange Green Blue Green Purple Brown Orange Blue Green Brown Orange Green
Row 4: Blue Yellow Orange Purple Green Brown Red Purple Gray Yellow Red Brown Brown Brown Brown Red Yellow Gray Purple Red Brown Green Purple Orange Yellow Blue
Row 5: Yellow Brown Black Black Red Black Gray Purple Red Brown Orange Blue Brown Brown Blue Orange Brown Red Purple Gray Black Red Black Black Brown Yellow
Row 6: Gray Blue Gray Blue Black Orange Black Blue Green Red Gray Blue Gray Gray Blue Gray Red Green Blue Black Orange Black Blue Gray Blue Gray
Row 7: Green Brown Brown Orange Yellow Gray Red Red Blue Yellow Red Purple Green Green Purple Red Yellow Blue Red Red Gray Yellow Orange Brown Brown Green
Row 8: Blue Yellow Black Orange Blue Purple Green Blue Red Green Yellow Green Green Green Green Yellow Green Red Blue Green Purple Blue Orange Black Yellow Blue
Row 9: Red Red Brown Blue Green Blue Green Yellow Black Gray Blue Brown Black Black Brown Blue Gray Black Yellow Green Blue Green Blue Brown Red Red
Row 10: Red Gray Purple Gray Purple Black Yellow Gray Blue Blue Gray Orange Brown Brown Orange Gray Blue Blue Gray Yellow Black Purple Gray Purple Gray Red
Row 11: Brown Orange Green Gray Orange Red Yellow Blue Orange Brown Blue Blue Gray Gray Blue Blue Brown Orange Blue Yellow Red Orange Gray Green Orange Brown
Row 12: Brown Orange Green Gray Orange Red Yellow Blue Orange Brown Blue Blue Gray Gray Blue Blue Brown Orange Blue Yellow Red Orange Gray Green Orange Brown
Row 13: Red Gray Purple Gray Purple Black Yellow Gray Blue Blue Gray Orange Brown Brown Orange Gray Blue Blue Gray Yellow Black Purple Gray Purple Gray Red
Row 14: Red Red Brown Blue Green Blue Green Yellow Black Gray Blue Brown Black Black Brown Blue Gray Black Yellow Green Blue Green Blue Brown Red Red
Row 15: Blue Yellow Black Orange Blue Purple Green Blue Red Green Yellow Green Green Green Green Yellow Green Red Blue Green Purple Blue Orange Black Yellow Blue
Row 16: Green Brown Brown Orange Yellow Gray Red Red Blue Yellow Red Purple Green Green Purple Red Yellow Blue Red Red Gray Yellow Orange Brown Brown Green
Row 17: Gray Blue Gray Blue Black Orange Black Blue Green Red Gray Blue Gray Gray Blue Gray Red Green Blue Black Orange Black Blue Gray Blue Gray
Row 18: Yellow Brown Black Black Red Black Gray Purple Red Brown Orange Blue Brown Brown Blue Orange Brown Red Purple Gray Black Red Black Black Brown Yellow
Row 19: Blue Yellow Orange Purple Green Brown Red Purple Gray Yellow Red Brown Brown Brown Brown Red Yellow Gray Purple Red Brown Green Purple Orange Yellow Blue
Row 20: Green Orange Brown Green Blue Orange Brown Purple Green Blue Green Orange Orange Orange Orange Green Blue Green Purple Brown Orange Blue Green Brown Orange Green
Row 21: Blue Orange Yellow Black Blue Orange Orange Brown Orange Gray Red Brown Black Black Brown Red Gray Orange Brown Orange Orange Blue Black Yellow Orange Blue
Row 22: Brown Orange Purple Orange Gray Orange Blue Yellow Black Gray Orange Black Blue Blue Black Orange Gray Black Yellow Blue Orange Gray Orange Purple Orange Brown
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Black Purple Pink Purple Purple Purple
Row 3: Blue Purple Pink Pink Pink Pink Purple Purple
Row 4: Pink Black Black Purple Blue Purple Purple Blue
Row 5: Pink Blue Pink Pink Purple Black Blue Purple
Row 6: Blue Purple Pink Black Black Black Pink Black
Row 7: Black Blue Pink Blue Pink Blue Purple Blue
Row 8: Purple Pink Blue Purple Blue Purple Blue Black
Row 9: Purple Blue Purple Blue Blue Pink Pink Purple
Row 10: Purple Purple Blue Purple Pink Purple Purple Purple
Row 11: Black Blue Blue Black Black Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Black Purple Pink Purple Purple Purple Purple Purple Purple Pink Purple Black Purple Purple
Blue Purple Pink Pink Pink Pink Purple Purple Purple Purple Pink Pink Pink Pink Purple Blue
Pink Black Black Purple Blue Purple Purple Blue Blue Purple Purple Blue Purple Black Black Pink
Pink Blue Pink Pink Purple Black Blue Purple Purple Blue Black Purple Pink Pink Blue Pink
Blue Purple Pink Black Black Black Pink Black Black Pink Black Black Black Pink Purple Blue
Black Blue Pink Blue Pink Blue Purple Blue Blue Purple Blue Pink Blue Pink Blue Black
Purple Pink Blue Purple Blue Purple Blue Black Black Blue Purple Blue Purple Blue Pink Purple
Purple Blue Purple Blue Blue Pink Pink Purple Purple Pink Pink Blue Blue Purple Blue Purple
Purple Purple Blue Purple Pink Purple Purple Purple Purple Purple Purple Pink Purple Blue Purple Purple
Black Blue Blue Black Black Purple Purple Purple Purple Purple Purple Black Black Blue Blue Black
Black Blue Blue Black Black Purple Purple Purple Purple Purple Purple Black Black Blue Blue Black
Purple Purple Blue Purple Pink Purple Purple Purple Purple Purple Purple Pink Purple Blue Purple Purple
Purple Blue Purple Blue Blue Pink Pink Purple Purple Pink Pink Blue Blue Purple Blue Purple
Purple Pink Blue Purple Blue Purple Blue Black Black Blue Purple Blue Purple Blue Pink Purple
Black Blue Pink Blue Pink Blue Purple Blue Blue Purple Blue Pink Blue Pink Blue Black
Blue Purple Pink Black Black Black Pink Black Black Pink Black Black Black Pink Purple Blue
Pink Blue Pink Pink Purple Black Blue Purple Purple Blue Black Purple Pink Pink Blue Pink
Pink Black Black Purple Blue Purple Purple Blue Blue Purple Purple Blue Purple Black Black Pink
Blue Purple Pink Pink Pink Pink Purple Purple Purple Purple Pink Pink Pink Pink Purple Blue
Purple Purple Black Purple Pink Purple Purple Purple Purple Purple Purple Pink Purple Black 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
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Green Green Green Green Green Green Pink
Row 7: Pink Pink Pink Pink Green Green Green Green Green Green Pink
Row 8: Pink Pink Pink Pink Green Pink Pink Green Green Green Pink
Row 9: Pink Pink Pink Pink Green Green Pink Pink Green Green Pink
Row 10: Pink Pink Pink Pink Green Pink Pink Green Green Green Pink
Row 11: Pink Pink Pink Pink Green Green Green Green Green Green Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 16: Pink Pink Pink Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink
Row 17: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 18: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 19: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: 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
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Green Green Green Green Green Green Pink
Row 7: Pink Pink Pink Pink Green Green Green Green Green Green Pink
Row 8: Pink Pink Pink Pink Green Pink Pink Green Green Green Pink
Row 9: Pink Pink Pink Pink Green Green Pink Pink Green Green Pink
Row 10: Pink Pink Pink Pink Green Pink Pink Green Green Green Pink
Row 11: Pink Pink Pink Pink Green Green Green Green Green Green Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 16: Pink Pink Pink Yellow Red Yellow Yellow Yellow Yellow Yellow Pink
Row 17: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 18: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 19: Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 7: Black Black Black Purple Black Black Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Gray Purple
Row 8: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Gray Purple
Row 9: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 10: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 11: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple 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
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 7: Black Black Black Red Black Black Purple Purple Purple Purple Gray Gray Gray Gray Red Red Gray Purple
Row 8: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Red Red Gray Purple
Row 9: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 10: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 11: Black Black Black Black Black Black Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Brown Orange Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Brown Brown Brown Brown Brown 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 Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 10: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 11: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 12: Orange Orange Orange Purple Purple Orange Orange Purple Purple Purple Orange Orange Orange
Row 13: Orange Orange Orange Purple Purple Orange Orange Purple Purple Purple Orange Orange Orange
Row 14: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange 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
Output:
Row 1: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Brown Red Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Brown Brown Brown Brown Brown 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 Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 10: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 11: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 12: Orange Orange Orange Purple Purple Red Red Purple Purple Purple Orange Orange Orange
Row 13: Orange Orange Orange Purple Purple Red Red Purple Purple Purple Orange Orange Orange
Row 14: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange 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
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Pink Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Pink Pink Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Black Black Black Black Black Black Black Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Black Purple Purple Purple Purple Black Black Purple Purple Purple Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Black Purple Purple Purple Purple Black Black Purple Purple Purple Orange Orange Purple Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Black Purple Purple Purple Purple Black Black Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Black Black Black Black Black Black Black 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Pink Pink Red Red Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Pink Pink Red Red Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Black Black Black Black Black Black Black Purple Purple Purple Orange Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple
Black Purple Purple Purple Purple Black Black Purple Purple Purple Orange Purple Purple Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Black Purple Purple Purple Purple Black Black Purple Purple Purple Orange Orange Purple Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Black Purple Purple Purple Purple Black Black Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple
Black Black Black Black Black Black Black Purple Purple Purple Orange Orange Orange Orange 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple 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: 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: Yellow Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Yellow Green Green Green Blue Blue Blue Blue Green Green Green Green Green
Row 5: Yellow Green Green Green Blue Blue Blue Blue Green Green Green Green Green
Row 6: Yellow Green Green Green Blue Blue Blue Blue Green Green Green Green Green
Row 7: Yellow Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow 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
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: Yellow Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Yellow Brown Brown Brown Blue Blue Blue Blue Green Green Green Green Green
Row 5: Yellow Brown Brown Brown Blue Blue Blue Blue Green Green Green Green Green
Row 6: Yellow Brown Brown Brown Blue Blue Blue Blue Green Green Green Green Green
Row 7: Yellow Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Yellow 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
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 14: Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 15: Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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 Yellow 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
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 14: Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange
Row 15: Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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 Orange
Example 3
Input:
Row 1: Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 2: Black Black Blue Blue Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 3: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Black Black Black 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 Black Black Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue Blue Blue Black Black Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 9: Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 10: Black Blue Blue Blue Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 11: Black Blue Gray Gray Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 12: Black Blue Gray Gray Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 13: Black Blue Gray Gray Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 14: Black Blue Gray Gray Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 15: Black Blue Blue Blue Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 16: Black Blue Blue Blue Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 17: Black Blue Blue Blue Blue Black Black Black Black Black Black Black Black Blue Black Black Blue Blue
Row 18: Black Blue Blue Blue Blue Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 19: Black Blue Blue Blue Blue Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 20: Black 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 Green Green Green Green Green Green Blue Blue
Row 22: Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Blue Blue
Row 23: Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Blue
Row 26: Blue Pink Pink Pink Pink Pink Pink Blue Blue Blue Black Black Black Black Black Black Black Blue
Output:
Row 1: Blue Blue Blue Blue Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 2: Black Black Brown Brown Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 3: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Black Black Black 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 Black Black Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Brown Brown Brown Black Black Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Blue Blue
Row 9: Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Blue Blue
Row 10: Black Brown Brown Brown Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 11: Black Brown Gray Gray Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 12: Black Brown Gray Gray Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 13: Black Brown Gray Gray Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 14: Black Brown Gray Gray Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 15: Black Brown Brown Brown Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 16: Black Brown Brown Brown Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 17: Black Brown Brown Brown Brown Black Black Black Black Black Black Black Black Brown Black Black Blue Blue
Row 18: Black Brown Brown Brown Brown Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 19: Black Brown Brown Brown Brown Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 20: Black 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 Green Green Green Green Green Green Blue Blue
Row 22: Blue Green Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Green Green Green Blue Blue
Row 23: Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Green Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Black Black Black Blue
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Black Blue
Row 26: Blue Pink Pink Pink Pink Pink Pink Blue Blue Blue Black Black Black Black Black Black Black Blue
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 Black Black Black
Row 5: Black Black Orange Orange Black Black Black Black
Row 6: Black Black Orange Orange Black Black Black Black
Row 7: Black Black Orange Orange Black Orange Black Black
Row 8: Black Black Orange Orange Black Orange Black Black
Row 9: Black Black Orange Orange Black Orange Black Black
Row 10: Black Black Black Black Black Orange Black Black
Row 11: Black Black Black Black Black Orange Black Black
Row 12: Black Black Green Green Black Orange Black Black
Row 13: Black Black Green Green Black Orange Black Black
Row 14: Black Black Green Green Black Black Black Black
Row 15: Black Black Green Green 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 Orange Orange Black Black Black Black
Black Black Orange Orange Black Black Black Black
Black Black Orange Orange Brown Orange Black Black
Black Black Orange Orange Brown Orange Black Black
Black Black Orange Orange Brown Orange Black Black
Black Black Black Black Black Orange Black Black
Black Black Black Black Black Orange Black Black
Black Black Green Green Brown Orange Black Black
Black Black Green Green Brown Orange Black Black
Black Black Green Green Black Black Black Black
Black Black Green Green 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
Row 2: Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Pink Blue Blue Blue Orange Orange Orange Blue Blue Blue Blue Blue
Row 4: Pink Blue Pink Blue Blue Orange Orange Blue Blue Blue Blue Red Red Blue
Row 5: Pink Blue Pink Pink Blue Blue Orange Blue Blue Blue Blue Red Blue Blue
Row 6: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue
Row 10: Blue Blue Orange Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Row 11: Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Black Black Blue Green Blue Blue Blue
Row 15: Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Black Blue Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue
Row 17: Blue Black Black Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue
Row 18: Blue Black Blue Blue Blue Orange Blue Blue Blue Blue Orange Orange Blue Blue
Row 19: Blue Black Blue Blue Blue Orange Orange Blue Blue Blue Orange Blue Blue Blue
Row 20: Black Black Blue Blue Blue Blue Orange Blue Blue Blue Orange Blue Blue Blue
Row 21: Blue Black Blue Black Blue Blue Orange Orange Orange Orange Orange Blue Blue Blue
Row 22: Blue Black Black Black Black Blue Blue Orange Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Black Black 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
Row 2: Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Pink Blue Blue Blue Orange Orange Orange Blue Blue Blue Blue Blue
Row 4: Pink Blue Pink Blue Blue Orange Orange Blue Blue Blue Blue Red Red Blue
Row 5: Pink Blue Pink Pink Blue Blue Orange Blue Blue Blue Blue Red Blue Blue
Row 6: Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue
Row 10: Blue Blue Orange Blue Blue Blue Blue Blue Yellow Yellow Blue Blue Blue Blue
Row 11: Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Black Black Blue Green Blue Blue Blue
Row 15: Blue Blue Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Black Blue Blue Blue Blue Purple Purple Blue Blue Blue Blue Blue
Row 17: Blue Black Black Blue Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue
Row 18: Blue Black Blue Blue Blue Purple Blue Blue Blue Blue Purple Purple Blue Blue
Row 19: Blue Black Blue Blue Blue Purple Purple Blue Blue Blue Purple Blue Blue Blue
Row 20: Black Black Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Blue
Row 21: Blue Black Blue Black Blue Blue Purple Purple Purple Purple Purple Blue Blue Blue
Row 22: Blue Black Black Black Black Blue Blue Purple Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Black Black Blue Blue 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 Black Black Black Black Black Black Black Black Red Black Black Red Black Black Black
Row 2: Black Red Red Black Black Black Black Black Black Black Black Black Blue Black Black Black Black Gray Black Black Red Red Red Red Red Red Black
Row 3: Red Red Red Red Black Black Black Blue Black Black Black Black Blue Black Black Gray Gray Gray Black Red Red Black Black Black Black Red Black
Row 4: Black Black Red Black Black Black Black Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black Red Red Black Black Black Black Red Black
Row 5: Black Black Red Red Black Black Black Blue Black Black Black Black Blue Black Black Black Black Black Black Black Red Red Red Red Red Red Black
Row 6: Black Black Red Black Black Black Black Blue Black Black Black Black Blue Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Blue Black Black Black Black Blue Black Black Black Black Yellow Black Black Black Red Red Red Black Black Black
Row 8: Blue Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Black Black Black Black Yellow Black Black Black Black Black Red Red Black Black
Row 9: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Green Black Red Red Black Black Black
Row 10: Blue Blue Blue Blue Blue Blue Black Black Black Black Orange Orange Orange Black Black Yellow Yellow Yellow Black Black Green Black Black Black Black Black Black
Row 11: Blue Black Black Black Black Black Black Black Black Black Orange Black Orange Black Black Black Black Black Black Black Green Black Black Black Black Green Black
Row 12: Blue Black Black Black Black Black Black Black Black Black Orange Black Orange Black Black Black Black Black Black Black Green Black Black Black Black Green Black
Row 13: Blue Black Black Black Black Black Black Black Black Black Orange Orange Orange Black Black Black Black Black Black Black Green Black Black Black Black Green Green
Row 14: Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Black Black Black Green Green Green Green Green Green Black
Row 15: Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Green Black Black Black Black Black Black
Row 16: Black Black Black Black Gray Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black Brown Brown Brown Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Yellow Black Black Black Yellow Black Black Brown Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Yellow Black Black Black Yellow Yellow Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 19: Black Black Green Black Black Black Black Black Black Yellow Black Black Black Yellow Black Black Brown Black Orange Black Black Black Black Black Black Black Black
Row 20: Black Black Green Green Green Green Green Black Black Yellow Black Black Black Yellow Black Black Brown Black Orange Black Black Black Orange Black Black Black Black
Row 21: Black Black Green Black Green Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Brown Black Orange Black Black Black Orange Black Black Black Black
Row 22: Black Black Green Green Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black
Row 23: Black Black Green Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange 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 Orange 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 Purple Black Black Purple Black Black Black
Row 2: Black Red Red Black Black Black Black Black Black Black Black Black Purple Black Black Black Black Gray Black Black Purple Purple Purple Purple Purple Purple Black
Row 3: Red Red Red Red Black Black Black Purple Black Black Black Black Purple Black Black Gray Gray Gray Black Purple Purple Black Black Black Black Purple Black
Row 4: Black Black Red Black Black Black Black Purple Purple Purple Purple Purple Purple Black Black Black Black Black Black Purple Purple Black Black Black Black Purple Black
Row 5: Black Black Red Red Black Black Black Purple Black Black Black Black Purple Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Black
Row 6: Black Black Red Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Yellow Black Black Black Red Red Red Black Black Black
Row 8: Blue Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Black Black Black Black Yellow Black Black Black Black Black Red Red Black Black
Row 9: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Black Black Green Black Red Red Black Black Black
Row 10: Blue Blue Blue Blue Blue Blue Black Black Black Black Purple Purple Purple Black Black Yellow Yellow Yellow Black Black Green Black Black Black Black Black Black
Row 11: Blue Black Black Black Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Green Black Black Black Black Green Black
Row 12: Blue Black Black Black Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Black Green Black Black Black Black Green Black
Row 13: Blue Black Black Black Black Black Black Black Black Black Purple Purple Purple Black Black Black Black Black Black Black Green Black Black Black Black Green Green
Row 14: Blue Blue Blue Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Black Black Black Green Green Green Green Green Green Black
Row 15: Black Black Black Black Gray Gray Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Green Black Black Black Black Black Black
Row 16: Black Black Black Black Gray Black Black Black Black Purple Purple Purple Purple Purple Black Brown Brown Brown Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Purple Black Black Black Purple Black Black Brown Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Purple Black Black Black Purple Purple Black Black Black Orange Orange Black Black Black Black Black Black Black
Row 19: Black Black Purple Black Black Black Black Black Black Purple Black Black Black Purple Black Black Brown Black Orange Black Black Black Black Black Black Black Black
Row 20: Black Black Purple Purple Purple Purple Purple Black Black Purple Black Black Black Purple Black Black Brown Black Orange Black Black Black Orange Black Black Black Black
Row 21: Black Black Purple Black Purple Black Black Black Black Purple Purple Purple Purple Purple Purple Black Brown Black Orange Black Black Black Orange Black Black Black Black
Row 22: Black Black Purple Purple Black Black Black Black Black Purple Black Black Black Black Black Black Black Black Orange Orange Orange Orange Orange Black Black Black Black
Row 23: Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange 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 Orange 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
Row 2: Gray Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray
Row 3: Gray Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray
Row 4: Gray Gray Black Black Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 5: Gray Gray Gray Black Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Orange
Row 6: Black Gray Gray Gray Gray Red Red Red Red Gray Gray Gray Gray Gray Gray Gray
Row 7: Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Black Gray Black Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray
Row 9: Black Black Gray Black Black Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Orange Orange Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Orange Gray Gray Gray Orange Orange Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Orange Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Black Gray Black Gray Gray Gray Gray Gray Gray Gray Gray Orange Gray Gray
Row 3: Gray Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray
Row 4: Gray Gray Black Black Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Orange
Row 5: Gray Gray Gray Black Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Orange
Row 6: Black Gray Gray Gray Gray Red Red Red Red Gray Gray Gray Gray Gray Gray Gray
Row 7: Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Black Gray Black Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray
Row 9: Black Black Gray Black Black Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Purple Purple Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Purple Purple Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Purple Gray Gray Gray Gray Gray
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
Row 2: Green Green Green Green Green Green Green Green Green Black Black Black Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Green
Row 3: Green Green Green Green Pink Green Green Green Green Green Green Black Green Green Green Green Green Green Green Blue Green Green Green Green Orange Green Green
Row 4: Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Black Green Green Green Green Green Green Green Blue Green Green Green Green Orange Green Green
Row 5: Green Green Green Pink Green Green Green Pink Green Green Green Black Black Black Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green
Row 6: Green Green Green Pink Green Green Green Pink Green Green Green Black Green Green Green Green Green Green Green Green Green Green Blue Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Black Green Green Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Black Black Black Black Black Black Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Black Green Green Green Green Black Green Green Green Green Green Green Gray Green Gray Gray Gray Green Green Green Green Green Gray Green Green
Row 10: Green Green Black Black Black Black Black Black Green Green Green Green Green Green Gray Gray Gray Green Green Green Yellow Yellow Yellow Green Gray Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Gray Gray Gray
Row 12: Green Green Green Green Green Green Green Green Green Black Green Black Green Green Green Green Green Gray Green Green Green Green Yellow Green Gray Gray Gray
Row 13: Brown Brown Brown Brown Brown Green Green Green Green Black Black Black Green Green Green Green Gray Gray Green Green Green Green Green Green Green Green Green
Row 14: Brown Green Green Green Brown Green Green Green Black Black Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Gray Gray Gray Gray
Row 15: Brown Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Gray Gray Gray Gray Gray Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green Green Green Green Green Green Green Green 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 Black Black Green Green Green Green Green Green Green Green Green Green Orange Orange Orange Orange Green
Green Green Green Green Pink Green Green Green Green Green Green Black Green Green Green Green Green Green Green Blue Green Green Green Green Orange Green Green
Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Black Green Green Green Green Green Green Green Blue Green Green Green Green Orange Green Green
Green Green Green Pink Green Green Green Pink Green Green Green Black Black Black Green Green Green Green Green Blue Blue Blue Blue Green Green Green Green
Green Green Green Pink Green Green Green Pink Green Green Green Black Green Green Green Green Green Green Green Green Green Green Blue Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Black Green Green 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 Purple Purple Purple Purple Green Green Green Green Green Green Green Green Green Green
Green Green Purple Green Green Green Green Purple Green Green Green Green Green Green Purple Green Purple Purple Purple Green Green Green Green Green Gray Green Green
Green Green Purple Purple Purple Purple Purple Purple Green Green Green Green Green Green Purple Purple Purple Green Green Green Yellow Yellow Yellow Green Gray Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Green Gray Gray Gray
Green Green Green Green Green Green Green Green Green Black Green Black Green Green Green Green Green Gray Green Green Green Green Yellow Green Gray Gray Gray
Purple Purple Purple Purple Purple Green Green Green Green Black Black Black Green Green Green Green Gray Gray Green Green Green Green Green Green Green Green Green
Purple Green Green Green Purple Green Green Green Black Black Green Green Green Green Green Gray Gray Gray Gray Green Green Green Green Gray Gray Gray Gray
Purple Purple Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Gray Green Green Green Gray Gray Gray Gray Gray 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 Yellow Blue Purple Purple Purple Purple Blue Purple Red Purple Purple Purple Black Purple Purple Green Purple
Row 2: Purple Purple Purple Red Purple Yellow Purple Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Yellow Purple Yellow Purple Purple Purple Green Black Green Red Purple Purple Purple Purple Purple Purple Purple Black Purple Green
Row 4: Purple Purple Red Purple Purple Purple Purple Black Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Black Purple Purple
Row 5: Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Red Purple Purple Purple Purple Red Purple Purple Purple Black Purple Purple Purple Purple Green Purple Purple Blue Purple Purple Yellow
Row 7: Purple Red Purple Red Purple Blue Purple Purple Purple Purple Gray Gray Gray Gray Black Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Green Purple Purple Yellow Purple Purple Purple Purple Gray Gray Gray Gray Purple Purple Purple Purple Green Purple Purple
Row 9: Purple Purple Purple Purple Purple Green Purple Purple Yellow Purple Gray Gray Gray Gray Red Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Gray Gray Gray Gray Purple Yellow Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Blue Purple Purple Yellow Purple Purple Purple Gray Gray Gray Red Purple Red Yellow Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Black Blue Purple Purple Blue Purple Purple Purple Black Purple Purple Blue Purple Black Purple Green Purple Purple Purple Purple Blue
Row 14: Purple Black Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Output:
Row 1: Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray
Row 5: Purple Gray Gray Gray
Example 2
Input:
Row 1: Red Red Red Green Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Pink Red Red Red Red Red Red
Row 3: Red Red Green Red Red Red Purple Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Yellow Purple Red Red Purple Red Purple Red Red Red Green
Row 5: Red Purple Red Red Red Red Pink Red Pink Red Red Purple Red Red Red Purple Red Red Red Red Red Red Red Red Red Pink Red Red Red Red
Row 6: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Purple Red Red Red Gray Pink
Row 7: Red Red Red Red Green Red Red Red Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Purple Red Red Red Gray 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 Red Pink Red Gray Gray Gray Gray Red
Row 9: Red Red Yellow Red Red Red Red Green Red Pink Red Red Red Red Red Red Red Purple Red Red Red Red Red Red Red Red Gray Red Red Red
Row 10: Red Purple Red Green Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Gray Gray Gray Gray Red
Row 11: Red Red Red Red Red Red Red Red Purple Red Red Red Red Red Red Red Red Red Purple Red Red Red Red Red Red Red Gray Gray Gray Pink
Row 12: Red Pink Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Purple Red Green Red Red Red Red Red Red Red Red Red Pink Purple
Row 13: Red Red Red Red Yellow Red Red Yellow Red Red Red Red Red Red Red Pink Red Red Red Red Red Red Green Red Red Red Red Purple Red Purple
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Pink Red Red Red Red Red Red Red Red Red Red Pink Yellow
Row 15: Red Red Red Yellow Red Yellow Red Red Red Pink Red Red Pink Red Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Yellow Purple Red Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Yellow Red Red Red Red Red Red Red Red Purple Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Green Pink Red Red Red Red Pink Red Red Red Red Red Red Red Red
Row 19: Red Red Purple Red Red Red Yellow Red Purple Red Red Red Red Purple Red Red Red Pink Red Red Red Pink Red Pink Red Red Red Purple Red Purple
Row 20: Red Red Red Red Purple Green Red Purple Purple Red Yellow Red Red Red Red Red Pink Red Red Purple Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Purple Red Pink Red Red Purple Red Green Red Green Pink Red Red Red Red Red Red Red Red Red Red Pink Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Pink Red Red Red Red Red Red Yellow Green Red Red Red Red Purple Red Red Red Pink Purple Green Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Purple Red Pink Red Red Red Red Red Red Red Red Purple Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Gray
Row 2: Red Gray Red Gray
Row 3: Gray Gray Gray Gray
Row 4: Red Gray Red Red
Row 5: Gray Gray Gray Gray
Row 6: Red Gray Gray Gray
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Blue Black Green Green Gray Green Green Green
Row 2: Green Gray Green Pink Green Green Green Green Green Green Green Green Black Green Green
Row 3: Green Gray Pink Green Green Green Green Green Blue Green Green Green Green Blue Green
Row 4: Green Green Green Green Green Green Green Blue Green Green Green Green Green Green Green
Row 5: Green Green Green Green Pink Green Black Gray Green Green Green Green Green Pink Green
Row 6: Orange Green Green Green Green Gray Green Green Gray Black Gray Green Green Green Green
Row 7: Orange Green Green Green Blue Green Gray Green Green Green Green Black Green Green Green
Row 8: Green Green Green Green Green Green Black Green Black Black Green Black Blue Green Green
Row 9: Green Green Green Green Pink Green Black Yellow Yellow Yellow Yellow Yellow Green Green Green
Row 10: Orange Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Green Black Green
Row 11: Green Green Blue Gray Blue Green Green Yellow Yellow Yellow Yellow Yellow Green Blue Green
Row 12: Green Green Green Orange Green Green Green Yellow Yellow Yellow Yellow Yellow Gray Blue Green
Row 13: Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Blue
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Black Brown
Row 2: Brown Brown Pink Brown Brown Brown Brown Brown Brown Black 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 Blue Brown Brown Brown Red Red Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Pink Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Red Brown Red Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Blue Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Red Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Pink
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Red Pink Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Black Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Black
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Black Pink Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Pink Blue Brown Blue 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 Blue Pink Pink Brown Red Brown
Row 12: Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Black Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 13: Pink Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Red Orange Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Orange Pink Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Blue Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown
Row 17: Brown Brown Blue Brown Blue Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Pink Brown Brown Blue Brown Brown Black Brown Brown Brown Blue Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Red Brown
Row 19: Red Brown Brown Black Brown Brown Pink Brown Red Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown
Row 20: Blue Orange Brown Pink Brown Black Brown Blue Brown Brown Brown Blue Brown Brown Brown Brown Brown Red Brown Brown Blue Brown Red Brown Brown Brown Brown Brown
Row 21: Brown Orange Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Black Red Brown Orange Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown
Row 23: Blue Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Blue Brown Pink Red Brown Brown Brown Blue Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Red Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Blue Brown Brown Brown Brown Brown Red Brown Pink Brown Brown Brown Brown
Row 26: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Brown Brown Blue Brown Brown Brown Brown Orange 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 Yellow Brown
Yellow Yellow Yellow Yellow Brown
Yellow Brown Brown 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: Red Purple Red
Row 2: Purple Purple Red
Row 3: Black Red Blue
Output:
Row 1: Red Red Red Purple Purple Purple Red Red Red
Row 2: Red Red Red Purple Purple Purple Red Red Red
Row 3: Red Red Red Purple Purple Purple Red Red Red
Row 4: Purple Purple Purple Purple Purple Purple Red Red Red
Row 5: Purple Purple Purple Purple Purple Purple Red Red Red
Row 6: Purple Purple Purple Purple Purple Purple Red Red Red
Row 7: Black Black Black Red Red Red Blue Blue Blue
Row 8: Black Black Black Red Red Red Blue Blue Blue
Row 9: Black Black Black Red Red Red Blue Blue Blue
Example 2
Input:
Row 1: Brown Gray Purple Brown
Row 2: Pink Gray Orange Orange
Output:
Row 1: Brown Brown Brown Brown Gray Gray Gray Gray Purple Purple Purple Purple Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Gray Gray Gray Gray Purple Purple Purple Purple Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Gray Gray Gray Gray Purple Purple Purple Purple Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Gray Gray Gray Gray Purple Purple Purple Purple Brown Brown Brown Brown
Row 5: Pink Pink Pink Pink Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Pink Pink Pink Pink Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Pink Pink Pink Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Pink Pink Pink Pink Gray Gray Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Yellow Blue Yellow Yellow
Row 2: Black Purple Purple Yellow
Row 3: Gray Pink Yellow Pink
Row 4: Black Purple Purple Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 7: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 8: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 9: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 10: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 11: Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 12: Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 13: Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 14: Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 15: Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 16: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 17: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 18: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 19: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Row 20: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Purple Black Purple
Row 2: Black Gray Gray
Row 3: Red Blue Red
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 Black Black Black Purple Purple Purple Purple
Purple Purple Purple Purple Black Black Black Black Purple Purple Purple Purple
Purple Purple Purple Purple Black Black Black Black Purple Purple Purple Purple
Purple Purple Purple Purple Black Black Black Black Purple Purple Purple Purple
Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray
Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray
Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray
Black Black Black Black Gray Gray Gray Gray Gray Gray Gray Gray
Red Red Red Red Blue Blue Blue Blue Red Red Red Red
Red Red Red Red Blue Blue Blue Blue Red Red Red Red
Red Red Red Red Blue Blue Blue Blue Red Red Red Red
Red Red Red Red Blue Blue Blue Blue Red Red Red Red |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Gray Gray Gray 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 Brown Blue 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 Brown Blue Gray Gray Gray
Output:
Row 1: Brown Blue
Row 2: Brown Blue
Example 2
Input:
Row 1: Red Red
Row 2: Red Red
Row 3: Red Red
Row 4: Red Red
Row 5: Red Red
Row 6: Red Red
Row 7: Red Red
Row 8: Red Red
Row 9: Red Red
Row 10: Red Red
Row 11: Red Red
Row 12: Red Red
Row 13: Red Red
Row 14: Red Red
Row 15: Red Red
Row 16: Red Red
Row 17: Red Red
Row 18: Red Red
Row 19: Red Red
Row 20: Yellow Red
Row 21: Green Red
Row 22: Green Red
Row 23: Red Red
Row 24: Red Red
Row 25: Red Red
Row 26: Red Red
Row 27: Red Red
Row 28: Red Red
Row 29: Red Red
Output:
Row 1: Yellow
Row 2: Green
Row 3: 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
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Green Brown Blue Blue Blue Green Yellow Yellow Orange Yellow Pink Green Green Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Brown Blue Orange Pink Blue Orange Blue Blue Blue Blue Orange Blue Red Pink Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Green Green Green Pink Green Green Red Blue Green Blue Blue Brown Blue Pink Orange Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Red Yellow Brown Blue Red Blue Blue Yellow Blue Red Blue Green Yellow Orange Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Yellow Pink Brown Blue Blue Blue Brown Blue Orange Brown Orange Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Pink Yellow Red Brown Green Blue Red Green Brown Pink Blue Blue Brown Brown Pink Blue Green Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Brown Yellow Blue Blue Red Orange Green Brown Brown Blue Blue Pink Red Orange Green Yellow Blue Orange
Row 9: Blue Blue Blue Blue Blue Blue Blue Pink Brown Blue Red Pink Blue Pink Red Red Yellow Yellow Green Orange Red Blue Green Yellow Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Brown Yellow Orange Orange Brown Yellow Brown Yellow Pink Orange Green Orange Pink Pink Brown Green Green Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Brown Green Brown Orange Brown Pink Green Brown Orange Green Orange Yellow Orange Blue Orange Pink Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Orange Yellow Red Yellow Yellow Orange Pink Green Yellow Green Brown Blue Yellow Pink Blue Orange Green Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Orange Blue Pink Orange Brown Red Orange Yellow Green Yellow Red Orange Blue Brown Green Brown Brown Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Pink Orange Green Brown Orange Orange Green Brown Red Pink Blue Blue Blue Blue Orange Yellow Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Red Green Yellow Red Green Pink Red Brown Yellow Yellow Green Green Blue Blue Orange Orange Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Orange Yellow Green Blue Yellow Orange Pink Green Brown Blue Orange Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Orange Orange Blue Green Green Pink Red Blue Brown Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Red Red Orange Red Yellow Orange Blue Blue Red Brown Pink Blue Blue Blue Blue Blue Blue
Output:
Row 1: Black Black Orange Green Brown Black Black Black Green Yellow Yellow Orange Yellow Pink Green Green Black Black
Row 2: Brown Black Orange Pink Black Orange Black Black Black Black Orange Black Red Pink Black Black Black Black
Row 3: Green Green Green Pink Green Green Red Black Green Black Black Brown Black Pink Orange Black Black Black
Row 4: Red Yellow Brown Black Red Black Black Yellow Black Red Black Green Yellow Orange Black Black Black Black
Row 5: Brown Black Black Yellow Pink Brown Black Black Black Brown Black Orange Brown Orange Black Black Black Black
Row 6: Pink Yellow Red Brown Green Black Red Green Brown Pink Black Black Brown Brown Pink Black Green Black
Row 7: Brown Yellow Black Black Red Orange Green Brown Brown Black Black Pink Red Orange Green Yellow Black Orange
Row 8: Pink Brown Black Red Pink Black Pink Red Red Yellow Yellow Green Orange Red Black Green Yellow Black
Row 9: Brown Yellow Orange Orange Brown Yellow Brown Yellow Pink Orange Green Orange Pink Pink Brown Green Green Black
Row 10: Brown Green Brown Orange Brown Pink Green Brown Orange Green Orange Yellow Orange Black Orange Pink Black Black
Row 11: Orange Yellow Red Yellow Yellow Orange Pink Green Yellow Green Brown Black Yellow Pink Black Orange Green Black
Row 12: Orange Black Pink Orange Brown Red Orange Yellow Green Yellow Red Orange Black Brown Green Brown Brown Black
Row 13: Pink Orange Green Brown Orange Orange Green Brown Red Pink Black Black Black Black Orange Yellow Black Black
Row 14: Red Green Yellow Red Green Pink Red Brown Yellow Yellow Green Green Black Black Orange Orange Black Black
Row 15: Orange Yellow Green Black Yellow Orange Pink Green Brown Black Orange Black Black Black Black Black Black Black
Row 16: Black Black Red Orange Orange Black Green Green Pink Red Black Brown Black Black Black Black Black Black
Row 17: Black Red Red Orange Red Yellow Orange Black Black Red Brown Pink Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Gray 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 Yellow Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Brown Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Yellow Red Pink Purple Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Red Blue Red Yellow Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Blue Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Orange Orange Pink Gray 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
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
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink 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>
| Black Black Black Black Gray Black Black
Black Black Black Black Black Yellow Orange
Black Black Black Black Black Brown Green
Yellow Red Black Purple Black Yellow Black
Black Red Blue Red Yellow Blue Black
Black Black Blue Black Black Yellow Black
Black Black Black Orange Orange Black Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Purple Pink Pink Yellow Purple Yellow Pink Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow
Row 3: Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink
Row 5: Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Pink Yellow Yellow Purple Yellow Pink Yellow Purple Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Pink Yellow Yellow Purple Purple Purple Purple Purple Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Purple Yellow Pink Pink Purple Purple Purple Purple Purple Purple Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 8: Pink Pink Pink Pink Purple Pink Pink Pink Purple Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Purple Pink Pink Pink Purple Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Yellow Yellow Yellow Yellow Purple Purple Purple Purple Purple Purple Yellow Pink Yellow Purple Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Purple Purple Purple Purple Purple Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
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 Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red Red Red Red Red Red Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red Red Brown Brown Brown Red Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red Red Brown Brown Brown Red Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Brown Brown Brown Red Brown Brown Brown Brown
Row 9: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Brown Brown Brown
Row 10: Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown Brown Red 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 Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Pink Brown Red Red Red Red Red Red Brown Brown Brown Brown
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Red Pink Pink Pink Red Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Red Pink Pink Pink Red Pink Pink Pink Pink
Row 8: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Red Brown Pink Brown Red Brown Brown Brown Brown
Row 9: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Red Red Red Red Red Brown Brown Brown Brown
Row 10: Red Brown Pink Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 11: Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Pink Brown Red Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Red Red Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Orange Orange Orange Orange Orange Yellow Yellow
Row 4: Orange Yellow Yellow Yellow Orange Yellow Yellow
Row 5: Orange Yellow Yellow Yellow Orange Yellow Yellow
Row 6: Orange Yellow Yellow Yellow Orange Yellow Yellow
Row 7: Orange Orange Orange Orange Orange Yellow Yellow
Row 8: Yellow Yellow Orange Orange Orange Orange Orange
Row 9: Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 10: Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 11: Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 12: Yellow Yellow Orange Orange Orange Orange Orange
Row 13: Yellow Orange Orange Orange Orange Orange Yellow
Row 14: Yellow Orange Yellow Yellow Yellow Orange Yellow
Row 15: Yellow Orange Yellow Yellow Yellow Orange Yellow
Row 16: Yellow Orange Yellow Yellow Yellow Orange Yellow
Row 17: Yellow Orange Orange Orange Orange Orange Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Orange Orange Orange Orange Orange
Row 21: Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 22: Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 23: Yellow Yellow Orange Yellow Yellow Yellow Orange
Row 24: Yellow Yellow Orange Orange Orange Orange Orange
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Pink Pink Pink Yellow Yellow
Row 2: Yellow Yellow Pink Pink Pink Yellow Yellow
Row 3: Orange Orange Orange Orange Orange Yellow Yellow
Row 4: Orange Yellow Pink Pink Orange Yellow Yellow
Row 5: Orange Pink Pink Pink Orange Pink Pink
Row 6: Orange Yellow Pink Pink Orange Yellow Yellow
Row 7: Orange Orange Orange Orange Orange Yellow Yellow
Row 8: Yellow Yellow Orange Orange Orange Orange Orange
Row 9: Yellow Yellow Orange Pink Pink Yellow Orange
Row 10: Pink Pink Orange Pink Pink Pink Orange
Row 11: Yellow Yellow Orange Pink Pink Yellow Orange
Row 12: Yellow Yellow Orange Orange Orange Orange Orange
Row 13: Yellow Orange Orange Orange Orange Orange Yellow
Row 14: Yellow Orange Pink Pink Pink Orange Yellow
Row 15: Pink Orange Pink Pink Pink Orange Pink
Row 16: Yellow Orange Pink Pink Pink Orange Yellow
Row 17: Yellow Orange Orange Orange Orange Orange Yellow
Row 18: Yellow Yellow Pink Pink Pink Yellow Yellow
Row 19: Yellow Yellow Pink Pink Pink Yellow Yellow
Row 20: Yellow Yellow Orange Orange Orange Orange Orange
Row 21: Yellow Yellow Orange Pink Pink Yellow Orange
Row 22: Pink Pink Orange Pink Pink Pink Orange
Row 23: Yellow Yellow Orange Pink Pink Yellow Orange
Row 24: Yellow Yellow Orange Orange Orange Orange Orange
Row 25: Yellow Yellow Pink Pink Pink Yellow Yellow
Row 26: Yellow Yellow Pink Pink Pink Yellow Yellow
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black
Row 2: Black Green Green Green Green Green Black Black Black
Row 3: Black Green Black Black Black Green Black Black Black
Row 4: Black Green Black Black Black Green Black Black Black
Row 5: Black Green Black Black Black Green Black Black Black
Row 6: Black Green Green Green Green Green 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
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 Pink Black Black Black Black Black
Black Green Green Green Green Green Black Black Black
Black Green Black Pink Black Green Black Black Black
Pink Green Pink Pink Pink Green Pink Pink Pink
Black Green Black Pink Black Green Black Black Black
Black Green Green Green Green Green Black Black Black
Black Black Black Pink Black Black Black Black Black
Black Black Black Pink 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 Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Orange Orange Orange Blue Orange Orange
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Blue Orange Blue Orange Orange Orange
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Blue Orange Orange Orange Orange Orange
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Blue Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Blue Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Pink Pink
Row 9: Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue
Row 10: Blue Blue Blue Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Blue Blue
Row 11: Pink Pink Blue Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Blue Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Blue Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Brown Brown Brown Brown Brown Brown Green Red Red Brown Red Brown Red
Row 17: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Row 18: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Row 19: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Row 20: Brown Brown Brown Brown Brown Brown Green Brown Red Brown Red Brown Red
Row 21: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Brown
Row 22: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Green Brown Red Red Red Red Red
Row 24: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Row 25: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Row 26: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Row 27: Brown Brown Brown Brown Brown Brown Green Red Red Red Brown Red Brown
Row 28: Brown Brown Brown Brown Brown Brown Green Red Brown Red Red Red Brown
Row 29: Brown Brown Brown Brown Brown Brown Green Red Red Red Red Red Red
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Brown Green Green Green Brown Green Green Brown Green Green Green Brown
Row 3: Brown Green Brown Green Green Green Green Green Green Brown Green Brown
Row 4: 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
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Brown Brown Green Green Green Green Green
Row 8: Brown Brown Green Green Green Green Green Green Green Green Brown Brown
Row 9: Brown Green Green Green Green Green Green Green Green Green Green Brown
Row 10: Green Brown Green Brown Green Brown Brown Green Brown Green Brown Green
Row 11: 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
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Brown Green Brown Green Green Green Green Brown Green Brown Green
Row 15: Green Brown Green Brown Green Green Green Green Brown Green Brown Green
Row 16: 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
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Brown Green Brown Green Brown Brown Green Brown Green Brown Green
Row 20: Brown Green Green Green Green Green Green Green Green Green Green Brown
Row 21: Brown Brown Green Green Green Green Green Green Green Green Brown Brown
Row 22: Green Green Green Green Green Brown Brown Green Green Green Green Green
Row 23: 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
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Brown Green Brown Green Green Green Green Green Green Brown Green Brown
Row 27: Brown Green Green Green Brown Green Green Brown Green Green Green Brown
Row 28: Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Red Red Red Red Red Red Red Red Red Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Red Red Red Red Red Red Red Red Red Orange Gray Gray Red Gray Gray Gray Gray Gray Gray
Row 4: Red Red Red Red Red Red Red Red Red Orange Gray Red Gray Gray Gray Gray Gray Gray Gray
Row 5: Red Red Red Red Red Red Red Red Red Orange Red Gray Red Gray Red Red Gray Gray Gray
Row 6: Red Red Red Red Red Red Red Red Red Orange Red Gray Gray Red Red Gray Red Gray Gray
Row 7: Red Red Red Red Red Red Red Red Red Orange Red Gray Red Gray Gray Red Red Gray Gray
Row 8: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Gray Red Gray Gray Red
Row 9: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Gray Red Red
Row 10: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Orange 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
Row 2: 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 Red Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Red Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Red Red Orange Red Orange Red Red Orange Red Orange Red Red Orange Orange Orange
Row 6: Orange Orange Red Orange Red Red Orange Orange Red Red Orange Orange Red Red Orange Red Orange Orange
Row 7: Orange Orange Red Red Orange Orange Red Orange Red Red Orange Red Orange Orange Red Red Orange Orange
Row 8: Red Orange Orange Red Orange Red Red Red Red Red Red Red Red Orange Red Orange Orange Red
Row 9: Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Orange Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red
Row 13: Red Orange Orange Red Orange Red Red Red Red Red Red Red Red Orange Red Orange Orange Red
Row 14: Orange Orange Red Red Orange Orange Red Orange Red Red Orange Red Orange Orange Red Red Orange Orange
Row 15: Orange Orange Red Orange Red Red Orange Orange Red Red Orange Orange Red Red Orange Red Orange Orange
Row 16: Orange Orange Orange Red Red Orange Red Orange Red Red Orange Red Orange Red Red Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Red Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Red 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
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 17: Red Pink Pink Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 18: Pink Pink Red Pink Red Red Red Yellow Red Red Red Red Red Red Red
Row 19: Red Pink Red Pink Red Red Red Yellow Red Red Red Red Red Red Red
Row 20: Pink Red Pink Red Red Red Red Yellow Red Red Red Red Red Red Red
Row 21: Pink Pink Pink Pink Pink Red Red Yellow 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>
| Yellow Yellow Yellow Yellow Yellow Red Red Red Red Yellow Yellow Yellow Yellow Yellow
Yellow Red Yellow Red Red Red Red Red Red Red Red Yellow Red Yellow
Red Yellow Red Yellow Red Red Red Red Red Red Yellow Red Yellow Red
Yellow Yellow Red Yellow Red Red Red Red Red Red Yellow Red Yellow Yellow
Red Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Yellow Yellow Red Red Red Red Red Red Red Red Yellow Yellow Red
Yellow Yellow Red Yellow Red Red Red Red Red Red Yellow Red Yellow Yellow
Red Yellow Red Yellow Red Red Red Red Red Red Yellow Red Yellow Red
Yellow Red Yellow Red Red Red Red Red Red Red Red Yellow Red Yellow
Yellow Yellow Yellow Yellow Yellow Red Red Red Red 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: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Red
Row 6: Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange 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 Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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
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 Gray Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Green Red Pink Red Green 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
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: 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 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: 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
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red
Row 27: 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
Output:
Row 1: Brown Gray Black
Row 2: Brown Orange Blue
Row 3: Pink Orange Green
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray 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 Gray Gray Brown Brown Brown Brown Brown Brown Brown Pink Yellow Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Gray Gray
Row 2: Gray Gray
Row 3: Pink Yellow
Row 4: Yellow 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 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 Orange Yellow 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 Orange 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 Black Black Black Black Black 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 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 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 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 Yellow 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 Brown 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 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 Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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 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 Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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 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
Row 28: Black Black Black Black Black Black 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 Yellow
Row 2: Orange 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
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 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 Blue Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Blue Black Black Black Black Black Black Black Black Black
Row 10: Black Black Orange Blue 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 Yellow Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Yellow Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Orange Black Yellow Yellow Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black 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
Row 18: 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
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Black Black Black Black Pink Black Pink Black Black Brown Brown Black Black Black Black
Row 22: Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black
Row 24: 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
Row 26: 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
Row 28: 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>
| Yellow Blue Brown Brown
Pink Yellow Pink Blue
Orange Blue 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: Yellow Yellow Yellow Blue Yellow Blue Gray
Row 2: Yellow Yellow Orange Yellow Yellow Yellow Green
Row 3: Orange Orange Yellow Blue Gray Gray Pink
Row 4: Yellow Gray Yellow Blue Orange Gray Yellow
Row 5: Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Green Yellow Gray Green Yellow Yellow Yellow
Row 7: Blue Green Blue Yellow Yellow Yellow Gray
Row 8: Yellow Yellow Yellow Blue Gray Yellow Gray
Row 9: Yellow Yellow Yellow Yellow Yellow Pink Yellow
Row 10: Gray Purple Yellow Yellow Gray Yellow Gray
Row 11: Gray Green Green Pink Yellow Orange Orange
Row 12: Yellow Orange Yellow Blue Gray Yellow Yellow
Row 13: Green Yellow Yellow Purple Yellow Gray Pink
Row 14: Yellow Yellow Yellow Green Yellow Orange Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Gray Purple Yellow Purple Orange Blue Blue
Row 18: Green Orange Yellow Yellow Blue Gray Orange
Row 19: Green Orange Orange Blue Gray Orange Yellow
Output:
Row 1: Green Orange Orange Blue Gray Orange Yellow
Row 2: Green Orange Yellow Yellow Blue Gray Orange
Row 3: Gray Purple Yellow Purple Orange Blue Blue
Row 4: Gray Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Green Yellow Orange Yellow
Row 7: Green Yellow Yellow Purple Yellow Gray Pink
Row 8: Yellow Orange Yellow Blue Gray Yellow Yellow
Row 9: Gray Green Green Pink Yellow Orange Orange
Row 10: Gray Purple Yellow Yellow Gray Yellow Gray
Row 11: Yellow Yellow Yellow Yellow Yellow Pink Yellow
Row 12: Yellow Yellow Yellow Blue Gray Yellow Gray
Row 13: Blue Green Blue Yellow Yellow Yellow Gray
Row 14: Green Yellow Gray Green Yellow Yellow Yellow
Row 15: Green Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Gray Yellow Blue Orange Gray Yellow
Row 17: Orange Orange Yellow Blue Gray Gray Pink
Row 18: Yellow Yellow Orange Yellow Yellow Yellow Green
Row 19: Yellow Yellow Yellow Blue Yellow Blue Gray
Example 2
Input:
Row 1: Red Purple Red Purple Purple Black
Row 2: Black Black Black Purple Black Red
Row 3: Black Purple Purple Purple Red Red
Row 4: Purple Purple Black Black Red Red
Row 5: Purple Purple Red Red Purple Red
Row 6: Black Red Black Black Purple Purple
Row 7: Black Red Red Purple Red Red
Row 8: Red Red Red Red Red Black
Row 9: Red Purple Red Red Purple Red
Row 10: Red Black Red Red Purple Purple
Row 11: Black Black Black Purple Red Red
Row 12: Purple Purple Red Purple Purple Red
Row 13: Black Purple Red Purple Purple Red
Row 14: Purple Purple Red Purple Red Purple
Row 15: Red Black Purple Red Red Red
Output:
Row 1: Red Black Purple Red Red Red
Row 2: Purple Purple Red Purple Red Purple
Row 3: Black Purple Red Purple Purple Red
Row 4: Purple Purple Red Purple Purple Red
Row 5: Black Black Black Purple Red Red
Row 6: Red Black Red Red Purple Purple
Row 7: Red Purple Red Red Purple Red
Row 8: Red Red Red Red Red Black
Row 9: Black Red Red Purple Red Red
Row 10: Black Red Black Black Purple Purple
Row 11: Purple Purple Red Red Purple Red
Row 12: Purple Purple Black Black Red Red
Row 13: Black Purple Purple Purple Red Red
Row 14: Black Black Black Purple Black Red
Row 15: Red Purple Red Purple Purple Black
Example 3
Input:
Row 1: Black Brown Brown Brown Brown Brown Brown Pink Black Pink Brown
Row 2: Brown Brown Green Pink Green Brown Brown Green Brown Brown Pink
Row 3: Brown Brown Brown Pink Brown Green Green Pink Brown Brown Brown
Row 4: Brown Brown Green Brown Brown Gray Brown Brown Green Brown Black
Row 5: Brown Green Pink Pink Brown Brown Brown Brown Gray Brown Green
Row 6: Brown Green Red Brown Brown Gray Brown Brown Pink Brown Brown
Row 7: Pink Brown Purple Brown Black Brown Pink Brown Brown Black Black
Row 8: Brown Black Brown Black Green Gray Brown Brown Brown Brown Gray
Row 9: Brown Brown Brown Black Brown Brown Brown Pink Brown Gray Brown
Row 10: Black Pink Purple Green Pink Brown Brown Brown Green Brown Brown
Row 11: Green Gray Black Green Brown Purple Brown Pink Brown Brown Brown
Row 12: Gray Gray Brown Purple Black Black Brown Gray Gray Brown Brown
Row 13: Brown Gray Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Pink
Row 15: Brown Brown Brown Gray Brown Brown Brown Brown Brown Gray Brown
Row 16: Gray Brown Gray Gray Black Black Purple Gray Brown Brown Brown
Output:
Row 1: Gray Brown Gray Gray Black Black Purple Gray Brown Brown Brown
Row 2: Brown Brown Brown Gray Brown Brown Brown Brown Brown Gray Brown
Row 3: Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Pink
Row 4: Brown Gray Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 5: Gray Gray Brown Purple Black Black Brown Gray Gray Brown Brown
Row 6: Green Gray Black Green Brown Purple Brown Pink Brown Brown Brown
Row 7: Black Pink Purple Green Pink Brown Brown Brown Green Brown Brown
Row 8: Brown Brown Brown Black Brown Brown Brown Pink Brown Gray Brown
Row 9: Brown Black Brown Black Green Gray Brown Brown Brown Brown Gray
Row 10: Pink Brown Purple Brown Black Brown Pink Brown Brown Black Black
Row 11: Brown Green Red Brown Brown Gray Brown Brown Pink Brown Brown
Row 12: Brown Green Pink Pink Brown Brown Brown Brown Gray Brown Green
Row 13: Brown Brown Green Brown Brown Gray Brown Brown Green Brown Black
Row 14: Brown Brown Brown Pink Brown Green Green Pink Brown Brown Brown
Row 15: Brown Brown Green Pink Green Brown Brown Green Brown Brown Pink
Row 16: Black Brown Brown Brown Brown Brown Brown Pink Black Pink Brown
Here is the input grid for the test example:
Input:
Row 1: Black Black Purple Black Red Black Red Black Black Black Black Black Purple Black Purple Orange Black Black Pink Black Black Black Black Black Black Red Black Red
Row 2: Red Black Pink Black Black Purple Black Black Purple Black Orange Black Orange Purple Purple Black Black Red Black Black Black Orange Pink Purple Black Black Black Black
Row 3: Black Black Pink Black Black Black Purple Black Red Black Orange Black Purple Black Black Black Black Black Red Black Black Black Black Red Black Black Black Black
Row 4: Black Black Black Purple Red Black Black Purple Black Black Orange Purple Black Black Black Purple Red Purple Black Black Orange Red Black Black Black Orange Black Purple
Row 5: Black Black Black Black Black Purple Black Black Black Purple Pink Purple Black Red Black Black Red Orange Black Black Black Black Black Black Black Pink Black Purple
Row 6: Purple Black Black Black Black Purple Black Black Black Black Black Red Black Orange Purple Purple Black Black Orange Pink Orange Black Purple Black Black Purple Black Black
Row 7: Orange Black Red Black Black Black Orange Black Purple Black Black Black Black Black Black Purple Black Purple Purple Purple Black Black Purple Black Black Orange Black Orange
Row 8: Black Orange Black Pink Orange Purple Red Purple Black Orange Red Purple Black Purple Black Black Black Purple Black Black Orange Black Black Black Red Purple Black Black
Row 9: Black Purple Black Orange Black Black Black Black Black Black Black Black Purple Black Black Black Black Purple Purple Black Black Black Purple Black Black Black Black Black
Row 10: Black Black Black Purple Black Black Black Purple Black Black Black Purple Orange Black Black Purple Black Red Black Black Orange Black Black Black Purple Purple Black Black
Row 11: Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Red Black Orange Black Black Purple Black Orange Black Purple Orange Black Black Black
Row 12: Purple Black Black Purple Black Black Purple Black Black Black Purple Black Black Black Black Black Black Black Black Black Red Black Black Purple Black Black Black Black
Row 13: Black Purple Pink Black Black Black Red Black Purple Black Black Black Black Black Black Black Black Black Black Red Orange Black Black Black Purple Purple Black Black
Row 14: Black Black Purple Black Black Purple Black Black Black Purple Red Purple Black Black Black Orange Black Purple Black Black Black Black Black Purple Purple Purple Purple Black
Row 15: Black Black Black Purple Black Purple Black Red Purple Orange Black Black Purple Orange Purple Black Black Black Black Purple Black Black Black Black Purple Red Black Purple
Row 16: Black Black Black Red Black Purple Purple Black Purple Black Purple Purple Red Black Purple Black Black Black Black Purple Red Black Red Black Black Black Purple Black
Row 17: Black Black Black Black Orange Purple Black Black Purple Purple Black Black Black Black Black Black Black Pink Black Red Black Black Black Orange Purple Black Black Red
Row 18: Orange Black Black Black Black Purple Purple Black Orange Black Black Black Black Black Purple Black Purple Orange Black Black Black Black Black Black Black Purple Black Orange
Row 19: Black Black Black Black Orange Black Black Orange Black Orange Black Purple Purple Orange Purple Black Purple Purple Black Black Purple Black Black Purple Black Purple Purple Black
Row 20: Black Black Orange Black Purple Black Black Purple Black Black Purple Purple Black Black Black Black Purple Black Black Black Black Orange Black Purple Purple Purple Purple Black
Row 21: Black Black Purple Purple Purple Purple Red Black Purple Black Purple Black Black Black Black Black Orange Black Purple Black Black Purple Purple Orange Black Purple Black Orange
Row 22: Black Black Black Purple Red Black Black Black Black Black Black Purple Purple Black Orange Purple Black Black Red Black Black Black Purple Red Purple Black Red Black
Row 23: Red Black Purple Black Black Purple Black Black Orange Black Orange Purple Black Black Purple Black Black Black Black Red Black Black Red Black Black Black Black Black
Row 24: Black Black Black Purple Black Purple Black Black Purple Orange Red Purple Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Red
Row 25: Red Black Black Black Black Black Black Black Purple Black Black Black Black Orange Black Black Black Black Black Purple Purple Black Orange Black Purple Black Purple Black
Row 26: Black Purple Black Black Black Red Black Purple Purple Orange Red Black Black Black Purple Black Orange Black Purple Purple Black Black Purple Black Black Purple Purple Black
Row 27: Black Black Black Black Black Black Black Black Purple Purple Purple Black Black Black Black Purple Purple Red Orange Purple Black Black Purple Black Black Black Black Purple
Row 28: Black Orange Red Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Purple Black Black Black Black Purple Orange Black Black Black
Row 29: Black Black Purple Black Black Red Black Black Purple Red Purple Black Black Black Black Purple Black Black Black Black Red Purple Black Black Black Black Purple 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 Purple Black Black Red Black Black Purple Red Purple Black Black Black Black Purple Black Black Black Black Red Purple Black Black Black Black Purple Red
Black Orange Red Black Black Black Black Black Black Purple Black Purple Black Black Black Black Black Black Purple Black Black Black Black Purple Orange Black Black Black
Black Black Black Black Black Black Black Black Purple Purple Purple Black Black Black Black Purple Purple Red Orange Purple Black Black Purple Black Black Black Black Purple
Black Purple Black Black Black Red Black Purple Purple Orange Red Black Black Black Purple Black Orange Black Purple Purple Black Black Purple Black Black Purple Purple Black
Red Black Black Black Black Black Black Black Purple Black Black Black Black Orange Black Black Black Black Black Purple Purple Black Orange Black Purple Black Purple Black
Black Black Black Purple Black Purple Black Black Purple Orange Red Purple Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Red
Red Black Purple Black Black Purple Black Black Orange Black Orange Purple Black Black Purple Black Black Black Black Red Black Black Red Black Black Black Black Black
Black Black Black Purple Red Black Black Black Black Black Black Purple Purple Black Orange Purple Black Black Red Black Black Black Purple Red Purple Black Red Black
Black Black Purple Purple Purple Purple Red Black Purple Black Purple Black Black Black Black Black Orange Black Purple Black Black Purple Purple Orange Black Purple Black Orange
Black Black Orange Black Purple Black Black Purple Black Black Purple Purple Black Black Black Black Purple Black Black Black Black Orange Black Purple Purple Purple Purple Black
Black Black Black Black Orange Black Black Orange Black Orange Black Purple Purple Orange Purple Black Purple Purple Black Black Purple Black Black Purple Black Purple Purple Black
Orange Black Black Black Black Purple Purple Black Orange Black Black Black Black Black Purple Black Purple Orange Black Black Black Black Black Black Black Purple Black Orange
Black Black Black Black Orange Purple Black Black Purple Purple Black Black Black Black Black Black Black Pink Black Red Black Black Black Orange Purple Black Black Red
Black Black Black Red Black Purple Purple Black Purple Black Purple Purple Red Black Purple Black Black Black Black Purple Red Black Red Black Black Black Purple Black
Black Black Black Purple Black Purple Black Red Purple Orange Black Black Purple Orange Purple Black Black Black Black Purple Black Black Black Black Purple Red Black Purple
Black Black Purple Black Black Purple Black Black Black Purple Red Purple Black Black Black Orange Black Purple Black Black Black Black Black Purple Purple Purple Purple Black
Black Purple Pink Black Black Black Red Black Purple Black Black Black Black Black Black Black Black Black Black Red Orange Black Black Black Purple Purple Black Black
Purple Black Black Purple Black Black Purple Black Black Black Purple Black Black Black Black Black Black Black Black Black Red Black Black Purple Black Black Black Black
Black Black Purple Black Black Black Black Black Black Black Black Black Black Black Red Black Orange Black Black Purple Black Orange Black Purple Orange Black Black Black
Black Black Black Purple Black Black Black Purple Black Black Black Purple Orange Black Black Purple Black Red Black Black Orange Black Black Black Purple Purple Black Black
Black Purple Black Orange Black Black Black Black Black Black Black Black Purple Black Black Black Black Purple Purple Black Black Black Purple Black Black Black Black Black
Black Orange Black Pink Orange Purple Red Purple Black Orange Red Purple Black Purple Black Black Black Purple Black Black Orange Black Black Black Red Purple Black Black
Orange Black Red Black Black Black Orange Black Purple Black Black Black Black Black Black Purple Black Purple Purple Purple Black Black Purple Black Black Orange Black Orange
Purple Black Black Black Black Purple Black Black Black Black Black Red Black Orange Purple Purple Black Black Orange Pink Orange Black Purple Black Black Purple Black Black
Black Black Black Black Black Purple Black Black Black Purple Pink Purple Black Red Black Black Red Orange Black Black Black Black Black Black Black Pink Black Purple
Black Black Black Purple Red Black Black Purple Black Black Orange Purple Black Black Black Purple Red Purple Black Black Orange Red Black Black Black Orange Black Purple
Black Black Pink Black Black Black Purple Black Red Black Orange Black Purple Black Black Black Black Black Red Black Black Black Black Red Black Black Black Black
Red Black Pink Black Black Purple Black Black Purple Black Orange Black Orange Purple Purple Black Black Red Black Black Black Orange Pink Purple Black Black Black Black
Black Black Purple Black Red Black Red Black Black Black Black Black Purple Black Purple Orange Black Black Pink Black Black Black Black Black Black Red Black 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 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
Row 3: 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
Row 5: Purple Purple 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
Row 7: 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
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: Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Red Red Red 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
Row 16: 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
Row 18: Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Red Red Red 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
Row 22: 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
Row 24: 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
Output:
Row 1: 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
Row 3: 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
Row 5: Purple Purple 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
Row 7: 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
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: Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Purple Purple Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: 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
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Purple Purple Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: 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
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
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: Black Black Black Black Black Black Black Black Black Black Black Black 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: Black Black Black Black Black Black Black Black Black Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
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: Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue
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: Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
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 Green Green Green Green Green Green Green Green
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: 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
Row 9: 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
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
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 Green Green Green Green Green Green Green Green
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: 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
Row 9: 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
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: 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
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: 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
Row 15: 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
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: 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
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Red Red Red Red Red Red Red Red Red Red Red Red 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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: 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 Yellow Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange
Row 7: Green Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Brown Orange
Row 10: Orange Orange Orange Orange Orange Orange
Row 11: Blue Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Brown Orange
Row 16: Orange Orange Green Orange Orange Orange
Row 17: Pink Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange
Row 20: Green Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Brown Orange
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
Output:
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 Yellow Yellow Yellow Yellow
Row 5: Orange Orange Orange Orange Orange Yellow
Row 6: Orange Orange Orange Orange Orange Yellow
Row 7: Green Green Green Green Green Green
Row 8: Orange Orange Orange Orange Orange Green
Row 9: Orange Orange Orange Orange Brown Brown
Row 10: Orange Orange Orange Orange Orange Brown
Row 11: Blue Blue Blue Blue Blue Blue
Row 12: Orange Orange Orange Orange Orange Blue
Row 13: Orange Orange Orange Orange Orange Blue
Row 14: Orange Orange Orange Orange Orange Blue
Row 15: Orange Orange Orange Orange Brown Brown
Row 16: Orange Orange Green Green Green Green
Row 17: Pink Pink Pink Pink Pink Pink
Row 18: Orange Orange Orange Orange Orange Pink
Row 19: Orange Orange Orange Orange Orange Pink
Row 20: Green Green Green Green Green Green
Row 21: Orange Orange Orange Orange Brown Brown
Row 22: Orange Orange Orange Orange Orange Brown
Row 23: Orange Orange Orange Orange Orange Brown
Row 24: Orange Orange Orange Orange Orange Brown
Row 25: Orange Orange Orange Orange Orange Brown
Row 26: Orange Orange Orange Orange Orange Brown
Example 2
Input:
Row 1: Purple Purple Purple Green Purple
Row 2: Purple Purple Purple Purple Purple
Row 3: Purple Purple Yellow Purple Purple
Row 4: Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple
Row 6: Gray Purple Purple Purple Purple
Row 7: Purple Purple Purple Blue Purple
Row 8: Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Green Green
Row 2: Purple Purple Purple Purple Green
Row 3: Purple Purple Yellow Yellow Yellow
Row 4: Purple Purple Purple Purple Yellow
Row 5: Purple Purple Purple Purple Yellow
Row 6: Gray Gray Gray Gray Gray
Row 7: Purple Purple Purple Blue Blue
Row 8: Purple Purple Purple Purple Blue
Row 9: Purple Purple Purple Purple Blue
Example 3
Input:
Row 1: Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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 Green Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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
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
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
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
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple 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 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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
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 Pink
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Green
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 Green
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink
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 Pink
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 Pink
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 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 Pink
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 Pink
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 Pink
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink
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 Pink
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 Pink
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Row 5: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: 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
Row 11: 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
Row 13: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange
Row 17: 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
Row 19: 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
Row 21: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Blue 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 Red 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 Orange Red Red Red Red Red
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 Orange Orange Orange Black
Orange 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 Orange Orange Black
Orange 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 Orange Orange Black
Orange 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 Orange Orange Black
Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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 Orange Orange Orange Yellow
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow
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 Orange Orange Orange Yellow
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 Orange Orange Orange Yellow
Orange Orange Orange Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink
Orange Orange Orange Orange Orange Orange Orange Orange Black Black Black Black Black Black Black
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Orange Orange Orange Orange 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: Red Red Red Red Red Red Red Red Red Red Red Green
Row 2: Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red
Row 3: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 4: Orange Orange Orange Orange Orange Orange Red Green Blue Blue Red Red
Row 5: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 6: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 7: Red Red Green Red Red Red Red Blue Blue Blue Red Red
Row 8: 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
Row 10: Blue Blue Blue Blue Red Orange Orange Red Red Red Red Red
Row 11: Blue Blue Blue Blue Red Orange Orange Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red
Row 3: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 4: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 5: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 6: Orange Orange Orange Orange Orange Orange Red Blue Blue Blue Red Red
Row 7: Red Red Red Red Red Red Red Blue Blue Blue Red Red
Row 8: 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
Row 10: Blue Blue Blue Blue Red Orange Orange Red Red Red Red Red
Row 11: Blue Blue Blue Blue Red Orange Orange Red Red Red Red Red
Example 2
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 Orange Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Orange Purple Purple
Row 4: 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 Purple Purple
Row 6: Orange Purple Purple Purple Purple Purple Orange 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 Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Orange 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 Orange Purple Purple Purple
Row 12: Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Orange Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Blue Blue Orange Blue Blue Blue Purple Purple Purple Pink
Row 15: Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Pink Purple Purple Purple Purple Pink Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Pink Purple Purple Purple Orange Purple Purple Purple Purple Orange Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple 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 Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Purple Purple Purple Gray 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 Orange Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Purple
Row 6: Purple Purple Yellow Purple Purple Purple Purple Blue Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Blue Purple Purple Purple Purple Purple Red Red Red Red
Row 9: Purple Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 10: Purple Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 11: Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple
Row 13: Purple Red Red Red Red Red Red Yellow Purple Purple Purple
Row 14: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 15: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 16: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 19: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 20: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 21: Purple Brown Brown Brown Orange Brown Brown Brown Purple Purple Purple
Row 22: Orange Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 23: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 24: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 25: Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: 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
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 Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 9: Purple Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 10: Purple Purple Purple Purple Purple Purple Purple Red Red Red Red
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 14: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 15: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 16: Purple Red Red Red Red Red Red Red Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 19: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 20: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 21: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 22: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 23: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 24: Purple Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 26: 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 Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Black Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Gray Orange Orange Pink Red Red Red Red Red
Row 3: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Red Red Red Gray Red
Row 4: Orange Pink Red Red Red Orange Orange Purple Pink Purple Purple Pink Purple Purple Orange Orange Orange Red Red Red Red Red
Row 5: Orange Orange Red Red Red Orange Black Purple Purple Purple Purple Purple Purple Purple Gray Orange Orange Orange Orange Orange Orange Pink
Row 6: Gray Orange Pink Red Gray Orange Orange Purple Purple Purple Purple Black Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange Pink Orange Orange Orange
Row 8: Orange Orange Orange Gray Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange
Row 9: Purple Gray Purple Orange Orange Orange Orange Gray Purple Purple Orange Orange Black Orange Orange Orange Orange Black Purple Purple Purple Orange
Row 10: Purple Purple Purple Orange Orange Black Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink 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 Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Red Red Red Red Red
Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Red Red Red Red Red
Orange Orange Red Red Red Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Red Red Red Red Red
Orange Orange Red Red Red Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Red Red Red Orange Orange Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange 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 Purple Purple Purple Orange
Purple Purple Purple Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange
Purple Purple Purple Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown Purple Purple Purple Purple Purple Brown
Row 4: Brown Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Brown Purple Brown Brown Brown Purple Brown
Row 5: Brown Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Brown Purple Brown
Row 6: Brown Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Purple Brown Brown Brown Purple Brown
Row 7: Brown Purple Brown Brown Brown Purple Purple Brown Brown Brown Purple Brown Purple Purple Purple Purple Purple Brown
Row 8: Brown Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Purple Brown Brown Brown Purple Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown Brown
Row 12: Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown Brown Purple Purple Purple Purple Purple Brown Brown
Row 13: Brown Brown Purple Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple
Row 14: Brown Brown Purple Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple
Row 15: Brown Brown Purple Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple
Row 16: Brown Brown Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple
Row 17: Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 18: Brown Brown Brown Purple Brown Brown Brown Purple Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 19: Brown Brown Brown Purple Brown Brown Brown Purple Purple Brown Brown Brown Purple Purple Brown Brown Brown Purple
Row 20: Brown Brown Brown Purple Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Purple
Row 21: Brown Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Pink Pink Pink Purple Purple Purple Purple Purple Brown Brown Pink Pink Pink Brown Brown
Row 2: Brown Brown Brown Pink Pink Pink Purple Brown Pink Brown Purple Brown Brown Pink Pink Pink Brown Brown
Row 3: Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple Pink Purple Purple Purple Purple Purple Pink
Row 4: Brown Purple Purple Purple Purple Purple Purple Brown Pink Brown Purple Brown Purple Pink Pink Pink Purple Brown
Row 5: Pink Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Purple Pink Pink Pink Purple Pink
Row 6: Pink Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Purple Pink Pink Pink Purple Pink
Row 7: Brown Purple Brown Pink Pink Purple Purple Brown Pink Brown Purple Brown Purple Purple Purple Purple Purple Brown
Row 8: Pink Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink
Row 9: Brown Brown Brown Pink Pink Pink Purple Brown Pink Brown Purple Purple Brown Pink Pink Purple Brown Brown
Row 10: Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple Pink Pink
Row 11: Brown Brown Brown Pink Pink Pink Brown Brown Pink Brown Pink Purple Brown Pink Pink Purple Brown Brown
Row 12: Brown Brown Purple Purple Purple Purple Purple Brown Pink Brown Pink Purple Purple Purple Purple Purple Brown Brown
Row 13: Brown Brown Purple Pink Pink Pink Purple Brown Pink Brown Pink Brown Brown Purple Purple Purple Purple Purple
Row 14: Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple
Row 15: Pink Pink Purple Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Purple
Row 16: Brown Brown Purple Purple Purple Purple Purple Brown Purple Purple Purple Purple Purple Purple Pink Pink Brown Purple
Row 17: Brown Brown Brown Purple Purple Purple Purple Purple Purple Brown Pink Brown Purple Purple Purple Purple Purple Purple
Row 18: Pink Pink Pink Purple Pink Pink Pink Purple Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple
Row 19: Pink Pink Pink Purple Pink Pink Pink Purple Purple Pink Pink Pink Purple Purple Pink Pink Pink Purple
Row 20: Pink Pink Pink Purple Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Pink Pink Pink Purple
Row 21: Brown Brown Brown Purple Purple Purple Purple Purple Pink Brown Pink Brown Brown Purple Pink Pink Brown Purple
Row 22: Brown Brown Brown Pink Pink Pink Brown Brown Pink Brown Pink Brown Brown Purple Purple Purple Purple Purple
Row 23: Brown Brown Brown Pink Pink Pink Brown Brown Pink Brown Pink Brown Brown Pink Pink Pink 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 Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Blue Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Blue Gray Gray Gray Blue Blue Gray Gray Gray Blue Gray Gray
Row 6: Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray
Row 7: Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray
Row 8: Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray
Row 9: Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 10: Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray
Row 16: Gray Gray Gray Blue Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray
Row 17: Gray Gray Gray Blue Gray Gray Gray Blue Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray
Row 18: Gray Gray Gray Blue Gray Gray Gray Blue Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray
Row 19: Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Blue Gray Gray Gray Blue Blue Blue Blue Blue Gray Gray
Row 20: Gray Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 21: Gray Blue Gray Gray Gray Blue Gray Gray Blue Blue Blue Blue Blue Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 22: Gray Blue Gray Gray Gray Blue Gray Gray Blue Gray Gray Gray Blue Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 23: Gray Blue Gray Gray Gray Blue Gray Gray Blue Gray Gray Gray Blue Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray
Row 24: Gray Blue Blue Blue Blue Blue Gray Gray Blue Gray Gray Gray Blue Gray Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 25: Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue 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
Row 27: Gray Gray Gray Gray Gray 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 Gray Gray Gray Gray Gray
Row 29: 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 Pink Pink Gray Pink Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray
Row 2: Gray Gray Pink Pink Gray Pink Blue Blue Blue Blue Blue Gray Gray Pink Gray Gray Blue Blue Blue Blue Blue Gray Gray
Row 3: Gray Gray Pink Pink Gray Pink Blue Gray Pink Gray Blue Gray Gray Pink Gray Gray Blue Gray Pink Gray Blue Gray Gray
Row 4: Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Pink Pink
Row 5: Gray Gray Pink Pink Gray Pink Blue Gray Pink Gray Blue Blue Gray Pink Gray Blue Blue Gray Pink Gray Blue Gray Gray
Row 6: Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Pink Pink Pink Blue Blue Blue Blue Blue Blue Pink Pink
Row 7: Blue Gray Pink Pink Blue Pink Gray Gray Pink Gray Pink Blue Gray Pink Gray Blue Pink Gray Pink Gray Gray Gray Gray
Row 8: Blue Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink
Row 9: Blue Gray Pink Pink Blue Pink Gray Gray Pink Gray Pink Gray Gray Pink Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 10: Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Gray Gray Pink Blue Gray Pink Gray Blue Gray Gray Gray Gray
Row 11: Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink
Row 13: Gray Gray Pink Pink Gray Pink Blue Gray Pink Gray Blue Gray Gray Pink Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 14: Gray Gray Pink Pink Gray Pink Blue Blue Blue Blue Blue Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray
Row 15: Gray Gray Pink Blue Blue Blue Blue Blue Pink Gray Pink Gray Gray Pink Gray Gray Blue Blue Blue Blue Blue Gray Gray
Row 16: Gray Gray Pink Blue Gray Pink Gray Blue Blue Blue Blue Blue Blue Pink Gray Gray Blue Gray Pink Gray Blue Gray Gray
Row 17: Pink Pink Pink Blue Pink Pink Pink Blue Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink
Row 18: Pink Pink Pink Blue Pink Pink Pink Blue Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink Pink Blue Pink Pink
Row 19: Gray Gray Pink Blue Blue Blue Blue Blue Blue Gray Pink Gray Blue Pink Gray Gray Blue Blue Blue Blue Blue Gray Gray
Row 20: Gray Blue Blue Blue Blue Blue Gray Gray Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 21: Gray Blue Pink Pink Gray Blue Gray Gray Blue Blue Blue Blue Blue Pink Blue Gray Pink Gray Blue Gray Gray Gray Gray
Row 22: Pink Blue Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Blue Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink
Row 23: Pink Blue Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Blue Pink Blue Pink Pink Pink Blue Pink Pink Pink Pink
Row 24: Gray Blue Blue Blue Blue Blue Gray Gray Blue Gray Pink Gray Blue Pink Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 25: Gray Gray Pink Pink Gray Pink Gray Gray Blue Blue Blue Blue Blue Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray
Row 26: Gray Gray Pink Pink Gray Pink Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray
Row 27: Gray Gray Pink Pink Gray Pink Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray
Row 28: Gray Gray Pink Pink Gray Pink Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray
Row 29: Gray Gray Pink Pink Gray Pink Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Gray Pink 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 Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow
Row 3: Brown Brown Yellow Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow
Row 4: Brown Brown Yellow Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow
Row 5: Brown Brown Yellow Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Pink Brown Brown Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Pink Brown Yellow
Row 3: Pink Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Yellow Pink Pink Pink Yellow Pink Pink Yellow Pink Pink Pink Yellow Yellow Pink Pink Pink Yellow
Row 4: Pink Pink Yellow Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Yellow Yellow Pink Pink Pink Yellow Pink Pink Yellow Pink Pink Pink Yellow Yellow Pink Pink Pink Yellow
Row 5: Brown Brown Yellow Brown Pink Brown Yellow Brown Yellow Brown Pink Brown Yellow Yellow Brown Pink Brown Yellow Brown Brown Yellow Brown Pink Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Pink Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Orange Brown Brown Brown Orange Brown Orange Orange Orange Orange Orange
Row 4: Brown Brown Brown Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown Brown Orange
Row 5: Brown Brown Brown Brown Orange Orange Orange Orange Orange Brown Orange Brown Brown Brown Orange
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Orange
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Brown Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Pink Brown Brown
Brown Brown Brown Brown Orange Brown Pink Brown Orange Brown Brown Brown Pink Brown Brown
Pink Pink Pink Pink Orange Pink Pink Pink Orange Pink Orange Orange Orange Orange Orange
Brown Brown Brown Brown Orange Brown Pink Brown Orange Brown Orange Brown Pink Brown Orange
Pink Pink Pink Pink Orange Orange Orange Orange Orange Pink Orange Pink Pink Pink Orange
Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Orange Brown Pink Brown Orange
Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Orange Orange Orange Orange Orange
Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink 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: Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Purple Black Black
Row 9: Red Black Black Black Black Black 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: Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Purple Black Black
Row 9: Red Yellow Yellow Yellow Yellow Yellow Black Black
Example 2
Input:
Row 1: Green Green Red 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 Purple 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 Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Red Yellow Yellow Yellow Green Green Green Green Green
Row 2: Green Green Green Green Green Yellow Green Green Green Green Green
Row 3: Green Green Green Green Green Yellow Green Green Green Green Green
Row 4: Green Green Green Green Green Yellow Green Green Green Green Green
Row 5: Green Green Green Green Green Yellow Green Green Green Green Green
Row 6: Green Green Green Green Green Yellow Green Green Green Green Green
Row 7: Green Green Green Green Green Yellow Green Green Green Green Green
Row 8: Green Green Green Green Green Yellow Green Green Green Green Green
Row 9: Green Green Green Green Green Purple 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 Green Green Green Green Green
Row 12: 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
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 Red
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 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: 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
Row 13: 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
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 Purple 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 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 Yellow Yellow Red
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple 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
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Red Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Purple Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Black Black Black Black
Row 21: 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 Red Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black Black Black
Black Black Black Black Black Black Yellow Black 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 Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black 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 Black Black Black Black Black Black Black Black Black Black
Row 2: Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black
Row 3: Black Brown Brown Brown Black Black Black Black Gray Gray Gray Black Black Black
Row 4: Black Brown Brown Brown Black Black Black Black Gray Gray Gray Black Black Black
Row 5: Black Black Black Green Green Green Green Green Gray Gray Gray Black Black Black
Row 6: Orange Orange Orange Green Green Green Green Green Black Black Black Black Black Black
Row 7: Orange Orange Orange Green Green Green Green Green Black Black Black Black Black Black
Row 8: Orange Orange Orange Green Green Green Green Green Black Black Black Black Black Black
Row 9: Orange Orange Orange Green Green Green Green Green Black Black Black Black Black Black
Row 10: Orange Orange Orange Green Green Green Green Green Black Black Black Black Black Black
Row 11: Orange Orange Orange Black Black Black Black Pink Pink Pink Pink Black Black Black
Row 12: Orange Orange Orange Black Black Black Black Pink Pink Pink Pink Black Black Black
Row 13: Black Black Blue Blue Blue Black Black Pink Pink Pink Pink Black Black Black
Row 14: Black Black Blue Blue Blue Black Black Pink Pink Pink Pink Black Black Black
Row 15: Black Black Blue Blue Blue Black Black Pink Pink Pink Pink Black Black Black
Row 16: Black Black Blue Blue Blue Black Black Pink Pink Pink Pink Black Black Black
Row 17: Black Black Blue Blue Blue Black Black Pink Pink Pink Pink Black Black Black
Row 18: Black Black Blue Blue Blue 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
Row 20: 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
Row 2: Black Brown Brown Brown Black Black Black Black Black Black Black Black Black Black
Row 3: Black Brown Purple Brown Black Black Black Black Gray Gray Gray Black Black Black
Row 4: Black Brown Brown Brown Black Black Black Black Gray Purple Gray Black Black Black
Row 5: Black Black Black Green Green Green Green Green Gray Gray Gray Black Black Black
Row 6: Orange Orange Orange Green Purple Purple Purple Green Black Black Black Black Black Black
Row 7: Orange Purple Orange Green Purple Purple Purple Green Black Black Black Black Black Black
Row 8: Orange Purple Orange Green Purple Purple Purple Green Black Black Black Black Black Black
Row 9: Orange Purple Orange Green Purple Purple Purple Green Black Black Black Black Black Black
Row 10: Orange Purple Orange Green Green Green Green Green Black Black Black Black Black Black
Row 11: Orange Purple Orange Black Black Black Black Pink Pink Pink Pink Black Black Black
Row 12: Orange Orange Orange Black Black Black Black Pink Purple Purple Pink Black Black Black
Row 13: Black Black Blue Blue Blue Black Black Pink Purple Purple Pink Black Black Black
Row 14: Black Black Blue Purple Blue Black Black Pink Purple Purple Pink Black Black Black
Row 15: Black Black Blue Purple Blue Black Black Pink Purple Purple Pink Black Black Black
Row 16: Black Black Blue Purple Blue Black Black Pink Purple Purple Pink Black Black Black
Row 17: Black Black Blue Purple Blue Black Black Pink Pink Pink Pink Black Black Black
Row 18: Black Black Blue Blue Blue 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
Row 20: Black Black Black Black Black Black Black Black Black Black Black Black Black Black
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
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Blue Blue Blue Blue Brown Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 8: Pink Pink Pink Pink Pink Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 9: Pink Pink Pink Pink Pink Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 10: Pink Pink Pink Pink Pink Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 11: Pink Pink Pink Pink Pink Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 12: Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 13: Yellow Yellow Yellow 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: Yellow Yellow Yellow 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: Yellow Yellow Yellow 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: Yellow Yellow Yellow 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: Yellow Yellow Yellow 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: Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Purple Purple Purple Purple Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Blue Purple Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Blue Purple Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Blue Blue Blue Blue Brown Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 8: Pink Pink Pink Pink Pink Brown Gray Purple Purple Purple Purple Purple Gray Brown Brown Brown Green Purple Green Brown Brown Brown Brown Brown Brown Brown
Row 9: Pink Purple Purple Purple Pink Brown Gray Purple Purple Purple Purple Purple Gray Brown Brown Brown Green Purple Green Brown Brown Brown Brown Brown Brown Brown
Row 10: Pink Purple Purple Purple Pink Brown Gray Purple Purple Purple Purple Purple Gray Brown Brown Brown Green Purple Green Brown Brown Brown Brown Brown Brown Brown
Row 11: Pink Pink Pink Pink Pink Brown Gray Gray Gray Gray Gray Gray Gray Brown Brown Brown Green Purple Green Brown Brown Brown Brown Brown Brown Brown
Row 12: Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Green Brown Brown Brown Brown Brown Brown Brown
Row 13: Yellow Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Yellow Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Yellow Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Yellow Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Yellow Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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
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 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
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
Row 7: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Red Red Red Red Red 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
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
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 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
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
Row 7: Gray Gray Gray Gray Red Red Red Red Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Red Purple Purple Purple Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Red Purple Purple Purple Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Red Purple Purple Purple Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Red Purple Purple Purple Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Red Purple Purple Purple Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Red Red Red Red Red 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
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
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Red Red Red Red Red Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: 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
Row 15: 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
Row 16: 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
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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
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 Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Orange Purple Purple Purple Purple Purple Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Red Red Red Red Orange Purple Purple Purple Purple Purple Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Purple Purple Purple Red Orange Purple Purple Purple Purple Purple Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Purple Purple Purple Red Orange Purple Purple Purple Purple Purple Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Purple Purple Purple Red Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Purple Purple Purple Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Purple Purple Purple Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Red Red Red Red Red Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Blue Purple Purple Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Blue Purple Purple Purple Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Pink Pink 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 Pink Purple Purple Purple Purple Purple Pink Brown 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 Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown 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: Blue Gray Blue Purple Blue Green Green Green Blue Blue Blue Blue Blue Blue Orange Orange Blue Blue Blue Blue Red Red Blue Blue
Row 2: Blue Gray Blue Purple Blue Green Green Green Green Green Blue Blue Orange Orange Blue Orange Blue Blue Blue Blue Red Red Blue Red
Row 3: Blue Gray Blue Blue Blue Blue Green Green Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Red Red Red Red
Row 4: Gray Gray Blue Yellow Yellow Blue Blue Blue Blue Green Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue Red Red Red Blue
Row 5: Blue Gray Blue Yellow Yellow Yellow Blue Blue Green Green Blue Yellow Blue Orange Blue Blue Brown Blue Brown Blue Blue Blue Red Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Green Green Blue Yellow Blue Blue Blue Brown Brown Brown Brown Brown Brown Blue Blue Blue
Output:
Row 1: Blue Blue Blue Orange Orange Blue Blue
Row 2: Blue Orange Orange Blue Orange Blue Blue
Row 3: Orange Orange Orange Orange Orange Orange Orange
Row 4: Blue Blue Orange Orange Blue Blue Blue
Row 5: Blue Blue Orange Blue Blue Blue Blue
Example 2
Input:
Row 1: Pink Pink Red Blue Blue Blue Blue Blue Blue Red Red Red Red Yellow Red Blue Blue Red Red Red Red Blue Blue Red Red Red Orange Orange Orange
Row 2: Red Red Red Blue Blue Red Red Red Red Red Pink Pink Red Yellow Red Blue Blue Blue Red Red Blue Blue Blue Red Blue Red Red Red Orange
Row 3: Green Green Red Red Red Red Gray Gray Gray Red Pink Red Red Red Red Red Blue Blue Blue Red Red Blue Blue Blue Blue Blue Red Red Orange
Row 4: Green Green Green Green Red Red Gray Gray Gray Red Red Red Gray Red Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Red Orange
Row 5: Green Green Green Red Red Red Red Red Gray Gray Red Red Red Red Red Blue Blue Red Red Red Blue Red Blue Red Red Blue Red Red Orange
Row 6: Red Red Red Red Red Red Red Gray Gray Gray Gray Gray Red Brown Red Red Blue Red Red Red Red Red Blue Red Red Red Red Orange Orange
Row 7: Blue Blue Red Red Red Blue Red Gray Gray Red Red Red Red Brown Brown Red Red Red Purple Red Purple Red Red Red Red Orange Orange Orange Orange
Row 8: Blue Blue Blue Red Blue Blue Red Red Gray Red Brown Red Brown Brown Red Red Red Purple Purple Purple Purple Red Red Red Red Red Red Orange Red
Row 9: Blue Red Red Red Blue Red Blue Red Red Red Brown Red Red Brown Red Red Red Purple Purple Red Purple Purple Purple Red Green Green Red Orange Red
Row 10: Blue Red Blue Red Blue Blue Blue Red Red Brown Brown Brown Brown Brown Brown Brown Red Purple Purple Red Purple Red Red Red Green Green Red Red Red
Row 11: Red Red Blue Blue Blue Red Red Red Red Red Brown Brown Red Brown Brown Red Red Purple Purple Red Red Red Green Green Green Green Green Green Green
Row 12: Blue Blue Blue Blue Blue Red Orange Orange Orange Red Red Red Red Red Red Red Red Red Purple Red Red Green Green Green Red Green Green Green Red
Output:
Row 1: Red Blue Blue Red Red Red Red
Row 2: Blue Blue Blue Red Blue Red Red
Row 3: Red Blue Blue Blue Blue Blue Red
Row 4: Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Red Blue Red Red Blue Red
Row 6: Red Red Blue Red Red Red Red
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Gray Gray Pink Red Pink Red Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Gray Gray Pink Red Red Red Red Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue Pink Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Pink Gray Pink Pink Pink Pink Black Black Black Pink Pink Pink
Row 5: Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Blue Pink Pink Blue Pink Pink Pink Gray Gray Gray Gray Pink Black Black Black Pink Pink Pink Pink
Row 6: Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Gray Gray Gray
Row 7: Red Pink Pink Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Gray Pink
Row 8: Red Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Brown Brown Brown Brown Pink Blue Blue Pink Pink Pink Gray Gray
Row 9: Red Red Pink Pink Yellow Yellow Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Brown Brown Pink Pink Blue Blue Pink Pink Pink Pink
Row 10: Red Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Brown Brown Brown Pink Brown Brown Pink Blue Blue Blue Blue Blue Pink Pink
Row 11: Red Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Pink Pink Brown Brown Pink Blue Pink Blue Blue Pink Pink Pink
Row 12: Red Pink Black Black Black Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 13: Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink
Output:
Row 1: Blue Blue Pink Pink Pink
Row 2: Pink Blue Blue Pink Pink
Row 3: Blue Blue Blue Blue Blue
Row 4: Blue Pink Blue Blue Pink
Row 5: Pink Pink Blue Pink Pink
Row 6: Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Red Red Red Red Red Red Pink Pink Pink Pink Pink Black Black Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue
Row 2: Pink Pink Red Red Red Red Red Red Red Red Pink Pink Pink Pink Black Black Pink Black Pink Pink Pink Pink Pink Blue Blue Blue Blue
Row 3: Pink Pink Pink Red Red Red Red Red Red Red Pink Pink Pink Pink Black Black Black Black Black Pink Pink Pink Pink Pink Blue Blue Blue
Row 4: Pink Red Red Red Red Red Red Red Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue
Row 5: Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 6: Pink Pink Pink Red Pink Pink Pink Pink Red Red Pink Pink Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 7: Pink Pink Pink Red Pink Pink Pink Pink Red Red Pink Pink Pink Yellow Pink Yellow Pink Pink Pink Gray Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Red Red Pink Pink Pink Yellow Pink Pink Pink Pink Gray Gray Gray Pink Red Pink Pink Red Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Yellow Yellow Pink Blue Blue Pink Gray Gray Gray Pink Red Red Pink Red Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray Gray Gray Pink Pink Red Red Red Pink
Row 11: Black Pink Black Black Black Pink Pink Pink Black Black Black Black Black Pink Black Pink Gray Gray Gray Gray Pink Pink Pink Red Pink Red Red
Row 12: Black Black Black Black Pink Pink Pink Pink Pink Black Black Black Pink Pink Black Pink Pink Pink Gray Pink Pink Pink Pink Pink Red Red Pink
Row 13: Black Black Black Black Black Pink Pink Pink Pink Black Black Black Black Black Black Black Pink Pink Gray Pink Brown Pink Pink Pink Pink Red Pink
Row 14: Black Black Black Black Black Pink Pink Yellow Pink Black Pink Black Pink Black Black Black Pink Pink Pink Pink Brown Brown Brown Pink Pink Pink Pink
Row 15: Black Pink Black Black Black Black Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Brown Pink Black Black Black
Row 16: Pink Pink Black Black Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Brown Brown Brown Pink Pink Black Black Black
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Black Black Pink Pink Brown Brown Pink Pink Black Black Black Black
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Brown Pink Pink Black Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Black Pink Pink Pink Brown Brown Pink Black Pink Purple Purple
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Purple Pink Purple Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Purple Purple
Row 21: Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Pink Purple Purple Purple Purple Pink Purple Purple Pink Brown Pink Pink Pink Purple Purple Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 23: Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Purple Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple
Row 24: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Purple Pink Purple Purple
Row 25: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Red Red Red Red Red Red Pink
Pink Red Red Red Red Red Red Red Red
Pink Pink Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Pink Pink
Pink Pink Red Pink Pink Pink Pink Pink Pink
Pink Pink Red Pink Pink Pink Pink Pink Pink
Pink Pink Red 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: Yellow 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 Brown Green
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Brown Black Purple Black Black Black Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Brown Black
Row 4: Black Brown Purple Purple Black Purple Black Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Purple Purple Black Brown Black
Row 5: Black Brown Black Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Brown Black
Row 6: Black Brown Purple Purple Purple Black Purple Black Purple Black Purple Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Black Black Black Purple Brown Black
Row 7: Black Brown Purple Purple Purple Black Purple Black Purple Purple Purple Purple Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black
Row 8: Black Brown Purple Black Purple Black Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Black Black Black Black Black Black Black Black Brown Black
Row 9: Black Brown Black Black Black Purple Black Purple Black Purple Purple Purple Black Purple Black Black Black Black Black Black Black Black Black Black Purple Black Brown Black
Row 10: Black Brown Purple Purple Purple Black Purple Black Purple Purple Purple Black Purple Black Black Black Purple Purple Black Black Black Purple Black Black Black Black Brown Black
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Orange 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 Brown Red
Output:
Row 1: Black Yellow Black Black Black Yellow Black Yellow Black Yellow Yellow Yellow Green Green Green Green Green Black Green Green Green Green Green Green
Row 2: Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Black Black Yellow Green Green Green Green Green Green Green Black Green Green Green Black
Row 3: Black Black Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Black Green Green Green Green Green Black Green Green Green Green Green Green
Row 4: Yellow Yellow Yellow Black Yellow Black Yellow Black Yellow Black Black Black Green Green Green Green Green Green Green Green Black Black Black Green
Row 5: Orange Orange Orange Black Orange Black Orange Orange Orange Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Orange Black Orange Black Orange Orange Orange Orange Orange Orange Black Orange Black Red Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Orange Black Orange Black Orange Orange Orange Black Orange Black Black Black Black Black Black Black Black Black Black Red Black
Row 8: Orange Orange Orange Black Orange Black Orange Orange Orange Black Orange Black Black Black Red Red Black Black Black Red Black Black Black Black
Example 2
Input:
Row 1: Black Purple Green Green Purple Blue
Row 2: Purple Purple Purple Purple Purple Purple
Row 3: Green Purple Red Red Purple Green
Row 4: Green Purple Red Green Purple Green
Row 5: Green Purple Green Green Purple Green
Row 6: Green Purple Green Red Purple Green
Row 7: Green Purple Red Red Purple Green
Row 8: Green Purple Red Red Purple Green
Row 9: Green Purple Red Red Purple Green
Row 10: Green Purple Green Red Purple Green
Row 11: Green Purple Red Green Purple Green
Row 12: Green Purple Red Green Purple Green
Row 13: Green Purple Green Red Purple Green
Row 14: Green Purple Green Red Purple Green
Row 15: Green Purple Green Red Purple Green
Row 16: Green Purple Green Red Purple Green
Row 17: Green Purple Green Red Purple Green
Row 18: Green Purple Red Red Purple Green
Row 19: Green Purple Green Red Purple Green
Row 20: Green Purple Red Red Purple Green
Row 21: Green Purple Green Red Purple Green
Row 22: Green Purple Green Red Purple Green
Row 23: Green Purple Red Green Purple Green
Row 24: Green Purple Red Green Purple Green
Row 25: Green Purple Red Green Purple Green
Row 26: Green Purple Red Red Purple Green
Row 27: Green Purple Red Green Purple Green
Row 28: Green Purple Red Red Purple Green
Row 29: Purple Purple Purple Purple Purple Purple
Row 30: Orange Purple Green Green Purple Pink
Output:
Row 1: Black Blue
Row 2: Black Green
Row 3: Green Green
Row 4: Green Blue
Row 5: Black Blue
Row 6: Black Blue
Row 7: Black Blue
Row 8: Green Blue
Row 9: Black Green
Row 10: Black Green
Row 11: Green Blue
Row 12: Green Blue
Row 13: Green Blue
Row 14: Green Pink
Row 15: Green Pink
Row 16: Orange Pink
Row 17: Green Pink
Row 18: Orange Pink
Row 19: Green Pink
Row 20: Green Pink
Row 21: Orange Green
Row 22: Orange Green
Row 23: Orange Green
Row 24: Orange Pink
Row 25: Orange Green
Row 26: Orange Pink
Example 3
Input:
Row 1: Red Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Blue
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Green Orange Green Green Green Green Green Brown Green Brown Brown Brown Green Brown Brown Green Orange Green
Row 4: Green Orange Green Brown Green Green Green Green Green Green Green Green Brown Brown Brown Green Orange Green
Row 5: Green Orange Brown Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Orange Green
Row 6: Green Orange Green Brown Green Green Green Brown Brown Brown Brown Green Brown Brown Green Green Orange Green
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Gray Orange Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange Yellow
Output:
Row 1: Green Green Green Green Green Red Green Blue Blue Blue Green Blue Blue Green
Row 2: Green Red Green Green Green Green Green Green Green Green Blue Blue Blue Green
Row 3: Gray Green Green Green Green Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Green Gray Green Green Green Gray Gray Yellow Yellow Green Yellow Yellow Green Green
Here is the input grid for the test example:
Input:
Row 1: Black Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Gray
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Pink Green Pink Pink Pink Pink Pink Pink Pink Red Red Red Pink Red Red Red Red Pink Green Pink
Row 4: Pink Green Red Pink Red Pink Pink Red Red Red Red Red Red Red Red Red Pink Pink Green Pink
Row 5: Pink Green Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Pink Red Pink Pink Pink Green Pink
Row 6: Pink Green Pink Pink Red Pink Pink Red Pink Red Pink Red Red Pink Pink Red Red Pink Green Pink
Row 7: Pink Green Pink Pink Pink Red Pink Pink Red Red Red Red Pink Red Pink Pink Pink Pink Green Pink
Row 8: Pink Green Pink Pink Pink Pink Pink Red Red Pink Pink Red Red Red Red Pink Red Red Green Pink
Row 9: Pink Green Pink Red Pink Red Pink Red Red Pink Red Pink Red Pink Pink Pink Red Red Green Pink
Row 10: Pink Green Pink Pink Red Pink Pink Red Pink Red Red Pink Pink Red Pink Red Red Red Green Pink
Row 11: Pink Green Pink Red Pink Red Pink Pink Red Red Red Red Pink Red Pink Pink Red Red Green Pink
Row 12: Pink Green Red Pink Pink Red Red Pink Red Pink Pink Red Red Red Red Pink Pink Pink Green Pink
Row 13: Pink Green Pink Pink Pink Pink Pink Red Red Pink Red Red Red Pink Red Red Red Pink Green Pink
Row 14: Pink Green Pink Pink Pink Red Pink Pink Pink Red Red Pink Pink Pink Red Pink Red Pink Green Pink
Row 15: Pink Green Pink Red Red Red Pink Red Pink Pink Red Red Pink Red Red Red Pink Red Green Pink
Row 16: Pink Green Pink Red Pink Pink Pink Pink Red Pink Red Red Pink Red Red Red Red Red Green Pink
Row 17: Pink Green Red Red Red Pink Pink Pink Red Red Red Red Red Pink Red Red Red Red Green Pink
Row 18: Pink Green Red Pink Pink Pink Pink Pink Pink Red Red Red Red Red Pink Pink Red Red Green Pink
Row 19: Pink Green Red Red Pink Pink Red Red Pink Pink Red Red Red Red Red Red Red Red Green Pink
Row 20: Pink Green Pink Pink Red Pink Pink Pink Red Pink Red Pink Red Red Red Red Red Red Green Pink
Row 21: Pink Green Pink Red Red Red Pink Red Pink Pink Red Pink Pink Red Red Red Red Red Green Pink
Row 22: Pink Green Pink Red Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Green Pink
Row 23: Pink Green Red Pink Pink Pink Red Pink Pink Red Red Red Red Red Pink Red Red Red Green Pink
Row 24: Pink Green Red Pink Red Pink Pink Red Pink Red Red Red Red Red Red Red Red Red Green Pink
Row 25: Pink Green Pink Red Pink Red Pink Pink Pink Red Red Red Red Red Red Pink Red Red Green Pink
Row 26: Pink Green Pink Pink Pink Red Pink Pink Pink Pink Red Red Red Red Red Red Red Red Green Pink
Row 27: Pink Green Pink Red Pink Red Pink Pink Red Pink Red Red Red Red Red Red Red Red Green Pink
Row 28: Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Red Red Red Red Red Red Red Red Green Pink
Row 29: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 30: Purple Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Orange
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 Black Gray Gray Pink Gray Gray Gray Gray Pink
Black Pink Black Pink Pink Black Black Black Gray Gray Gray Gray Gray Gray Pink Pink
Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Gray Pink Gray Pink Pink Pink
Pink Pink Black Pink Pink Black Pink Black Pink Gray Gray Pink Pink Gray Gray Pink
Pink Pink Pink Black Pink Pink Black Black Gray Gray Pink Gray Pink Pink Pink Pink
Pink Pink Pink Pink Pink Black Black Pink Pink Gray Gray Gray Gray Pink Gray Gray
Pink Black Pink Black Pink Black Black Pink Gray Pink Gray Pink Pink Pink Gray Gray
Pink Pink Black Pink Pink Black Pink Black Gray Pink Pink Gray Pink Gray Gray Gray
Pink Black Pink Black Pink Pink Black Black Gray Gray Pink Gray Pink Pink Gray Gray
Black Pink Pink Black Black Pink Black Pink Pink Gray Gray Gray Gray Pink Pink Pink
Pink Pink Pink Pink Pink Black Black Pink Gray Gray Gray Pink Gray Gray Gray Pink
Pink Pink Pink Black Pink Pink Pink Black Gray Pink Pink Pink Gray Pink Gray Pink
Pink Black Black Black Pink Black Pink Pink Gray Gray Pink Gray Gray Gray Pink Gray
Pink Purple Pink Pink Pink Pink Purple Pink Orange Orange Pink Orange Orange Orange Orange Orange
Purple Purple Purple Pink Pink Pink Purple Purple Orange Orange Orange Pink Orange Orange Orange Orange
Purple Pink Pink Pink Pink Pink Pink Purple Orange Orange Orange Orange Pink Pink Orange Orange
Purple Purple Pink Pink Purple Purple Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Pink Pink Purple Pink Pink Pink Purple Pink Orange Pink Orange Orange Orange Orange Orange Orange
Pink Purple Purple Purple Pink Purple Pink Pink Orange Pink Pink Orange Orange Orange Orange Orange
Pink Purple Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange
Purple Pink Pink Pink Purple Pink Pink Purple Orange Orange Orange Orange Pink Orange Orange Orange
Purple Pink Purple Pink Pink Purple Pink Purple Orange Orange Orange Orange Orange Orange Orange Orange
Pink Purple Pink Purple Pink Pink Pink Purple Orange Orange Orange Orange Orange Pink Orange Orange
Pink Pink Pink Purple Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange
Pink Purple Pink Purple Pink Pink Purple Pink Orange Orange Orange Orange Orange Orange Orange Orange
Pink Pink Pink Pink Pink Pink Pink Pink 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 Pink Black Black Orange Purple Black Purple Green Orange Black Black Green Black Pink Blue Purple Black Black Pink Black Pink Green Blue Black Black Blue Black Black
Row 2: Blue Green Black Purple Green Black Black Black Black Green Black Black Black Blue Green Blue Blue Black Orange Green Pink Green Green Purple Black Black Black Black Black
Row 3: Purple Blue Black Black Orange Black Black Black Blue Blue Orange Black Black Purple Black Black Blue Black Black Purple Orange Purple Blue Black Black Orange Green Pink Green
Row 4: Pink Black Purple Purple Pink Pink Black Black Pink Black Green Black Blue Purple Black Purple Black Black Black Black Pink Pink Orange Black Purple Black Green Black Black
Row 5: Black Orange Black Black Black Black Pink Pink Black Black Blue Black Purple Purple Green Pink Orange Green Black Orange Green Pink Black Blue Purple Black Black Black Black
Row 6: Black Black Green Black Pink Black Green Black Black Purple Black Blue Black Purple Green Blue Blue Black Green Black Green Pink Blue Black Green Black Black Black Black
Row 7: Purple Blue Green Black Blue Black Black Black Orange Purple Green Black Green Green Black Black Black Orange Blue Black Black Blue Green Orange Black Black Pink Green Pink
Row 8: Pink Pink Orange Black Purple Black Orange Pink Orange Black Purple Black Black Black Black Green Black Purple Black Black Green Green Black Black Black Green Purple Blue Black
Row 9: Blue Black Pink Green Black Green Black Black Green Pink Black Black Green Blue Green Purple Black Black Black Purple Black Blue Black Black Green Green Purple Black Black
Row 10: Blue Purple Orange Black Pink Black Black Black Purple Blue Black Black Black Black Orange Black Black Pink Black Black Orange Green Black Purple Pink Black Black Black Purple
Row 11: Black Pink Black Black Orange Black Black Pink Orange Black Black Black Pink Black Orange Black Pink Purple Black Black Black Purple Black Orange Black Black Pink Black Black
Output:
Row 1: Orange Pink Black Black Orange Purple Black Purple Green Orange Black Black Green Black Pink Blue Purple Black Black Pink Black Pink Green Blue Black Black Blue Black Black
Row 2: Blue Green Black Purple Green Black Black Black Black Green Black Black Black Blue Green Blue Blue Black Orange Green Pink Green Green Purple Black Black Black Black Black
Row 3: Purple Blue Black Black Orange Black Black Black Blue Blue Orange Black Black Purple Black Black Blue Black Black Purple Orange Purple Blue Black Black Orange Green Pink Green
Row 4: Pink Black Purple Purple Pink Pink Black Black Pink Black Green Black Blue Purple Black Purple Black Black Black Black Pink Pink Orange Black Purple Black Green Black Black
Row 5: Black Orange Black Black Black Black Pink Pink Black Black Blue Black Purple Purple Green Pink Orange Green Black Orange Green Pink Black Blue Purple Black Black Black Black
Row 6: Black Black Green Black Pink Black Green Black Black Purple Black Blue Black Purple Green Blue Blue Black Green Black Green Pink Blue Black Green Black Black Black Black
Row 7: Purple Blue Green Black Blue Black Black Black Orange Purple Green Black Green Green Black Black Black Orange Blue Black Black Blue Green Orange Black Black Pink Green Pink
Row 8: Pink Pink Orange Black Purple Black Orange Pink Orange Black Purple Black Black Black Black Green Black Purple Black Black Green Green Black Black Black Green Purple Blue Black
Row 9: Blue Black Pink Green Black Green Black Black Green Pink Black Black Green Blue Green Purple Black Black Black Purple Black Blue Black Black Green Green Purple Black Black
Row 10: Blue Purple Orange Black Pink Black Black Black Purple Blue Black Black Black Black Orange Black Black Pink Black Black Orange Green Black Purple Pink Black Black Black Purple
Row 11: Black Pink Black Black Orange Black Black Pink Orange Black Black Black Pink Black Orange Black Pink Purple Black Black Black Purple Black Orange Black Black Pink Black Black
Row 12: Black Pink Black Black Orange Black Black Pink Orange Black Black Black Pink Black Orange Black Pink Purple Black Black Black Purple Black Orange Black Black Pink Black Black
Row 13: Blue Purple Orange Black Pink Black Black Black Purple Blue Black Black Black Black Orange Black Black Pink Black Black Orange Green Black Purple Pink Black Black Black Purple
Row 14: Blue Black Pink Green Black Green Black Black Green Pink Black Black Green Blue Green Purple Black Black Black Purple Black Blue Black Black Green Green Purple Black Black
Row 15: Pink Pink Orange Black Purple Black Orange Pink Orange Black Purple Black Black Black Black Green Black Purple Black Black Green Green Black Black Black Green Purple Blue Black
Row 16: Purple Blue Green Black Blue Black Black Black Orange Purple Green Black Green Green Black Black Black Orange Blue Black Black Blue Green Orange Black Black Pink Green Pink
Row 17: Black Black Green Black Pink Black Green Black Black Purple Black Blue Black Purple Green Blue Blue Black Green Black Green Pink Blue Black Green Black Black Black Black
Row 18: Black Orange Black Black Black Black Pink Pink Black Black Blue Black Purple Purple Green Pink Orange Green Black Orange Green Pink Black Blue Purple Black Black Black Black
Row 19: Pink Black Purple Purple Pink Pink Black Black Pink Black Green Black Blue Purple Black Purple Black Black Black Black Pink Pink Orange Black Purple Black Green Black Black
Row 20: Purple Blue Black Black Orange Black Black Black Blue Blue Orange Black Black Purple Black Black Blue Black Black Purple Orange Purple Blue Black Black Orange Green Pink Green
Row 21: Blue Green Black Purple Green Black Black Black Black Green Black Black Black Blue Green Blue Blue Black Orange Green Pink Green Green Purple Black Black Black Black Black
Row 22: Orange Pink Black Black Orange Purple Black Purple Green Orange Black Black Green Black Pink Blue Purple Black Black Pink Black Pink Green Blue Black Black Blue Black Black
Example 2
Input:
Row 1: Yellow Yellow Blue Blue Pink Red Yellow Blue Yellow Yellow Blue Yellow Red Yellow Yellow Blue Blue Yellow Yellow Pink Pink Pink Blue Red Red Yellow Red Red Pink
Row 2: Yellow Blue Blue Yellow Pink Blue Yellow Yellow Yellow Pink Pink Blue Blue Blue Pink Red Red Blue Red Blue Red Red Red Red Blue Blue Pink Red Red
Row 3: Yellow Blue Yellow Blue Blue Red Red Red Blue Red Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Yellow Blue Blue Red Blue Blue Blue Yellow Blue
Row 4: Blue Yellow Pink Red Red Yellow Blue Blue Blue Red Red Blue Blue Yellow Blue Yellow Yellow Blue Blue Yellow Yellow Blue Blue Yellow Blue Red Yellow Blue Blue
Row 5: Blue Yellow Yellow Red Blue Red Red Blue Blue Blue Yellow Red Red Red Red Pink Yellow Blue Yellow Pink Blue Red Red Blue Yellow Yellow Blue Blue Blue
Row 6: Blue Blue Blue Pink Red Yellow Blue Blue Red Yellow Red Pink Red Blue Blue Blue Blue Yellow Blue Blue Blue Red Blue Yellow Yellow Red Yellow Yellow Pink
Row 7: Red Pink Red Blue Red Blue Yellow Blue Yellow Yellow Pink Pink Red Blue Blue Red Red Blue Yellow Blue Blue Red Blue Blue Blue Red Yellow Blue Red
Row 8: Blue Blue Yellow Blue Yellow Blue Red Blue Pink Red Blue Blue Blue Yellow Blue Red Yellow Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Yellow
Row 9: Blue Blue Blue Red Yellow Red Yellow Blue Yellow Blue Blue Red Blue Blue Pink Pink Red Blue Blue Blue Blue Blue Blue Yellow Red Red Blue Blue Red
Row 10: Blue Yellow Blue Red Blue Yellow Blue Yellow Red Yellow Red Blue Red Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Red Pink Yellow Blue Red Red Blue
Row 11: Blue Red Yellow Blue Red Yellow Yellow Blue Yellow Red Yellow Blue Pink Pink Blue Red Pink Red Blue Blue Red Blue Blue Red Pink Blue Pink Blue Blue
Row 12: Red Pink Red Pink Blue Blue Red Blue Red Red Red Blue Blue Yellow Red Yellow Pink Blue Red Red Blue Red Red Blue Yellow Blue Blue Blue Blue
Row 13: Red Red Yellow Blue Pink Yellow Red Pink Red Pink Red Blue Blue Red Yellow Yellow Red Blue Red Blue Yellow Yellow Blue Blue Yellow Blue Red Blue Blue
Row 14: Blue Blue Blue Blue Yellow Blue Red Red Blue Blue Pink Blue Blue Yellow Blue Yellow Yellow Blue Red Red Red Blue Red Yellow Red Yellow Pink Blue Yellow
Output:
Row 1: Yellow Yellow Blue Blue Pink Red Yellow Blue Yellow Yellow Blue Yellow Red Yellow Yellow Blue Blue Yellow Yellow Pink Pink Pink Blue Red Red Yellow Red Red Pink
Row 2: Yellow Blue Blue Yellow Pink Blue Yellow Yellow Yellow Pink Pink Blue Blue Blue Pink Red Red Blue Red Blue Red Red Red Red Blue Blue Pink Red Red
Row 3: Yellow Blue Yellow Blue Blue Red Red Red Blue Red Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Yellow Blue Blue Red Blue Blue Blue Yellow Blue
Row 4: Blue Yellow Pink Red Red Yellow Blue Blue Blue Red Red Blue Blue Yellow Blue Yellow Yellow Blue Blue Yellow Yellow Blue Blue Yellow Blue Red Yellow Blue Blue
Row 5: Blue Yellow Yellow Red Blue Red Red Blue Blue Blue Yellow Red Red Red Red Pink Yellow Blue Yellow Pink Blue Red Red Blue Yellow Yellow Blue Blue Blue
Row 6: Blue Blue Blue Pink Red Yellow Blue Blue Red Yellow Red Pink Red Blue Blue Blue Blue Yellow Blue Blue Blue Red Blue Yellow Yellow Red Yellow Yellow Pink
Row 7: Red Pink Red Blue Red Blue Yellow Blue Yellow Yellow Pink Pink Red Blue Blue Red Red Blue Yellow Blue Blue Red Blue Blue Blue Red Yellow Blue Red
Row 8: Blue Blue Yellow Blue Yellow Blue Red Blue Pink Red Blue Blue Blue Yellow Blue Red Yellow Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Yellow
Row 9: Blue Blue Blue Red Yellow Red Yellow Blue Yellow Blue Blue Red Blue Blue Pink Pink Red Blue Blue Blue Blue Blue Blue Yellow Red Red Blue Blue Red
Row 10: Blue Yellow Blue Red Blue Yellow Blue Yellow Red Yellow Red Blue Red Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Red Pink Yellow Blue Red Red Blue
Row 11: Blue Red Yellow Blue Red Yellow Yellow Blue Yellow Red Yellow Blue Pink Pink Blue Red Pink Red Blue Blue Red Blue Blue Red Pink Blue Pink Blue Blue
Row 12: Red Pink Red Pink Blue Blue Red Blue Red Red Red Blue Blue Yellow Red Yellow Pink Blue Red Red Blue Red Red Blue Yellow Blue Blue Blue Blue
Row 13: Red Red Yellow Blue Pink Yellow Red Pink Red Pink Red Blue Blue Red Yellow Yellow Red Blue Red Blue Yellow Yellow Blue Blue Yellow Blue Red Blue Blue
Row 14: Blue Blue Blue Blue Yellow Blue Red Red Blue Blue Pink Blue Blue Yellow Blue Yellow Yellow Blue Red Red Red Blue Red Yellow Red Yellow Pink Blue Yellow
Row 15: Blue Blue Blue Blue Yellow Blue Red Red Blue Blue Pink Blue Blue Yellow Blue Yellow Yellow Blue Red Red Red Blue Red Yellow Red Yellow Pink Blue Yellow
Row 16: Red Red Yellow Blue Pink Yellow Red Pink Red Pink Red Blue Blue Red Yellow Yellow Red Blue Red Blue Yellow Yellow Blue Blue Yellow Blue Red Blue Blue
Row 17: Red Pink Red Pink Blue Blue Red Blue Red Red Red Blue Blue Yellow Red Yellow Pink Blue Red Red Blue Red Red Blue Yellow Blue Blue Blue Blue
Row 18: Blue Red Yellow Blue Red Yellow Yellow Blue Yellow Red Yellow Blue Pink Pink Blue Red Pink Red Blue Blue Red Blue Blue Red Pink Blue Pink Blue Blue
Row 19: Blue Yellow Blue Red Blue Yellow Blue Yellow Red Yellow Red Blue Red Yellow Blue Blue Yellow Blue Blue Blue Blue Blue Red Pink Yellow Blue Red Red Blue
Row 20: Blue Blue Blue Red Yellow Red Yellow Blue Yellow Blue Blue Red Blue Blue Pink Pink Red Blue Blue Blue Blue Blue Blue Yellow Red Red Blue Blue Red
Row 21: Blue Blue Yellow Blue Yellow Blue Red Blue Pink Red Blue Blue Blue Yellow Blue Red Yellow Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Yellow
Row 22: Red Pink Red Blue Red Blue Yellow Blue Yellow Yellow Pink Pink Red Blue Blue Red Red Blue Yellow Blue Blue Red Blue Blue Blue Red Yellow Blue Red
Row 23: Blue Blue Blue Pink Red Yellow Blue Blue Red Yellow Red Pink Red Blue Blue Blue Blue Yellow Blue Blue Blue Red Blue Yellow Yellow Red Yellow Yellow Pink
Row 24: Blue Yellow Yellow Red Blue Red Red Blue Blue Blue Yellow Red Red Red Red Pink Yellow Blue Yellow Pink Blue Red Red Blue Yellow Yellow Blue Blue Blue
Row 25: Blue Yellow Pink Red Red Yellow Blue Blue Blue Red Red Blue Blue Yellow Blue Yellow Yellow Blue Blue Yellow Yellow Blue Blue Yellow Blue Red Yellow Blue Blue
Row 26: Yellow Blue Yellow Blue Blue Red Red Red Blue Red Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Yellow Blue Blue Red Blue Blue Blue Yellow Blue
Row 27: Yellow Blue Blue Yellow Pink Blue Yellow Yellow Yellow Pink Pink Blue Blue Blue Pink Red Red Blue Red Blue Red Red Red Red Blue Blue Pink Red Red
Row 28: Yellow Yellow Blue Blue Pink Red Yellow Blue Yellow Yellow Blue Yellow Red Yellow Yellow Blue Blue Yellow Yellow Pink Pink Pink Blue Red Red Yellow Red Red Pink
Example 3
Input:
Row 1: Gray Red Gray Red Red Gray Purple Purple Purple Gray Gray Gray Gray Gray Brown Blue Red Gray Yellow Yellow Gray Gray Red Gray Gray Gray Gray Gray Gray Blue
Row 2: Gray Yellow Gray Gray Purple Red Red Gray Orange Gray Gray Yellow Gray Gray Blue Red Brown Gray Brown Gray Orange Blue Blue Purple Gray Gray Gray Gray Yellow Brown
Output:
Row 1: Gray Red Gray Red Red Gray Purple Purple Purple Gray Gray Gray Gray Gray Brown Blue Red Gray Yellow Yellow Gray Gray Red Gray Gray Gray Gray Gray Gray Blue
Row 2: Gray Yellow Gray Gray Purple Red Red Gray Orange Gray Gray Yellow Gray Gray Blue Red Brown Gray Brown Gray Orange Blue Blue Purple Gray Gray Gray Gray Yellow Brown
Row 3: Gray Yellow Gray Gray Purple Red Red Gray Orange Gray Gray Yellow Gray Gray Blue Red Brown Gray Brown Gray Orange Blue Blue Purple Gray Gray Gray Gray Yellow Brown
Row 4: Gray Red Gray Red Red Gray Purple Purple Purple Gray Gray Gray Gray Gray Brown Blue Red Gray Yellow Yellow Gray Gray Red Gray Gray Gray Gray Gray Gray Blue
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: 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 |
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
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 Orange Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink 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
Row 17: 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
Row 19: 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
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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: 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
Row 28: 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
Output:
Row 1: Yellow Green Green Green Yellow
Row 2: Gray Orange Yellow Yellow Black
Row 3: Gray Yellow Orange Yellow Black
Row 4: Gray Yellow Orange Black Black
Row 5: Gray Yellow Pink Yellow Black
Row 6: Yellow Pink Pink Pink Yellow
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Gray Yellow Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray 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
Row 16: 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
Row 18: 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 Red Red Red Red Red Red Gray
Row 2: Purple Yellow Red Red Red Gray Yellow Brown
Row 3: Purple Yellow Blue Blue Blue Blue Gray Brown
Row 4: Gray Blue Blue Blue Blue Blue Blue Gray
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
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 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
Row 8: 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
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Gray Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Purple Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Purple Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Purple Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue 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 Orange Orange Orange
Row 16: Orange Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Gray Gray Gray Orange
Row 2: Green Black Gray Orange Purple
Row 3: Green Orange Black Purple Purple
Row 4: Green Black Orange Orange Purple
Row 5: Orange Blue Blue Blue Orange
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
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray
Row 5: 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
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Brown Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Brown Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray Gray Purple Gray Gray Gray Brown Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Gray Gray Gray
Row 12: 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
Row 14: 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
Row 16: 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
Row 18: 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
Row 20: 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 Black Black Black Gray
Purple Gray Black Green Brown
Purple Purple Gray Gray Brown
Purple Green Gray Gray Brown
Gray Yellow Yellow Yellow Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Orange Black Red Gray Black Black Black Gray Black Brown Green Gray Black Yellow Black Black Black Black
Row 2: Black Black Black Black Black Blue Brown Black Green Purple Purple Green Gray Black Black Black Black Black Orange Black Black
Row 3: Black Black Black Green Black Black Black Red Black Green Black Black Black Blue Orange Gray Brown Black Black Black Black
Row 4: Black Red Black Orange Black Black Black Black Black Black Black Black Black Black Black Red Black Green Black Purple Brown
Row 5: Black Black Black Black Black Purple Black Black Black Red Black Yellow Black Black Black Yellow Red Black Black Black Black
Row 6: Black Purple Black Black Yellow Orange Black Black Black Black Yellow Black Black Black Black Orange Black Black Black Green Black
Output:
Row 1: Pink Pink Pink Orange Black Red Gray Black Black Black Gray Black Brown Green Gray Black Yellow Black Black Black Black
Row 2: Pink Pink Pink Black Black Blue Brown Black Green Purple Purple Green Gray Black Black Black Black Black Orange Black Black
Row 3: Pink Pink Pink Green Black Black Black Red Black Green Black Black Black Blue Orange Gray Brown Black Black Black Black
Row 4: Black Red Black Orange Black Black Pink Pink Pink Black Black Black Pink Pink Pink Red Black Green Black Purple Brown
Row 5: Black Black Black Black Black Purple Pink Pink Pink Red Black Yellow Pink Pink Pink Yellow Red Black Black Black Black
Row 6: Black Purple Black Black Yellow Orange Pink Pink Pink Black Yellow Black Pink Pink Pink Orange Black Black Black Green Black
Example 2
Input:
Row 1: Gray Gray Black Yellow Gray Gray
Row 2: Gray Gray Yellow Yellow Yellow Gray
Row 3: Yellow Black Yellow Black Black Black
Row 4: Black Black Gray Black Yellow Gray
Row 5: Black Black Yellow Yellow Gray Black
Row 6: Gray Yellow Black Yellow Gray Gray
Row 7: Gray Black Black Black Yellow Gray
Row 8: Yellow Yellow Gray Gray Yellow Yellow
Row 9: Yellow Black Black Yellow Gray Black
Row 10: Gray Black Gray Black Yellow Gray
Row 11: Black Gray Yellow Gray Yellow Gray
Row 12: Gray Gray Black Gray Gray Gray
Row 13: Gray Black Gray Gray Yellow Gray
Row 14: Gray Yellow Gray Black Gray Gray
Row 15: Gray Yellow Yellow Yellow Yellow Black
Row 16: Yellow Black Gray Gray Yellow Black
Row 17: Black Yellow Black Gray Yellow Gray
Row 18: Gray Gray Yellow Gray Gray Gray
Row 19: Gray Black Black Yellow Gray Black
Row 20: Black Yellow Black Black Black Yellow
Row 21: Black Black Yellow Gray Yellow Yellow
Row 22: Gray Yellow Black Black Gray Yellow
Output:
Row 1: Gray Gray Black Yellow Gray Gray
Row 2: Gray Gray Yellow Yellow Yellow Gray
Row 3: Yellow Black Yellow Black Black Black
Row 4: Pink Pink Gray Black Yellow Gray
Row 5: Pink Pink Yellow Yellow Gray Black
Row 6: Gray Yellow Black Yellow Gray Gray
Row 7: Gray Black Black Black Yellow Gray
Row 8: Yellow Yellow Gray Gray Yellow Yellow
Row 9: Yellow Black Black Yellow Gray Black
Row 10: Gray Black Gray Black Yellow Gray
Row 11: Black Gray Yellow Gray Yellow Gray
Row 12: Gray Gray Black Gray Gray Gray
Row 13: Gray Black Gray Gray Yellow Gray
Row 14: Gray Yellow Gray Black Gray Gray
Row 15: Gray Yellow Yellow Yellow Yellow Black
Row 16: Yellow Black Gray Gray Yellow Black
Row 17: Black Yellow Black Gray Yellow Gray
Row 18: Gray Gray Yellow Gray Gray Gray
Row 19: Gray Black Black Yellow Gray Black
Row 20: Black Yellow Black Black Black Yellow
Row 21: Black Black Yellow Gray Yellow Yellow
Row 22: Gray Yellow Black Black Gray Yellow
Example 3
Input:
Row 1: Black Black Black Red Black Black Red Black
Row 2: Black Black Red Black Black Red Gray Red
Row 3: Black Gray Black Black Red Red Gray Black
Row 4: Black Black Gray Black Black Black Black Black
Row 5: Black Green Red Black Black Red Red Black
Row 6: Black Black Black Red Black Black Black Red
Row 7: Green Black Black Black Red Gray Gray Black
Row 8: Green Gray Black Green Black Black Black Black
Row 9: Red Red Black Gray Green Green Black Gray
Row 10: Green Black Black Red Black Black Black Black
Row 11: Black Black Black Black Gray Black Gray Green
Row 12: Black Black Black Black Green Black Black Green
Row 13: Gray Black Black Red Black Black Black Black
Row 14: Green Black Red Red Black Red Green Black
Row 15: Red Black Black Black Black Black Black Black
Row 16: Black Black Red Black Black Black Black Black
Row 17: Green Black Black Black Black Black Green Black
Row 18: Black Black Black Green Black Black Black Green
Row 19: Black Black Black Black Black Black Black Gray
Output:
Row 1: Black Black Black Red Black Black Red Black
Row 2: Black Black Red Black Black Red Gray Red
Row 3: Black Gray Black Black Red Red Gray Black
Row 4: Black Black Gray Black Black Black Black Black
Row 5: Black Green Red Black Black Red Red Black
Row 6: Black Black Black Red Black Black Black Red
Row 7: Green Black Black Black Red Gray Gray Black
Row 8: Green Gray Black Green Black Black Black Black
Row 9: Red Red Black Gray Green Green Black Gray
Row 10: Green Black Black Red Black Black Black Black
Row 11: Black Black Black Black Gray Black Gray Green
Row 12: Black Black Black Black Green Black Black Green
Row 13: Gray Black Black Red Black Black Black Black
Row 14: Green Black Red Red Black Red Green Black
Row 15: Red Black Black Pink Pink Pink Pink Pink
Row 16: Black Black Red Pink Pink Pink Pink Pink
Row 17: Green Black Black Black Pink Pink Green Black
Row 18: Black Black Black Green Pink Pink Black Green
Row 19: Black Black Black Black Pink Pink Black Gray
Here is the input grid for the test example:
Input:
Row 1: Brown Red Yellow Yellow Black Yellow Red Brown Red Brown Yellow Orange Yellow Orange Brown Yellow Yellow Red
Row 2: Red Yellow Orange Brown Red Red Red Red Black Brown Red Black Black Yellow Orange Yellow Black Brown
Row 3: Orange Brown Orange Yellow Orange Orange Red Black Orange Black Red Black Black Red Red Red Yellow Yellow
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Red Yellow Yellow Black Yellow Red Brown Red Brown Yellow Orange Yellow Orange Brown Yellow Yellow Red
Red Yellow Orange Brown Red Red Red Red Black Brown Red Pink Pink Yellow Orange Yellow Black Brown
Orange Brown Orange Yellow Orange Orange Red Black Orange Black Red Pink Pink Red Red Red 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Black Purple Orange Yellow Pink Pink Pink Pink Orange Yellow Orange Orange Black
Row 3: Orange Yellow Brown Red Green Orange Pink Pink Pink Pink Green Orange Orange Yellow Brown
Row 4: Orange Orange Red Gray Green Blue Pink Pink Pink Pink Green Blue Orange Orange Red
Row 5: Orange Red Red Pink Pink Pink Pink Pink Pink Pink Yellow Purple Orange Red Red
Row 6: Orange Yellow Purple Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Orange Yellow Purple
Row 7: Orange Gray Pink Pink Pink Pink Pink Pink Pink Pink Red Black Orange Gray Yellow
Row 8: Orange Pink Pink Pink Pink Pink Pink Pink Gray Red Red Blue Orange Red Gray
Row 9: Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Gray
Row 10: Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Purple
Row 11: Orange Purple Purple Purple Blue Black Orange Purple Purple Purple Blue Black Orange Purple Purple
Row 12: Orange Orange Yellow Purple Gray Orange Orange Orange Yellow Purple Gray Orange Orange Orange Yellow
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Black Purple Orange Yellow Orange Orange Black Purple Orange Yellow Orange Orange Black
Row 15: Orange Yellow Brown Red Green Orange Orange Yellow Brown Red Green Orange Orange Yellow Brown
Row 16: Orange Orange Red Pink Pink Pink Orange Orange Red Gray Green Blue Pink Pink Red
Row 17: Orange Red Red Pink Pink Pink Orange Red Red Black Yellow Purple Pink Pink Red
Row 18: Orange Yellow Purple Pink Pink Pink Orange Yellow Purple Blue Yellow Yellow Orange Yellow Purple
Row 19: Orange Gray Yellow Pink Pink Pink Orange Gray Yellow Purple Red Black Orange Gray Yellow
Row 20: Orange Red Gray Pink Pink Pink Orange Red Gray Red Red Blue Orange Red Gray
Row 21: Orange Orange Gray Pink Pink Pink Orange Orange Gray Black Orange Black Orange Orange Gray
Row 22: Orange Purple Purple Black Blue Blue Orange Purple Purple Black Blue Blue Orange Purple Purple
Row 23: Orange Purple Purple Purple Blue Black Orange Purple Purple Purple Blue Black Orange Purple Purple
Row 24: Orange Orange Yellow Purple Gray Orange Orange Orange Yellow Purple Gray Orange Orange Orange Yellow
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Black Purple Orange Yellow Orange Pink Pink Pink Pink Yellow Orange Orange Black
Row 27: Orange Yellow Brown Red Green Orange Orange Pink Pink Pink Pink Orange Orange Yellow Brown
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Black Purple Orange Yellow Orange Orange Black Purple Orange Yellow Orange Orange Black
Row 3: Orange Yellow Brown Red Green Orange Orange Yellow Brown Red Green Orange Orange Yellow Brown
Row 4: Orange Orange Red Gray Green Blue Orange Orange Red Gray Green Blue Orange Orange Red
Row 5: Orange Red Red Black Yellow Purple Orange Red Red Black Yellow Purple Orange Red Red
Row 6: Orange Yellow Purple Blue Yellow Yellow Orange Yellow Purple Blue Yellow Yellow Orange Yellow Purple
Row 7: Orange Gray Yellow Purple Red Black Orange Gray Yellow Purple Red Black Orange Gray Yellow
Row 8: Orange Red Gray Red Red Blue Orange Red Gray Red Red Blue Orange Red Gray
Row 9: Orange Orange Gray Black Orange Black Orange Orange Gray Black Orange Black Orange Orange Gray
Row 10: Orange Purple Purple Black Blue Blue Orange Purple Purple Black Blue Blue Orange Purple Purple
Row 11: Orange Purple Purple Purple Blue Black Orange Purple Purple Purple Blue Black Orange Purple Purple
Row 12: Orange Orange Yellow Purple Gray Orange Orange Orange Yellow Purple Gray Orange Orange Orange Yellow
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Black Purple Orange Yellow Orange Orange Black Purple Orange Yellow Orange Orange Black
Row 15: Orange Yellow Brown Red Green Orange Orange Yellow Brown Red Green Orange Orange Yellow Brown
Row 16: Orange Orange Red Gray Green Blue Orange Orange Red Gray Green Blue Orange Orange Red
Row 17: Orange Red Red Black Yellow Purple Orange Red Red Black Yellow Purple Orange Red Red
Row 18: Orange Yellow Purple Blue Yellow Yellow Orange Yellow Purple Blue Yellow Yellow Orange Yellow Purple
Row 19: Orange Gray Yellow Purple Red Black Orange Gray Yellow Purple Red Black Orange Gray Yellow
Row 20: Orange Red Gray Red Red Blue Orange Red Gray Red Red Blue Orange Red Gray
Row 21: Orange Orange Gray Black Orange Black Orange Orange Gray Black Orange Black Orange Orange Gray
Row 22: Orange Purple Purple Black Blue Blue Orange Purple Purple Black Blue Blue Orange Purple Purple
Row 23: Orange Purple Purple Purple Blue Black Orange Purple Purple Purple Blue Black Orange Purple Purple
Row 24: Orange Orange Yellow Purple Gray Orange Orange Orange Yellow Purple Gray Orange Orange Orange Yellow
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Black Purple Orange Yellow Orange Orange Black Purple Orange Yellow Orange Orange Black
Row 27: Orange Yellow Brown Red Green Orange Orange Yellow Brown Red Green Orange Orange Yellow Brown
Example 2
Input:
Row 1: Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink
Row 2: Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Green Green Green Green Green Pink Red Brown Brown Pink
Row 3: Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Green Green Green Green Green Pink Brown Red Yellow Pink
Row 4: Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Green Green Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Green Green Green Green Green Pink Yellow Orange Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Yellow Pink Brown Brown Yellow Green Green Green Yellow Green Green Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink
Row 7: Brown Pink Brown Brown Brown Green Green Green Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink
Row 8: Pink Pink Yellow Pink Pink Green Green Green Pink Pink Yellow Pink Pink Pink Yellow Pink Green Green Green Green Green Green Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 9: Pink Pink Yellow Brown Green Green Green Green Green Green Green Brown Pink Pink Yellow Brown Green Green Green Green Green Green Yellow Brown Green Green Green Green Green Green
Row 10: Brown Pink Red Brown Green Green Green Green Green Green Green Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Green Green Green Green Green Green
Row 11: Yellow Pink Brown Red Green Green Green Green Green Green Green Red Yellow Pink Brown Red Yellow Pink Brown Green Green Green Green Red Yellow Pink Brown Red Yellow Pink
Row 12: Pink Pink Yellow Orange Green Green Green Green Green Green Green Orange Pink Pink Yellow Orange Pink Pink Yellow Green Green Green Green Orange Pink Pink Yellow Orange Pink Pink
Row 13: Pink Pink Pink Pink Green Green Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Green Green Green Green Green Pink Pink Pink Pink Pink Pink Pink
Row 14: Yellow Pink Brown Brown Green Green Green Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Green Green Green Green Green Brown Yellow Pink Brown Brown Yellow Pink
Row 15: Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Green Green Green Green Green Brown Brown Pink Green Green Green Green Green Brown Brown Pink Brown Brown Brown Pink
Row 16: Pink Pink Yellow Pink Pink Pink Yellow Green Green Green Green Green Green Green Green Pink Pink Pink Green Green Green Green Green Pink Pink Pink Yellow Pink Pink Pink
Row 17: Pink Pink Yellow Brown Pink Pink Yellow Green Green Green Green Green Green Green Green Brown Pink Pink Green Green Green Green Green Brown Pink Pink Yellow Brown Pink Pink
Row 18: Brown Pink Red Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Pink Green Green Green Green Green Brown Brown Pink Red Brown Brown Pink
Row 19: Yellow Pink Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink
Row 20: Pink Pink Green Green Green Green Green Green Green Green Green Orange Pink Green Green Green Green Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink
Row 21: Pink Pink Green Green Green Green Green Green Green Green Green Pink Pink Green Green Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 22: Yellow Pink Green Green Green Green Green Green Green Pink Brown Brown Yellow Green Green Green Green Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink
Row 23: Brown Pink Green Green Green Green Green Green Green Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink
Row 24: Pink Pink Green Green Green Green Green Green Pink Pink Yellow Green Green Green Green Green Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 25: Pink Pink Yellow Brown Pink Pink Yellow Brown Green Green Green Green Green Green Green Green Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink
Row 26: Brown Pink Red Brown Brown Pink Red Brown Green Green Green Green Green Green Green Green Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink
Row 27: Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Green Green Green Green Green Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink
Row 28: Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange 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 Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink
Row 2: Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink
Row 3: Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink
Row 4: Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange 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 Pink
Row 6: Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink
Row 7: Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink
Row 8: Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 9: Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink
Row 10: Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink
Row 11: Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink
Row 12: Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange 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 Pink Pink
Row 14: Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink
Row 15: Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink
Row 16: Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 17: Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink
Row 18: Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink
Row 19: Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink
Row 20: Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange 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 Pink Pink Pink
Row 22: Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink Brown Brown Yellow Pink
Row 23: Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink Brown Brown Brown Pink
Row 24: Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 25: Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink Yellow Brown Pink Pink
Row 26: Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink Red Brown Brown Pink
Row 27: Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink Brown Red Yellow Pink
Row 28: Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange Pink Pink Yellow Orange 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 3
Input:
Row 1: Orange Orange Green Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Black Orange Green Green Green Green Green Green Green Green Green Yellow Yellow Black Brown Blue Black Orange
Row 3: Red Green Green Green Green Green Green Green Green Green Green Yellow Brown Black Brown Black Red Orange
Row 4: Red Green Green Green Green Green Green Green Red Orange Black Yellow Blue Black Red Red Red Orange
Row 5: Yellow Orange Green Green Green Green Green Green Yellow Orange Black Red Red Brown Red Red Yellow Orange
Row 6: Red Orange Yellow Brown Red Red Brown Red Red Orange Yellow Brown Red Red Brown Red Red Orange
Row 7: Red Orange Brown Brown Red Red Black Red Red Orange Brown Brown Green Green Green Green Green Green
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green
Row 9: Black Orange Blue Yellow Yellow Black Brown Blue Black Orange Blue Yellow Green Green Green Green Green Orange
Row 10: Red Orange Yellow Yellow Brown Black Brown Black Red Orange Yellow Yellow Green Green Green Green Green Orange
Row 11: Red Orange Black Yellow Blue Black Red Red Red Orange Black Yellow Green Green Green Green Green Orange
Row 12: Yellow Orange Black Red Red Brown Red Red Yellow Orange Black Red Green Green Green Green Green Orange
Row 13: Red Orange Yellow Brown Red Red Brown Red Red Orange Yellow Brown Green Green Green Green Green Orange
Row 14: Red Orange Brown Brown Red Red Black Red Red Orange Brown Brown Green Green Green Green Green Green
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green
Row 16: Black Orange Blue Yellow Yellow Black Brown Blue Black Orange Blue Yellow Green Green Green Green Green Green
Row 17: Red Orange Yellow Yellow Brown Green Green Green Red Orange Yellow Yellow Green Green Green Green Green Green
Row 18: Red Orange Black Yellow Blue Green Green Green Red Orange Black Yellow Green Green Green Green Green Green
Row 19: Yellow Green Green Green Green Green Green Green Yellow Orange Black Red Green Green Green Green Green Green
Row 20: Red Green Green Green Green Green Green Green Red Orange Yellow Brown Green Green Green Green Green Green
Row 21: Red Green Green Green Green Green Green Green Green Orange Brown Brown Green Green Green Green Green Green
Row 22: Orange Orange Green Green Green Green Green Green Green Orange Orange Orange Green Green Green Orange Orange Orange
Row 23: Black Orange Green Green Green Green Green Green Green Orange Blue Yellow Green Green Green Blue Black Orange
Row 24: Red Orange Yellow Yellow Brown Black Brown Black Red Orange Yellow Yellow Green Green Green Black Red Orange
Row 25: Red Orange Black Yellow Blue Black Red Red Red Orange Black Yellow Blue Black Red Red Red Orange
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Black Orange Blue Yellow Yellow Black Brown Blue Black Orange Blue Yellow Yellow Black Brown Blue Black Orange
Row 3: Red Orange Yellow Yellow Brown Black Brown Black Red Orange Yellow Yellow Brown Black Brown Black Red Orange
Row 4: Red Orange Black Yellow Blue Black Red Red Red Orange Black Yellow Blue Black Red Red Red Orange
Row 5: Yellow Orange Black Red Red Brown Red Red Yellow Orange Black Red Red Brown Red Red Yellow Orange
Row 6: Red Orange Yellow Brown Red Red Brown Red Red Orange Yellow Brown Red Red Brown Red Red Orange
Row 7: Red Orange Brown Brown Red Red Black Red Red Orange Brown Brown Red Red Black Red Red Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Black Orange Blue Yellow Yellow Black Brown Blue Black Orange Blue Yellow Yellow Black Brown Blue Black Orange
Row 10: Red Orange Yellow Yellow Brown Black Brown Black Red Orange Yellow Yellow Brown Black Brown Black Red Orange
Row 11: Red Orange Black Yellow Blue Black Red Red Red Orange Black Yellow Blue Black Red Red Red Orange
Row 12: Yellow Orange Black Red Red Brown Red Red Yellow Orange Black Red Red Brown Red Red Yellow Orange
Row 13: Red Orange Yellow Brown Red Red Brown Red Red Orange Yellow Brown Red Red Brown Red Red Orange
Row 14: Red Orange Brown Brown Red Red Black Red Red Orange Brown Brown Red Red Black Red Red Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Black Orange Blue Yellow Yellow Black Brown Blue Black Orange Blue Yellow Yellow Black Brown Blue Black Orange
Row 17: Red Orange Yellow Yellow Brown Black Brown Black Red Orange Yellow Yellow Brown Black Brown Black Red Orange
Row 18: Red Orange Black Yellow Blue Black Red Red Red Orange Black Yellow Blue Black Red Red Red Orange
Row 19: Yellow Orange Black Red Red Brown Red Red Yellow Orange Black Red Red Brown Red Red Yellow Orange
Row 20: Red Orange Yellow Brown Red Red Brown Red Red Orange Yellow Brown Red Red Brown Red Red Orange
Row 21: Red Orange Brown Brown Red Red Black Red Red Orange Brown Brown Red Red Black Red Red Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Black Orange Blue Yellow Yellow Black Brown Blue Black Orange Blue Yellow Yellow Black Brown Blue Black Orange
Row 24: Red Orange Yellow Yellow Brown Black Brown Black Red Orange Yellow Yellow Brown Black Brown Black Red Orange
Row 25: Red Orange Black Yellow Blue Black Red Red Red Orange Black Yellow Blue Black Red Red Red Orange
Here is the input grid for the test example:
Input:
Row 1: Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Blue Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue
Row 2: Purple Blue Blue Blue Blue Blue Blue Blue Blue Green Brown Yellow Brown Blue Blue Blue Blue Blue Green Brown Brown Red Red Green Blue Blue Blue Blue Blue
Row 3: Purple Blue Blue Blue Blue Blue Blue Blue Blue Brown Black Blue Blue Blue Blue Blue Blue Blue Red Green Black Green Black Brown Blue Blue Blue Blue Blue
Row 4: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Red Yellow Black Green Yellow Brown Blue Blue Blue Blue Blue
Row 5: Purple Black Yellow Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Brown Black Black Purple Green Green Brown Black Purple Purple Purple
Row 6: Purple Red Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Purple Blue Blue Green Purple Red Yellow Green Black Purple Red Purple Black Brown Purple Purple
Row 7: Purple Green Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Black Green Brown Black Red Red Brown Green Purple Green Purple
Row 8: Purple Green Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Brown Brown Yellow Brown Purple Green Red Yellow Yellow Black Purple
Row 9: Purple Green Blue Blue Green Red Green Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Purple Black Brown Purple
Row 10: Purple Purple Red Yellow Black Red Yellow Green Yellow Brown Red Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Red Black Black Brown Purple
Row 11: Purple Red Black Green Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Purple Yellow Purple Yellow Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Purple Purple Brown Green Green Green Green Red Purple Purple Yellow Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Purple Red Green Brown Black Brown Brown Black Purple Purple Red Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Purple Purple Purple
Row 16: Purple Yellow Purple Yellow Green Brown Brown Red Red Green Brown Yellow Brown Yellow Purple Yellow Purple Yellow Green Brown Brown Red Blue Blue Blue Blue Brown Yellow Purple
Row 17: Purple Green Green Black Red Green Black Green Black Brown Black Black Yellow Red Purple Green Green Black Red Green Black Green Blue Blue Blue Blue Yellow Red Purple
Row 18: Purple Purple Yellow Purple Red Yellow Black Green Yellow Brown Green Red Black Purple Purple Purple Yellow Purple Red Yellow Black Green Yellow Blue Blue Blue Blue Blue Purple
Row 19: Purple Black Yellow Purple Brown Black Black Purple Green Green Brown Black Purple Purple Purple Black Yellow Blue Blue Blue Blue Purple Green Green Blue Blue Blue Blue Purple
Row 20: Purple Red Green Purple Red Yellow Green Black Purple Red Purple Black Brown Purple Purple Red Green Blue Blue Blue Blue Black Purple Red Purple Black Brown Purple Purple
Row 21: Purple Green Red Red Black Green Brown Black Red Red Brown Green Purple Green Purple Green Red Blue Blue Blue Blue Black Red Red Brown Green Purple Green Purple
Row 22: Purple Green Yellow Green Brown Brown Yellow Brown Purple Green Red Yellow Yellow Black Purple Green Yellow Blue Blue Blue Blue Brown Purple Green Red Yellow Yellow Black Purple
Row 23: Purple Green Green Green Green Red Green Purple Green Purple Purple Purple Black Brown Purple Green Green Blue Blue Blue Blue Purple Blue Blue Blue Blue Black Brown Purple
Row 24: Purple Purple Red Yellow Black Red Yellow Green Yellow Brown Red Black Black Brown Blue Blue Red Blue Blue Blue Blue Green Blue Blue Blue Blue Black Brown Purple
Row 25: Purple Red Black Green Purple Green Brown Brown Purple Yellow Red Red Red Yellow Blue Blue Black Green Purple Green Brown Brown Blue Blue Blue Blue Blue Yellow Purple
Row 26: Purple Yellow Purple Yellow Brown Purple Black Brown Red Red Red Red Black Red Blue Blue Purple Yellow Brown Purple Black Brown Blue Blue Blue Blue Blue Red Purple
Row 27: Purple Purple Brown Green Green Green Green Red Purple Purple Yellow Black Yellow Red Purple Purple Brown Green Green Green Green Red Blue Blue Blue Blue Blue Red Purple
Row 28: Purple Red Green Brown Black Brown Brown Black Purple Purple Red Green Purple Red Purple Red Green Brown Black Brown Brown Black Purple Purple Red Green Purple Red Purple
Row 29: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Yellow Green Brown Brown Red Red Green Brown Yellow Brown Yellow Purple Yellow Purple Yellow Green Brown Brown Red Red Green Brown Yellow Brown Yellow Purple
Purple Green Green Black Red Green Black Green Black Brown Black Black Yellow Red Purple Green Green Black Red Green Black Green Black Brown Black Black Yellow Red Purple
Purple Purple Yellow Purple Red Yellow Black Green Yellow Brown Green Red Black Purple Purple Purple Yellow Purple Red Yellow Black Green Yellow Brown Green Red Black Purple Purple
Purple Black Yellow Purple Brown Black Black Purple Green Green Brown Black Purple Purple Purple Black Yellow Purple Brown Black Black Purple Green Green Brown Black Purple Purple Purple
Purple Red Green Purple Red Yellow Green Black Purple Red Purple Black Brown Purple Purple Red Green Purple Red Yellow Green Black Purple Red Purple Black Brown Purple Purple
Purple Green Red Red Black Green Brown Black Red Red Brown Green Purple Green Purple Green Red Red Black Green Brown Black Red Red Brown Green Purple Green Purple
Purple Green Yellow Green Brown Brown Yellow Brown Purple Green Red Yellow Yellow Black Purple Green Yellow Green Brown Brown Yellow Brown Purple Green Red Yellow Yellow Black Purple
Purple Green Green Green Green Red Green Purple Green Purple Purple Purple Black Brown Purple Green Green Green Green Red Green Purple Green Purple Purple Purple Black Brown Purple
Purple Purple Red Yellow Black Red Yellow Green Yellow Brown Red Black Black Brown Purple Purple Red Yellow Black Red Yellow Green Yellow Brown Red Black Black Brown Purple
Purple Red Black Green Purple Green Brown Brown Purple Yellow Red Red Red Yellow Purple Red Black Green Purple Green Brown Brown Purple Yellow Red Red Red Yellow Purple
Purple Yellow Purple Yellow Brown Purple Black Brown Red Red Red Red Black Red Purple Yellow Purple Yellow Brown Purple Black Brown Red Red Red Red Black Red Purple
Purple Purple Brown Green Green Green Green Red Purple Purple Yellow Black Yellow Red Purple Purple Brown Green Green Green Green Red Purple Purple Yellow Black Yellow Red Purple
Purple Red Green Brown Black Brown Brown Black Purple Purple Red Green Purple Red Purple Red Green Brown Black Brown Brown Black Purple Purple Red Green Purple Red Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Yellow Purple Yellow Green Brown Brown Red Red Green Brown Yellow Brown Yellow Purple Yellow Purple Yellow Green Brown Brown Red Red Green Brown Yellow Brown Yellow Purple
Purple Green Green Black Red Green Black Green Black Brown Black Black Yellow Red Purple Green Green Black Red Green Black Green Black Brown Black Black Yellow Red Purple
Purple Purple Yellow Purple Red Yellow Black Green Yellow Brown Green Red Black Purple Purple Purple Yellow Purple Red Yellow Black Green Yellow Brown Green Red Black Purple Purple
Purple Black Yellow Purple Brown Black Black Purple Green Green Brown Black Purple Purple Purple Black Yellow Purple Brown Black Black Purple Green Green Brown Black Purple Purple Purple
Purple Red Green Purple Red Yellow Green Black Purple Red Purple Black Brown Purple Purple Red Green Purple Red Yellow Green Black Purple Red Purple Black Brown Purple Purple
Purple Green Red Red Black Green Brown Black Red Red Brown Green Purple Green Purple Green Red Red Black Green Brown Black Red Red Brown Green Purple Green Purple
Purple Green Yellow Green Brown Brown Yellow Brown Purple Green Red Yellow Yellow Black Purple Green Yellow Green Brown Brown Yellow Brown Purple Green Red Yellow Yellow Black Purple
Purple Green Green Green Green Red Green Purple Green Purple Purple Purple Black Brown Purple Green Green Green Green Red Green Purple Green Purple Purple Purple Black Brown Purple
Purple Purple Red Yellow Black Red Yellow Green Yellow Brown Red Black Black Brown Purple Purple Red Yellow Black Red Yellow Green Yellow Brown Red Black Black Brown Purple
Purple Red Black Green Purple Green Brown Brown Purple Yellow Red Red Red Yellow Purple Red Black Green Purple Green Brown Brown Purple Yellow Red Red Red Yellow Purple
Purple Yellow Purple Yellow Brown Purple Black Brown Red Red Red Red Black Red Purple Yellow Purple Yellow Brown Purple Black Brown Red Red Red Red Black Red Purple
Purple Purple Brown Green Green Green Green Red Purple Purple Yellow Black Yellow Red Purple Purple Brown Green Green Green Green Red Purple Purple Yellow Black Yellow Red Purple
Purple Red Green Brown Black Brown Brown Black Purple Purple Red Green Purple Red Purple Red Green Brown Black Brown Brown Black Purple Purple Red Green Purple Red Purple
Purple Purple Purple Purple Purple 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: Red Gray Red
Row 2: Pink Pink Pink
Row 3: Black Pink Pink
Output:
Row 1: Red Gray Red
Row 2: Pink Pink Pink
Row 3: Black Pink Pink
Row 4: Pink Pink Pink
Row 5: Red Gray Red
Row 6: Pink Pink Pink
Row 7: Black Pink Pink
Row 8: Pink Pink Pink
Row 9: Red Gray Red
Example 2
Input:
Row 1: Red Gray Red Red Red Pink Black Red Pink Red Purple Pink Red Purple Gray Red Black Red Pink Red Yellow
Row 2: Gray Red Purple Purple Red Yellow Black Purple Red Black Pink Black Red Red Black Red Red Gray Red Gray Red
Row 3: Black Red Red Red Red Red Purple Gray Yellow Black Purple Yellow Gray Red Gray Gray Red Pink Red Pink Black
Row 4: Yellow Gray Red Red Yellow Gray Purple Red Black Black Yellow Purple Yellow Purple Red Red Yellow Yellow Pink Yellow Purple
Output:
Row 1: Red Gray Red Red Red Pink Black Red Pink Red Purple Pink Red Purple Gray Red Black Red Pink Red Yellow
Row 2: Gray Red Purple Purple Red Yellow Black Purple Red Black Pink Black Red Red Black Red Red Gray Red Gray Red
Row 3: Black Red Red Red Red Red Purple Gray Yellow Black Purple Yellow Gray Red Gray Gray Red Pink Red Pink Black
Row 4: Yellow Gray Red Red Yellow Gray Purple Red Black Black Yellow Purple Yellow Purple Red Red Yellow Yellow Pink Yellow Purple
Row 5: Black Red Red Red Red Red Purple Gray Yellow Black Purple Yellow Gray Red Gray Gray Red Pink Red Pink Black
Row 6: Gray Red Purple Purple Red Yellow Black Purple Red Black Pink Black Red Red Black Red Red Gray Red Gray Red
Row 7: Red Gray Red Red Red Pink Black Red Pink Red Purple Pink Red Purple Gray Red Black Red Pink Red Yellow
Row 8: Gray Red Purple Purple Red Yellow Black Purple Red Black Pink Black Red Red Black Red Red Gray Red Gray Red
Row 9: Black Red Red Red Red Red Purple Gray Yellow Black Purple Yellow Gray Red Gray Gray Red Pink Red Pink Black
Row 10: Yellow Gray Red Red Yellow Gray Purple Red Black Black Yellow Purple Yellow Purple Red Red Yellow Yellow Pink Yellow Purple
Row 11: Black Red Red Red Red Red Purple Gray Yellow Black Purple Yellow Gray Red Gray Gray Red Pink Red Pink Black
Row 12: Gray Red Purple Purple Red Yellow Black Purple Red Black Pink Black Red Red Black Red Red Gray Red Gray Red
Row 13: Red Gray Red Red Red Pink Black Red Pink Red Purple Pink Red Purple Gray Red Black Red Pink Red Yellow
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Blue Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 5: Brown Brown Brown Brown Orange 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 Black Brown Brown Brown Blue Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Blue Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 5: Brown Brown Brown Brown Orange 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 Black Brown Brown Brown Blue Brown
Row 7: Brown Brown Brown Brown Orange 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 Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 9: Brown Brown Blue Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Blue Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 15: Brown Brown Brown Brown Orange 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 Black Brown Brown Brown Blue Brown
Row 17: Brown Brown Brown Brown Orange 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 Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Row 19: Brown Brown Blue Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown
Row 2: Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Row 3: Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
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 Black Black Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown
Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown
Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Brown Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red
Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Yellow Brown
Brown Brown Brown Brown Black Black Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Blue Blue Blue Blue Blue Blue Blue
Row 3: Pink Blue Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Pink Blue Yellow Gray Gray Gray Gray Gray
Row 5: Pink Blue Yellow Gray Yellow Yellow Yellow Yellow
Row 6: Pink Blue Yellow Gray Yellow Pink Pink Pink
Row 7: Pink Blue Yellow Gray Yellow Pink Blue Blue
Row 8: Pink Blue Yellow Gray Yellow Pink Blue Yellow
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Pink Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Pink Blue Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Pink Blue Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Pink Blue Yellow Gray Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Blue Yellow Gray Yellow Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Pink Blue Yellow Gray Yellow Pink Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Blue Blue Blue Blue Blue Blue
Row 11: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Yellow Gray Gray Gray Gray Gray
Row 13: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Yellow Gray Yellow Yellow Yellow Yellow
Row 14: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Yellow Gray Yellow Pink Pink Pink
Row 15: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Yellow Gray Yellow Pink Blue Blue
Row 16: Pink Blue Yellow Gray Yellow Pink Blue Yellow Pink Blue Yellow Gray Yellow Pink Blue Yellow
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple
Row 2: Yellow Yellow Yellow Yellow Purple
Row 3: Green Green Green Yellow Purple
Row 4: Blue Blue Green Yellow Purple
Row 5: Blue Blue Green Yellow Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple
Row 3: Green Green Green Green Green Green Green Green Yellow Purple
Row 4: Blue Blue Blue Blue Blue Blue Blue Green Yellow Purple
Row 5: Blue Blue Blue Blue Blue Blue Blue Green Yellow Purple
Row 6: Purple Purple Purple Purple Purple Blue Blue Green Yellow Purple
Row 7: Yellow Yellow Yellow Yellow Purple Blue Blue Green Yellow Purple
Row 8: Green Green Green Yellow Purple Blue Blue Green Yellow Purple
Row 9: Blue Blue Green Yellow Purple Blue Blue Green Yellow Purple
Row 10: Blue Blue Green Yellow Purple Blue Blue Green Yellow Purple
Example 3
Input:
Row 1: Yellow Yellow Gray Black Black Black Black Black Black
Row 2: Yellow Yellow Gray Black Black Black Black Black Black
Row 3: Gray Gray Gray Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Black Black Black
Row 6: Black Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black
Output:
Row 1: Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 2: Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 3: Gray Gray Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 4: Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 5: Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 6: Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray Yellow Yellow Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray Yellow Yellow Gray
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Gray
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray
Row 18: 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: Purple Purple Red Purple Purple Black Black Black
Row 2: Purple Purple Red Purple Purple Black Black Black
Row 3: Red Red Red Purple Purple Black Black Black
Row 4: Purple Purple Purple Purple Purple Black Black Black
Row 5: Purple Purple Purple Purple Purple Black Black Black
Row 6: Black Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Red Red Red Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Red Purple Purple Purple
Red Red Red Red Red Red Red Red Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Purple
Red Red Red Red Red Red Red Red Red Red Red Red Red Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Purple Purple Purple Purple Purple Purple Purple Purple 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: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Pink Pink Purple Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Blue Purple
Row 8: Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue
Row 9: Purple Purple Purple Pink Pink Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Blue Blue Purple
Row 10: Purple Purple Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple 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
Row 15: 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
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Pink Pink Purple Pink Purple Purple Purple Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Blue Purple
Row 8: Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue
Row 9: Purple Purple Purple Pink Pink Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Blue Blue Purple
Row 10: Purple Purple Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Pink Pink Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Pink Pink Purple Pink Purple Purple Purple Pink 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
Row 2: 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
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: 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
Row 8: Yellow Pink Pink Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow
Row 9: Pink Pink Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow
Row 10: Yellow Pink Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: 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
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: 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
Row 3: 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
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow
Row 8: Yellow Pink Pink Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow
Row 9: Pink Pink Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow
Row 10: Yellow Pink Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: 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
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Black Red Black Black Black Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Black Red Black Black Black Black Black Black Red Black Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green
Row 5: Green Brown Brown Brown Brown Brown Green Blue Green
Row 6: Brown Brown Brown Brown Brown Brown Green Blue Blue
Row 7: Brown Brown Brown Brown Green Brown Blue Blue Green
Row 8: Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green
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 Brown Brown Brown Brown Brown Green Blue Green
Brown Brown Brown Brown Brown Brown Green Blue Blue
Brown Brown Brown Brown Green Brown Blue Blue Green
Brown Brown Brown Brown Green Brown Green Green Green
Brown Brown Brown Brown Brown Brown Green Green Green
Green Brown Brown Brown Brown Brown 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 Yellow Orange Orange Orange Red
Row 2: Orange Orange Orange Orange Yellow Red Orange Orange Orange
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Red Orange Orange Orange Yellow Orange Orange Red Red
Row 5: Red Red Orange Orange Yellow Orange Orange Red Orange
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Red Orange Red Orange Yellow Orange Red Orange Orange
Row 8: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Red Red Red Red Yellow Red Red Red Red
Row 5: Red Red Red Red Yellow Red Red Red Red
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Yellow Orange Orange Orange Orange
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Red Gray Purple Purple Purple Gray Red Purple Gray Purple Purple Purple
Row 2: Purple Gray Purple Gray Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 3: Purple Gray Purple Purple Purple Red Purple Purple Purple Gray Purple Red Gray Purple Purple Gray Gray
Row 4: Gray Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Gray Purple Gray Purple Purple
Row 7: Purple Purple Purple Gray Purple Red Gray Gray Purple Gray Purple Red Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Gray Purple Red Purple Purple Purple Purple Purple Red Purple Purple Gray Purple Purple
Row 9: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Output:
Row 1: Gray Gray Gray Gray Gray Red Purple Purple Purple Purple Purple Red Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Red Purple Purple Purple Purple Purple Red Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Red Purple Purple Purple Purple Purple Red Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Red Purple Purple Purple Purple Purple Red Gray Gray Gray Gray Gray
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple Red Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Orange Black Orange Black Blue Black Black Orange Black Blue Black Black Black Black
Row 2: Orange Black Orange Black Blue Orange Black Black Orange Blue Black Orange Orange Black
Row 3: Black Black Black Orange Blue Orange Black Black Orange Blue Orange Black Orange Black
Row 4: Black Black Black Orange Blue Black Black Black Orange Blue Black Orange Black Black
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Black Black Black Black Blue Black Orange Black Black Blue Orange Black Orange Orange
Row 7: Black Black Black Orange Blue Orange Black Black Orange Blue Black Black Black Black
Row 8: Black Black Black Black Blue Black Orange Orange Black Blue Black Black Black Black
Row 9: Black Black Black Black Blue Black Black Black Orange Blue Black Orange Black Orange
Output:
Row 1: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 2: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 3: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 4: Orange Orange Orange Orange Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 5: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Black Black Black Black Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 7: Black Black Black Black Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 8: Black Black Black Black Blue Orange Orange Orange Orange Blue Black Black Black Black
Row 9: Black Black Black Black Blue Orange Orange Orange Orange Blue Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray
Row 2: Gray Gray Gray Purple Gray Gray Black Purple Gray Gray Gray
Row 3: Gray Gray Gray Purple Gray Gray Gray Purple Black Black Gray
Row 4: Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Gray Gray Black Purple Gray Gray Gray Purple Gray Gray Gray
Row 7: Gray Gray Gray Purple Gray Gray Black Purple Gray Gray Gray
Row 8: Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray
Row 9: Gray Black Gray Purple Gray Gray Gray Purple Gray Gray Black
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray
Row 12: Gray Gray Gray Purple Gray Black Gray Purple Gray Gray Gray
Row 13: Gray Gray Gray Purple Gray Gray Gray Purple Gray Gray Gray
Row 14: Gray Gray Gray Purple Black Gray Gray Purple 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 Purple Gray Gray Gray Purple Black Black Black
Gray Gray Gray Purple Gray Gray Gray Purple Black Black Black
Gray Gray Gray Purple Gray Gray Gray Purple Black Black Black
Gray Gray Gray Purple Gray Gray Gray Purple Black Black Black
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Black Black Black Purple Gray Gray Gray Purple Gray Gray Gray
Black Black Black Purple Gray Gray Gray Purple Gray Gray Gray
Black Black Black Purple Gray Gray Gray Purple Gray Gray Gray
Black Black Black Purple Gray Gray Gray Purple Gray Gray Gray
Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Gray Gray Gray Purple Black Black Black Purple Gray Gray Gray
Gray Gray Gray Purple Black Black Black Purple Gray Gray Gray
Gray Gray Gray Purple Black Black Black Purple Gray Gray Gray
Gray Gray Gray Purple Black Black Black Purple 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: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 2: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 3: Brown Brown Gray Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 4: Purple Purple Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 5: Pink Pink Pink Gray Gray Gray Purple Gray Gray Gray Gray Gray
Row 6: Purple Purple Purple Purple 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 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
Output:
Row 1: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 2: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 3: Brown Brown Yellow Brown Brown Yellow Yellow Brown Brown Brown Yellow Brown
Row 4: Purple Purple Yellow Purple Purple Yellow Yellow Purple Purple Purple Yellow Purple
Row 5: Pink Pink Yellow Pink Pink Yellow Yellow Pink Pink Pink Yellow Pink
Row 6: Purple Purple Yellow Purple Purple Yellow Yellow Purple Purple Purple Yellow Purple
Row 7: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 8: Pink Pink Yellow Pink Pink Yellow Yellow Pink Pink Pink Yellow Pink
Row 9: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 10: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 11: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 12: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Row 13: Gray Gray Purple Gray Gray Pink Purple Gray Gray Gray Brown Gray
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 3: Blue Blue Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 4: Black Black Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 5: Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 7: Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Red Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Red Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 3: Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Yellow Blue Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 4: Black Black Black Black Black Black Black Yellow Black Black Yellow Yellow Black Black Yellow Yellow Yellow Black Black Black Black Black Black
Row 5: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Yellow Yellow Orange Orange Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange
Row 6: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 7: Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Yellow Gray Gray Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Row 8: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 13: Black Black Black Black Black Black Black Yellow Black Black Yellow Yellow Black Black Yellow Yellow Yellow Black Black Black Black Black Black
Row 14: Blue Blue Blue Blue Blue Blue Blue Yellow Blue Blue Yellow Yellow Blue Blue Yellow Yellow Yellow Blue Blue Blue Blue Blue Blue
Row 15: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Red Purple Purple Green Black Purple Purple Green Red Gray Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Red Red Brown Red Red
Row 2: Red Red Brown Red Red
Row 3: Red Red Red Pink Pink
Row 4: Red Red Red Red Red
Row 5: Red Red Red Red Red
Output:
Row 1: Red Red Brown Red Red
Row 2: Red Red Brown Red Red
Row 3: Pink Pink Yellow Pink Pink
Row 4: Red Red Brown Red Red
Row 5: Red Red Brown Red Red
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Brown Black
Row 2: Black Black Black Brown Black
Row 3: Black Black Black Brown Black
Row 4: Black Black Black Black Black
Row 5: Orange Orange Orange Black Black
Row 6: Black Black Black Black Black
Row 7: Brown Brown Brown Black Black
Row 8: Black Black Black Black Black
Row 9: Orange Orange Orange Orange Orange
Row 10: Brown Brown Brown Black Black
Row 11: Black Black Black Black Black
Row 12: Black Black Black Black Black
Row 13: Black Black Black Black Black
Row 14: Black Black Black Black Black
Row 15: Black Black Black Black Black
Row 16: 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 Brown Black
Black Black Black Brown Black
Black Black Black Brown Black
Black Black Black Brown Black
Orange Orange Orange Yellow Orange
Black Black Black Brown Black
Brown Brown Brown Yellow Brown
Black Black Black Brown Black
Orange Orange Orange Yellow Orange
Brown Brown Brown Yellow Brown
Black Black Black Brown Black
Black Black Black Brown Black
Black Black Black Brown Black
Black Black Black Brown Black
Black Black Black Brown Black
Black Black Black Brown Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Green Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Red Pink Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Yellow Pink Red Green Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Pink Green Pink Yellow Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Orange Pink Red Pink Red Yellow Orange Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Green Pink Green Yellow Pink Orange Orange Pink Green Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Red Pink Yellow Yellow Yellow Yellow Green Green Red Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Yellow Orange Red Red Red Red Green Orange Orange Red Pink Pink Orange Pink
Row 10: Pink Pink Pink Pink Green Yellow Yellow Orange Yellow Red Orange Yellow Yellow Red Pink Red Orange Green
Row 11: Pink Pink Pink Green Orange Green Yellow Yellow Red Green Red Yellow Pink Orange Pink Pink Yellow Yellow
Row 12: Pink Pink Pink Pink Red Red Green Red Red Yellow Yellow Green Orange Pink Orange Green Pink Green
Row 13: Pink Pink Pink Pink Red Orange Green Green Red Red Pink Pink Yellow Yellow Orange Pink Yellow Pink
Row 14: Pink Pink Pink Green Pink Orange Pink Red Green Orange Orange Pink Pink Green Green Pink Pink Pink
Row 15: Pink Pink Pink Pink Red Orange Pink Pink Red Pink Pink Orange Orange Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Red Green Red Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Green Red Red Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Yellow Red Orange Orange 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
Row 20: 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
Row 22: 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
Output:
Row 1: Black Black Black Black Green Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Yellow Green Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Red Black Yellow Black Black Black Black Black Black Black Black
Row 4: Black Black Black Yellow Black Red Green Black Black Black Black Black Black Black Black
Row 5: Black Black Black Black Black Black Yellow Black Green Black Yellow Black Black Black Black
Row 6: Black Black Black Black Orange Black Red Black Red Yellow Orange Black Black Black Black
Row 7: Black Black Black Green Black Green Yellow Black Orange Orange Black Green Black Black Black
Row 8: Black Black Red Black Yellow Yellow Yellow Yellow Green Green Red Black Black Black Black
Row 9: Black Yellow Orange Red Red Red Red Green Orange Orange Red Black Black Orange Black
Row 10: Black Green Yellow Yellow Orange Yellow Red Orange Yellow Yellow Red Black Red Orange Green
Row 11: Green Orange Green Yellow Yellow Red Green Red Yellow Black Orange Black Black Yellow Yellow
Row 12: Black Red Red Green Red Red Yellow Yellow Green Orange Black Orange Green Black Green
Row 13: Black Red Orange Green Green Red Red Black Black Yellow Yellow Orange Black Yellow Black
Row 14: Green Black Orange Black Red Green Orange Orange Black Black Green Green Black Black Black
Row 15: Black Red Orange Black Black Red Black Black Orange Orange Black Black Black Black Black
Row 16: Black Black Black Yellow Yellow Yellow Red Green Red Black Black Black Black Black Black
Row 17: Black Black Black Green Red Red Yellow Black Black Black Black Black Black Black Black
Row 18: Black Black Black Black Yellow Red Orange Orange Black Black Black Black Black Black Black
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Yellow Pink Pink Pink Pink Pink Pink Pink
Row 4: Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 5: Yellow Yellow Yellow Pink Pink Pink Pink Pink
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink
Row 7: Pink Yellow Yellow Yellow Yellow Pink Pink Pink
Row 8: Yellow Yellow Yellow Yellow Pink Pink Pink Pink
Row 9: Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink
Row 10: Yellow Yellow Pink Yellow Yellow Yellow Yellow Pink
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 12: Yellow Yellow Yellow Yellow Yellow Pink Yellow Pink
Row 13: Yellow Pink Yellow Pink Pink Yellow Yellow 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
Output:
Row 1: Yellow Black Black Black Black Black Black
Row 2: Yellow Yellow Yellow Black Black Black Black
Row 3: Yellow Yellow Yellow Black Black Black Black
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 5: Black Yellow Yellow Yellow Yellow Black Black
Row 6: Yellow Yellow Yellow Yellow Black Black Black
Row 7: Yellow Yellow Yellow Yellow Yellow Black Yellow
Row 8: Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Black Yellow
Row 11: Yellow Black Yellow Black Black Yellow Yellow
Example 3
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 Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Pink Brown
Row 9: Brown Brown Brown Brown Brown Gray Brown Brown Green Red Red Brown Brown
Row 10: Brown Brown Brown Brown Brown Green Brown Pink Green Green Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Pink Gray Brown Brown Red Pink Brown Brown
Row 12: Brown Brown Brown Brown Brown Gray Red Gray Gray Gray Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Pink Green Green Red Green Gray Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Gray Green Pink Pink Brown Red
Row 15: Brown Brown Brown Brown Brown Brown Pink Pink Green Pink Brown Gray Brown
Row 16: Brown Brown Brown Brown Brown Pink Brown Brown Gray Pink Green Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Red Brown Gray Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Green Green Red Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: 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
Row 25: 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
Row 27: 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
Row 29: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 30: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Black Black Black Black Black Green Green Black
Row 2: Black Black Black Green Black Black Pink Black
Row 3: Gray Black Black Green Red Red Black Black
Row 4: Green Black Pink Green Green Black Black Black
Row 5: Pink Gray Black Black Red Pink Black Black
Row 6: Gray Red Gray Gray Gray Black Black Black
Row 7: Black Pink Green Green Red Green Gray Black
Row 8: Black Black Gray Green Pink Pink Black Red
Row 9: Black Pink Pink Green Pink Black Gray Black
Row 10: Pink Black Black Gray Pink Green Black Black
Row 11: Black Black Red Black Gray Black Black Black
Row 12: Black Green Green Red Black Black Black Black
Row 13: Black Black Black Pink Black Black Black Black
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
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Blue Yellow Blue Yellow Green Green Green Green Green Green
Row 8: Green Green Green Green Purple Blue Pink Yellow Yellow Pink Green Green Green
Row 9: Green Green Green Green Yellow Blue Green Green Green Yellow Yellow Blue Green
Row 10: Green Blue Pink Pink Green Green Yellow Blue Green Blue Purple Purple Green
Row 11: Green Green Yellow Green Blue Yellow Green Purple Purple Purple Pink Yellow Green
Row 12: Green Pink Purple Blue Purple Yellow Pink Yellow Yellow Purple Purple Pink Green
Row 13: Green Purple Blue Blue Pink Green Purple Purple Blue Blue Green Pink Green
Row 14: Green Yellow Green Yellow Pink Green Blue Green Pink Yellow Green Purple Green
Row 15: Green Blue Pink Blue Purple Yellow Yellow Blue Blue Pink Pink Purple Green
Row 16: Green Purple Blue Yellow Purple Pink Purple Green Green Pink Purple Blue Green
Row 17: Green Green Green Blue Pink Pink Yellow Pink Blue Pink Green Green Green
Row 18: Green Green Purple Purple Pink Blue Green Green Purple Green Blue Blue Green
Row 19: Green Green Green Pink Green Green Yellow Blue Purple Pink Yellow Green Green
Row 20: Green Pink Blue Purple Pink Green Green Purple Pink Green Green Pink Green
Row 21: Green Green Green Green Green Green Green Pink Blue Green Purple Purple Green
Row 22: Green Green Green Green Green Green Purple Purple Blue Green Green Green Green
Row 23: Green Green Green Green Green Green Purple Pink Green Green Green Green Green
Row 24: 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
Row 26: 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
Row 28: 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Black Blue Yellow Blue Yellow Black Black Black Black Black
Black Black Black Purple Blue Pink Yellow Yellow Pink Black Black
Black Black Black Yellow Blue Black Black Black Yellow Yellow Blue
Blue Pink Pink Black Black Yellow Blue Black Blue Purple Purple
Black Yellow Black Blue Yellow Black Purple Purple Purple Pink Yellow
Pink Purple Blue Purple Yellow Pink Yellow Yellow Purple Purple Pink
Purple Blue Blue Pink Black Purple Purple Blue Blue Black Pink
Yellow Black Yellow Pink Black Blue Black Pink Yellow Black Purple
Blue Pink Blue Purple Yellow Yellow Blue Blue Pink Pink Purple
Purple Blue Yellow Purple Pink Purple Black Black Pink Purple Blue
Black Black Blue Pink Pink Yellow Pink Blue Pink Black Black
Black Purple Purple Pink Blue Black Black Purple Black Blue Blue
Black Black Pink Black Black Yellow Blue Purple Pink Yellow Black
Pink Blue Purple Pink Black Black Purple Pink Black Black Pink
Black Black Black Black Black Black Pink Blue Black Purple Purple
Black Black Black Black Black Purple Purple Blue Black Black Black
Black Black Black Black Black Purple 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: Black Black Yellow Gray Black Black Black Gray Black Black Black Gray Black Black Black
Row 2: Black Black Black Gray Black Black Red Gray Black Yellow Black Gray Yellow Black Black
Row 3: Black Black Black Gray Black Black Black Gray Black Black Black Gray Black Black Black
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Black Black Black Gray Black Black Blue Gray Black Blue Black Gray Black Yellow Black
Row 6: Black Black Black Gray Black Black Black Gray Black Black Black Gray Black Black Black
Row 7: Black Black Blue Gray Black Black Black Gray Black Black Black Gray Black Black Black
Output:
Row 1: Brown Brown Brown Gray Orange Orange Orange Gray Brown Brown Brown Gray Brown Brown Brown
Row 2: Brown Brown Brown Gray Orange Orange Orange Gray Brown Brown Brown Gray Brown Brown Brown
Row 3: Brown Brown Brown Gray Orange Orange Orange Gray Brown Brown Brown Gray Brown Brown Brown
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Gray Brown Brown Brown
Row 6: Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Gray Brown Brown Brown
Row 7: Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Gray Brown Brown Brown
Example 2
Input:
Row 1: Gray Red Gray Gray Gray Black Gray Gray Yellow Gray Gray
Row 2: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 5: Yellow Gray Gray Gray Gray Black Gray Gray Gray Green Gray
Row 6: Black Black Black Black Black Black Black Black Black Black Black
Row 7: Gray Gray Gray Gray Red Black Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Black Gray Blue Gray Gray Gray
Row 9: Black Black Black Black Black Black Black Black Black Black Black
Row 10: Gray Green Gray Gray Gray Black Gray Gray Red Gray Gray
Row 11: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 12: Black Black Black Black Black Black Black Black Black Black Black
Row 13: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Yellow Gray Black Gray Gray Gray Gray Green
Row 15: Black Black Black Black Black Black Black Black Black Black Black
Row 16: Gray Gray Gray Blue Gray Black Gray Blue Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 18: Black Black Black Black Black Black Black Black Black Black Black
Row 19: Gray Gray Green Gray Gray Black Gray Gray Gray Gray Gray
Row 20: Gray Gray Gray Gray Gray Black Gray Gray Blue Gray Gray
Row 21: Black Black Black Black Black Black Black Black Black Black Black
Row 22: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 23: Gray Blue Gray Gray Gray Black Gray Gray Gray Gray Blue
Row 24: Black Black Black Black Black Black Black Black Black Black Black
Row 25: Gray Gray Gray Green Gray Black Gray Gray Gray Gray Green
Row 26: Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Output:
Row 1: Orange Orange Orange Orange Orange Black Brown Brown Brown Brown Brown
Row 2: Orange Orange Orange Orange Orange Black Brown Brown Brown Brown Brown
Row 3: Black Black Black Black Black Black Black Black Black Black Black
Row 4: Brown Brown Brown Brown Brown Black Purple Purple Purple Purple Purple
Row 5: Brown Brown Brown Brown Brown Black Purple Purple Purple Purple Purple
Row 6: Black Black Black Black Black Black Black Black Black Black Black
Row 7: Orange Orange Orange Orange Orange Black Pink Pink Pink Pink Pink
Row 8: Orange Orange Orange Orange Orange Black Pink Pink Pink Pink Pink
Row 9: Black Black Black Black Black Black Black Black Black Black Black
Row 10: Purple Purple Purple Purple Purple Black Orange Orange Orange Orange Orange
Row 11: Purple Purple Purple Purple Purple Black Orange Orange Orange Orange Orange
Row 12: Black Black Black Black Black Black Black Black Black Black Black
Row 13: Brown Brown Brown Brown Brown Black Purple Purple Purple Purple Purple
Row 14: Brown Brown Brown Brown Brown Black Purple Purple Purple Purple Purple
Row 15: Black Black Black Black Black Black Black Black Black Black Black
Row 16: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 18: Black Black Black Black Black Black Black Black Black Black Black
Row 19: Purple Purple Purple Purple Purple Black Pink Pink Pink Pink Pink
Row 20: Purple Purple Purple Purple Purple Black Pink Pink Pink Pink Pink
Row 21: Black Black Black Black Black Black Black Black Black Black Black
Row 22: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink
Row 24: Black Black Black Black Black Black Black Black Black Black Black
Row 25: Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple
Row 26: Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Gray Gray Black Gray Gray Black Yellow Gray Black Gray Gray Black Gray Gray Black Yellow Gray
Row 2: Gray Gray Black Gray Gray Black Gray Gray Black Gray Gray Black Gray Gray Black Gray Gray
Row 3: Gray Blue Black Green Gray Black Gray Gray Black Red Gray Black Blue Gray Black Gray Gray
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Gray Gray Black Gray Gray Black Gray Gray Black Blue Gray Black Gray Gray Black Gray Gray
Row 6: Gray Green Black Gray Gray Black Gray Blue Black Gray Gray Black Gray Gray Black Gray Gray
Row 7: Gray Gray Black Green Gray Black Gray Gray Black Gray Gray Black Yellow Gray Black Gray Blue
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Gray Gray Black Yellow Gray Black Gray Gray Black Gray Gray Black Gray Gray Black Gray Gray
Row 10: Gray Gray Black Gray Gray Black Yellow Gray Black Gray Red Black Gray Gray Black Gray Gray
Row 11: Gray Green Black Gray Gray Black Gray Gray Black Gray Gray Black Gray Red Black Yellow Gray
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Gray Red Black Gray Gray Black Green Gray Black Gray Blue Black Gray Gray Black Gray Gray
Row 14: Gray Gray Black Gray Blue Black Gray Gray Black Gray Gray Black Gray Gray Black Gray Gray
Row 15: Gray Gray Black Gray Gray Black Gray Gray Black Gray Gray Black Gray Red Black Blue Gray
Output:
Row 1: Pink Pink Black Purple Purple Black Brown Brown Black Orange Orange Black Pink Pink Black Brown Brown
Row 2: Pink Pink Black Purple Purple Black Brown Brown Black Orange Orange Black Pink Pink Black Brown Brown
Row 3: Pink Pink Black Purple Purple Black Brown Brown Black Orange Orange Black Pink Pink Black Brown Brown
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Purple Purple Black Purple Purple Black Pink Pink Black Pink Pink Black Brown Brown Black Pink Pink
Row 6: Purple Purple Black Purple Purple Black Pink Pink Black Pink Pink Black Brown Brown Black Pink Pink
Row 7: Purple Purple Black Purple Purple Black Pink Pink Black Pink Pink Black Brown Brown Black Pink Pink
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Purple Purple Black Brown Brown Black Brown Brown Black Orange Orange Black Orange Orange Black Brown Brown
Row 10: Purple Purple Black Brown Brown Black Brown Brown Black Orange Orange Black Orange Orange Black Brown Brown
Row 11: Purple Purple Black Brown Brown Black Brown Brown Black Orange Orange Black Orange Orange Black Brown Brown
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Orange Orange Black Pink Pink Black Purple Purple Black Pink Pink Black Orange Orange Black Pink Pink
Row 14: Orange Orange Black Pink Pink Black Purple Purple Black Pink Pink Black Orange Orange Black Pink Pink
Row 15: Orange Orange Black Pink Pink Black Purple Purple Black Pink Pink Black Orange Orange Black Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Black Red Black Black Gray Black Black Black Blue
Row 2: Black Black Black Black Gray Black Black Black Black
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Black Black Black Black Gray Black Black Black Black
Row 5: Yellow Black Black Black Gray Black Black Red Black
Row 6: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Black Black Green Black Gray Black Black Black Black
Row 8: Black Black Black Black Gray Black Black Green Black
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Green Black Black Black Gray Black Black Black Black
Row 11: Black Black Black Black Gray Black Black Yellow Black
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Black Black Black Black Gray Black Yellow Black Black
Row 14: Black Red Black Black Gray Black Black Black Black
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Black Black Black Black Gray Black Black Black Black
Row 17: Black Black Blue Black Gray Black Blue Black Black
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Orange Orange Orange Gray Pink Pink Pink Pink
Orange Orange Orange Orange Gray Pink Pink Pink Pink
Gray Gray Gray Gray Gray Gray Gray Gray Gray
Brown Brown Brown Brown Gray Orange Orange Orange Orange
Brown Brown Brown Brown Gray Orange Orange Orange Orange
Gray Gray Gray Gray Gray Gray Gray Gray Gray
Purple Purple Purple Purple Gray Purple Purple Purple Purple
Purple Purple Purple Purple Gray Purple Purple Purple Purple
Gray Gray Gray Gray Gray Gray Gray Gray Gray
Purple Purple Purple Purple Gray Brown Brown Brown Brown
Purple Purple Purple Purple Gray Brown Brown Brown Brown
Gray Gray Gray Gray Gray Gray Gray Gray Gray
Orange Orange Orange Orange Gray Brown Brown Brown Brown
Orange Orange Orange Orange Gray Brown Brown Brown Brown
Gray Gray Gray Gray Gray Gray Gray Gray Gray
Pink Pink Pink Pink Gray Pink Pink Pink Pink
Pink Pink Pink Pink Gray 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 Red Red Red Red Red Red Red Red Red Red Red
Row 2: Green Red Red Red Red Red Red Red Red Red Red Red
Row 3: Green Red Red Red Red Red Red Red Red Red Red Red
Row 4: Green Red Red Red Red Red Red Red Red Red Red Red
Row 5: Green Red Red Red Red Red Red Red Red Red Red Red
Row 6: 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
Row 8: Red Red Red Red Red Red Red Red Red Red Red Green
Row 9: Red Red Red Red Red Red Red Red Red Red Red Green
Row 10: Red Brown Red Red Red Red Red Red Red Red Red Green
Row 11: Red Red Red Red Red Red Red Red Red Red Red Green
Row 12: Red Red Red Red Red Brown Red Red Red Red Red Green
Output:
Row 1: Green Red Red Red Red Red Red Red Red Red Red Red
Row 2: Green Red Red Red Red Red Red Red Red Red Red Red
Row 3: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Green Red Red Red Red Red Red Red Red Red Red Red
Row 5: Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: 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
Row 8: Red Red Red Red Red Red Red Red Red Red Red Green
Row 9: Red Red Red Red Red Red Red Red Red Red Red Green
Row 10: Red Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 11: Red Red Red Red Red Red Red Red Red Red Red Green
Row 12: Red Red Red Red Red Yellow Brown Brown Brown Brown Brown Green
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 Brown Brown Brown Brown
Row 2: Pink Pink Pink Blue Blue 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 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
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
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Brown Brown Brown Brown 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 Brown Brown Brown Brown
Row 2: Pink Pink Pink Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 3: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 4: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 5: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 6: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 7: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 8: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 9: Pink Pink Pink Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 10: Pink Pink Pink Blue Blue Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 11: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 12: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 13: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 14: Pink Pink Pink Blue Blue Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Row 15: Pink Pink Pink Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Pink
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange
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 Blue Blue Blue Black
Row 5: 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
Row 7: 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
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 Black Blue
Row 13: 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
Row 15: 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
Row 17: 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
Row 19: 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
Row 21: 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
Row 23: 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
Row 25: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange
Row 2: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Black
Row 3: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Black
Row 4: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Yellow
Row 5: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 6: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 7: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 8: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 9: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 10: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 11: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Black Blue
Row 12: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Yellow Blue
Row 13: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 14: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 25: Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 26: Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 4: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 5: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 6: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 8: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Row 11: 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
Row 13: 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
Row 15: 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
Row 17: 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
Row 19: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Pink Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black Black Black
Row 22: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Pink Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black Black Black Black
Row 24: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Pink Black Black Black Black Brown Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 28: Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 29: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
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 Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Black Black Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Brown Brown Brown Brown Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown 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 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
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 3: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 5: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 7: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 8: Brown Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow
Row 9: Gray Yellow Gray Yellow Gray Yellow Yellow Yellow Yellow Yellow Yellow Yellow Gray Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 11: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 12: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 13: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 14: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 15: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 16: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Row 17: Pink Yellow Green Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow
Example 2
Input:
Row 1: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
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
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
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
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
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
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
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
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 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 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 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 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
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 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 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 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
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 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 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 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
Row 23: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Output:
Row 1: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 2: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 3: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 4: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 5: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 6: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 7: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 8: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 9: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 10: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 11: Pink Pink Red Purple Red Pink Purple Pink Pink Pink Pink Red Pink Purple Pink Orange Pink Pink Purple Pink Orange Red Pink Pink Pink Purple Pink Orange
Row 12: Pink Pink Gray Gray Gray Pink Gray Pink Pink Pink Pink Gray Pink Gray Pink Gray Pink Pink Gray Pink Gray Gray Pink Pink Pink Gray Pink Gray
Row 13: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 14: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 15: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 16: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 17: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 18: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 19: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 20: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 21: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 22: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Row 23: Pink Pink Purple Red Orange Pink Red Pink Pink Pink Pink Orange Pink Red Pink Orange Pink Pink Red Pink Purple Orange Pink Pink Pink Purple Pink Red
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: 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
Row 6: 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
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Blue Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Red
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Pink Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Orange
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: 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
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: 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
Row 6: 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
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Red Red Red Red Red Red Red Red Red Red Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Red Red Red Red Red Red Red Red Red Red
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Gray 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 Green Green Green Green Green
Row 16: Red Red Red Red Red Red Red Red Red Red Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green 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
Row 19: 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
Row 21: 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 Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Row 2: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 3: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Row 4: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 5: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Yellow
Row 6: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Row 7: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 8: Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue Pink
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Black
Row 11: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Pink Pink Pink Pink Pink Gray Green Green Green Green Green
Green Green Green Green Green Gray Black Black Black Black Black
Pink Pink Pink Pink Pink Gray Green Green Green Green Green
Yellow Yellow Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Gray Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Gray Green Green Green Green Green
Green Green Green Green Green Gray Black Black Black Black Black
Yellow Yellow Yellow Yellow Yellow Gray Pink Pink Pink Pink Pink
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Pink Pink Pink Pink Pink Gray Black Black Black Black Black
Green Green Green Green Green Gray Green Green Green Green Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Purple Purple
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Purple Purple
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Purple Purple
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Purple Purple
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Purple Purple
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Purple Purple
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 11: 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
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Red Red Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 16: Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 17: Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 18: Purple Purple Purple Yellow Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 21: Red Red Red Red Yellow Yellow Purple Purple Purple Purple Yellow Orange Yellow
Row 22: Red Red Red Red Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 23: Red Red Red Red Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Purple Purple
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow
Row 11: 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
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Red Red Brown Purple Purple Purple Purple Brown Orange Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Brown Orange Yellow
Row 16: Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Brown Orange Yellow
Row 17: Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Brown Orange Yellow
Row 18: Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Brown Orange Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Brown Orange Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Brown Orange Yellow
Row 21: Red Red Red Red Brown Brown Purple Purple Purple Purple Brown Orange Yellow
Row 22: Red Red Red Red Brown Brown Purple Purple Purple Purple Yellow Yellow Yellow
Row 23: Red Red Red Red Brown Brown Purple Purple Purple Purple Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Row 29: Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Purple Yellow Yellow Yellow
Example 2
Input:
Row 1: Gray Gray Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 4: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 5: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 6: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 7: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 8: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 9: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 10: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 11: Blue Blue Gray Yellow Yellow Yellow Yellow Gray Gray Gray Green Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray
Row 13: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Green Gray Gray
Row 14: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Green Gray Gray
Row 15: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 4: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 5: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 6: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 7: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 8: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 9: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 10: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 11: Blue Blue Brown Yellow Yellow Yellow Yellow Brown Brown Brown Green Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray
Row 13: Gray Gray Gray Gray Gray Purple Purple Brown Brown Brown Green Gray Gray
Row 14: Gray Gray Gray Gray Gray Purple Purple Brown Brown Brown Green Gray Gray
Row 15: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Purple Purple Gray Gray Gray Gray Gray Gray
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Red Red Red Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Red Red Red Red Pink
Row 4: Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 5: Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 6: Red Red Red Red Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 7: Red Red Red Red Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 8: Red Red Red Red Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 9: Pink Pink Pink Pink Pink Purple Purple Purple Pink Blue Pink Pink Pink Pink Red Red Red Red Pink
Row 10: Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 11: Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Pink Pink Red Red Red Red Pink
Row 12: Pink Pink Pink Pink Pink Purple Purple Purple Pink Pink Pink Pink Blue Pink Red Red Red Red Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Red Red Red Red Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Red Red Red Red Pink
Row 15: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 16: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 17: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 18: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 19: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 20: Purple Purple Purple Purple Purple Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Blue Blue Blue Blue Blue Pink Pink Pink Pink Blue 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
Row 25: 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
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Brown Brown Red Red Red Red Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red Brown Brown Red Red Red Red Pink
Row 4: Pink Pink Pink Pink Pink Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 5: Pink Pink Pink Pink Pink Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 6: Red Red Red Red Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 7: Red Red Red Red Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 8: Red Red Red Red Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 9: Pink Pink Pink Pink Pink Purple Purple Purple Brown Blue Brown Brown Brown Brown Red Red Red Red Pink
Row 10: Pink Pink Pink Pink Pink Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 11: Pink Pink Pink Pink Pink Purple Purple Purple Brown Brown Brown Brown Brown Brown Red Red Red Red Pink
Row 12: Pink Pink Pink Pink Pink Purple Purple Purple Brown Brown Brown Brown Blue Brown Red Red Red Red Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Brown Red Red Red Red Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Brown Red Red Red Red Pink
Row 15: Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink
Row 16: Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink
Row 17: Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink
Row 18: Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink
Row 19: Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink
Row 20: Purple Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Blue Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Pink Pink Pink Pink Pink Pink
Row 23: Pink Pink Pink Blue Blue Blue Blue Blue Brown Brown Brown Brown Blue 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
Row 25: 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
Here is the input grid for the test example:
Input:
Row 1: Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black
Row 2: Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black
Row 3: Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Black Black Green Green Green Green
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 Orange Orange Orange Orange Orange Black Black Black Black
Row 9: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 10: Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black
Row 11: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 12: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 13: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 14: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 15: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 16: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 17: Blue Blue Blue Blue Blue Blue Blue Black Black Black Green Green Black
Row 18: Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Green Green Black Black Red Red Red Red Red Red Red Red Black
Row 21: Green Green Black Black Red Red Red Red Red Red Red Red Black
Row 22: Green Green Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Row 24: Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Row 25: Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Row 26: 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
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 Orange Orange Orange Orange Black Black Black Black Black
Black Black Black Orange Orange Orange Orange Orange Black Black Black Black Black
Black Black Black Orange Orange Orange Orange Orange 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 Orange Orange Orange Orange Orange Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Black Black Black Black Black Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Green Green Black
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
Green Green Brown Brown Red Red Red Red Red Red Red Red Black
Green Green Brown Brown Red Red Red Red Red Red Red Red Black
Green Green Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Black Black Black
Black Black Black Yellow Yellow Yellow Yellow Yellow 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 |
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 Gray Yellow Yellow
Row 2: Orange Orange Yellow Orange Orange Gray
Row 3: Orange Yellow Gray Orange Yellow Orange
Row 4: Orange Yellow Orange Yellow Orange Orange
Row 5: Yellow Orange Yellow Gray Yellow Orange
Row 6: Orange Orange Orange Orange Orange Orange
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Orange Orange Gray Yellow Orange
Row 9: Gray Orange Orange Yellow Yellow Yellow
Row 10: Gray Yellow Orange Orange Orange Gray
Row 11: Yellow Orange Orange Yellow Yellow Yellow
Row 12: Orange Yellow Orange Yellow Orange Orange
Row 13: Orange Yellow Orange Orange Orange Orange
Row 14: Yellow Orange Yellow Yellow Orange Yellow
Row 15: Orange Gray Orange Yellow Yellow Yellow
Row 16: Orange Yellow Gray Yellow Yellow Gray
Row 17: Yellow Yellow Orange Yellow Orange Yellow
Row 18: Orange Yellow Yellow Orange Yellow Gray
Row 19: Orange Yellow Yellow Yellow Orange Orange
Row 20: Yellow Orange Gray Orange Orange Orange
Row 21: Yellow Orange Gray Yellow Orange Yellow
Row 22: Orange Orange Yellow Orange Orange Yellow
Row 23: Orange Yellow Gray Orange Yellow Yellow
Row 24: Orange Yellow Yellow Yellow Orange Gray
Row 25: Orange Orange Yellow Yellow Orange Yellow
Row 26: Yellow Orange Yellow Yellow Yellow Yellow
Row 27: Gray Yellow Orange Yellow Orange Orange
Output:
Row 1: Yellow Yellow Yellow Purple Yellow Yellow
Row 2: Orange Orange Yellow Orange Orange Purple
Row 3: Orange Yellow Purple Orange Yellow Orange
Row 4: Orange Yellow Orange Yellow Orange Orange
Row 5: Yellow Orange Yellow Purple Yellow Orange
Row 6: Orange Orange Orange Orange Orange Orange
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Orange Orange Purple Yellow Orange
Row 9: Purple Orange Orange Yellow Yellow Yellow
Row 10: Purple Yellow Orange Orange Orange Purple
Row 11: Yellow Orange Orange Yellow Yellow Yellow
Row 12: Orange Yellow Orange Yellow Orange Orange
Row 13: Orange Yellow Orange Orange Orange Orange
Row 14: Yellow Orange Yellow Yellow Orange Yellow
Row 15: Orange Purple Orange Yellow Yellow Yellow
Row 16: Orange Yellow Purple Yellow Yellow Purple
Row 17: Yellow Yellow Orange Yellow Orange Yellow
Row 18: Orange Yellow Yellow Orange Yellow Purple
Row 19: Orange Yellow Yellow Yellow Orange Orange
Row 20: Yellow Orange Purple Orange Orange Orange
Row 21: Yellow Orange Purple Yellow Orange Yellow
Row 22: Orange Orange Yellow Orange Orange Yellow
Row 23: Orange Yellow Purple Orange Yellow Yellow
Row 24: Orange Yellow Yellow Yellow Orange Purple
Row 25: Orange Orange Yellow Yellow Orange Yellow
Row 26: Yellow Orange Yellow Yellow Yellow Yellow
Row 27: Purple Yellow Orange Yellow Orange Orange
Example 2
Input:
Row 1: Blue Red Gray
Row 2: Blue Orange Blue
Row 3: Red Gray Red
Row 4: Orange Red Yellow
Row 5: Orange Yellow Yellow
Row 6: Pink Orange Gray
Row 7: Blue Pink Yellow
Row 8: Blue Orange Orange
Row 9: Red Blue Pink
Row 10: Gray Red Gray
Row 11: Purple Red Orange
Row 12: Gray Orange Pink
Row 13: Gray Orange Gray
Row 14: Pink Orange Yellow
Row 15: Orange Pink Orange
Output:
Row 1: Blue Red Purple
Row 2: Blue Orange Blue
Row 3: Red Purple Red
Row 4: Orange Red Yellow
Row 5: Orange Yellow Yellow
Row 6: Pink Orange Purple
Row 7: Blue Pink Yellow
Row 8: Blue Orange Orange
Row 9: Red Blue Pink
Row 10: Purple Red Purple
Row 11: Gray Red Orange
Row 12: Purple Orange Pink
Row 13: Purple Orange Purple
Row 14: Pink Orange Yellow
Row 15: Orange Pink Orange
Example 3
Input:
Row 1: Orange Purple Orange Purple Black Gray Orange Green Purple Black Orange Gray Gray Black Black Orange
Row 2: Orange Orange Orange Green Purple Purple Black Black Purple Purple Black Black Green Green Purple Purple
Row 3: Gray Green Purple Purple Orange Green Green Green Green Purple Orange Orange Black Purple Black Purple
Row 4: Purple Black Orange Gray Black Purple Orange Orange Black Green Green Purple Black Black Green Black
Row 5: Purple Black Gray Gray Purple Green Purple Green Orange Purple Orange Purple Purple Green Orange Green
Row 6: Green Orange Green Purple Purple Orange Purple Green Gray Gray Purple Black Orange Gray Black Purple
Row 7: Gray Purple Green Orange Orange Black Purple Black Orange Green Orange Gray Black Green Gray Purple
Row 8: Orange Purple Green Black Purple Purple Gray Black Purple Black Green Purple Orange Green Black Purple
Row 9: Gray Purple Gray Gray Purple Gray Orange Black Gray Black Green Purple Green Green Purple Black
Row 10: Black Green Purple Purple Purple Green Purple Orange Purple Purple Purple Orange Black Orange Orange Black
Row 11: Gray Gray Green Green Black Orange Orange Orange Black Orange Purple Gray Black Purple Green Green
Row 12: Purple Purple Black Gray Green Gray Orange Black Orange Black Green Purple Green Black Green Gray
Row 13: Black Purple Gray Black Orange Purple Purple Orange Purple Purple Green Gray Black Purple Green Purple
Row 14: Purple Orange Green Purple Orange Gray Purple Purple Gray Orange Black Orange Orange Gray Green Gray
Output:
Row 1: Orange Gray Orange Gray Black Purple Orange Green Gray Black Orange Purple Purple Black Black Orange
Row 2: Orange Orange Orange Green Gray Gray Black Black Gray Gray Black Black Green Green Gray Gray
Row 3: Purple Green Gray Gray Orange Green Green Green Green Gray Orange Orange Black Gray Black Gray
Row 4: Gray Black Orange Purple Black Gray Orange Orange Black Green Green Gray Black Black Green Black
Row 5: Gray Black Purple Purple Gray Green Gray Green Orange Gray Orange Gray Gray Green Orange Green
Row 6: Green Orange Green Gray Gray Orange Gray Green Purple Purple Gray Black Orange Purple Black Gray
Row 7: Purple Gray Green Orange Orange Black Gray Black Orange Green Orange Purple Black Green Purple Gray
Row 8: Orange Gray Green Black Gray Gray Purple Black Gray Black Green Gray Orange Green Black Gray
Row 9: Purple Gray Purple Purple Gray Purple Orange Black Purple Black Green Gray Green Green Gray Black
Row 10: Black Green Gray Gray Gray Green Gray Orange Gray Gray Gray Orange Black Orange Orange Black
Row 11: Purple Purple Green Green Black Orange Orange Orange Black Orange Gray Purple Black Gray Green Green
Row 12: Gray Gray Black Purple Green Purple Orange Black Orange Black Green Gray Green Black Green Purple
Row 13: Black Gray Purple Black Orange Gray Gray Orange Gray Gray Green Purple Black Gray Green Gray
Row 14: Gray Orange Green Gray Orange Purple Gray Gray Purple Orange Black Orange Orange Purple Green Purple
Here is the input grid for the test example:
Input:
Row 1: Green Black Brown Black Gray Gray Brown Gray Gray Green Brown Gray Yellow Brown Brown Gray Gray Brown Green Brown Orange Red Orange Green Brown Red Yellow Red Red Gray
Row 2: Gray Gray Red Gray Red Gray Gray Green Orange Black Black Green Gray Gray Yellow Gray Gray Red Gray Gray Gray Red Green Brown Gray Brown Orange Orange Gray Yellow
Row 3: Black Gray Orange Yellow Green Brown Orange Red Black Black Gray Black Green Yellow Green Green Green Brown Gray Orange Gray Green Gray Gray Black Brown Yellow Black Gray Black
Row 4: Brown Brown Gray Black Gray Green Gray Gray Green Red Green Purple Gray Gray Gray Yellow Gray Orange Green Green Green Red Red Red Red Gray Gray Orange Black Black
Row 5: Gray Red Gray Gray Orange Red Red Yellow Gray Green Red Orange Green Gray Black Gray Gray Red Gray Brown Gray Green Gray Black Gray Green Yellow Gray Green Brown
Row 6: Yellow Gray Black Brown Green Yellow Brown Red Gray Orange Yellow Gray Green Red Orange Yellow Black Orange Yellow Black Orange Gray Yellow Green Green Black Gray Gray Gray Gray
Row 7: Orange Red Yellow Red Gray Green Red Green Gray Gray Gray Gray Green Gray Black Gray Gray Gray Orange Black Gray Orange Gray Gray Orange Gray Yellow Orange Brown Gray
Row 8: Gray Gray Red Orange Green Gray Gray Red Orange Orange Gray Gray Red Gray Gray Orange Gray Brown Gray Green Black Yellow Gray Gray Gray Gray Gray Gray Orange Red
Row 9: Gray Yellow Gray Gray Gray Orange Orange Gray Gray Red Red Orange Gray Gray Orange Brown Black Gray Gray Orange Green Gray Orange Brown Gray Gray Black Purple Orange Black
Row 10: Red Yellow Orange Gray Orange Black Black Brown Green Black Gray Gray Black Yellow Black Black Gray Gray Green Gray Yellow Gray Black Gray Orange Black Gray Orange Purple Gray
Row 11: Gray Red Gray Yellow Brown Orange Black Black Gray Gray Yellow Gray Yellow Gray Gray Brown Gray Gray Black Black Green Black Gray Black Yellow Orange Gray Green Red Brown
Row 12: Red Red Gray Gray Gray Gray Gray Brown Gray Gray Red Gray Gray Purple Green Orange Gray Black Gray Gray Brown Brown Gray Green Gray Black Gray Brown Gray Yellow
Row 13: Gray Green Gray Orange Green Green Gray Gray Black Yellow Red Gray Red Red Yellow Orange Brown Gray Orange Green Purple Brown Brown Black Gray Orange Black Gray Yellow Yellow
Row 14: Gray Green Green Orange Gray Purple Gray Red Gray Gray Brown Green Red Green Black Orange Yellow Gray Orange Yellow Black Gray Brown Red Orange Black Red Gray Gray Gray
Row 15: Yellow Yellow Gray Orange Red Black Gray Yellow Green Black Orange Red Red Brown Gray Black Purple Orange Black Black Gray Gray Orange Brown Orange Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Brown Gray Yellow Orange Orange Green Gray Brown Gray Red Black Black Brown Red Orange Red Brown Gray Brown Red Gray Red Gray Gray Gray Gray Green
Row 17: Yellow Gray Green Gray Gray Gray Black Gray Brown Red Brown Purple Red Black Green Brown Brown Gray Gray Gray Orange Green Green Gray Gray Orange Green Gray Gray Yellow
Row 18: Red Red Green Brown Black Gray Yellow Yellow Brown Gray Orange Gray Black Black Red Gray Red Green Red Purple Red Gray Gray Red Gray Green Gray Gray Brown Gray
Row 19: Red Green Orange Gray Black Green Yellow Brown Gray Yellow Red Green Brown Green Gray Green Gray Brown Black Gray Brown Black Red Brown Yellow Gray Green Orange Gray Yellow
Row 20: Orange Yellow Black Gray Purple Red Gray Red Green Red Orange Brown Orange Gray Brown Brown Gray Gray Green Gray Gray Gray Gray Gray Red Orange Gray Gray Orange Yellow
Row 21: Gray Gray Yellow Gray Red Orange Gray Yellow Gray Green Black Yellow Brown Black Brown Orange Brown Gray Orange Gray Purple Orange Brown Gray Black Orange Yellow Red Green Red
Row 22: Gray Brown Purple Orange Red Green Black Gray Gray Orange Yellow Red Gray Gray Brown Gray Brown Red Purple Gray Gray Gray Yellow Gray Red Green Gray Black Brown Black
Row 23: Gray Green Red Gray Gray Gray Green Yellow Red Gray Gray Gray Green Purple Gray Orange Black Black Purple Gray Gray Orange Yellow Yellow Gray Brown Gray Black Gray Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Black Brown Black Purple Purple Brown Purple Purple Green Brown Purple Yellow Brown Brown Purple Purple Brown Green Brown Orange Red Orange Green Brown Red Yellow Red Red Purple
Purple Purple Red Purple Red Purple Purple Green Orange Black Black Green Purple Purple Yellow Purple Purple Red Purple Purple Purple Red Green Brown Purple Brown Orange Orange Purple Yellow
Black Purple Orange Yellow Green Brown Orange Red Black Black Purple Black Green Yellow Green Green Green Brown Purple Orange Purple Green Purple Purple Black Brown Yellow Black Purple Black
Brown Brown Purple Black Purple Green Purple Purple Green Red Green Gray Purple Purple Purple Yellow Purple Orange Green Green Green Red Red Red Red Purple Purple Orange Black Black
Purple Red Purple Purple Orange Red Red Yellow Purple Green Red Orange Green Purple Black Purple Purple Red Purple Brown Purple Green Purple Black Purple Green Yellow Purple Green Brown
Yellow Purple Black Brown Green Yellow Brown Red Purple Orange Yellow Purple Green Red Orange Yellow Black Orange Yellow Black Orange Purple Yellow Green Green Black Purple Purple Purple Purple
Orange Red Yellow Red Purple Green Red Green Purple Purple Purple Purple Green Purple Black Purple Purple Purple Orange Black Purple Orange Purple Purple Orange Purple Yellow Orange Brown Purple
Purple Purple Red Orange Green Purple Purple Red Orange Orange Purple Purple Red Purple Purple Orange Purple Brown Purple Green Black Yellow Purple Purple Purple Purple Purple Purple Orange Red
Purple Yellow Purple Purple Purple Orange Orange Purple Purple Red Red Orange Purple Purple Orange Brown Black Purple Purple Orange Green Purple Orange Brown Purple Purple Black Gray Orange Black
Red Yellow Orange Purple Orange Black Black Brown Green Black Purple Purple Black Yellow Black Black Purple Purple Green Purple Yellow Purple Black Purple Orange Black Purple Orange Gray Purple
Purple Red Purple Yellow Brown Orange Black Black Purple Purple Yellow Purple Yellow Purple Purple Brown Purple Purple Black Black Green Black Purple Black Yellow Orange Purple Green Red Brown
Red Red Purple Purple Purple Purple Purple Brown Purple Purple Red Purple Purple Gray Green Orange Purple Black Purple Purple Brown Brown Purple Green Purple Black Purple Brown Purple Yellow
Purple Green Purple Orange Green Green Purple Purple Black Yellow Red Purple Red Red Yellow Orange Brown Purple Orange Green Gray Brown Brown Black Purple Orange Black Purple Yellow Yellow
Purple Green Green Orange Purple Gray Purple Red Purple Purple Brown Green Red Green Black Orange Yellow Purple Orange Yellow Black Purple Brown Red Orange Black Red Purple Purple Purple
Yellow Yellow Purple Orange Red Black Purple Yellow Green Black Orange Red Red Brown Purple Black Gray Orange Black Black Purple Purple Orange Brown Orange Purple Purple Purple Purple Purple
Purple Purple Purple Brown Purple Yellow Orange Orange Green Purple Brown Purple Red Black Black Brown Red Orange Red Brown Purple Brown Red Purple Red Purple Purple Purple Purple Green
Yellow Purple Green Purple Purple Purple Black Purple Brown Red Brown Gray Red Black Green Brown Brown Purple Purple Purple Orange Green Green Purple Purple Orange Green Purple Purple Yellow
Red Red Green Brown Black Purple Yellow Yellow Brown Purple Orange Purple Black Black Red Purple Red Green Red Gray Red Purple Purple Red Purple Green Purple Purple Brown Purple
Red Green Orange Purple Black Green Yellow Brown Purple Yellow Red Green Brown Green Purple Green Purple Brown Black Purple Brown Black Red Brown Yellow Purple Green Orange Purple Yellow
Orange Yellow Black Purple Gray Red Purple Red Green Red Orange Brown Orange Purple Brown Brown Purple Purple Green Purple Purple Purple Purple Purple Red Orange Purple Purple Orange Yellow
Purple Purple Yellow Purple Red Orange Purple Yellow Purple Green Black Yellow Brown Black Brown Orange Brown Purple Orange Purple Gray Orange Brown Purple Black Orange Yellow Red Green Red
Purple Brown Gray Orange Red Green Black Purple Purple Orange Yellow Red Purple Purple Brown Purple Brown Red Gray Purple Purple Purple Yellow Purple Red Green Purple Black Brown Black
Purple Green Red Purple Purple Purple Green Yellow Red Purple Purple Purple Green Gray Purple Orange Black Black Gray Purple Purple Orange Yellow Yellow Purple Brown Purple Black 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: Pink Pink Pink 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
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
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 Gray Gray 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 Gray Pink Pink Orange Orange 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 Orange 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 Gray Pink Orange Orange Orange 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: Pink Pink Pink 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
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
Row 4: Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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: Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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 Gray Gray 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 Gray 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 Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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 Gray 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 Gray 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 Gray Gray Gray 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: Gray Pink Pink Gray Gray Pink Pink Gray Gray Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Gray Pink Pink Pink Gray Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Gray Pink Gray Gray Gray Pink Gray Gray Gray Pink Orange Orange Orange 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
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
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 Black 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 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 Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown 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 Red 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
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 21: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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
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
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
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
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
Row 2: Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Black Black 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 Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Black Black 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 Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black 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 Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown 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 Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red 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 Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Gray Gray 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 Gray Gray Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Brown Brown Red Brown Brown Red Brown Brown Red Brown Brown Red Brown Brown Red Gray Gray Red Red Red Red Red Red Red Red
Row 12: Red Brown Brown Red Brown Brown Red Brown Brown Red Brown Brown Red Brown Brown Red Gray Gray Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Brown 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 Brown Brown Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Brown Brown Red Red
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 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 Pink Pink Pink Black Black Black Black Black
Row 10: Black Black Black Black Black Pink Pink Pink Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Brown Black Brown Black Blue Black Black Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black Black
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 Pink Pink Pink Black Black Black Black Black
Black Black Black Black Black Pink Pink Pink Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Brown Brown Brown Black Blue Blue Blue Black Black Black Black Black
Black Brown Brown Brown Black 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 Blue Blue Blue 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: 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 Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Pink
Row 3: Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red 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
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: Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Red
Row 3: Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink 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
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Row 3: Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Output:
Row 1: 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 Purple
Row 3: Purple Green Green Green Green Green Green Green Green Green Green Green Green Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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 Green Green Green Green 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
Row 3: Gray 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 Green Gray
Row 4: Gray Green 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 Red Green Gray
Row 5: Gray Green 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 Red Green Gray
Row 6: Gray 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 Green Gray
Row 7: Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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 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 Blue Blue Blue Blue Blue
Row 2: Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue
Row 3: Blue 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 Red Blue
Row 4: Blue Red 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 Green Red Blue
Row 5: Blue Red 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 Green Red Blue
Row 6: Blue 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 Red Blue
Row 7: Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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
Row 2: Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 3: Gray Blue Green Green Green Green Green Green Green Green Green Green Green Green Blue Gray
Row 4: Gray Blue Green Black Black Black Black Black Black Black Black Black Black Green Blue Gray
Row 5: Gray Blue Green Black Gray Gray Gray Gray Gray Gray Gray Gray Black Green Blue Gray
Row 6: Gray Blue Green Black Gray Purple Purple Purple Purple Purple Purple Gray Black Green Blue Gray
Row 7: Gray Blue Green Black Gray Purple Pink Pink Pink Pink Purple Gray Black Green Blue Gray
Row 8: Gray Blue Green Black Gray Purple Pink Pink Pink Pink Purple Gray Black Green Blue Gray
Row 9: Gray Blue Green Black Gray Purple Purple Purple Purple Purple Purple Gray Black Green Blue Gray
Row 10: Gray Blue Green Black Gray Gray Gray Gray Gray Gray Gray Gray Black Green Blue Gray
Row 11: Gray Blue Green Black Black Black Black Black Black Black Black Black Black Green Blue Gray
Row 12: Gray Blue Green Green Green Green Green Green Green Green Green Green Green Green Blue Gray
Row 13: Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray
Row 14: 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>
| Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Pink
Pink Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Pink
Pink Purple Gray Black Black Black Black Black Black Black Black Black Black Gray Purple Pink
Pink Purple Gray Black Green Green Green Green Green Green Green Green Black Gray Purple Pink
Pink Purple Gray Black Green Blue Blue Blue Blue Blue Blue Green Black Gray Purple Pink
Pink Purple Gray Black Green Blue Gray Gray Gray Gray Blue Green Black Gray Purple Pink
Pink Purple Gray Black Green Blue Gray Gray Gray Gray Blue Green Black Gray Purple Pink
Pink Purple Gray Black Green Blue Blue Blue Blue Blue Blue Green Black Gray Purple Pink
Pink Purple Gray Black Green Green Green Green Green Green Green Green Black Gray Purple Pink
Pink Purple Gray Black Black Black Black Black Black Black Black Black Black Gray Purple Pink
Pink Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Pink
Pink Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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: Red Green Green Yellow Green Green Green Green Gray Green Green Blue Green
Row 2: Green Red Green Green Blue Blue Green Black Green Green Blue Gray Pink
Row 3: Green Green Blue Green Green Gray Blue Gray Gray Purple Yellow Red Green
Row 4: Green Green Green Red Blue Gray Green Pink Green Purple Green Green Blue
Row 5: Pink Green Green Black Gray Black Gray Blue Green Green Green Green Green
Row 6: Green Gray Green Blue Green Green Red Green Yellow Green Green Gray Green
Row 7: Yellow Green Red Green Black Red Green Purple Green Blue Red Gray Green
Row 8: Green Yellow Blue Red Black Pink Green Green Yellow Red Green Green Blue
Row 9: Green Green Green Green Gray Green Green Green Green Green Purple Yellow Green
Row 10: Red Black Green Black Green Green Green Blue Green Purple Black Blue Purple
Row 11: Red Green Green Yellow Green Green Green Green Gray Green Green Blue Green
Row 12: Green Red Green Green Blue Blue Green Black Green Green Blue Gray Pink
Row 13: Green Green Blue Green Green Gray Blue Gray Gray Purple Yellow Red Green
Row 14: Green Green Green Red Blue Gray Green Pink Green Purple Green Green Blue
Row 15: Pink Green Green Black Gray Black Gray Blue Green Green Green Green Green
Row 16: Green Gray Green Blue Green Green Red Green Yellow Green Green Gray Green
Row 17: Yellow Green Red Green Black Red Green Purple Green Blue Red Gray Green
Row 18: Green Yellow Blue Red Black Pink Green Green Yellow Red Green Green Blue
Row 19: Green Green Green Green Gray Green Green Green Green Green Purple Yellow Green
Row 20: Red Black Green Black Green Green Green Blue Green Purple Black Blue Purple
Output:
Row 1: Red Green Green Yellow Green Green Green Green Gray Green Green Blue Green
Row 2: Green Red Green Green Blue Blue Green Black Green Green Blue Gray Pink
Row 3: Green Green Blue Green Green Gray Blue Gray Gray Purple Yellow Red Green
Row 4: Green Green Green Red Blue Gray Green Pink Green Purple Green Green Blue
Row 5: Pink Green Green Black Gray Black Gray Blue Green Green Green Green Green
Row 6: Green Gray Green Blue Green Green Red Green Yellow Green Green Gray Green
Row 7: Yellow Green Red Green Black Red Green Purple Green Blue Red Gray Green
Row 8: Green Yellow Blue Red Black Pink Green Green Yellow Red Green Green Blue
Row 9: Green Green Green Green Gray Green Green Green Green Green Purple Yellow Green
Row 10: Red Black Green Black Green Green Green Blue Green Purple Black Blue Purple
Example 2
Input:
Row 1: Pink Green Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Green Pink Orange Pink Pink Pink Pink Pink Pink Pink
Row 2: Gray Black Pink Yellow Pink Pink Pink Black Pink Blue Yellow Gray Black Pink Yellow Pink Pink Pink Black Pink Blue Yellow
Output:
Row 1: Pink Green Pink Orange Pink Pink Pink Pink Pink Pink Pink
Row 2: Gray Black Pink Yellow Pink Pink Pink Black Pink Blue Yellow
Example 3
Input:
Row 1: Pink Pink Pink Black Brown Pink Brown Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown
Row 2: Brown Pink Brown Brown Brown Pink Brown Brown Pink Pink Brown Brown Pink Pink Brown Pink Brown
Row 3: Pink Pink Pink Brown Pink Brown Pink Brown Brown Pink Brown Brown Pink Pink Pink Pink Pink
Row 4: Pink Pink Brown Brown Pink Brown Pink Pink Brown Brown Pink Pink Brown Pink Brown Pink Brown
Row 5: Pink Pink Pink Pink Brown Brown Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Brown
Row 6: Brown Black Brown Pink Pink Black Pink Pink Brown Brown Pink Pink Brown Pink Pink Brown Black
Row 7: Brown Pink Pink Pink Pink Black Black Pink Brown Brown Pink Brown Brown Pink Brown Pink Brown
Row 8: Pink Pink Pink Black Brown Pink Brown Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown
Row 9: Brown Pink Brown Brown Brown Pink Brown Brown Pink Pink Brown Brown Pink Pink Brown Pink Brown
Row 10: Pink Pink Pink Brown Pink Brown Pink Brown Brown Pink Brown Brown Pink Pink Pink Pink Pink
Row 11: Pink Pink Brown Brown Pink Brown Pink Pink Brown Brown Pink Pink Brown Pink Brown Pink Brown
Row 12: Pink Pink Pink Pink Brown Brown Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Brown
Row 13: Brown Black Brown Pink Pink Black Pink Pink Brown Brown Pink Pink Brown Pink Pink Brown Black
Row 14: Brown Pink Pink Pink Pink Black Black Pink Brown Brown Pink Brown Brown Pink Brown Pink Brown
Output:
Row 1: Pink Pink Pink Black Brown Pink Brown Pink Brown Pink Brown Pink Brown Brown Brown Pink Brown
Row 2: Brown Pink Brown Brown Brown Pink Brown Brown Pink Pink Brown Brown Pink Pink Brown Pink Brown
Row 3: Pink Pink Pink Brown Pink Brown Pink Brown Brown Pink Brown Brown Pink Pink Pink Pink Pink
Row 4: Pink Pink Brown Brown Pink Brown Pink Pink Brown Brown Pink Pink Brown Pink Brown Pink Brown
Row 5: Pink Pink Pink Pink Brown Brown Pink Pink Pink Brown Brown Pink Pink Pink Pink Pink Brown
Row 6: Brown Black Brown Pink Pink Black Pink Pink Brown Brown Pink Pink Brown Pink Pink Brown Black
Row 7: Brown Pink Pink Pink Pink Black Black Pink Brown Brown Pink Brown Brown Pink Brown Pink Brown
Here is the input grid for the test example:
Input:
Row 1: Blue Pink Orange Blue Blue Blue Blue Purple Blue Blue Pink Orange Blue Blue Blue Blue Purple Blue
Row 2: Blue Blue Blue Blue Blue Blue Pink Red Blue Blue Blue Blue Blue Blue Blue Pink Red Blue
Row 3: Blue Blue Blue Red Blue Pink Blue Blue Pink Blue Blue Blue Red Blue Pink Blue Blue Pink
Row 4: Blue Orange Blue Blue Purple Orange Red Blue Blue Blue Orange Blue Blue Purple Orange Red Blue Blue
Row 5: Blue Blue Blue Blue Blue Orange Blue Blue Purple Blue Blue Blue Blue Blue Orange Blue Blue Purple
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Purple Blue Blue Orange Pink Blue Blue Pink Blue Purple Blue Blue Orange Pink Blue Blue Pink Blue
Row 8: Red Blue Blue Blue Blue Blue Pink Blue Blue Red Blue Blue Blue Blue Blue Pink Blue Blue
Row 9: Blue Blue Red Purple Pink Blue Blue Pink Orange Blue Blue Red Purple Pink Blue Blue Pink Orange
Row 10: Blue Red Blue Orange Red Pink Blue Blue Purple Blue Red Blue Orange Red Pink Blue Blue Purple
Row 11: Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Purple Orange Blue Blue Blue Blue Blue Blue Blue Purple Orange Blue Blue Blue Blue
Row 13: Purple Blue Red Orange Blue Blue Blue Pink Blue Purple Blue Red Orange Blue Blue Blue Pink Blue
Row 14: Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue
Row 15: Red Blue Blue Blue Orange Blue Blue Blue Blue Red Blue Blue Blue Orange Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Pink Blue Blue Blue Blue
Row 17: Brown Blue Blue Green Pink Blue Blue Blue Blue Brown Blue Blue Green Pink Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Red Blue Pink Blue Brown Blue Blue Blue Blue Red Blue Pink Blue Brown
Row 19: Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Purple 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 Pink Orange Blue Blue Blue Blue Purple Blue
Blue Blue Blue Blue Blue Blue Pink Red Blue
Blue Blue Blue Red Blue Pink Blue Blue Pink
Blue Orange Blue Blue Purple Orange Red Blue Blue
Blue Blue Blue Blue Blue Orange Blue Blue Purple
Blue Blue Blue Blue Blue Blue Blue Blue Blue
Purple Blue Blue Orange Pink Blue Blue Pink Blue
Red Blue Blue Blue Blue Blue Pink Blue Blue
Blue Blue Red Purple Pink Blue Blue Pink Orange
Blue Red Blue Orange Red Pink Blue Blue Purple
Blue Purple Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Purple Orange Blue Blue Blue Blue
Purple Blue Red Orange Blue Blue Blue Pink Blue
Blue Blue Blue Blue Blue Blue Pink Blue Blue
Red Blue Blue Blue Orange Blue Blue Blue Blue
Blue Blue Blue Blue Pink Blue Blue Blue Blue
Brown Blue Blue Green Pink Blue Blue Blue Blue
Blue Blue Blue Blue Red Blue Pink Blue Brown
Blue Blue Blue Blue Blue Blue Purple 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: 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
Row 3: Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Row 4: Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Gray Brown Gray Brown Brown Brown
Row 5: Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Row 6: Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Gray Brown Brown Brown
Row 10: Brown Brown Black Black Black Black Black Brown Brown Gray Gray Gray Brown Brown Brown
Row 11: Brown Brown Black Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Black Brown Brown Brown Black Brown Brown Brown Black Black Black Black Brown
Row 13: Brown Brown Black Brown Brown Brown Black Brown Brown Brown Black Brown Brown Black Brown
Row 14: Brown Brown Black Black Black Black Black Brown Brown Brown Black Brown Brown Black Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Brown
Row 16: Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Gray Brown Gray Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown
Row 19: 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
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Row 4: Yellow Orange Orange Orange Yellow Brown Brown Brown Brown Gray Orange Gray Brown Brown Brown
Row 5: Yellow Orange Orange Orange Yellow Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Row 6: Yellow Orange Orange Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Orange Gray Brown Brown Brown
Row 10: Brown Brown Black Black Black Black Black Brown Brown Gray Gray Gray Brown Brown Brown
Row 11: Brown Brown Black Orange Orange Orange Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Black Orange Orange Orange Black Brown Brown Brown Black Black Black Black Brown
Row 13: Brown Brown Black Orange Orange Orange Black Brown Brown Brown Black Red Red Black Brown
Row 14: Brown Brown Black Black Black Black Black Brown Brown Brown Black Red Red Black Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Black Black Black Brown
Row 16: Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Gray Orange Gray Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Gray Gray Gray Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Brown Brown Brown Brown Brown 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 Brown Green Green Green Brown 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 Brown Green Green Green Brown 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 Brown Green Green Green Brown 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 Brown Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple Purple 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 Purple Green Green Green Purple 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 Purple Green Green Green Purple 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 Purple Green Green Green Purple 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 Purple Purple Purple Purple Purple 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 Green
Output:
Row 1: Green Green Green Green Green Green Green Brown Brown Brown Brown Brown 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 Brown Orange Orange Orange Brown 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 Brown Orange Orange Orange Brown 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 Brown Orange Orange Orange Brown 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 Brown Brown Brown Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Purple Purple Purple 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 Purple Orange Orange Orange Purple 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 Purple Orange Orange Orange Purple 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 Purple Orange Orange Orange Purple 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 Purple Purple Purple Purple Purple 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 Green
Example 3
Input:
Row 1: Blue Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Green Blue Blue Blue Blue Blue Green Blue Brown Brown Brown Brown Blue Blue
Row 5: Blue Green Blue Blue Blue Blue Blue Green Blue Brown Blue Blue Brown Blue Blue
Row 6: Blue Green Blue Blue Blue Blue Blue Green Blue Brown Blue Blue Brown Blue Blue
Row 7: Blue Green Green Green Green Green Green Green Blue Brown Brown Brown Brown 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
Output:
Row 1: Blue Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Green Orange Orange Orange Orange Orange Green Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Green Orange Orange Orange Orange Orange Green Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Green Orange Orange Orange Orange Orange Green Blue Brown Brown Brown Brown Blue Blue
Row 5: Blue Green Orange Orange Orange Orange Orange Green Blue Brown Red Red Brown Blue Blue
Row 6: Blue Green Orange Orange Orange Orange Orange Green Blue Brown Red Red Brown Blue Blue
Row 7: Blue Green Green Green Green Green Green Green Blue Brown Brown Brown Brown 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
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
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Yellow Yellow Yellow 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
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
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
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
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
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 Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray 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
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 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 Yellow Red Red Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Yellow Red Red Yellow 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Red Red Red Red Blue Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Red Red Red Red Blue Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Red Red Red Red Blue Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Red Red Red Red Blue Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray 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: 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 Blue Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Orange 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 Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Orange 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 Orange 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 Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Blue 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 Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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
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
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
Row 18: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Yellow Orange 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 Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 24: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 27: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 28: Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Green Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Blue Yellow Yellow Yellow Yellow Yellow Blue
Row 2: Green Yellow Yellow Yellow Yellow Orange Orange
Row 3: Green Yellow Yellow Yellow Orange Orange Orange
Row 4: Green Green Green Orange Orange Orange Orange
Row 5: Green Green Green Orange Orange Orange Orange
Row 6: Green Green Green Orange Orange Orange Orange
Row 7: Green Green Green Orange Orange Orange Orange
Row 8: Green Green Green Orange Orange Orange Orange
Row 9: Green Green Yellow Orange Orange Orange Orange
Row 10: Green Green Green Orange Orange Orange Orange
Row 11: Blue Yellow Yellow Yellow Yellow Yellow Blue
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 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 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
Row 10: 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 Purple Gray Gray Gray Gray Gray Gray Purple 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 Purple Green Green Green Green Green Green Purple Blue
Row 19: Blue Blue Blue Blue Blue Blue Green Blue Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Green Green Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Green Green Green Blue Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Gray Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 23: Blue Blue Blue Blue Blue Blue Gray Blue Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Blue Blue Blue Blue Gray Blue Blue Blue Gray 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
Row 26: 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: Purple Gray Gray Gray Gray Gray Gray Purple
Row 2: Blue Blue Gray Blue Blue Blue Gray Blue
Row 3: Blue Blue Blue Gray Blue Gray Blue Blue
Row 4: Blue Gray Gray Blue Blue Gray Blue Blue
Row 5: Blue Green Green Green Blue Blue Green Blue
Row 6: Blue Blue Blue Green Green Blue Green Blue
Row 7: Blue Blue Blue Green Blue Green Green Blue
Row 8: Purple Green Green Green Green Green Green Purple
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: 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
Row 6: Red Red Red Red Yellow Blue Blue Yellow Red Red Red Red Red
Row 7: 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
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Yellow Black Black Yellow 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
Row 14: 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
Row 16: 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
Row 18: 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 Blue Red Red
Row 20: Red Red Red Red Red Red Red Red Red Blue Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Black Black Red Red
Row 22: Red Red Red Red Red Red Red Red Red Black Black Red Red
Output:
Row 1: Yellow Blue Blue Yellow
Row 2: Red Red Blue Red
Row 3: Red Blue Red Red
Row 4: Red Black Black Red
Row 5: Red Black Black Red
Row 6: Yellow Black Black Yellow
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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 Green Green Orange Green Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Green Green Green Orange Red Green Green Green Green Green Red Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Black 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 Orange Orange
Row 15: 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 Red Black Black Black Black Black Red 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
Row 18: 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
Row 20: 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
Row 22: 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>
| Red Green Green Green Green Green Red
Orange Green Green Orange Green Green Orange
Orange Orange Orange Green Green Green Orange
Orange Orange Orange Black Black Black Orange
Orange Orange Orange Orange Black Black Orange
Orange Orange Orange Black Orange Orange Orange
Red Black Black Black Black Black 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 Yellow Yellow Brown Purple Purple Brown Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Gray Gray Gray Gray Yellow Yellow Yellow
Row 3: Yellow Yellow Brown Brown Gray Gray Brown Brown Yellow Yellow
Row 4: Brown Gray Brown Yellow Yellow Yellow Yellow Brown Gray Brown
Row 5: Black Black Black Black Yellow Yellow Yellow Gray Gray Purple
Row 6: Purple Gray Gray Yellow Yellow Yellow Yellow Gray Gray Purple
Row 7: Brown Gray Brown Yellow Yellow Yellow Yellow Brown Gray Brown
Row 8: Yellow Yellow Brown Brown Gray Gray Brown Brown Yellow Yellow
Row 9: Yellow Yellow Yellow Gray Gray Gray Gray Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Brown Purple Purple Brown Yellow Yellow Yellow
Output:
Row 1: Purple Gray Gray Yellow
Example 2
Input:
Row 1: Green Blue Pink Blue Orange Yellow Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Yellow Orange Blue Pink Blue Green
Row 2: Blue Yellow Blue Blue Brown Pink Orange Blue Yellow Purple Purple Gray Gray Purple Purple Yellow Blue Orange Pink Brown Blue Blue Yellow Blue
Row 3: Pink Blue Orange Blue Orange Pink Purple Green Purple Purple Orange Yellow Yellow Orange Purple Purple Green Purple Pink Orange Blue Orange Blue Pink
Row 4: Blue Blue Blue Pink Yellow Purple Gray Blue Gray Blue Purple Orange Orange Purple Blue Gray Blue Gray Purple Yellow Pink Blue Blue Blue
Row 5: Orange Brown Orange Yellow Purple Green Purple Gray Blue Blue Purple Purple Purple Purple Blue Blue Gray Purple Green Purple Yellow Orange Brown Orange
Row 6: Yellow Pink Pink Purple Green Blue Pink Purple Pink Purple Purple Purple Purple Purple Purple Pink Purple Pink Blue Green Purple Pink Pink Yellow
Row 7: Gray Orange Purple Gray Purple Pink Yellow Yellow Pink Pink Purple Purple Purple Purple Pink Pink Yellow Yellow Pink Purple Gray Purple Orange Gray
Row 8: Gray Blue Green Blue Gray Purple Yellow Yellow Pink Gray Green Gray Gray Green Gray Pink Yellow Yellow Purple Gray Blue Green Blue Gray
Row 9: Gray Yellow Purple Gray Blue Pink Pink Pink Pink Pink Green Pink Pink Green Pink Pink Pink Pink Pink Blue Gray Purple Yellow Gray
Row 10: Purple Purple Purple Blue Blue Purple Pink Gray Pink Purple Brown Pink Pink Brown Purple Pink Gray Pink Purple Blue Blue Purple Purple Purple
Row 11: Purple Purple Orange Purple Purple Purple Purple Green Green Brown Purple Blue Blue Purple Brown Green Black Black Black Purple Purple Orange Purple Purple
Row 12: Purple Gray Yellow Orange Purple Purple Purple Gray Pink Pink Blue Purple Purple Blue Pink Pink Black Black Black Purple Orange Yellow Gray Purple
Row 13: Purple Gray Yellow Orange Purple Purple Purple Gray Pink Pink Blue Purple Purple Blue Pink Pink Black Black Black Purple Orange Yellow Gray Purple
Row 14: Purple Purple Orange Purple Purple Purple Purple Green Green Brown Purple Blue Blue Purple Brown Green Black Black Black Purple Purple Orange Purple Purple
Row 15: Purple Purple Purple Blue Blue Purple Pink Gray Pink Purple Brown Pink Pink Brown Purple Pink Black Black Black Blue Blue Purple Purple Purple
Row 16: Gray Yellow Purple Gray Blue Pink Pink Pink Pink Pink Green Pink Pink Green Pink Pink Black Black Black Blue Gray Purple Yellow Gray
Row 17: Gray Blue Green Blue Gray Purple Yellow Yellow Pink Gray Green Gray Gray Green Gray Pink Black Black Black Gray Blue Green Blue Gray
Row 18: Gray Orange Purple Gray Purple Pink Yellow Yellow Pink Pink Purple Purple Purple Purple Pink Pink Black Black Black Purple Gray Purple Orange Gray
Row 19: Yellow Pink Pink Purple Green Blue Pink Purple Pink Purple Purple Purple Purple Purple Purple Pink Black Black Black Green Purple Pink Pink Yellow
Row 20: Orange Brown Orange Yellow Purple Green Purple Gray Blue Blue Purple Purple Purple Purple Blue Blue Black Black Black Purple Yellow Orange Brown Orange
Row 21: Blue Blue Blue Pink Yellow Purple Gray Blue Gray Blue Purple Orange Orange Purple Blue Gray Black Black Black Yellow Pink Blue Blue Blue
Row 22: Pink Blue Orange Blue Orange Pink Purple Green Purple Purple Orange Yellow Yellow Orange Purple Purple Black Black Black Orange Blue Orange Blue Pink
Row 23: Blue Yellow Blue Blue Brown Pink Orange Blue Yellow Purple Purple Gray Gray Purple Purple Yellow Blue Orange Pink Brown Blue Blue Yellow Blue
Row 24: Green Blue Pink Blue Orange Yellow Gray Gray Gray Purple Purple Purple Purple Purple Purple Gray Gray Gray Yellow Orange Blue Pink Blue Green
Output:
Row 1: Green Purple Purple
Row 2: Gray Purple Purple
Row 3: Gray Purple Purple
Row 4: Green Purple Purple
Row 5: Gray Pink Purple
Row 6: Pink Pink Pink
Row 7: Yellow Yellow Purple
Row 8: Yellow Yellow Pink
Row 9: Purple Pink Blue
Row 10: Gray Purple Green
Row 11: Blue Gray Purple
Row 12: Green Purple Pink
Example 3
Input:
Row 1: Brown Green Green Green Green Green Green Green Brown Green Green Brown Green Green Green Green Green Green Green Brown
Row 2: Green Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 3: Green Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Brown Green Green Green Green
Row 6: Green Green Green Green Green Green Brown Green Green Green Green Green Green Brown Green Green Green Green Green Green
Row 7: Green Green Green Green Green Brown Green Green Green Green Green Green Green Green Brown Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Brown Green Green Green Green Brown Green Green Green Green Green Green Green
Row 9: Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown
Row 13: Green Green Green Green Green Green Green Brown Green Green Green Green Brown Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Brown Green Green Green Green Green Green Green Green Brown Green Green Green Green Green
Row 15: Green Green Green Green Green Green Brown Green Green Green Green Green Green Brown Green Green Green Green Green Green
Row 16: Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Brown Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Green Green
Row 18: Green Brown Green Green Green Green Green Green Green Black Green Green Green Green Green Green Green Green Brown Green
Row 19: Green Brown Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Green
Row 20: Brown Green Green Green Green Green Green Green Brown Green Green Brown Green Green Green Green Green Green Green Brown
Output:
Row 1: Green
Row 2: Green
Here is the input grid for the test example:
Input:
Row 1: Blue Gray Gray Brown Brown Green Blue Brown Gray Green Green Green Green Gray Brown Blue Green Brown Brown Gray Gray Blue
Row 2: Gray Blue Gray Brown Brown Gray Green Green Blue Green Purple Purple Green Blue Green Green Gray Brown Brown Gray Blue Gray
Row 3: Gray Gray Gray Gray Gray Brown Blue Purple Green Brown Green Green Brown Green Purple Blue Brown Gray Gray Gray Gray Gray
Row 4: Brown Brown Gray Purple Blue Blue Brown Blue Purple Purple Brown Brown Purple Purple Blue Brown Blue Blue Purple Gray Brown Brown
Row 5: Brown Brown Gray Blue Blue Gray Blue Green Purple Purple Blue Blue Purple Purple Green Blue Gray Blue Blue Gray Brown Brown
Row 6: Green Gray Brown Blue Gray Green Brown Purple Brown Gray Gray Gray Gray Brown Purple Brown Green Gray Blue Brown Gray Green
Row 7: Blue Green Blue Brown Blue Brown Green Purple Gray Green Purple Purple Green Gray Purple Green Brown Blue Brown Blue Green Blue
Row 8: Brown Green Purple Blue Green Purple Purple Purple Blue Brown Purple Purple Brown Blue Purple Purple Purple Green Blue Purple Green Brown
Row 9: Gray Blue Green Purple Purple Brown Gray Blue Blue Purple Purple Purple Purple Blue Blue Gray Brown Purple Purple Green Blue Gray
Row 10: Green Green Brown Purple Purple Gray Green Brown Purple Blue Gray Gray Blue Purple Brown Green Gray Purple Purple Brown Green Green
Row 11: Green Purple Green Brown Blue Gray Purple Purple Purple Gray Green Green Gray Purple Purple Purple Gray Blue Brown Green Purple Green
Row 12: Green Purple Green Brown Blue Gray Purple Purple Purple Gray Green Green Gray Purple Purple Purple Gray Blue Brown Green Purple Green
Row 13: Green Green Brown Purple Purple Gray Green Brown Purple Blue Gray Gray Blue Purple Brown Green Gray Purple Purple Brown Green Green
Row 14: Gray Blue Green Purple Purple Brown Gray Blue Black Black Purple Purple Purple Blue Blue Gray Brown Purple Purple Green Blue Gray
Row 15: Brown Green Purple Blue Green Purple Purple Purple Black Black Purple Purple Brown Blue Purple Purple Purple Green Blue Purple Green Brown
Row 16: Blue Green Blue Brown Blue Brown Green Purple Gray Green Purple Purple Green Gray Purple Green Brown Blue Brown Blue Green Blue
Row 17: Green Gray Brown Blue Gray Green Brown Purple Brown Gray Gray Gray Gray Brown Purple Brown Green Gray Blue Brown Gray Green
Row 18: Brown Brown Gray Blue Blue Gray Blue Green Purple Purple Blue Blue Purple Purple Green Blue Gray Blue Blue Gray Brown Brown
Row 19: Brown Brown Gray Purple Blue Blue Brown Blue Purple Purple Brown Brown Purple Purple Blue Brown Blue Blue Purple Gray Brown Brown
Row 20: Gray Gray Gray Gray Gray Brown Blue Purple Green Brown Green Green Brown Green Purple Blue Brown Gray Gray Gray Gray Gray
Row 21: Gray Blue Gray Brown Brown Gray Green Green Blue Green Purple Purple Green Blue Green Green Gray Brown Brown Gray Blue Gray
Row 22: Blue Gray Gray Brown Brown Green Blue Brown Gray Green Green Green Green Gray Brown Blue Green Brown Brown Gray Gray 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
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 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 Gray Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Yellow Gray 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 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
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Yellow Yellow 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
Row 18: 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
Row 20: 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 Gray Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Gray Yellow 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
Row 28: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow
Row 30: 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
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 Gray Gray Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Gray Gray Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Gray Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Yellow Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Yellow Yellow Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Yellow Yellow Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Yellow Yellow Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Yellow Yellow Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Yellow Yellow Orange Orange Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Yellow Yellow Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Yellow Yellow Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Gray Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Gray Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Yellow Yellow Orange Orange Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Yellow Yellow Orange Orange Gray Gray 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 Yellow Yellow Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Orange Orange
Row 28: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray
Row 29: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow
Row 30: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Gray Orange Orange
Example 2
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Blue 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 Green Blue 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
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
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 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 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
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 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 Black
Row 10: Black Black Black Black Black Black Black Black Orange Brown 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 Yellow Pink 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
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
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
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
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
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 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
Row 19: Black Black Black Black Black Black Black Black Purple Blue 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 Brown Orange 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
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Brown Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Orange Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Orange Pink 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 Brown Orange 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
Output:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Blue 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 Green Blue 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 Blue Blue Black Black Brown Brown 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 Blue Blue Black Black Brown Brown 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 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 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
Row 8: Black Black Black Black Black Black Pink Pink Black Black Yellow Yellow 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 Pink Pink Black Black Yellow Yellow 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 Orange Brown 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 Yellow Pink 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 Brown Brown Black Black Orange 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 Black Brown Brown Black Black Orange 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 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
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
Row 17: Black Black Black Black Black Black Orange Orange Black Black Brown Brown 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 Orange Orange Black Black Brown Brown 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 Purple Blue 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 Brown Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Orange Black Black Blue Blue
Row 21: Black Black Black Black Black Black Blue Blue Black Black Purple Purple Black Black Black Black Black Black Black Black Black Black Black Orange Orange Black Black Blue Blue
Row 22: Black Black Black Black Black Black Blue Blue Black Black Purple Purple Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Brown Black Black
Row 23: Black Black Orange Orange Black Black Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Blue Orange Black Black
Row 24: Black Black Orange Orange Black Black Brown Brown Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Black Black Yellow Yellow
Row 25: Black Black Black Black Orange Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Brown Black Black Yellow Yellow
Row 26: Black Black Black Black Brown Orange 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 Pink Pink Black Black Orange Orange 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: 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 Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow 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
Row 5: 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
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Yellow Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Green Brown Brown
Row 9: Pink Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Green 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
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Red Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Brown Brown Orange Orange Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown Yellow Yellow
Row 7: Brown Brown Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Green Brown Brown Yellow Yellow
Row 8: Yellow Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Green Brown Brown
Row 9: Pink Yellow Brown Brown Brown Brown Brown Brown Brown Red Red Brown Brown Pink Pink Brown Brown Yellow Green Brown Brown
Row 10: Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Red Red Brown Brown Pink Pink Green Green Brown Brown Yellow Yellow
Row 11: Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Yellow Orange Brown Brown Green Green Brown Brown Yellow Yellow
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Red Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Blue Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Blue Gray Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: 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 Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Blue
Brown Brown Brown Brown Brown Brown Gray Gray Brown Brown Blue
Brown Brown Brown Brown Brown Brown Brown Brown Yellow Blue Brown
Brown Brown Brown Brown Brown Brown Brown Brown Blue Gray Brown
Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Yellow
Brown Brown Brown Brown Brown Brown Blue Blue Brown Brown Yellow
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown 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: Green Green Green Green Yellow Yellow Green
Row 2: Green Green Green Green Yellow Yellow Green
Row 3: Green Green Green Yellow 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
Output:
Row 1: Green
Example 2
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 Blue Blue
Row 6: Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue
Row 9: Brown Blue Brown Blue
Row 10: Blue Brown Blue Blue
Row 11: Brown Blue Brown Blue
Row 12: Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue
Output:
Row 1: Red
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
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: 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
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: 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
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Brown Brown Brown Brown Orange Orange Orange Orange 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
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown 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
Output:
Row 1: Red
Here is the input grid for the test example:
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 Black Black Black Green Green Green Green Green
Row 7: Green Green Green Black Black Black Green Green Green Green Green
Row 8: Green Green Green Black Black Black Green Green Green Green Green
Row 9: Black Black Black Black Black Black Black Black Black Green Green
Row 10: Black Black Black Black Black Black Black Black Black Green Green
Row 11: Black Black Black Black Black Black Black Black Black Green Green
Row 12: Green Green Green Black Black Black Green Green Green Green Green
Row 13: Green Green Green Black Black Black Green Green Green Green Green
Row 14: Green Green Green Black Black Black Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green
Row 23: 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>
| Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Brown Black Brown Brown Blue Red
Output:
Row 1: Red Blue Brown Brown Black Brown Blue Blue Brown Black Brown Brown Blue Red
Row 2: Red Blue Brown Brown Black Brown Blue Blue Brown Black Brown Brown Blue Red
Row 3: Red Blue Brown Brown Black Brown Blue Blue Brown Black Brown Brown Blue Red
Example 2
Input:
Row 1: Orange Green Green Orange Orange Pink Brown Orange
Row 2: Orange Orange Orange Red Orange Orange Brown Orange
Row 3: Orange Orange Black Green Orange Red Orange Orange
Row 4: Orange Orange Green Pink Orange Yellow Orange Orange
Row 5: Green Gray Orange Pink Brown Orange Pink Orange
Row 6: Orange Red Orange Gray Orange Orange Orange Black
Output:
Row 1: Black Orange Orange Orange Gray Orange Red Orange Orange Red Orange Gray Orange Orange Orange Black
Row 2: Orange Pink Orange Brown Pink Orange Gray Green Green Gray Orange Pink Brown Orange Pink Orange
Row 3: Orange Orange Yellow Orange Pink Green Orange Orange Orange Orange Green Pink Orange Yellow Orange Orange
Row 4: Orange Orange Red Orange Green Black Orange Orange Orange Orange Black Green Orange Red Orange Orange
Row 5: Orange Brown Orange Orange Red Orange Orange Orange Orange Orange Orange Red Orange Orange Brown Orange
Row 6: Orange Brown Pink Orange Orange Green Green Orange Orange Green Green Orange Orange Pink Brown Orange
Row 7: Orange Brown Pink Orange Orange Green Green Orange Orange Green Green Orange Orange Pink Brown Orange
Row 8: Orange Brown Orange Orange Red Orange Orange Orange Orange Orange Orange Red Orange Orange Brown Orange
Row 9: Orange Orange Red Orange Green Black Orange Orange Orange Orange Black Green Orange Red Orange Orange
Row 10: Orange Orange Yellow Orange Pink Green Orange Orange Orange Orange Green Pink Orange Yellow Orange Orange
Row 11: Orange Pink Orange Brown Pink Orange Gray Green Green Gray Orange Pink Brown Orange Pink Orange
Row 12: Black Orange Orange Orange Gray Orange Red Orange Orange Red Orange Gray Orange Orange Orange Black
Row 13: Black Orange Orange Orange Gray Orange Red Orange Orange Red Orange Gray Orange Orange Orange Black
Row 14: Orange Pink Orange Brown Pink Orange Gray Green Green Gray Orange Pink Brown Orange Pink Orange
Row 15: Orange Orange Yellow Orange Pink Green Orange Orange Orange Orange Green Pink Orange Yellow Orange Orange
Row 16: Orange Orange Red Orange Green Black Orange Orange Orange Orange Black Green Orange Red Orange Orange
Row 17: Orange Brown Orange Orange Red Orange Orange Orange Orange Orange Orange Red Orange Orange Brown Orange
Row 18: Orange Brown Pink Orange Orange Green Green Orange Orange Green Green Orange Orange Pink Brown Orange
Example 3
Input:
Row 1: Black Green Yellow Black Yellow Yellow Yellow Yellow Green Yellow
Row 2: Black Green Yellow Yellow Yellow Orange Yellow Blue Yellow Black
Row 3: Yellow Yellow Yellow Yellow Blue Yellow Yellow Black Red Yellow
Row 4: Yellow Yellow Yellow Yellow Blue Yellow Yellow Pink Blue Green
Row 5: Orange Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Pink Green Yellow Yellow Orange Yellow Blue Yellow
Row 7: Yellow Black Yellow Green Green Green Yellow Yellow Yellow Yellow
Row 8: Yellow Pink Green Yellow Yellow Yellow Orange Yellow Green Red
Output:
Row 1: Red Green Yellow Orange Yellow Yellow Yellow Green Pink Yellow Yellow Pink Green Yellow Yellow Yellow Orange Yellow Green Red
Row 2: Yellow Yellow Yellow Yellow Green Green Green Yellow Black Yellow Yellow Black Yellow Green Green Green Yellow Yellow Yellow Yellow
Row 3: Yellow Blue Yellow Orange Yellow Yellow Green Pink Yellow Yellow Yellow Yellow Pink Green Yellow Yellow Orange Yellow Blue Yellow
Row 4: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Orange Orange Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 5: Green Blue Pink Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Pink Blue Green
Row 6: Yellow Red Black Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Black Red Yellow
Row 7: Black Yellow Blue Yellow Orange Yellow Yellow Yellow Green Black Black Green Yellow Yellow Yellow Orange Yellow Blue Yellow Black
Row 8: Yellow Green Yellow Yellow Yellow Yellow Black Yellow Green Black Black Green Yellow Black Yellow Yellow Yellow Yellow Green Yellow
Row 9: Yellow Green Yellow Yellow Yellow Yellow Black Yellow Green Black Black Green Yellow Black Yellow Yellow Yellow Yellow Green Yellow
Row 10: Black Yellow Blue Yellow Orange Yellow Yellow Yellow Green Black Black Green Yellow Yellow Yellow Orange Yellow Blue Yellow Black
Row 11: Yellow Red Black Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Black Red Yellow
Row 12: Green Blue Pink Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Pink Blue Green
Row 13: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Orange Orange Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Blue Yellow Orange Yellow Yellow Green Pink Yellow Yellow Yellow Yellow Pink Green Yellow Yellow Orange Yellow Blue Yellow
Row 15: Yellow Yellow Yellow Yellow Green Green Green Yellow Black Yellow Yellow Black Yellow Green Green Green Yellow Yellow Yellow Yellow
Row 16: Red Green Yellow Orange Yellow Yellow Yellow Green Pink Yellow Yellow Pink Green Yellow Yellow Yellow Orange Yellow Green Red
Row 17: Red Green Yellow Orange Yellow Yellow Yellow Green Pink Yellow Yellow Pink Green Yellow Yellow Yellow Orange Yellow Green Red
Row 18: Yellow Yellow Yellow Yellow Green Green Green Yellow Black Yellow Yellow Black Yellow Green Green Green Yellow Yellow Yellow Yellow
Row 19: Yellow Blue Yellow Orange Yellow Yellow Green Pink Yellow Yellow Yellow Yellow Pink Green Yellow Yellow Orange Yellow Blue Yellow
Row 20: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Orange Orange Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 21: Green Blue Pink Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Pink Blue Green
Row 22: Yellow Red Black Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Black Red Yellow
Row 23: Black Yellow Blue Yellow Orange Yellow Yellow Yellow Green Black Black Green Yellow Yellow Yellow Orange Yellow Blue Yellow Black
Row 24: Yellow Green Yellow Yellow Yellow Yellow Black Yellow Green Black Black Green Yellow Black Yellow Yellow Yellow Yellow Green Yellow
Here is the input grid for the test example:
Input:
Row 1: Yellow Brown Yellow Blue Purple Black Green
Row 2: Yellow Pink Yellow Yellow Gray Yellow 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 Gray Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Gray Yellow Red
Green Black Purple Blue Yellow Brown Yellow Yellow Brown Yellow Blue Purple Black Green
Green Black Purple Blue Yellow Brown Yellow Yellow Brown Yellow Blue Purple Black Green
Red Yellow Gray Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Gray Yellow Red
Red Yellow Gray Yellow Yellow Pink Yellow Yellow Pink Yellow Yellow Gray Yellow Red
Green Black Purple Blue Yellow Brown Yellow Yellow Brown Yellow Blue Purple 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: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red 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
Row 3: 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 Red Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue 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
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue 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 Red Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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
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
Row 4: Orange Orange Pink 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 Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow 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 Yellow 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
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Gray
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Orange 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 Black
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Gray Red Purple Purple Purple Black Purple Purple
Row 11: Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Red 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 Orange
Row 15: Purple Purple Purple Purple Brown Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Gray
Row 4: Purple Purple Purple Purple Purple Purple Purple Gray Purple
Row 5: Purple Purple Purple Purple Purple Purple Gray Purple Purple
Row 6: Orange Purple Purple Purple Purple Gray Purple Purple Purple
Row 7: Purple Orange Purple Purple Gray Purple Purple Purple Purple
Row 8: Purple Purple Orange Gray Purple Purple Purple Purple Black
Row 9: Purple Purple Gray Orange Purple Purple Purple Black Purple
Row 10: Purple Gray Red Purple Orange Purple Black Purple Purple
Row 11: Brown Red Purple Purple Purple Orange Purple Purple Purple
Row 12: Red Brown Purple Purple Purple Purple Orange Purple Purple
Row 13: Purple Purple Brown Purple Purple Purple Purple Orange Purple
Row 14: Purple Purple Purple Brown Purple Purple Purple Purple Orange
Row 15: Purple Purple Purple Purple Brown Purple Purple Purple Purple
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Gray Pink Pink Pink Green Pink Blue Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Pink
Row 3: 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 Red Pink Pink Pink Blue
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Orange
Row 7: Gray 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
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Red Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Yellow
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Purple Yellow 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 Gray Pink Pink Pink Green Pink Blue Pink Pink Pink
Pink Pink Pink Pink Pink Gray Pink Pink Pink Green Pink Orange Pink Blue Pink Pink
Pink Pink Pink Pink Gray Pink Pink Pink Green Pink Pink Pink Orange Pink Blue Pink
Pink Pink Pink Gray Pink Pink Pink Green Pink Pink Pink Red Pink Orange Pink Blue
Pink Pink Gray Pink Pink Pink Green Pink Pink Pink Red Pink Pink Pink Orange Pink
Purple Gray Pink Pink Pink Green Pink Pink Pink Red Black Pink Pink Pink Pink Orange
Gray Purple Pink Pink Green Pink Pink Pink Red Black Pink Pink Pink Pink Pink Pink
Pink Pink Purple Green Pink Pink Pink Red Black Pink Pink Pink Pink Pink Pink Pink
Pink Pink Green Purple Pink Pink Red Black Pink Pink Pink Pink Pink Pink Pink Pink
Pink Green Pink Pink Purple Red Black Pink Pink Pink Pink Pink Pink Pink Pink Pink
Green Pink Pink Pink Red Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Red Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Red Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink Pink
Pink Red Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Purple Pink Pink Pink Pink Yellow
Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Purple Pink Pink Yellow Pink
Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Purple Yellow Pink Pink |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Red Red Red Red Red
Row 2: Red Red Red Red Red Red
Row 3: Blue Red Orange Red Red Blue
Row 4: Red Red Orange Red Red Red
Output:
Row 1: Blue Red Purple Red Red Purple Blue Red Purple Red Red Purple
Row 2: Purple Red Purple Red Red Purple Purple Red Purple Red Red Purple
Row 3: Blue Red Orange Red Red Blue Blue Red Orange Red Red Blue
Row 4: Purple Red Orange Red Red Purple Purple Red Orange Red Red Purple
Row 5: Blue Red Purple Red Red Purple Blue Red Purple Red Red Purple
Row 6: Purple Red Purple Red Red Purple Purple Red Purple Red Red Purple
Row 7: Blue Red Orange Red Red Blue Blue Red Orange Red Red Blue
Row 8: Purple Red Orange Red Red Purple Purple Red Orange Red Red Purple
Example 2
Input:
Row 1: Brown Pink Brown Brown Brown Pink Brown Black Black Black Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Pink
Row 3: Pink Brown Pink Brown Brown Brown Brown Brown Brown Pink Brown Black Brown Brown
Row 4: Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown
Row 5: Brown Pink 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 Pink
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink
Output:
Row 1: Purple Pink Purple Brown Brown Pink Brown Black Black Black Brown Purple Brown Purple Purple Pink Purple Brown Brown Pink Brown Black Black Black Brown Purple Brown Purple
Row 2: Purple Purple Purple Brown Brown Purple Brown Purple Purple Pink Brown Purple Brown Pink Purple Purple Purple Brown Brown Purple Brown Purple Purple Pink Brown Purple Brown Pink
Row 3: Pink Purple Pink Brown Brown Purple Brown Purple Purple Pink Brown Black Brown Purple Pink Purple Pink Brown Brown Purple Brown Purple Purple Pink Brown Black Brown Purple
Row 4: Purple Purple Black Brown Brown Purple Brown Purple Purple Purple Brown Pink Brown Purple Purple Purple Black Brown Brown Purple Brown Purple Purple Purple Brown Pink Brown Purple
Row 5: Purple Pink Purple Brown Brown Purple Brown Purple Black Purple Brown Purple Brown Purple Purple Pink Purple Brown Brown Purple Brown Purple Black Purple Brown Purple Brown Purple
Row 6: Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink
Row 7: Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink
Row 8: Purple Pink Purple Brown Brown Pink Brown Black Black Black Brown Purple Brown Purple Purple Pink Purple Brown Brown Pink Brown Black Black Black Brown Purple Brown Purple
Row 9: Purple Purple Purple Brown Brown Purple Brown Purple Purple Pink Brown Purple Brown Pink Purple Purple Purple Brown Brown Purple Brown Purple Purple Pink Brown Purple Brown Pink
Row 10: Pink Purple Pink Brown Brown Purple Brown Purple Purple Pink Brown Black Brown Purple Pink Purple Pink Brown Brown Purple Brown Purple Purple Pink Brown Black Brown Purple
Row 11: Purple Purple Black Brown Brown Purple Brown Purple Purple Purple Brown Pink Brown Purple Purple Purple Black Brown Brown Purple Brown Purple Purple Purple Brown Pink Brown Purple
Row 12: Purple Pink Purple Brown Brown Purple Brown Purple Black Purple Brown Purple Brown Purple Purple Pink Purple Brown Brown Purple Brown Purple Black Purple Brown Purple Brown Purple
Row 13: Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink
Row 14: Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink Purple Purple Purple Brown Brown Purple Brown Purple Purple Purple Brown Purple Brown Pink
Example 3
Input:
Row 1: Orange Orange Orange Yellow Orange
Row 2: Orange Orange Orange Orange Green
Row 3: Pink Orange Orange Orange Orange
Row 4: Pink Orange Orange Orange Pink
Row 5: Green Orange Yellow Orange Orange
Row 6: Orange Orange Brown Orange Orange
Row 7: Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Green Brown
Row 9: Green Orange Blue Yellow Orange
Row 10: Orange Orange Orange Orange Brown
Output:
Row 1: Purple Orange Purple Yellow Purple Purple Orange Purple Yellow Purple
Row 2: Purple Orange Purple Purple Green Purple Orange Purple Purple Green
Row 3: Pink Orange Purple Purple Purple Pink Orange Purple Purple Purple
Row 4: Pink Orange Purple Purple Pink Pink Orange Purple Purple Pink
Row 5: Green Orange Yellow Purple Purple Green Orange Yellow Purple Purple
Row 6: Purple Orange Brown Purple Purple Purple Orange Brown Purple Purple
Row 7: Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple
Row 8: Purple Orange Purple Green Brown Purple Orange Purple Green Brown
Row 9: Green Orange Blue Yellow Purple Green Orange Blue Yellow Purple
Row 10: Purple Orange Purple Purple Brown Purple Orange Purple Purple Brown
Row 11: Purple Orange Purple Yellow Purple Purple Orange Purple Yellow Purple
Row 12: Purple Orange Purple Purple Green Purple Orange Purple Purple Green
Row 13: Pink Orange Purple Purple Purple Pink Orange Purple Purple Purple
Row 14: Pink Orange Purple Purple Pink Pink Orange Purple Purple Pink
Row 15: Green Orange Yellow Purple Purple Green Orange Yellow Purple Purple
Row 16: Purple Orange Brown Purple Purple Purple Orange Brown Purple Purple
Row 17: Purple Orange Purple Purple Purple Purple Orange Purple Purple Purple
Row 18: Purple Orange Purple Green Brown Purple Orange Purple Green Brown
Row 19: Green Orange Blue Yellow Purple Green Orange Blue Yellow Purple
Row 20: Purple Orange Purple Purple Brown Purple Orange Purple Purple Brown
Here is the input grid for the test example:
Input:
Row 1: Brown Pink Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Gray Brown Brown Brown Brown Brown Black Brown Gray Orange Brown
Row 3: Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown
Row 5: 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>
| Purple Pink Orange Brown Brown Purple Purple Brown Purple Purple Brown Purple Pink Orange Brown Brown Purple Purple Brown Purple Purple Brown
Gray Purple Purple Brown Brown Purple Black Brown Gray Orange Brown Gray Purple Purple Brown Brown Purple Black Brown Gray Orange Brown
Purple Black Purple Brown Brown Purple Purple Brown Purple Purple Brown Purple Black Purple Brown Brown Purple Purple Brown Purple Purple Brown
Purple Purple Purple Brown Brown Black Purple Brown Purple Purple Brown Purple Purple Purple Brown Brown Black Purple Brown Purple Purple Brown
Purple Purple Purple Brown Brown Purple Purple Brown Purple Purple Brown Purple Purple Purple Brown Brown Purple Purple Brown Purple Purple Brown
Purple Pink Orange Brown Brown Purple Purple Brown Purple Purple Brown Purple Pink Orange Brown Brown Purple Purple Brown Purple Purple Brown
Gray Purple Purple Brown Brown Purple Black Brown Gray Orange Brown Gray Purple Purple Brown Brown Purple Black Brown Gray Orange Brown
Purple Black Purple Brown Brown Purple Purple Brown Purple Purple Brown Purple Black Purple Brown Brown Purple Purple Brown Purple Purple Brown
Purple Purple Purple Brown Brown Black Purple Brown Purple Purple Brown Purple Purple Purple Brown Brown Black Purple Brown Purple Purple Brown
Purple Purple Purple Brown Brown Purple Purple Brown Purple Purple Brown Purple Purple Purple Brown Brown Purple Purple Brown Purple Purple Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Brown Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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
Output:
Row 1: Brown Brown Pink
Row 2: Brown Brown Brown
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: Yellow Yellow 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 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
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Orange 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 Orange 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 Orange Orange Orange 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 Orange Orange Orange 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 Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Yellow Yellow Orange Yellow Orange 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 Orange Yellow Yellow
Row 2: Yellow Yellow Orange Yellow
Row 3: Yellow Orange Orange Orange
Row 4: Yellow Orange Orange Orange
Row 5: Yellow Orange Orange Orange
Row 6: Orange Orange Orange Orange
Row 7: Orange Yellow Orange Yellow
Example 3
Input:
Row 1: Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray
Row 3: Gray 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 Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Pink Gray Gray Gray
Row 14: Gray Pink Pink Gray Gray Gray
Row 15: Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Gray Gray Gray Gray
Row 17: Gray Gray Gray Gray Gray Gray
Row 18: Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Pink
Row 2: Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: 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
Row 4: 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
Row 6: 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
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown
Row 9: 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
Row 11: 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
Row 13: 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
Row 15: 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Blue Blue Blue Pink Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Pink Pink Blue Blue Gray Blue Blue Gray Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Yellow Yellow Blue Black Blue Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Yellow Yellow Blue Black Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Blue Blue 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
Row 14: 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
Row 16: 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
Output:
Row 1: Blue Blue Pink Pink Blue Gray Gray Blue Gray Gray Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Pink Pink Blue Gray Gray Blue Gray Gray Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Yellow Yellow Blue Black Black Blue Black Black Blue Black Black
Row 5: Blue Blue Blue Blue Blue Yellow Yellow Blue Black Black Blue Black Black Blue Black Black
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Purple 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
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: 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
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue 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 Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black 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
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 Brown Black Black Black Black Orange 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 Brown Black Black Orange 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 Brown Black Black Green 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 Green 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 Green Green Black Orange 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 Green Black Black Orange 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 Orange Black Black Brown 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 Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black 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
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 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
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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 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
Row 22: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black 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
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
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
Output:
Row 1: Brown Black Black Black Black Brown Brown Black Black Black Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Black Black Black Brown Black Black Black Black Black Orange 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 Brown Black Black Brown Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 5: Black Black Brown Black Black Brown Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 6: Black Black Brown Brown Black Brown Brown Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Black Brown Black Black Brown Black Black Orange 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: Brown Black Black Brown Black Black Green Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange
Row 10: Black Black Brown Black Black Green Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black
Row 11: Brown Black Brown Brown Black Green Green Black Orange Orange Black Orange Orange Black Orange Orange Black Orange Orange Black Orange Orange Black Orange Orange Black Orange Orange
Row 12: Black Black Brown Black Black Green Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange Black Black Orange 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 Orange Black Black Brown Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Orange Black Black Brown Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Black Orange Orange Black Brown Brown Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Black Orange Black Black Brown Black Black Orange 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 Black
Row 19: Orange Black Black Black Black Black Brown Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Brown Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 21: Orange Black Black Black Black Brown Brown Black Black Black Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Black Black Black Black Brown Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 23: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 24: Black Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 25: Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 26: Black Black Black Black Black Brown Brown Black Black Black Black Black Black Black Orange Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 27: Black Black Black Black Black Brown Black Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: 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
Row 7: 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
Row 9: 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
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Gray Pink Red Red Pink Yellow Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Red Red Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Orange 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
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: 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
Row 7: 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
Row 9: 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
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Gray Gray Pink Red Red Pink Yellow Yellow Pink Yellow Yellow Pink Yellow
Row 13: Pink Gray Pink Pink Red Pink Pink Yellow Pink Pink Yellow Pink Pink
Row 14: Gray Gray Pink Red Red Pink Yellow Yellow Pink Yellow Yellow Pink Yellow
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Orange Orange 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
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
Row 2: 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
Row 4: 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
Row 6: Gray Gray Gray Gray Yellow Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Yellow Gray Green Gray Green Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Yellow Gray Green Green Green 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
Row 10: Gray Gray Gray Gray Gray Gray Red Red Red Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Yellow Gray Yellow Yellow Yellow Gray Green Green Green Gray Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Gray
Yellow Gray Yellow Gray Yellow Gray Green Gray Green Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray
Yellow Gray Yellow Yellow Yellow Gray Green Green Green Gray Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Red Red Red Gray Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Red Gray Red Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Red Red Red Gray Blue Blue Blue 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: Gray Yellow Red
Row 2: Gray Red Red
Row 3: Gray Red Gray
Row 4: Gray Yellow Red
Row 5: Gray Black Yellow
Row 6: Gray Gray Gray
Row 7: Gray Red Black
Row 8: Red Yellow Gray
Row 9: Gray Gray Purple
Row 10: Yellow Black Gray
Row 11: Yellow Yellow Gray
Row 12: Yellow Red Black
Row 13: Gray Gray Gray
Row 14: Gray Gray Gray
Row 15: Red Gray Red
Row 16: Purple Gray Yellow
Row 17: Gray Yellow Gray
Row 18: Yellow Red Yellow
Row 19: Black Yellow Gray
Row 20: Black Gray Gray
Row 21: Red Gray Yellow
Row 22: Red Black Red
Output:
Row 1: Purple Yellow Red
Row 2: Purple Red Red
Row 3: Purple Red Purple
Row 4: Purple Yellow Red
Row 5: Purple Black Yellow
Row 6: Purple Purple Purple
Row 7: Purple Red Black
Row 8: Red Yellow Purple
Row 9: Purple Purple Gray
Row 10: Yellow Black Purple
Row 11: Yellow Yellow Purple
Row 12: Yellow Red Black
Row 13: Purple Purple Purple
Row 14: Purple Purple Purple
Row 15: Red Purple Red
Row 16: Gray Purple Yellow
Row 17: Purple Yellow Purple
Row 18: Yellow Red Yellow
Row 19: Black Yellow Purple
Row 20: Black Purple Purple
Row 21: Red Purple Yellow
Row 22: Red Black Red
Example 2
Input:
Row 1: Green Green Blue Purple Blue Green Brown Pink Red Purple Pink Purple Red Gray Brown Green Orange Blue Purple Purple Gray Brown Blue Yellow Red Orange Blue Yellow
Row 2: Pink Black Purple Red Purple Green Black Blue Green Yellow Black Green Gray Brown Orange Red Orange Green Black Blue Yellow Purple Pink Black Purple Yellow Blue Blue
Row 3: Red Purple Purple Black Brown Yellow Yellow Blue Red Brown Red Green Green Red Pink Red Red Black Black Gray Purple Blue Blue Yellow Black Pink Purple Green
Row 4: Black Red Red Brown Yellow Red Brown Red Black Gray Gray Purple Black Blue Green Purple Blue Green Orange Green Green Black Brown Green Brown Red Purple Orange
Row 5: Orange Orange Yellow Pink Purple Green Orange Orange Gray Brown Black Brown Orange Brown Green Orange Blue Red Red Yellow Green Blue Gray Pink Yellow Orange Orange Brown
Row 6: Gray Brown Purple Green Brown Orange Black Red Gray Gray Purple Black Purple Red Yellow Pink Red Black Red Purple Red Purple Red Orange Yellow Black Green Pink
Row 7: Brown Pink Black Red Green Pink Purple Blue Orange Green Purple Brown Red Brown Gray Orange Purple Black Gray Pink Yellow Green Blue Pink Green Purple Pink Orange
Row 8: Yellow Yellow Yellow Black Black Blue Purple Black Orange Pink Pink Purple Orange Red Purple Orange Purple Purple Purple Orange Blue Purple Pink Black Brown Black Purple Red
Row 9: Gray Gray Brown Pink Red Green Black Gray Black Purple Green Pink Orange Purple Blue Orange Orange Green Yellow Orange Red Yellow Orange Pink Brown Red Orange Purple
Row 10: Green Purple Red Green Brown Orange Purple Gray Red Pink Black Blue Purple Brown Brown Blue Blue Blue Black Black Blue Blue Brown Brown Red Red Purple Purple
Row 11: Green Green Orange Purple Purple Orange Gray Black Purple Purple Gray Black Yellow Purple Orange Purple Pink Red Purple Pink Brown Blue Pink Orange Blue Pink Pink Purple
Row 12: Green Green Blue Yellow Orange Blue Brown Blue Brown Green Yellow Yellow Pink Purple Orange Brown Green Pink Gray Brown Gray Purple Purple Brown Blue Green Blue Blue
Row 13: Green Gray Yellow Purple Blue Orange Purple Purple Black Purple Brown Purple Blue Orange Red Orange Yellow Purple Brown Green Purple Brown Green Gray Brown Black Orange Green
Row 14: Orange Orange Gray Purple Blue Brown Green Brown Gray Yellow Orange Black Orange Purple Brown Gray Orange Red Red Red Purple Blue Gray Red Brown Blue Green Pink
Row 15: Brown Pink Brown Red Red Black Gray Yellow Orange Pink Blue Blue Gray Red Black Green Brown Black Brown Brown Yellow Brown Orange Orange Green Purple Purple Yellow
Row 16: Green Gray Yellow Yellow Black Pink Pink Purple Brown Purple Black Orange Gray Purple Black Blue Red Red Black Blue Green Purple Brown Green Purple Green Purple Red
Output:
Row 1: Green Green Blue Gray Blue Green Brown Pink Red Gray Pink Gray Red Purple Brown Green Orange Blue Gray Gray Purple Brown Blue Yellow Red Orange Blue Yellow
Row 2: Pink Black Gray Red Gray Green Black Blue Green Yellow Black Green Purple Brown Orange Red Orange Green Black Blue Yellow Gray Pink Black Gray Yellow Blue Blue
Row 3: Red Gray Gray Black Brown Yellow Yellow Blue Red Brown Red Green Green Red Pink Red Red Black Black Purple Gray Blue Blue Yellow Black Pink Gray Green
Row 4: Black Red Red Brown Yellow Red Brown Red Black Purple Purple Gray Black Blue Green Gray Blue Green Orange Green Green Black Brown Green Brown Red Gray Orange
Row 5: Orange Orange Yellow Pink Gray Green Orange Orange Purple Brown Black Brown Orange Brown Green Orange Blue Red Red Yellow Green Blue Purple Pink Yellow Orange Orange Brown
Row 6: Purple Brown Gray Green Brown Orange Black Red Purple Purple Gray Black Gray Red Yellow Pink Red Black Red Gray Red Gray Red Orange Yellow Black Green Pink
Row 7: Brown Pink Black Red Green Pink Gray Blue Orange Green Gray Brown Red Brown Purple Orange Gray Black Purple Pink Yellow Green Blue Pink Green Gray Pink Orange
Row 8: Yellow Yellow Yellow Black Black Blue Gray Black Orange Pink Pink Gray Orange Red Gray Orange Gray Gray Gray Orange Blue Gray Pink Black Brown Black Gray Red
Row 9: Purple Purple Brown Pink Red Green Black Purple Black Gray Green Pink Orange Gray Blue Orange Orange Green Yellow Orange Red Yellow Orange Pink Brown Red Orange Gray
Row 10: Green Gray Red Green Brown Orange Gray Purple Red Pink Black Blue Gray Brown Brown Blue Blue Blue Black Black Blue Blue Brown Brown Red Red Gray Gray
Row 11: Green Green Orange Gray Gray Orange Purple Black Gray Gray Purple Black Yellow Gray Orange Gray Pink Red Gray Pink Brown Blue Pink Orange Blue Pink Pink Gray
Row 12: Green Green Blue Yellow Orange Blue Brown Blue Brown Green Yellow Yellow Pink Gray Orange Brown Green Pink Purple Brown Purple Gray Gray Brown Blue Green Blue Blue
Row 13: Green Purple Yellow Gray Blue Orange Gray Gray Black Gray Brown Gray Blue Orange Red Orange Yellow Gray Brown Green Gray Brown Green Purple Brown Black Orange Green
Row 14: Orange Orange Purple Gray Blue Brown Green Brown Purple Yellow Orange Black Orange Gray Brown Purple Orange Red Red Red Gray Blue Purple Red Brown Blue Green Pink
Row 15: Brown Pink Brown Red Red Black Purple Yellow Orange Pink Blue Blue Purple Red Black Green Brown Black Brown Brown Yellow Brown Orange Orange Green Gray Gray Yellow
Row 16: Green Purple Yellow Yellow Black Pink Pink Gray Brown Gray Black Orange Purple Gray Black Blue Red Red Black Blue Green Gray Brown Green Gray Green Gray Red
Example 3
Input:
Row 1: Brown Red Black Black Black Red Orange Pink Pink Blue Blue Orange Blue Pink Pink Blue Pink Blue Black Red Orange Black Pink Pink Black
Row 2: Red Brown Orange Green Blue Green Black Black Brown Blue Orange Blue Blue Brown Blue Red Pink Black Pink Green Red Orange Black Brown Brown
Row 3: Black Pink Black Green Blue Brown Red Orange Red Orange Black Green Orange Black Blue Green Orange Black Red Brown Green Red Blue Pink Blue
Row 4: Orange Orange Red Blue Black Red Green Black Blue Pink Red Black Blue Red Black Red Red Brown Pink Brown Pink Brown Green Blue Gray
Row 5: Black Red Green Orange Orange Black Orange Brown Pink Orange Orange Black Black Brown Black Brown Pink Black Blue Orange Pink Green Pink Gray Red
Row 6: Brown Pink Pink Black Pink Gray Red Green Blue Pink Green Blue Pink Brown Black Red Orange Black Orange Orange Red Red Brown Orange Black
Row 7: Black Orange Brown Orange Pink Green Orange Orange Black Pink Brown Red Orange Black Blue Black Orange Green Blue Orange Pink Orange Brown Green Black
Row 8: Brown Blue Pink Black Green Orange Green Orange Black Gray Brown Black Blue Green Black Red Blue Blue Blue Brown Pink Black Black Orange Green
Row 9: Blue Blue Black Green Blue Red Green Orange Blue Orange Gray Black Green Green Black Green Green Orange Black Gray Black Black Pink Brown Black
Row 10: Red Red Blue Brown Brown Blue Gray Orange Red Red Red Gray Orange Pink Orange Pink Brown Brown Gray Black Brown Green Pink Orange Black
Row 11: Pink Blue Blue Black Brown Blue Orange Gray Orange Pink Black Gray Pink Red Brown Pink Black Green Brown Red Blue Red Pink Red Orange
Row 12: Brown Blue Brown Green Orange Orange Orange Orange Blue Blue Blue Pink Brown Gray Black Brown Green Black Green Green Pink Orange Black Brown Orange
Row 13: Brown Red Brown Orange Green Green Brown Blue Pink Red Brown Black Brown Brown Brown Red Pink Orange Green Green Blue Brown Blue Black Blue
Row 14: Pink Blue Blue Pink Red Green Orange Black Pink Orange Red Brown Blue Gray Green Green Pink Blue Orange Orange Black Blue Green Green Blue
Row 15: Blue Brown Black Red Brown Green Brown Orange Red Orange Orange Pink Red Green Green Black Orange Green Green Green Blue Green Blue Black Orange
Row 16: Black Blue Pink Pink Orange Black Orange Brown Green Blue Brown Red Green Gray Orange Brown Red Green Brown Pink Orange Green Black Black Green
Row 17: Red Green Red Green Pink Orange Blue Red Red Red Black Brown Brown Blue Red Blue Blue Blue Gray Brown Red Red Green Brown Orange
Row 18: Orange Pink Pink Green Pink Brown Orange Blue Blue Orange Blue Red Black Black Red Red Blue Blue Black Gray Pink Pink Brown Red Brown
Row 19: Brown Black Brown Blue Red Red Blue Red Black Blue Gray Red Black Green Brown Blue Green Pink Brown Red Orange Black Black Red Blue
Row 20: Blue Pink Blue Brown Red Blue Orange Pink Brown Brown Black Red Orange Pink Blue Blue Blue Pink Pink Orange Orange Green Green Orange Blue
Row 21: Pink Black Red Green Black Red Green Green Brown Red Gray Brown Black Red Black Blue Orange Green Pink Pink Green Green Brown Orange Pink
Output:
Row 1: Brown Red Black Black Black Red Orange Pink Pink Blue Blue Orange Blue Pink Pink Blue Pink Blue Black Red Orange Black Pink Pink Black
Row 2: Red Brown Orange Green Blue Green Black Black Brown Blue Orange Blue Blue Brown Blue Red Pink Black Pink Green Red Orange Black Brown Brown
Row 3: Black Pink Black Green Blue Brown Red Orange Red Orange Black Green Orange Black Blue Green Orange Black Red Brown Green Red Blue Pink Blue
Row 4: Orange Orange Red Blue Black Red Green Black Blue Pink Red Black Blue Red Black Red Red Brown Pink Brown Pink Brown Green Blue Purple
Row 5: Black Red Green Orange Orange Black Orange Brown Pink Orange Orange Black Black Brown Black Brown Pink Black Blue Orange Pink Green Pink Purple Red
Row 6: Brown Pink Pink Black Pink Purple Red Green Blue Pink Green Blue Pink Brown Black Red Orange Black Orange Orange Red Red Brown Orange Black
Row 7: Black Orange Brown Orange Pink Green Orange Orange Black Pink Brown Red Orange Black Blue Black Orange Green Blue Orange Pink Orange Brown Green Black
Row 8: Brown Blue Pink Black Green Orange Green Orange Black Purple Brown Black Blue Green Black Red Blue Blue Blue Brown Pink Black Black Orange Green
Row 9: Blue Blue Black Green Blue Red Green Orange Blue Orange Purple Black Green Green Black Green Green Orange Black Purple Black Black Pink Brown Black
Row 10: Red Red Blue Brown Brown Blue Purple Orange Red Red Red Purple Orange Pink Orange Pink Brown Brown Purple Black Brown Green Pink Orange Black
Row 11: Pink Blue Blue Black Brown Blue Orange Purple Orange Pink Black Purple Pink Red Brown Pink Black Green Brown Red Blue Red Pink Red Orange
Row 12: Brown Blue Brown Green Orange Orange Orange Orange Blue Blue Blue Pink Brown Purple Black Brown Green Black Green Green Pink Orange Black Brown Orange
Row 13: Brown Red Brown Orange Green Green Brown Blue Pink Red Brown Black Brown Brown Brown Red Pink Orange Green Green Blue Brown Blue Black Blue
Row 14: Pink Blue Blue Pink Red Green Orange Black Pink Orange Red Brown Blue Purple Green Green Pink Blue Orange Orange Black Blue Green Green Blue
Row 15: Blue Brown Black Red Brown Green Brown Orange Red Orange Orange Pink Red Green Green Black Orange Green Green Green Blue Green Blue Black Orange
Row 16: Black Blue Pink Pink Orange Black Orange Brown Green Blue Brown Red Green Purple Orange Brown Red Green Brown Pink Orange Green Black Black Green
Row 17: Red Green Red Green Pink Orange Blue Red Red Red Black Brown Brown Blue Red Blue Blue Blue Purple Brown Red Red Green Brown Orange
Row 18: Orange Pink Pink Green Pink Brown Orange Blue Blue Orange Blue Red Black Black Red Red Blue Blue Black Purple Pink Pink Brown Red Brown
Row 19: Brown Black Brown Blue Red Red Blue Red Black Blue Purple Red Black Green Brown Blue Green Pink Brown Red Orange Black Black Red Blue
Row 20: Blue Pink Blue Brown Red Blue Orange Pink Brown Brown Black Red Orange Pink Blue Blue Blue Pink Pink Orange Orange Green Green Orange Blue
Row 21: Pink Black Red Green Black Red Green Green Brown Red Purple Brown Black Red Black Blue Orange Green Pink Pink Green Green Brown Orange Pink
Here is the input grid for the test example:
Input:
Row 1: Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown
Row 2: Gray Brown Yellow Brown Gray Gray Brown Gray Brown
Row 3: Gray Gray Brown Brown Gray Gray Gray Gray Gray
Row 4: Brown Yellow Brown Brown Brown Brown Gray Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow
Row 6: Yellow Brown Yellow Gray Brown Gray Yellow Brown Gray
Row 7: Brown Gray Gray Yellow Brown Yellow Brown Yellow Gray
Row 8: Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown
Row 9: Gray Brown Brown Brown Brown Gray Brown Gray Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Brown Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown
Purple Brown Yellow Brown Purple Purple Brown Purple Brown
Purple Purple Brown Brown Purple Purple Purple Purple Purple
Brown Yellow Brown Brown Brown Brown Purple Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow
Yellow Brown Yellow Purple Brown Purple Yellow Brown Purple
Brown Purple Purple Yellow Brown Yellow Brown Yellow Purple
Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Brown
Purple Brown Brown Brown Brown Purple Brown Purple Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 2: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 5: Orange Orange Orange Orange Orange Purple Purple Purple Orange Orange Orange Black Orange Black Orange
Row 6: Orange Orange Orange Black Orange Purple Black Purple Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Purple Black Purple Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Black Orange Orange Orange Purple Purple Purple Orange Orange Orange Orange Orange Black Orange
Row 9: Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Black Orange
Row 2: Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Purple Purple Purple Purple Orange Black Orange Orange Orange Orange Orange Orange Purple Purple Purple
Row 4: Purple Black Black Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Black Purple
Row 5: Purple Purple Purple Purple Orange Purple Purple Purple Orange Orange Orange Black Purple Black Purple
Row 6: Orange Orange Orange Black Orange Purple Black Purple Orange Orange Orange Orange Purple Purple Purple
Row 7: Purple Purple Purple Orange Orange Purple Black Purple Orange Orange Orange Orange Purple Purple Purple
Row 8: Purple Black Purple Orange Orange Purple Purple Purple Orange Orange Orange Orange Purple Black Purple
Row 9: Purple Black Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Black Purple
Row 10: Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Black Brown Brown Brown Brown Brown Black Black Brown
Row 3: Brown Black Brown Brown Black Brown Black Black Black Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown
Row 5: Brown Brown Brown Brown Brown Black Black Brown Brown Black Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Black Brown Black Black Brown Brown Brown Brown
Row 8: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Black Brown Brown Black Brown Black Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 12: Brown Black Brown Brown Brown Brown Brown Brown Brown Blue Black Blue
Row 13: Brown Brown Brown Brown Brown Brown Brown Black Brown Blue Blue Blue
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Black Blue
Row 15: Brown Brown Brown Black Brown Brown Brown Brown Brown Blue Blue Blue
Row 16: Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 17: Brown Black Brown Black Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Black Brown
Row 19: Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Row 22: Brown Brown Brown Brown Black Brown Black Brown Brown Black Brown Black
Row 23: Black Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Black Brown Brown Brown Brown Brown Black Black Brown
Row 3: Brown Black Brown Brown Black Brown Black Black Black Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Black Brown
Row 5: Brown Brown Brown Brown Brown Black Black Brown Brown Black Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Black Brown Black Black Brown Brown Brown Brown
Row 8: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown Brown
Row 10: Blue Black Blue Blue Black Blue Black Blue Brown Brown Brown Brown
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue
Row 12: Blue Black Blue Brown Brown Brown Brown Brown Brown Blue Black Blue
Row 13: Blue Blue Blue Brown Brown Brown Brown Black Brown Blue Blue Blue
Row 14: Brown Brown Blue Blue Blue Brown Brown Brown Brown Blue Black Blue
Row 15: Brown Brown Blue Black Blue Brown Brown Brown Brown Blue Blue Blue
Row 16: Brown Brown Blue Blue Blue Black Brown Brown Brown Brown Brown Brown
Row 17: Brown Black Blue Black Blue Brown Brown Brown Brown Blue Blue Blue
Row 18: Brown Black Blue Blue Blue Brown Brown Brown Brown Blue Black Blue
Row 19: Brown Brown Brown Brown Brown Black Brown Brown Brown Blue Blue Blue
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Black Blue
Row 21: Brown Brown Brown Blue Blue Blue Blue Blue Black Blue Blue Blue
Row 22: Brown Brown Brown Blue Black Blue Black Blue Brown Black Brown Black
Row 23: Black Brown Brown Blue Blue Blue Blue Blue Black Brown Brown Brown
Example 3
Input:
Row 1: Pink 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 Pink Pink Pink
Row 2: Pink Pink Pink Pink Brown Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Brown Pink Pink Pink Pink Pink Pink Pink Yellow Brown Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Brown Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink
Row 5: Pink 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 Pink Pink Pink
Row 6: Pink Pink Pink Pink Brown Pink 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 Brown 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 Brown Pink Brown Pink Pink Pink Pink Brown
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 Brown Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Brown Pink Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown 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 Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink
Row 14: Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Brown Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Brown 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 Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Brown 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 Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink
Row 19: 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 Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink
Row 21: Pink Pink Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown
Output:
Row 1: Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Pink Pink Yellow Brown Yellow Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Brown Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 3: Pink Brown Pink Yellow Yellow Yellow Pink Pink Pink Yellow Brown Yellow Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Brown Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink
Row 4: Brown Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Yellow Brown Yellow Pink Yellow Yellow Yellow Yellow Brown Yellow Pink Yellow Brown Yellow Pink
Row 5: Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink Yellow Brown Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink
Row 6: Pink Pink Pink Yellow Brown Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Brown Yellow Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow
Row 8: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Brown
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow
Row 10: Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Yellow Yellow Yellow Pink Pink Brown Brown Pink Pink Pink Yellow Brown Yellow Pink Pink Yellow Yellow Yellow Yellow Pink
Row 11: Pink Pink Pink Pink Yellow Brown Yellow Pink Yellow Yellow Yellow Brown Yellow Brown Brown Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Brown Yellow Pink
Row 12: Pink Pink Pink Pink Yellow Yellow Yellow Pink Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Brown Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Pink Pink Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Brown Yellow Pink
Row 14: Yellow Yellow Yellow Pink Pink Brown Pink Pink Pink Yellow Yellow Yellow Pink Yellow Yellow Yellow Brown Yellow Pink Pink Pink Yellow Yellow Yellow Pink Pink Yellow Yellow Yellow Pink
Row 15: Yellow Brown Yellow Pink Brown Pink Pink Pink Pink Yellow Brown Yellow Pink Yellow Brown Yellow Yellow Yellow Pink Pink Pink Yellow Brown Yellow Pink Pink Pink Pink Pink Pink
Row 16: Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Yellow Brown Yellow
Row 19: Pink Pink Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Brown Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 20: Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Pink Pink Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Brown Yellow Yellow Brown Yellow Pink Pink Pink
Row 21: Pink Pink Yellow Brown Yellow Yellow Brown Yellow Yellow Yellow Pink Pink Pink Pink Pink Yellow Brown Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Pink Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Brown Green 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 Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Row 3: Brown Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Row 4: Brown Green Brown Purple Green Green Purple Brown Brown Brown Green Green Brown Brown Brown Brown Brown Green Green Brown Green Brown Brown Brown Brown
Row 5: Brown Brown Brown Purple Purple Purple Purple Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Green 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 Green Brown Green Brown Brown Brown Brown Green 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 Green Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Green 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 Green
Row 10: Brown Green Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Green Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Purple Green Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green
Purple Purple Purple Purple Purple Purple Purple Brown Brown Purple Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Brown
Brown Green Brown Purple Green Green Purple Brown Brown Purple Green Green Purple Brown Brown Brown Brown Green Green Brown Green Brown Brown Brown Brown
Brown Brown Brown Purple Purple Purple Purple Brown Green Purple Purple Purple Purple Brown Brown Brown Brown Green Brown Brown Brown Brown Purple Purple Purple
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Green Brown Brown Brown Purple Green Purple
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Green Purple
Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Brown Green Brown 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 Brown Brown Brown Brown Brown Brown Green
Brown Green Brown Brown Brown Brown Brown Brown Green 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: 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
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 Blue Blue Blue Blue Gray Gray Gray Orange Orange Orange Gray Gray
Row 6: Gray Gray Gray Blue Green Green Blue Gray Gray Gray Orange Green Orange Gray Gray
Row 7: Gray Gray Gray Blue Green Green Blue Gray Gray Gray Orange Orange Orange Gray Gray
Row 8: Gray Gray Gray Blue Blue Blue Blue 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
Row 10: 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
Row 12: 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
Row 14: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 16: Gray Gray Green Black Black Green Gray Gray Gray Gray Gray Purple Purple Purple Gray
Row 17: Gray Gray Green Green Green Green Gray Gray Gray Gray Gray Purple Orange Purple Gray
Row 18: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Orange Purple Gray
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Purple Gray
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Gray Blue Purple Purple Blue Gray Gray Gray Gray Gray Gray Gray
Row 23: Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray
Row 24: 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
Row 26: 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
Row 28: 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Orange Orange Orange Gray Gray
Row 5: Gray Blue Blue Green Green Green Green Blue Blue Orange Green Green Green Orange Gray
Row 6: Gray Blue Blue Green Blue Blue Green Blue Blue Orange Green Orange Green Orange Gray
Row 7: Gray Blue Blue Green Blue Blue Green Blue Blue Orange Green Green Green Orange Gray
Row 8: Gray Blue Blue Green Green Green Green Blue Blue Gray Orange Orange Orange Gray Gray
Row 9: Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray
Row 10: Gray Gray Gray Blue Blue Blue Blue 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
Row 12: 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
Row 14: Gray Gray Green Green Green Green Gray Gray Gray Gray Gray Purple Purple Purple Gray
Row 15: Green Green Black Black Black Black Green Green Gray Gray Gray Purple Purple Purple Gray
Row 16: Green Green Black Green Green Black Green Green Gray Gray Purple Orange Orange Orange Purple
Row 17: Green Green Black Black Black Black Green Green Gray Gray Purple Orange Purple Orange Purple
Row 18: Gray Gray Green Green Green Green Gray Gray Gray Gray Purple Orange Purple Orange Purple
Row 19: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Orange Orange Orange Purple
Row 20: Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Purple Purple Purple Gray
Row 21: Gray Gray Blue Blue Purple Purple Purple Purple Blue Blue Gray Purple Purple Purple Gray
Row 22: Gray Gray Blue Blue Purple Blue Blue Purple Blue Blue Gray Gray Gray Gray Gray
Row 23: Gray Gray Blue Blue Purple Purple Purple Purple Blue Blue Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Gray Blue Blue Blue Blue Gray Gray Gray Gray Gray Gray Gray
Row 25: 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
Row 27: 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
Example 2
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 Gray Gray Gray Purple Purple Purple Brown Brown Brown Brown Purple Purple Purple
Row 5: Purple Purple Gray Yellow Gray Purple Purple Purple Brown Pink Pink Brown Purple Purple Purple
Row 6: Purple Purple Gray Yellow Gray Purple Purple Purple Brown Pink Pink Brown Purple Purple Purple
Row 7: Purple Purple Gray Gray Gray Purple Purple Purple Brown Brown Brown Brown 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
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Gray Gray Gray Purple Purple Purple Brown Brown Brown Brown Purple Purple Purple
Row 3: Purple Purple Gray Gray Gray Purple Purple Purple Brown Brown Brown Brown Purple Purple Purple
Row 4: Purple Gray Yellow Yellow Yellow Gray Brown Brown Pink Pink Pink Pink Brown Brown Purple
Row 5: Purple Gray Yellow Gray Yellow Gray Brown Brown Pink Brown Brown Pink Brown Brown Purple
Row 6: Purple Gray Yellow Gray Yellow Gray Brown Brown Pink Brown Brown Pink Brown Brown Purple
Row 7: Purple Gray Yellow Yellow Yellow Gray Brown Brown Pink Pink Pink Pink Brown Brown Purple
Row 8: Purple Purple Gray Gray Gray Purple Purple Purple Brown Brown Brown Brown Purple Purple Purple
Row 9: Purple Purple Gray Gray Gray Purple Purple Purple Brown Brown Brown Brown 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
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Green Brown Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Red Red Green Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green 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
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
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
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Green Red Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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 Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Green Brown Brown Brown Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Green Brown Green Brown Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Green Brown Brown Brown Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Green Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Red Red Red Red Green Green Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Red Green Green Red Green Green Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Red Red Red Red Green Green Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green Green Green Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Green Green Green Red Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Green Red Green Red Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Green Green Green Red Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Red Red Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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: Gray Gray Gray 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 Green Green Green Green 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 Green Brown Brown Green 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 Green Brown Brown Green 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 Green Green Green Green 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
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Gray Gray Gray 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray 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 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 Green Green Green Green Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Brown Brown Brown Brown Green Green Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Brown Green Green Brown Green Green Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Brown Green Green Brown Green Green Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Brown Brown Brown Brown Green Green Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green 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 Green Green 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 Gray Gray Gray Gray Gray
Gray Gray Gray 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: Green Green Green Brown Green Green Green Green Green Green Green
Row 2: Brown Brown Green Brown Green Brown Brown Brown Black Purple Green
Row 3: Green Brown Green Brown Green Brown Green Green Green Green Green
Row 4: Green Brown Green Brown Brown Brown Green Brown Brown Brown Green
Row 5: Green Green Green Green Green Green Green Brown Green Green Green
Output:
Row 1: Green Green Green Black Green Green Green Green Green Green Green
Row 2: Brown Brown Green Purple Green Purple Black Purple Black Purple Green
Row 3: Green Brown Green Black Green Black Green Green Green Green Green
Row 4: Green Brown Green Purple Black Purple Green Brown Brown Brown Green
Row 5: Green Green Green Green Green Green Green Brown Green Green Green
Example 2
Input:
Row 1: 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
Row 2: Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow
Row 3: Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Yellow
Row 4: Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Red Black Red Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Purple
Row 5: Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 6: Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow
Row 8: Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 9: Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow
Row 10: Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow
Row 11: Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 12: Yellow Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 13: Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Purple
Row 15: Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 16: Yellow Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Purple
Row 17: Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 18: Yellow Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Yellow
Row 19: Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow
Row 20: Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Yellow
Row 21: Yellow Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow
Row 22: Purple Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Yellow
Row 23: Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: 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
Row 2: Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow
Row 3: Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Yellow
Row 4: Yellow Purple Purple Purple Purple Purple Yellow Black Red Black Red Black Red Black Yellow Purple Yellow Purple Purple Purple Yellow Purple Yellow Purple Purple
Row 5: Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Purple Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 6: Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Black Yellow Purple Purple Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Red Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow
Row 8: Yellow Purple Purple Purple Purple Purple Yellow Black Red Black Red Black Yellow Purple Yellow Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 9: Yellow Yellow Yellow Purple Yellow Yellow Yellow Red Yellow Yellow Yellow Red Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow
Row 10: Yellow Purple Purple Purple Yellow Black Red Black Red Black Yellow Black Yellow Purple Yellow Purple Purple Purple Purple Purple Yellow Purple Yellow Purple Yellow
Row 11: Yellow Purple Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Purple Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 12: Yellow Purple Yellow Black Red Black Yellow Black Red Black Yellow Black Yellow Purple Purple Purple Yellow Purple Purple Purple Purple Purple Purple Purple Yellow
Row 13: Yellow Purple Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Purple Yellow Black Yellow Black Yellow Black Red Black Red Black Red Black Yellow Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Purple
Row 15: Yellow Purple Yellow Red Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 16: Yellow Purple Yellow Black Red Black Yellow Black Yellow Purple Yellow Black Red Black Red Black Yellow Purple Purple Purple Yellow Purple Purple Purple Purple
Row 17: Yellow Purple Yellow Yellow Yellow Red Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Purple Yellow Yellow Yellow
Row 18: Yellow Purple Purple Purple Yellow Black Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Purple Purple Yellow Purple Yellow
Row 19: Yellow Purple Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow
Row 20: Yellow Purple Yellow Black Red Black Red Black Red Black Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Purple Yellow
Row 21: Yellow Purple Yellow Red Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Purple Yellow Purple Yellow
Row 22: Purple Purple Yellow Black Yellow Black Yellow Purple Yellow Black Red Black Red Black Yellow Purple Yellow Purple Purple Purple Yellow Purple Purple Purple Yellow
Row 23: Yellow Yellow Yellow Red Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Red
Row 3: Red Red Red Red Red Red Red Yellow Red Yellow Red Yellow Red Red Red Yellow Red Yellow Red
Row 4: Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 5: Red Yellow Red Red Red Yellow Red Yellow Red Red Red Yellow Red Yellow Red Red Red Yellow Red
Row 6: Red Yellow Yellow Yellow Red Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Red
Row 7: Red Red Red Yellow Red Red Red Red Red Yellow Red Red Red Yellow Red Yellow Red Red Red
Row 8: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 9: Red Red Red Yellow Red Red Red Red Red Yellow Red Yellow Red Yellow Red Red Red Yellow Red
Row 10: Red Yellow Yellow Yellow Red Yellow Yellow Yellow Red Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red
Row 11: Red Yellow Red Red Red Yellow Red Red Red Yellow Red Blue Red Red Red Yellow Red Red Red
Row 12: Red Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Red Pink Blue Yellow Red Yellow Red Yellow Yellow
Row 13: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Yellow Red Yellow Red Red Red
Row 14: Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Red
Row 15: Red Yellow Red Red Red Red Red Yellow Red Red Red Yellow Red Red Red Yellow Red Yellow Red
Row 16: Yellow Yellow Red Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Red Yellow Red
Row 17: Red Red Red Yellow Red Red Red Red Red Red Red Red Red Yellow 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 Yellow Red
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Red
Row 3: Red Red Red Red Red Red Red Yellow Red Yellow Red Yellow Red Red Red Yellow Red Yellow Red
Row 4: Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 5: Red Yellow Red Red Red Yellow Red Yellow Red Red Red Yellow Red Yellow Red Red Red Yellow Red
Row 6: Red Yellow Yellow Yellow Red Yellow Red Yellow Red Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Red
Row 7: Red Red Red Yellow Red Red Red Red Red Yellow Red Red Red Yellow Red Yellow Red Red Red
Row 8: Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red Pink Red Yellow Red Yellow Red Yellow Red
Row 9: Red Red Red Yellow Red Red Red Red Red Yellow Red Blue Red Yellow Red Red Red Yellow Red
Row 10: Red Yellow Yellow Yellow Red Pink Blue Pink Red Yellow Red Pink Red Yellow Yellow Yellow Yellow Yellow Red
Row 11: Red Yellow Red Red Red Blue Red Red Red Yellow Red Blue Red Red Red Yellow Red Red Red
Row 12: Red Yellow Red Pink Blue Pink Red Yellow Yellow Yellow Red Pink Blue Pink Red Yellow Red Yellow Yellow
Row 13: Red Red Red Red Red Blue Red Red Red Red Red Red Red Blue Red Yellow Red Red Red
Row 14: Red Pink Blue Pink Blue Pink Blue Pink Red Pink Blue Pink Blue Pink Red Yellow Yellow Yellow Red
Row 15: Red Blue Red Red Red Red Red Blue Red Red Red Blue Red Red Red Yellow Red Yellow Red
Row 16: Blue Pink Red Yellow Yellow Yellow Red Pink Blue Pink Blue Pink Red Yellow Yellow Yellow Red Yellow Red
Row 17: Red Red Red Yellow Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Red
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
Row 2: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Row 3: Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue
Row 4: Blue Gray Blue Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray
Row 5: Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 6: Gray Gray Gray Green Pink Green Blue Gray Gray Gray Gray Gray Gray
Row 7: Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue
Row 8: Blue Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray Gray Blue
Row 9: Blue Gray Blue Blue Blue Gray Blue Gray Blue Blue Blue Gray Blue
Row 10: Blue Gray Blue Gray Blue Gray Gray Gray Gray Gray Blue Gray Blue
Row 11: Blue Gray Blue Gray Blue Gray Blue Blue Blue Gray Blue Gray Blue
Row 12: Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue
Row 13: Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue Gray 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue
Blue Blue Blue Gray Blue Blue Blue Blue Blue Gray Blue Blue Blue
Blue Green Blue Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray
Blue Pink Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue
Pink Green Pink Green Pink Green Blue Gray Gray Gray Gray Gray Gray
Blue Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Blue
Blue Gray Gray Gray Gray Gray Blue Gray Blue Gray Gray Gray Blue
Blue Gray Blue Blue Blue Gray Blue Gray Blue Blue Blue Gray Blue
Blue Gray Blue Gray Blue Gray Gray Gray Gray Gray Blue Gray Blue
Blue Gray Blue Gray Blue Gray Blue Blue Blue Gray Blue Gray Blue
Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue
Blue Blue Blue Gray Blue Blue Blue Gray Blue Blue Blue 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
Row 2: Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink
Row 8: Pink Pink Pink Pink
Row 9: Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink
Row 17: Pink Pink Black Pink
Row 18: Pink Black Pink Pink
Row 19: Pink Black Black Black
Row 20: Pink Black Black Black
Row 21: Pink Pink Pink Pink
Row 22: Pink Pink Pink Pink
Output:
Row 1: Pink Black Pink Pink Black Pink
Row 2: Black Pink Pink Black Pink Pink
Row 3: Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Orange Orange Orange Brown Orange Orange Brown Brown
Row 3: Brown Orange Orange Orange Orange Orange Orange Brown Brown
Row 4: Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 5: Brown Brown Brown Orange Orange Orange Orange Brown Brown
Row 6: Brown Orange Orange Orange Brown Brown Orange Brown Brown
Row 7: Brown Orange Orange Orange Orange Orange Orange Brown Brown
Row 8: Brown Brown Orange Brown Orange Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Orange Brown Brown Brown Brown
Row 10: Brown Brown Brown Orange Orange Orange Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Orange Orange Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Orange Orange Orange Brown Orange Orange Orange Orange Orange Brown Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Brown Brown Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange
Row 4: Brown Brown Orange Orange Orange Orange Brown Brown Orange Orange Orange Orange
Row 5: Orange Orange Orange Brown Brown Orange Orange Orange Orange Brown Brown Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Brown Orange Brown Orange Brown Brown Brown Orange Brown Orange Brown Brown
Row 8: Brown Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown
Row 9: Brown Brown Orange Orange Orange Brown Brown Brown Orange Orange Orange Brown
Row 10: Brown Brown Brown Brown Orange Orange Brown Brown Brown Brown Orange Orange
Example 3
Input:
Row 1: Brown Brown 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 Green Brown
Row 8: Brown Brown Brown Brown Brown Brown Green Brown
Row 9: Brown Brown Brown Brown Brown Green Brown Brown
Row 10: Brown Brown Brown Brown Brown Green Green 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
Output:
Row 1: Brown Green Brown Green
Row 2: Brown Green Brown Green
Row 3: Green Brown Green Brown
Row 4: Green Green Green Green
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: 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
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Blue Blue Blue Blue Red Blue Blue Blue Red Red Red
Row 6: Red Blue Blue Blue Blue Blue Blue Red Blue Blue Red Red
Row 7: Red Blue Blue Blue Blue Blue Red Blue Blue Red Blue Red
Row 8: Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue
Row 9: Red Blue Blue Blue Blue Red Blue Blue Red Red Red Red
Row 10: Red Blue Blue Blue Blue Blue Blue Red Red Red Red Red
Row 11: Red Blue Blue Blue Blue Blue Red Red Blue Blue Red Red
Row 12: Red Blue Blue Blue Blue Red Blue Blue Red Red Red Red
Row 13: 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
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 Red Blue Blue Blue Red Red Red Blue Blue Blue Blue Red Blue Blue Blue Red Red Red
Blue Blue Blue Blue Blue Blue Red Blue Blue Red Red Blue Blue Blue Blue Blue Blue Red Blue Blue Red Red
Blue Blue Blue Blue Blue Red Blue Blue Red Blue Red Blue Blue Blue Blue Blue Red Blue Blue Red Blue Red
Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue
Blue Blue Blue Blue Red Blue Blue Red Red Red Red Blue Blue Blue Blue Red Blue Blue Red Red Red Red
Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Red Red Red Red Red
Blue Blue Blue Blue Blue Red Red Blue Blue Red Red Blue Blue Blue Blue Blue Red Red Blue Blue Red Red
Blue Blue Blue Blue Red Blue Blue Red Red Red Red Blue Blue Blue Blue Red Blue Blue 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: Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange
Row 2: Pink Pink Green Green Green Green Pink Blue Pink Pink Pink Pink Blue Pink Pink
Row 3: Pink Black Green Green Green Green Black Black Blue Black Pink Black Black Blue Black
Row 4: Pink Orange Green Green Green Green Orange Black Orange Orange Pink Orange Black Orange Orange
Row 5: Pink Pink Green Green Green Green Pink Pink Pink Blue Pink Pink Pink Pink Blue
Row 6: Blue Black Green Green Green Green Black Pink Black Black Blue Black Pink Black Black
Row 7: Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black
Row 8: Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink
Row 9: Black Black Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink
Row 10: Orange Black Orange Orange Pink Orange Black Green Green Pink Orange Black Orange Orange Pink
Row 11: Pink Pink Pink Blue Pink Pink Pink Green Green Green Green Green Green Green Pink
Row 12: Black Pink Black Black Blue Black Pink Green Green Green Green Green Green Green Blue
Row 13: Orange Pink Orange Black Orange Orange Pink Green Green Green Green Green Green Green Orange
Row 14: Blue Pink Pink Pink Pink Blue Pink Pink Pink Green Green Green Green Green Green
Row 15: Black Blue Black Pink Black Black Blue Black Pink Green Green Green Green Green Green
Row 16: Black Orange Orange Pink Orange Black Orange Orange Pink Green Green Green Green Green Green
Row 17: Pink Pink Blue Pink Pink Pink Pink Blue Pink Green Green Green Green Green Green
Row 18: Pink Black Black Blue Black Pink Black Black Blue Black Pink Green Green Green Green
Row 19: Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange
Row 20: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue
Row 21: Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink Black Black
Row 22: Orange Orange Pink Orange Black Green Green Green Green Green Orange Orange Pink Orange Black
Row 23: Pink Blue Pink Pink Pink Green Green Green Green Green Pink Blue Pink Pink Pink
Row 24: Black Black Blue Black Pink Green Green Green Green Green Black Black Blue Black Pink
Output:
Row 1: Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange
Row 2: Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink
Row 3: Pink Black Black Blue Black Pink Black Black Blue Black Pink Black Black Blue Black
Row 4: Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange
Row 5: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue
Row 6: Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink Black Black
Row 7: Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black
Row 8: Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink
Row 9: Black Black Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink
Row 10: Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink
Row 11: Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink
Row 12: Black Pink Black Black Blue Black Pink Black Black Blue Black Pink Black Black Blue
Row 13: Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange
Row 14: Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink
Row 15: Black Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink Black
Row 16: Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange
Row 17: Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink
Row 18: Pink Black Black Blue Black Pink Black Black Blue Black Pink Black Black Blue Black
Row 19: Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange
Row 20: Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue
Row 21: Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink Black Black
Row 22: Orange Orange Pink Orange Black Orange Orange Pink Orange Black Orange Orange Pink Orange Black
Row 23: Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink Pink Blue Pink Pink Pink
Row 24: Black Black Blue Black Pink Black Black Blue Black Pink Black Black Blue Black Pink
Example 2
Input:
Row 1: Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow
Row 2: Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow
Row 3: Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow
Row 4: Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown
Row 5: Yellow Green Yellow Pink Brown Orange Gray Gray Gray Gray Gray Gray Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange
Row 6: Yellow Brown Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown
Row 7: Yellow Brown Green Yellow Gray Gray Gray Gray Gray Gray Gray Gray Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple
Row 8: Brown Purple Green Brown Gray Gray Gray Gray Gray Gray Gray Gray Brown Green Brown Yellow Brown Purple Green Brown Brown Green
Row 9: Orange Brown Brown Yellow Gray Gray Gray Gray Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow
Row 10: Brown Purple Yellow Yellow Gray Gray Gray Gray Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange
Row 11: Purple Yellow Gray Gray Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Gray Gray Gray Gray Gray
Row 12: Green Brown Gray Gray Purple Green Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Gray Gray Gray Gray Gray
Row 13: Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Gray Gray Gray Gray Gray
Row 14: Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow
Row 15: Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink
Output:
Row 1: Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow
Row 2: Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow
Row 3: Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow
Row 4: Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown
Row 5: Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange
Row 6: Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown
Row 7: Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple
Row 8: Brown Purple Green Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green
Row 9: Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow
Row 10: Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange
Row 11: Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green
Row 12: Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown Purple Green Brown Brown Green Brown Yellow Brown Purple Green
Row 13: Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown Yellow Green Yellow Pink Brown Orange Brown Brown
Row 14: Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow Yellow Brown Orange Orange Orange Brown Purple Yellow
Row 15: Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink Yellow Brown Green Yellow Pink Purple Yellow Pink
Example 3
Input:
Row 1: Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple
Row 2: Purple Black Purple Black Purple Yellow Yellow Purple Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black
Row 3: Purple Black Black Purple Black Yellow Yellow Purple Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black
Row 4: Black Black Purple Purple Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 5: Black Purple Purple Purple Black Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Black Purple Yellow Yellow Black Purple Purple Purple Purple
Row 6: Purple Black Purple Black Purple Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Black Yellow Yellow Purple Black Black Purple Black
Row 7: Purple Black Black Purple Black Yellow Yellow Purple Yellow Yellow Yellow Yellow Yellow Yellow Purple Purple Purple Black Yellow Yellow Black Purple Purple Purple Black
Row 8: Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black Black Yellow Yellow Purple Purple Purple Purple Purple
Row 9: Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black Purple Yellow Yellow Black Purple Purple Purple Purple
Row 10: Purple Black Purple Black Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black
Row 11: Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black
Output:
Row 1: Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple
Row 2: Purple Black Purple Black Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black
Row 3: Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black
Row 4: Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 5: Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple
Row 6: Purple Black Purple Black Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black
Row 7: Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black
Row 8: Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple
Row 9: Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple
Row 10: Purple Black Purple Black Purple Black Black Purple Black Black Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Black Black Purple Black
Row 11: Purple Black Black Purple Black Purple Purple Purple Black Purple Purple Purple Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Purple Black
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange
Row 2: Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow
Row 3: Orange Red Orange Orange Red Yellow Orange Red Orange Orange Black Black Orange Red Orange Orange Red Yellow Orange Red
Row 4: Orange Orange Red Orange Orange Orange Orange Orange Red Orange Black Black Orange Orange Red Orange Orange Orange Orange Orange
Row 5: Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Black Black Red Black Black Black Black Black Red Yellow
Row 6: Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Black Black Black Black Black Red Orange
Row 7: Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Black Black Black Black Black Black Black Black Red Orange
Row 8: Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Black Black Black Black Yellow Orange Red Orange Orange Red
Row 9: Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Black Black Black Black Orange Orange Orange Red Orange Orange
Row 10: Red Red Yellow Red Yellow Yellow Red Red Yellow Red Black Black Black Black Yellow Red Yellow Yellow Red Red
Row 11: Orange Orange Red Red Orange Yellow Orange Orange Red Red Black Black Orange Orange Red Red Orange Yellow Orange Orange
Row 12: Yellow Yellow Black Black Black Red Yellow Yellow Orange Red Orange Red Yellow Yellow Black Black Black Red Yellow Yellow
Row 13: Orange Red Black Black Black Yellow Orange Red Orange Orange Red Yellow Orange Red Black Black Black Yellow Orange Red
Row 14: Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Black Black Black Black Black Black Orange Orange Orange
Row 15: Red Yellow Black Black Red Yellow Red Yellow Yellow Red Red Black Black Black Black Black Black Yellow Red Yellow
Row 16: Red Orange Black Black Orange Red Red Orange Yellow Orange Orange Red Red Orange Black Black Black Red Red Orange
Row 17: Black Black Black Black Yellow Orange Red Orange Black Black Black Orange Red Orange Red Yellow Yellow Orange Red Orange
Row 18: Black Black Black Black Red Orange Orange Red Black Black Black Orange Orange Red Yellow Orange Red Orange Orange Red
Row 19: Black Black Black Orange Orange Red Black Black Black Black Black Red Orange Orange Orange Orange Orange Red Orange Orange
Row 20: Black Black Black Red Yellow Yellow Black Black Black Black Black Yellow Red Red Yellow Red Yellow Yellow Red Red
Row 21: Black Black Black Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange
Row 22: Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow
Row 23: Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red
Row 24: Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 25: Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow
Row 26: Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange
Row 27: Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow 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>
| Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange
Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow
Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red
Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow
Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange
Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange
Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red
Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange
Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red
Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange
Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow
Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red
Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow
Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange
Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange
Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red
Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange
Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red
Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange
Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow
Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red Orange Orange Red Yellow Orange Red
Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange
Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow Yellow Red Red Yellow Red Yellow
Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange Yellow Orange Orange Red Red Orange
Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red Orange Red Yellow Yellow Orange Red 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 Black Orange Orange Orange Orange
Row 2: Orange Pink Orange Orange Black Orange Pink Orange Orange
Row 3: Orange Orange Pink Orange Black Orange Orange Pink Orange
Row 4: Orange Orange Pink Orange Black Orange Pink Pink Orange
Row 5: Orange Pink Pink Orange Black Orange Pink Pink Orange
Row 6: Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Black Orange Pink Orange Orange
Row 10: Orange Orange Orange Orange Black Orange Orange Pink Orange
Row 11: Orange Orange Orange Orange Black Orange Pink Pink Orange
Row 12: Orange Orange Pink Orange Black Orange Pink Pink Orange
Row 13: Orange Orange Orange Orange Black Orange Orange Orange Orange
Output:
Row 1: Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 2: Orange Pink Orange Orange Black Orange Pink Orange Orange
Row 3: Orange Orange Pink Orange Black Orange Orange Pink Orange
Row 4: Orange Black Pink Orange Black Orange Pink Pink Orange
Row 5: Orange Pink Pink Orange Black Orange Pink Pink Orange
Row 6: Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 7: Black Black Black Black Black Black Black Black Black
Row 8: Orange Orange Orange Orange Black Orange Orange Orange Orange
Row 9: Orange Black Orange Orange Black Orange Pink Orange Orange
Row 10: Orange Orange Black Orange Black Orange Orange Pink Orange
Row 11: Orange Black Black Orange Black Orange Pink Pink Orange
Row 12: Orange Black Pink Orange Black Orange Pink Pink Orange
Row 13: Orange Orange Orange Orange Black Orange Orange Orange Orange
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue
Row 7: Purple Purple Purple Purple Purple
Row 8: Blue Blue Blue Blue Blue
Row 9: Blue Blue Green Blue Blue
Row 10: Blue Green Green Blue Blue
Row 11: Blue Green Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue
Row 2: Blue Blue Purple Blue Blue
Row 3: Blue Purple Purple Blue Blue
Row 4: Blue Purple Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue
Row 7: Purple Purple Purple Purple Purple
Row 8: Blue Blue Blue Blue Blue
Row 9: Blue Blue Green Blue Blue
Row 10: Blue Green Green Blue Blue
Row 11: Blue Green Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Green Brown Orange Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Green Brown Orange Brown Brown Brown Green Brown
Row 10: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Green Brown Orange Brown Brown Brown Orange Brown
Row 3: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Green Brown Orange Brown Brown Brown Green Brown
Row 10: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Green Green
Row 2: Green Green Green Green Green
Row 3: Green Black Green Green Green
Row 4: Green Black Black Green Green
Row 5: Green Green Green Green Green
Row 6: Brown Brown Brown Brown Brown
Row 7: Green Green Green Green Green
Row 8: Green Green Green Green Green
Row 9: Green Green Green Green Green
Row 10: Green Black Green Green Green
Row 11: Green Green Green Green Green
Row 12: Brown Brown Brown Brown Brown
Row 13: Green Green Green Green Green
Row 14: Green Green Green Green Green
Row 15: Green Black Green Green Green
Row 16: Green Black Black Green Green
Row 17: Green Green Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Green Green
Green Green Green Green Green
Green Black Green Green Green
Green Black Black Green Green
Green Green Green Green Green
Brown Brown Brown Brown Brown
Green Green Green Green Green
Green Green Green Green Green
Green Brown Green Green Green
Green Black Brown Green Green
Green Green Green Green Green
Brown Brown Brown Brown Brown
Green Green Green Green Green
Green Green Green Green Green
Green Black Green Green Green
Green Black Black 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 Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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
Row 18: Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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 Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 2: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 3: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 4: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 5: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 6: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 7: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 8: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 9: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 10: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 11: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 12: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 13: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 14: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 15: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 16: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 17: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 18: Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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 Purple Purple Purple Purple Purple Purple
Row 27: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 28: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Green 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
Output:
Row 1: Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown
Row 2: Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown Yellow Brown
Row 3: Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 2: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 3: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 4: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 5: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 6: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 7: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 8: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 9: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 10: Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red
Row 11: Red Red Red Red Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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: 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
Row 7: 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
Row 9: 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
Row 11: 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
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 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
Row 18: 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
Row 20: 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
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Black Red Red Red Red
Row 25: 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
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 29: 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 Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow Red Yellow
Red Red 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 Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red 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: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Purple Purple
Row 2: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Purple Purple
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Green Green Blue Black Black Blue Black Black Blue Black Black Blue Green Green Blue Black Black Blue Black Black Blue Black Black Blue Black Black
Row 5: Green Green Blue Black Black Blue Black Black Blue Black Black Blue Green Green Blue Black Black Blue Black Black Blue Black Black Blue Black Black
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: Black Black Blue Orange Orange Blue Black Black Blue Orange Orange Blue Black Black Blue Black Black Blue Orange Orange Blue Black Black Blue Purple Purple
Row 8: Black Black Blue Orange Orange Blue Black Black Blue Orange Orange Blue Black Black Blue Black Black Blue Orange Orange Blue Black Black Blue Purple Purple
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: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Black Black
Row 11: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Black Black
Output:
Row 1: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Purple Purple
Row 2: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Purple Purple
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Green Green Blue Green Green Blue Green Green Blue Green Green Blue Green Green Blue Black Black Blue Black Black Blue Pink Pink Blue Purple Purple
Row 5: Green Green Blue Green Green Blue Green Green Blue Green Green Blue Green Green Blue Black Black Blue Black Black Blue Pink Pink Blue Purple Purple
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Black Black Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Pink Pink Blue Purple Purple
Row 8: Black Black Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Orange Orange Blue Pink Pink Blue Purple Purple
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: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Black Black
Row 11: Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Black Black Blue Pink Pink Blue Black Black
Example 2
Input:
Row 1: Green Green Red Green Green Red Green Green Red Green Green
Row 2: Green Green Red Green Green Red Green Green Red Green Green
Row 3: Green Green Red Green Green Red Green Green Red Green Green
Row 4: Red Red Red Red Red Red Red Red Red Red Red
Row 5: Green Green Red Green Green Red Green Green Red Blue Blue
Row 6: Green Green Red Green Green Red Green Green Red Blue Blue
Row 7: Green Green Red Green Green Red Green Green Red Blue Blue
Row 8: Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Red Green Green Red Green Green Red Green Green
Row 10: Green Green Red Green Green Red Green Green Red Green Green
Row 11: Green Green Red Green Green Red Green Green Red Green Green
Row 12: Red Red Red Red Red Red Red Red Red Red Red
Row 13: Green Green Red Green Green Red Green Green Red Green Green
Row 14: Green Green Red Green Green Red Green Green Red Green Green
Row 15: Green Green Red Green Green Red Green Green Red Green Green
Row 16: Red Red Red Red Red Red Red Red Red Red Red
Row 17: Green Green Red Green Green Red Green Green Red Green Green
Row 18: Green Green Red Green Green Red Green Green Red Green Green
Row 19: Green Green Red Green Green Red Green Green Red Green Green
Row 20: Red Red Red Red Red Red Red Red Red Red Red
Row 21: Green Green Red Green Green Red Green Green Red Green Green
Row 22: Green Green Red Green Green Red Green Green Red Green Green
Row 23: Green Green Red Green Green Red Green Green Red Green Green
Row 24: Red Red Red Red Red Red Red Red Red Red Red
Row 25: Green Green Red Green Green Red Green Green Red Blue Blue
Row 26: Green Green Red Green Green Red Green Green Red Blue Blue
Row 27: Green Green Red Green Green Red Green Green Red Blue Blue
Output:
Row 1: Green Green Red Green Green Red Green Green Red Green Green
Row 2: Green Green Red Green Green Red Green Green Red Green Green
Row 3: Green Green Red Green Green Red Green Green Red Green Green
Row 4: Red Red Red Red Red Red Red Red Red Red Red
Row 5: Green Green Red Green Green Red Green Green Red Blue Blue
Row 6: Green Green Red Green Green Red Green Green Red Blue Blue
Row 7: Green Green Red Green Green Red Green Green Red Blue Blue
Row 8: Red Red Red Red Red Red Red Red Red Red Red
Row 9: Green Green Red Green Green Red Green Green Red Blue Blue
Row 10: Green Green Red Green Green Red Green Green Red Blue Blue
Row 11: Green Green Red Green Green Red Green Green Red Blue Blue
Row 12: Red Red Red Red Red Red Red Red Red Red Red
Row 13: Green Green Red Green Green Red Green Green Red Blue Blue
Row 14: Green Green Red Green Green Red Green Green Red Blue Blue
Row 15: Green Green Red Green Green Red Green Green Red Blue Blue
Row 16: Red Red Red Red Red Red Red Red Red Red Red
Row 17: Green Green Red Green Green Red Green Green Red Blue Blue
Row 18: Green Green Red Green Green Red Green Green Red Blue Blue
Row 19: Green Green Red Green Green Red Green Green Red Blue Blue
Row 20: Red Red Red Red Red Red Red Red Red Red Red
Row 21: Green Green Red Green Green Red Green Green Red Blue Blue
Row 22: Green Green Red Green Green Red Green Green Red Blue Blue
Row 23: Green Green Red Green Green Red Green Green Red Blue Blue
Row 24: Red Red Red Red Red Red Red Red Red Red Red
Row 25: Green Green Red Green Green Red Green Green Red Blue Blue
Row 26: Green Green Red Green Green Red Green Green Red Blue Blue
Row 27: Green Green Red Green Green Red Green Green Red Blue Blue
Example 3
Input:
Row 1: Black Black Black Black Purple Yellow Yellow Yellow Yellow Purple Black Black Black Black Purple Yellow Yellow Yellow Yellow
Row 2: Black Black Black Black Purple Yellow Yellow Yellow Yellow Purple Black Black Black Black Purple Yellow Yellow Yellow Yellow
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Purple Green Green Green Green
Row 5: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Purple Green Green Green Green
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Black Black Black Black Purple Green Green Green Green
Row 14: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Black Black Black Black Purple Green Green Green Green
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Gray Gray Gray Gray
Row 17: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Gray Gray Gray Gray
Output:
Row 1: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Yellow Yellow Yellow Yellow
Row 2: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Yellow Yellow Yellow Yellow
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Black Black Black Black Purple Green Green Green Green
Row 5: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Black Black Black Black Purple Green Green Green Green
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Black Black Black Black Purple Green Green Green Green
Row 8: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Black Black Black Black Purple Green Green Green Green
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Black Black Black Black Purple Green Green Green Green
Row 11: Yellow Yellow Yellow Yellow Purple Red Red Red Red Purple Black Black Black Black Purple Green Green Green Green
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Black Black Black Black Purple Green Green Green Green
Row 14: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Black Black Black Black Purple Green Green Green Green
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Gray Gray Gray Gray
Row 17: Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Yellow Pink Pink Pink Yellow Orange Orange Orange Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 2: Orange Orange Orange Yellow Pink Pink Pink Yellow Orange Orange Orange Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 3: Orange Orange Orange Yellow Pink Pink Pink Yellow Orange Orange Orange Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Pink Pink Pink Yellow Green Green Green Yellow Pink Pink Pink Yellow Green Green Green Yellow Pink Pink Pink
Row 6: Pink Pink Pink Yellow Green Green Green Yellow Pink Pink Pink Yellow Green Green Green Yellow Pink Pink Pink
Row 7: Pink Pink Pink Yellow Green Green Green Yellow Pink Pink Pink Yellow Green Green Green Yellow Pink Pink Pink
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 10: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 11: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 12: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 14: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 15: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Gray Gray Gray Yellow Pink Pink Pink
Row 18: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Gray Gray Gray Yellow Pink Pink Pink
Row 19: Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Gray Gray Gray Yellow 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 Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Yellow Pink Pink Pink Yellow Pink Pink Pink
Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Yellow Pink Pink Pink Yellow Pink Pink Pink
Orange Orange Orange Yellow Orange Orange Orange Yellow Orange Orange Orange Yellow Pink Pink Pink Yellow Pink Pink Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Pink Pink Pink Yellow Green Green Green Yellow Green Green Green Yellow Green Green Green Yellow Pink Pink Pink
Pink Pink Pink Yellow Green Green Green Yellow Green Green Green Yellow Green Green Green Yellow Pink Pink Pink
Pink Pink Pink Yellow Green Green Green Yellow Green Green Green Yellow Green Green Green Yellow Pink Pink Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink
Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Gray Gray Gray Yellow Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Gray Gray Gray Yellow Pink Pink Pink
Pink Pink Pink Yellow Pink Pink Pink Yellow Pink Pink Pink Yellow Gray Gray Gray Yellow 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 Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Black Red Black Black Black Black Purple Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Red Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Blue Black Black Black Black Black Black Black Black Black Black Black Black Black Black Orange Black
Row 5: Black Black Blue Black Black Black Black Black Black Black Black Black Black Black Orange Black Black
Row 6: Black Black Black Black Black Black Gray Black Black Black Black Purple Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Brown Black Black
Row 8: Black Black Black Green Black Black Black Black Brown Black Black Black Black Black Black Black Black
Row 9: Black Green Black Black Black Gray Black Black Black Black Black Black Black Black Black Pink Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Black Black
Row 11: 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
Row 2: Black Black Red Red Red Black Black Purple Purple Purple Purple Purple Black Black Black Black Black
Row 3: Black Black Red Red Red Black Black Purple Purple Purple Purple Purple Black Black Black Black Black
Row 4: Blue Blue Blue Black Black Black Black Purple Purple Purple Purple Purple Black Black Orange Orange Black
Row 5: Blue Blue Blue Black Black Black Black Purple Purple Purple Purple Purple Black Black Orange Orange Black
Row 6: Black Black Black Black Black Gray Gray Purple Purple Purple Purple Purple Black Black Black Black Black
Row 7: Black Black Black Black Black Gray Gray Black Brown Brown Brown Brown Brown Brown Brown Black Black
Row 8: Black Green Green Green Black Gray Gray Black Brown Brown Brown Brown Brown Brown Brown Black Black
Row 9: Black Green Green Green Black Gray Gray Black Black Black Black Black Black Black Pink Pink Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Pink Pink Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Example 2
Input:
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 Blue Yellow Yellow Yellow Yellow
Row 6: 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
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue 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 Yellow Yellow Yellow Yellow Yellow Yellow Red 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
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Black 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
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 Blue Blue Blue Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Blue Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Red Red Red Yellow Blue Blue Blue Yellow Yellow Yellow Yellow
Row 11: Yellow Yellow Yellow Yellow Yellow Red Red Red Yellow Blue Blue Blue Yellow Yellow Yellow Yellow
Row 12: Yellow Yellow Yellow Yellow Yellow Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Red Red Red 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
Row 15: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 17: Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 18: Yellow Yellow Yellow Yellow Yellow Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Example 3
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Pink Black Black
Row 2: Black Black Black Red Black Black Black Black Black Black Black Black Black
Row 3: Black Black Black Black Gray Black Black Black Black Black Black Black Black
Row 4: Black Red Black Black Black Black Gray Black Black Black Black Black Black
Row 5: Black Black Green 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 Pink Black Black Black Black Black
Row 8: Black Black Black Black Black Black Black Black Purple Black Black Black Black
Row 9: Black Black Black Black Black Black Green Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Black Black Black Purple Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Black Black Black Black Pink Pink Pink Pink Black Black
Row 2: Black Red Red Red Black Black Black Pink Pink Pink Pink Black Black
Row 3: Black Red Red Red Gray Gray Gray Pink Pink Pink Pink Black Black
Row 4: Black Red Red Red Gray Gray Gray Pink Pink Pink Pink Black Black
Row 5: Black Black Green Green Green Green Green Pink Pink Pink Pink Black Black
Row 6: Black Black Green Green Green Green Green Pink Pink Pink Pink Black Black
Row 7: Black Black Green Green Green Green Green Pink Pink Pink Pink Black Black
Row 8: Black Black Green Green Green Green Green Black Purple Purple Black Black Black
Row 9: Black Black Green Green Green Green Green Black Purple Purple Black Black Black
Row 10: Black Black Black Black Black Black Black Black Purple Purple Black Black Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Black Black Black Black
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
Row 2: Green Green Green Green Green Green Green Green Green Green Red 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
Row 4: Green Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 5: Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Red Green Green Green Green Green
Row 6: Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green Green Green Gray Green Green
Row 7: Green Green Green Green Green Green Green Green Green Brown Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Green Blue 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 Gray Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Purple 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
Row 16: Green Green Green Green Green Green Green Green Green Blue Green Green Green Green Green Green Purple 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
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 Red Red Red Red Red Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Red Red Red Red Red Green Green Green Green Green
Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Red Red Red Red Red Green Green Green Green Green
Green Yellow Yellow Yellow Yellow Yellow Yellow Green Green Green Red Red Red Red Red Green Green Green Green Green
Green Green Green Green Brown Brown Brown Brown Brown Brown Green Green Gray Gray Gray Gray Gray Gray Green Green
Green Green Green Green Brown Brown Brown Brown Brown Brown Green Green Gray Gray Gray Gray Gray Gray Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Gray Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Gray Gray Gray Gray Gray Gray Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue Green Green Gray Gray Gray Gray Gray Gray Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue Green Green Gray Gray Gray Gray Gray Gray Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue Green Green Green Green Green Green Green Green Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue Green Purple Purple Purple Purple Purple Purple Green Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue Green Purple Purple Purple Purple Purple Purple Green Green Green
Green Green Green Blue Blue Blue Blue Blue Blue Blue 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 |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue 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
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 23: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange 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 Orange 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 Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange 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 Orange 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 Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange 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 Orange 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange 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 Orange 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 Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 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 Orange 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 Orange 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 Orange Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange 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 Orange 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Purple Purple Purple Purple Purple Purple Purple Purple
Example 3
Input:
Row 1: Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 6: Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Brown Brown Brown Brown
Row 8: Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 10: Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 11: Gray Brown Gray Gray Gray Brown Brown Brown Brown
Row 12: Gray Brown Gray Gray Gray Brown Gray Brown Gray
Row 13: Gray Brown Gray Gray Gray Brown Gray Brown Gray
Row 14: Gray Brown Gray Gray Gray Brown Gray Brown Gray
Row 15: Brown Brown Brown Brown Brown Brown Gray Brown Gray
Row 16: Gray Gray Brown Gray Gray Brown Gray Brown Gray
Row 17: Brown Brown Brown Gray Gray Brown Gray Brown Gray
Row 18: Gray Gray Brown Gray Gray Brown Gray Brown Gray
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Gray Gray Gray Brown Gray Gray Gray Gray Gray
Row 21: Gray Gray Gray Brown Gray Gray Gray Gray Gray
Row 22: Gray Gray Gray Brown Brown Brown Brown Brown Brown
Row 23: Gray Gray Gray Brown Gray Gray Gray Gray Gray
Row 24: Gray Gray Gray Brown Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Brown Gray Gray Gray Gray
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Gray Gray Gray Gray Gray Brown Gray Gray Gray
Row 6: Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 7: Blue Blue Blue Blue Blue Brown Brown Brown Brown
Row 8: Blue Blue Blue Blue Blue Brown Gray Gray Gray
Row 9: Blue Blue Blue Blue Blue Brown Gray Gray Gray
Row 10: Brown Brown Brown Brown Brown Brown Gray Gray Gray
Row 11: Gray Brown Gray Gray Gray Brown Brown Brown Brown
Row 12: Gray Brown Gray Gray Gray Brown Gray Brown Gray
Row 13: Gray Brown Gray Gray Gray Brown Gray Brown Gray
Row 14: Gray Brown Gray Gray Gray Brown Gray Brown Gray
Row 15: Brown Brown Brown Brown Brown Brown Gray Brown Gray
Row 16: Purple Purple Brown Gray Gray Brown Gray Brown Gray
Row 17: Brown Brown Brown Gray Gray Brown Gray Brown Gray
Row 18: Purple Purple Brown Gray Gray Brown Gray Brown Gray
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Blue Blue Blue Brown Gray Gray Gray Gray Gray
Row 21: Blue Blue Blue Brown Gray Gray Gray Gray Gray
Row 22: Blue Blue Blue Brown Brown Brown Brown Brown Brown
Row 23: Blue Blue Blue Brown Gray Gray Gray Gray Gray
Row 24: Blue Blue Blue Brown Gray Gray Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Pink Black Pink Black Pink Pink
Row 2: Black Black Pink Black Pink Pink
Row 3: Pink Black Pink Black Pink Pink
Row 4: Pink Black Pink Black Pink Pink
Row 5: Black Black Black Black Black Black
Row 6: Pink Pink Pink Pink Pink Pink
Row 7: Pink Pink Pink Pink Pink Pink
Row 8: Black Black Black Black Black Black
Row 9: Pink Pink Pink Black Pink Pink
Row 10: Pink Pink Pink Black Black Black
Row 11: Pink Pink Pink Black Pink Pink
Row 12: Black Black Black Black Black Black
Row 13: Pink Black Pink Black Pink Pink
Row 14: Black Black Black Black Black Black
Row 15: Pink Pink Black Pink Pink Pink
Row 16: Pink Pink Black Pink Pink Pink
Row 17: Black Black Black Black Black Black
Row 18: Pink Black Pink Pink 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 Black Pink Black Pink Pink
Black Black Pink Black Pink Pink
Pink Black Pink Black Pink Pink
Pink Black Pink Black Pink Pink
Black Black Black Black Black Black
Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue
Black Black Black Black Black Black
Pink Pink Pink Black Pink Pink
Pink Pink Pink Black Black Black
Pink Pink Pink Black Pink Pink
Black Black Black Black Black Black
Purple Black Purple Black Pink Pink
Black Black Black Black Black Black
Pink Pink Black Pink Pink Pink
Pink Pink Black Pink Pink Pink
Black Black Black Black Black Black
Purple Black Pink Pink 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: Purple Purple Purple Black Purple Brown Purple
Row 2: Purple Purple Red Purple Black Brown Orange
Output:
Row 1: Purple Purple Purple Black Purple Brown Purple Purple Brown Purple Black Purple Purple Purple
Row 2: Purple Purple Red Purple Black Brown Orange Orange Brown Black Purple Red Purple Purple
Row 3: Purple Purple Red Purple Black Brown Orange Orange Brown Black Purple Red Purple Purple
Row 4: Purple Purple Purple Black Purple Brown Purple Purple Brown Purple Black Purple Purple Purple
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow
Row 3: Yellow Yellow Purple Yellow Yellow
Row 4: Yellow Yellow Brown Yellow Purple
Row 5: Yellow Yellow Purple Blue Pink
Row 6: Black Blue Purple Gray Yellow
Output:
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 Purple Yellow Yellow Yellow Yellow Purple Yellow Yellow
Row 4: Yellow Yellow Brown Yellow Purple Purple Yellow Brown Yellow Yellow
Row 5: Yellow Yellow Purple Blue Pink Pink Blue Purple Yellow Yellow
Row 6: Black Blue Purple Gray Yellow Yellow Gray Purple Blue Black
Row 7: Black Blue Purple Gray Yellow Yellow Gray Purple Blue Black
Row 8: Yellow Yellow Purple Blue Pink Pink Blue Purple Yellow Yellow
Row 9: Yellow Yellow Brown Yellow Purple Purple Yellow Brown Yellow Yellow
Row 10: Yellow Yellow Purple Yellow Yellow Yellow Yellow Purple 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
Example 3
Input:
Row 1: Gray Green Gray Red Black Blue Gray Black
Row 2: Green Gray Red Red Green Red Black Gray
Row 3: Green Red Black Black Red Green Gray Red
Row 4: Red Red Gray Gray Green Black Red Gray
Row 5: Red Gray Gray Black Black Black Gray Black
Row 6: Black Black Green Green Red Red Black Red
Output:
Row 1: Gray Green Gray Red Black Blue Gray Black Black Gray Blue Black Red Gray Green Gray
Row 2: Green Gray Red Red Green Red Black Gray Gray Black Red Green Red Red Gray Green
Row 3: Green Red Black Black Red Green Gray Red Red Gray Green Red Black Black Red Green
Row 4: Red Red Gray Gray Green Black Red Gray Gray Red Black Green Gray Gray Red Red
Row 5: Red Gray Gray Black Black Black Gray Black Black Gray Black Black Black Gray Gray Red
Row 6: Black Black Green Green Red Red Black Red Red Black Red Red Green Green Black Black
Row 7: Black Black Green Green Red Red Black Red Red Black Red Red Green Green Black Black
Row 8: Red Gray Gray Black Black Black Gray Black Black Gray Black Black Black Gray Gray Red
Row 9: Red Red Gray Gray Green Black Red Gray Gray Red Black Green Gray Gray Red Red
Row 10: Green Red Black Black Red Green Gray Red Red Gray Green Red Black Black Red Green
Row 11: Green Gray Red Red Green Red Black Gray Gray Black Red Green Red Red Gray Green
Row 12: Gray Green Gray Red Black Blue Gray Black Black Gray Blue Black Red Gray Green Gray
Here is the input grid for the test example:
Input:
Row 1: Red Pink Purple Green Brown Pink Blue Yellow Yellow Green Black
Row 2: Green Red Orange Orange Purple Yellow Pink Green Yellow Purple Purple
Row 3: Red Green Yellow Orange Black Green Purple Black Purple Red Brown
Row 4: Orange Brown Purple Black Red Brown Black Purple Purple Red Pink
Row 5: Red Pink Orange Orange Green Orange Purple Red Blue Brown Yellow
Row 6: Black Yellow Green Orange Green Orange Orange Brown Pink Blue Pink
Row 7: Brown Red Black Black Black Red Red Brown Pink Black Yellow
Row 8: Orange Pink Purple Black Red Red Orange Green Yellow Orange Yellow
Row 9: Yellow Black Red Orange Black Pink Red Purple Pink Pink Red
Row 10: Green Red Purple Green Orange Brown Blue Pink Orange Orange Yellow
Row 11: Yellow Pink Purple Yellow Yellow Purple Purple Black Green Brown Black
Row 12: Red Yellow Yellow Pink Black Black Brown Yellow Black Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Pink Purple Green Brown Pink Blue Yellow Yellow Green Black Black Green Yellow Yellow Blue Pink Brown Green Purple Pink Red
Green Red Orange Orange Purple Yellow Pink Green Yellow Purple Purple Purple Purple Yellow Green Pink Yellow Purple Orange Orange Red Green
Red Green Yellow Orange Black Green Purple Black Purple Red Brown Brown Red Purple Black Purple Green Black Orange Yellow Green Red
Orange Brown Purple Black Red Brown Black Purple Purple Red Pink Pink Red Purple Purple Black Brown Red Black Purple Brown Orange
Red Pink Orange Orange Green Orange Purple Red Blue Brown Yellow Yellow Brown Blue Red Purple Orange Green Orange Orange Pink Red
Black Yellow Green Orange Green Orange Orange Brown Pink Blue Pink Pink Blue Pink Brown Orange Orange Green Orange Green Yellow Black
Brown Red Black Black Black Red Red Brown Pink Black Yellow Yellow Black Pink Brown Red Red Black Black Black Red Brown
Orange Pink Purple Black Red Red Orange Green Yellow Orange Yellow Yellow Orange Yellow Green Orange Red Red Black Purple Pink Orange
Yellow Black Red Orange Black Pink Red Purple Pink Pink Red Red Pink Pink Purple Red Pink Black Orange Red Black Yellow
Green Red Purple Green Orange Brown Blue Pink Orange Orange Yellow Yellow Orange Orange Pink Blue Brown Orange Green Purple Red Green
Yellow Pink Purple Yellow Yellow Purple Purple Black Green Brown Black Black Brown Green Black Purple Purple Yellow Yellow Purple Pink Yellow
Red Yellow Yellow Pink Black Black Brown Yellow Black Brown Brown Brown Brown Black Yellow Brown Black Black Pink Yellow Yellow Red
Red Yellow Yellow Pink Black Black Brown Yellow Black Brown Brown Brown Brown Black Yellow Brown Black Black Pink Yellow Yellow Red
Yellow Pink Purple Yellow Yellow Purple Purple Black Green Brown Black Black Brown Green Black Purple Purple Yellow Yellow Purple Pink Yellow
Green Red Purple Green Orange Brown Blue Pink Orange Orange Yellow Yellow Orange Orange Pink Blue Brown Orange Green Purple Red Green
Yellow Black Red Orange Black Pink Red Purple Pink Pink Red Red Pink Pink Purple Red Pink Black Orange Red Black Yellow
Orange Pink Purple Black Red Red Orange Green Yellow Orange Yellow Yellow Orange Yellow Green Orange Red Red Black Purple Pink Orange
Brown Red Black Black Black Red Red Brown Pink Black Yellow Yellow Black Pink Brown Red Red Black Black Black Red Brown
Black Yellow Green Orange Green Orange Orange Brown Pink Blue Pink Pink Blue Pink Brown Orange Orange Green Orange Green Yellow Black
Red Pink Orange Orange Green Orange Purple Red Blue Brown Yellow Yellow Brown Blue Red Purple Orange Green Orange Orange Pink Red
Orange Brown Purple Black Red Brown Black Purple Purple Red Pink Pink Red Purple Purple Black Brown Red Black Purple Brown Orange
Red Green Yellow Orange Black Green Purple Black Purple Red Brown Brown Red Purple Black Purple Green Black Orange Yellow Green Red
Green Red Orange Orange Purple Yellow Pink Green Yellow Purple Purple Purple Purple Yellow Green Pink Yellow Purple Orange Orange Red Green
Red Pink Purple Green Brown Pink Blue Yellow Yellow Green Black Black Green Yellow Yellow Blue Pink Brown Green Purple Pink 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 Black Black Red
Row 2: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 3: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 4: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 5: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 6: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 7: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 8: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 9: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 10: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 11: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 12: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange
Row 19: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 20: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 21: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 22: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 23: Red Red Red Red Red Red Red Red Red Red Black Black Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 2: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 3: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 4: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 5: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 6: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 7: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 8: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 9: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 10: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 11: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 12: Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow
Row 13: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Black Black Yellow
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Black Black Yellow
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Black Black Yellow
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Black Black Yellow
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Black Black Yellow
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Black Black Yellow
Row 19: Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow
Row 20: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 21: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 22: Red Red Red Red Red Red Red Red Red Red Black Black Red
Row 23: Red Red Red Red Red Red Red Red Red Red Black Black Red
Example 2
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Blue 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 Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Blue Blue 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 Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Blue 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 Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Blue Blue Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Blue Blue Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Blue Blue Yellow Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Green Green Green Green Green Green Green Green Green Yellow Yellow Yellow Yellow Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 20: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 21: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 24: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 25: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Row 26: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 2: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 3: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 4: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 5: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 6: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 7: Purple Purple Purple Pink Pink Purple Purple Purple Purple
Row 8: Purple Purple Purple Pink Pink Purple Purple Purple Purple
Row 9: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 10: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 11: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 12: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 13: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 2: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 3: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 4: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 5: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 6: Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue
Row 7: Purple Purple Yellow Pink Pink Yellow Purple Purple Purple
Row 8: Purple Purple Yellow Pink Pink Yellow Purple Purple Purple
Row 9: Blue Blue Yellow Yellow Yellow Yellow Blue Blue Blue
Row 10: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 11: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 12: Blue Blue Blue Pink Pink Blue Blue Blue Blue
Row 13: Blue Blue Blue Pink Pink Blue Blue Blue Blue
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 Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown Orange Orange Orange
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown Brown Brown 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 Brown Brown 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 Brown Brown 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 Brown Brown 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 Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Yellow Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Yellow Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Yellow Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Red Red Red Red Yellow Red Red
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange
Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Brown 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 Brown Brown 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 Brown Brown Brown Brown 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: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 3: Red Red Red Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray
Row 4: Red Red Red Gray Purple Purple Purple Gray Gray Purple Purple Gray Purple
Row 5: Red Red Red Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple
Row 6: Red Red Red Purple Gray Gray Purple Purple Purple Purple Purple Gray Purple
Row 7: Red Red Red Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Gray Purple Purple Purple Purple Gray Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray
Row 3: Gray Purple Purple Purple Gray Gray Purple Purple Gray Purple
Row 4: Purple Purple Purple Purple Purple Gray Purple Purple Gray Purple
Row 5: Purple Gray Gray Purple Purple Purple Purple Purple Gray Purple
Row 6: Purple Purple Gray Purple Purple Purple Gray Purple Purple Purple
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Pink Purple Purple Pink Purple Purple Purple Pink Purple Brown Brown Brown Brown
Row 3: Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown
Row 4: Brown Brown Pink Purple Purple Purple Pink Purple Pink Purple Pink Brown Brown Brown Brown
Row 5: Brown Brown Purple Purple Purple Purple Purple Purple Purple Pink Purple Brown Brown Brown Brown
Row 6: Brown Brown Pink Purple Purple Purple Purple Purple Purple Pink Purple Brown Brown Brown Brown
Row 7: Brown Brown Pink Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown Brown Brown
Row 8: Brown Brown Purple Pink Purple Pink Purple Pink Pink Purple Pink Brown Brown Brown Brown
Row 9: 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
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Pink Purple Purple Pink Purple Purple Purple Pink Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Pink Purple Purple Purple Pink Purple Pink Purple Pink
Row 4: Purple Purple Purple Purple Purple Purple Purple Pink Purple
Row 5: Pink Purple Purple Purple Purple Purple Purple Pink Purple
Row 6: Pink Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Pink Purple Pink Purple Pink Pink Purple Pink
Example 3
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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 Yellow Yellow Yellow Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Gray Gray Yellow Gray Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Yellow Gray Gray Yellow Gray Gray Gray Yellow Gray Yellow Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Yellow Gray Gray Gray Gray Yellow Yellow Gray Gray Gray 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Yellow Gray Gray Yellow Gray Gray Gray Yellow Gray Yellow
Row 2: Yellow Gray Gray Gray Gray Yellow Yellow Gray Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange Orange Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Black Yellow Black Yellow Black Yellow Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Yellow Yellow Black Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow 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
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 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 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
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 Orange
Row 10: Orange Orange Orange Orange Orange Orange Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Black Black Yellow Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Yellow Yellow Black Yellow Yellow Yellow Black Black Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Yellow Yellow Yellow Yellow Yellow 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 Orange Orange Orange Orange
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Black Yellow Black Yellow Black Yellow
Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Black Yellow Yellow Black Yellow Yellow Yellow
Yellow Yellow Yellow Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Black 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: Pink Pink Pink Pink Pink Green Pink Pink Pink Pink Green Pink Green Pink Green Green Pink Orange Blue Pink Green Green Orange Pink Pink Pink Pink Orange Pink
Row 2: Pink Pink Orange Orange Pink Pink Pink Pink Green Orange Pink Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink Orange Pink Pink
Row 3: Green Pink Orange Orange Orange Green Pink Pink Green Orange Orange Pink Green Pink Orange Pink Pink Pink Orange Pink Orange Pink Pink Pink Pink Green Pink Pink Pink
Row 4: Pink Pink Blue Orange Orange Pink Pink Green Pink Orange Orange Pink Pink Orange Orange Pink Green Pink Pink Pink Green Pink Pink Green Pink Green Orange Pink Pink
Row 5: Orange Orange Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Orange Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Green Orange Orange Pink Pink Pink
Row 6: Pink Pink Green Pink Pink Pink Pink Pink Pink Pink Orange Pink Pink Pink Orange Orange Green Green Orange Pink Green Orange Orange Pink Pink Green Pink Pink Green
Output:
Row 1: Red Red Pink
Row 2: Pink Pink Pink
Row 3: Pink Pink Pink
Example 2
Input:
Row 1: Yellow Yellow Green Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Pink
Row 2: Yellow Pink Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Green Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Pink
Row 3: Yellow Yellow Yellow Orange Yellow Pink Yellow Blue Orange Yellow Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow
Row 4: Yellow Yellow Yellow Orange 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 Pink Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow
Row 6: Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Green Yellow Orange Yellow Yellow Yellow Yellow Yellow Blue Yellow Green Pink
Row 7: Pink Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Orange Green Yellow Yellow Yellow Orange Yellow Yellow
Row 8: Yellow Green Yellow Orange Green Orange Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Yellow Green Yellow Yellow Pink Pink Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Green Yellow Yellow Yellow Orange Orange Yellow Orange Yellow Green Yellow Yellow Yellow Orange Yellow
Row 10: Yellow Orange Yellow Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Green Orange Yellow Green Green Yellow Green Yellow Yellow Yellow Green
Row 11: Orange Yellow Yellow Yellow Yellow Green Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Orange Yellow Yellow Yellow Yellow Orange Yellow
Row 12: Yellow Yellow Yellow Yellow Green Yellow Yellow Blue Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Pink Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Pink Yellow Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Green Yellow Yellow Pink Green Yellow Orange Yellow Yellow Yellow Yellow Yellow
Row 15: Yellow Orange Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 16: Yellow Yellow Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Green Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green
Row 17: Green Yellow Yellow Yellow Yellow Yellow Pink Pink Yellow Yellow Green Yellow Orange Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow Green Yellow
Row 18: Yellow Green Yellow Yellow Blue Yellow Yellow Pink Yellow Pink Yellow Yellow Yellow Green Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Red Red Red
Row 2: Yellow Red Yellow
Row 3: Yellow Yellow Yellow
Example 3
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Black Brown Orange Brown Yellow Orange Orange Pink Orange Orange Orange Orange Orange Orange
Row 2: Gray Orange Orange Gray Orange Gray Orange Black Yellow Orange Orange Orange Green Orange Yellow Orange Orange Brown Orange Orange Green
Row 3: Orange Orange Pink Orange Brown Brown Orange Orange Gray Gray Black Orange Orange Orange Orange Orange Green Orange Orange Green Orange
Row 4: Green Orange Green Green Orange Orange Orange Pink Orange Gray Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange
Row 5: Orange Green Orange Black Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Gray Orange Orange Orange
Row 6: Black Yellow Gray Orange Orange Orange Orange Green Blue Orange Orange Pink Green Brown Orange Orange Orange Pink Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Gray Orange Gray Orange Orange Orange Black Orange Orange Orange Orange Black Orange Orange Orange
Row 8: Orange Orange Black Gray Orange Pink Orange Gray Orange Green Orange Orange Orange Orange Orange Pink Orange Orange Orange Gray Gray
Row 9: Gray Orange Orange Gray Orange Black Gray Orange Orange Orange Green Pink Orange Black Black Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Pink Black Orange Orange Orange Orange Orange Orange Orange Orange Black Black Orange Orange Orange Orange Orange
Row 11: Orange Orange Gray Orange Brown Orange Yellow Orange Yellow Orange Yellow Orange Orange Gray Orange Yellow Orange Orange Orange Pink Orange
Row 12: Black Orange Orange Orange Pink Orange Orange Blue Pink Orange Pink Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 13: Orange Blue Orange Orange Orange Brown Orange Orange Pink Orange Orange Black Orange Orange Orange Orange Pink Orange Yellow Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Brown Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Black Orange Orange Green Gray Green
Row 16: Orange Orange Green Orange Black Orange Orange Gray Orange Orange Green Orange Orange Orange Orange Gray Orange Green Green Orange Orange
Row 17: Gray Yellow Gray Green Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Green Orange Brown
Row 18: Orange Orange Gray Black Pink Orange Orange Yellow Orange Green Brown Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange
Row 19: Orange Green Orange Yellow Orange Orange Green Orange Brown Orange Orange Orange Orange Orange Green Orange Orange Pink Yellow Orange Gray
Row 20: Orange Brown Gray Orange Orange Orange Brown Orange Orange Orange Brown Orange Orange Orange Pink Orange Orange Orange Brown Orange Orange
Row 21: Orange Orange Brown 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 Green Orange Black Orange Orange Orange Orange Pink Orange Orange Pink Orange Green Orange
Output:
Row 1: Red Red Red
Row 2: Orange Red Orange
Row 3: Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Gray Brown Brown Orange Brown
Row 2: Green Brown Pink Brown Brown Brown Brown Brown Brown Green Brown Green Brown Brown Purple Brown Brown Pink Purple Brown Brown Brown Brown
Row 3: Brown Brown Brown Gray Brown Brown Brown Gray Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Pink Pink Brown Brown Orange Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Green Brown Brown Pink Brown Green
Row 5: Brown Orange Brown Brown Brown Pink Brown Blue Brown Purple Orange Pink Brown Brown Brown Brown Yellow Brown Brown Gray Gray Brown Brown
Row 6: Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Purple Brown Brown Orange Brown Green Brown Green Brown
Row 7: Purple Brown Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Orange Brown Brown Gray
Row 8: Brown Brown Gray Brown Green Green Brown Brown Brown Gray Brown Yellow Brown Brown Gray Purple Brown Gray Brown Green Brown Brown Brown
Row 9: Brown Brown Orange Brown Green Green Brown Pink Brown Brown Brown Gray Brown Brown Brown Brown Gray Brown Brown Brown Green Brown Gray
Row 10: Brown Green Brown Brown Brown Green Orange Brown Brown Purple Brown Brown Purple Yellow Brown Pink Brown Purple Green Brown Brown Brown Brown
Row 11: Purple Brown Brown Gray Brown Brown Green Yellow Brown Green Brown Brown Brown Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Yellow Brown Yellow Brown Brown Brown Orange Brown Brown Orange Brown Brown Brown Brown Brown Brown Gray Brown Brown Brown Brown Orange
Row 13: Green Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Green Brown Yellow Brown Green
Row 14: Brown Brown Brown Purple Brown Brown Brown Brown Brown Brown Purple Pink Green Brown Brown Brown Gray Brown Brown Brown Yellow Brown Brown
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red 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: Gray Gray Blue Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Blue Blue Gray Gray Gray Gray Blue Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Blue Blue Gray Gray Gray Gray Blue Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
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: Gray Gray Blue Blue Blue Blue Gray Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Blue Blue Gray Gray Gray Gray Blue Gray Blue Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray
Row 7: Gray Gray Blue Blue Gray Blue Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Gray Gray Blue Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 10: Gray Gray Blue Blue Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Red Red Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Red Red Gray Gray Gray Gray Red Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Red Red Gray Gray Gray Gray Red Gray Blue Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Gray Gray Red Red Blue Blue Gray Gray Red Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Red Red Gray Gray Gray Gray Red Gray Blue Gray Gray Blue Gray Gray Gray Gray Blue Gray Gray Gray
Row 7: Gray Gray Red Red Gray Blue Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
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: Gray Gray Red Red Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray
Row 10: Gray Gray Red Red Gray Gray Gray Gray Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Example 2
Input:
Row 1: Purple Black Black Black Purple Purple Purple Black Purple Purple Purple Black
Row 2: Purple Purple Black Black Purple Black Purple Purple Purple Purple Purple Black
Row 3: Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Black
Row 4: Purple Black Purple Purple Purple Purple Purple Black Purple Purple Purple Black
Row 5: Purple Black Purple Purple Purple Purple Purple Purple Black Black Purple Black
Row 6: Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Black
Row 7: Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Black
Row 9: Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Black
Row 10: Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Black
Row 11: Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple Black
Row 13: Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Black
Row 14: Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Black
Row 15: Black Black Black Black Black Black Black Black Black Black Black Black
Row 16: Black Purple Black Black Purple Purple Purple Purple Black Purple Purple Black
Output:
Row 1: Purple Black Black Black Purple Purple Purple Black Purple Purple Purple Red
Row 2: Purple Purple Black Black Purple Black Purple Purple Purple Purple Purple Red
Row 3: Purple Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Red
Row 4: Purple Black Purple Purple Purple Purple Purple Black Purple Purple Purple Red
Row 5: Purple Black Purple Purple Purple Purple Purple Purple Black Black Purple Red
Row 6: Purple Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Purple Purple Purple Purple Purple Purple Black Black Purple Purple Purple Red
Row 9: Purple Purple Purple Black Purple Purple Purple Purple Black Purple Purple Red
Row 10: Black Purple Purple Purple Purple Black Black Purple Black Purple Purple Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Purple Black Purple Black Purple Purple Purple Purple Purple Purple Purple Red
Row 13: Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Red
Row 14: Purple Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Black Purple Black Black Purple Purple Purple Purple Black Purple Purple Red
Example 3
Input:
Row 1: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Orange Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple
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: Purple Purple Purple Orange Purple Orange Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange
Row 5: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Orange Orange Purple Purple Purple Purple Orange
Row 6: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Orange Purple
Row 7: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Orange Purple Purple Purple
Row 8: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Orange Purple
Row 9: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Orange Purple Purple Purple
Row 12: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 15: Orange Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Orange Purple Purple
Row 16: Purple Purple Purple Orange Purple Purple Purple Orange Purple Orange Purple Purple Orange Orange Purple Purple Purple Purple Purple Orange Purple
Output:
Row 1: Purple Purple Purple Red Purple Purple Purple Red Purple Red Orange Purple Red Red Purple Purple Purple Purple Purple Purple Purple
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Purple Purple Purple Red Purple Orange Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Orange Red Red Orange Purple Purple Purple Purple Orange Orange
Row 5: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Orange Orange Purple Purple Purple Purple Orange
Row 6: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Orange Purple
Row 7: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Orange Purple Purple Purple
Row 8: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Orange Purple
Row 9: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red 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
Row 11: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Orange Purple Purple Purple
Row 12: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Orange Red Red Purple Purple Purple Purple Purple Purple Purple
Row 15: Orange Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Orange Purple Purple
Row 16: Purple Purple Purple Red Purple Purple Purple Red Purple Red Purple Purple Red Red Purple Purple Purple Purple Purple Orange Purple
Here is the input grid for the test example:
Input:
Row 1: Green Purple Purple Purple Green Green Green Green Green Green Purple Green Green Purple Green Green Green Green Green
Row 2: Green Purple Purple Purple Green Purple Green Purple Green Green Green Purple Purple Green Green Purple Purple Green Green
Row 3: Purple Purple Purple Purple Green Green Green Purple Green Green Green Green Green Purple Green Green Green Green Green
Row 4: Green Purple Purple Purple Green Green Green Green Green Purple Purple Green Green Green Purple Purple Green Green Green
Row 5: Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Green
Row 6: Green Purple Purple Purple Green Green Green Green Purple Purple Green Purple Green Green Green Green Green Green Green
Row 7: Green Purple Purple Purple Green Purple Green Green Green Green Green Purple Purple Green Green Green Green Green Green
Row 8: Green Purple Purple Purple Green Green Purple Green Green Purple Green Green Green Green Purple Green Green Green Green
Row 9: Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green
Row 10: Green Purple Purple Purple Green Green Purple Green Purple Green Green Green Purple Green Green Green Green Green Green
Row 11: Green Purple Purple Purple Green Green Purple Green Purple Green Green Purple Green Green Green Green Green Green Purple
Row 12: Green Purple Purple Purple Purple Green Purple Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Purple Purple Purple Green Purple Green Green Green Green Purple Green Green Green Green Green Green Green Green
Row 14: Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Green Purple Purple Purple Green Green Green Green Purple Green Green Purple Green Purple Green Purple Green Green Purple
Row 17: Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green
Row 18: Purple Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: Green Purple Purple Purple Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green
Row 20: Purple Purple Purple Purple Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green
Row 21: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 22: Green Purple Purple Purple Green Green Green Green Purple Green Purple Green Green Green Green Purple Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Red Red Red Green Green Green Green Green Green Purple Green Green Purple Green Green Green Green Green
Green Red Red Red Green Purple Green Purple Green Green Green Purple Purple Green Green Purple Purple Green Green
Purple Red Red Red Green Green Green Purple Green Green Green Green Green Purple Green Green Green Green Green
Green Red Red Red Green Green Green Green Green Purple Purple Green Green Green Purple Purple Green Green Green
Green Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Purple Purple Green
Green Red Red Red Green Green Green Green Purple Purple Green Purple Green Green Green Green Green Green Green
Green Red Red Red Green Purple Green Green Green Green Green Purple Purple Green Green Green Green Green Green
Green Red Red Red Green Green Purple Green Green Purple Green Green Green Green Purple Green Green Green Green
Green Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Purple Green
Green Red Red Red Green Green Purple Green Purple Green Green Green Purple Green Green Green Green Green Green
Green Red Red Red Green Green Purple Green Purple Green Green Purple Green Green Green Green Green Green Purple
Green Red Red Red Purple Green Purple Green Green Green Green Green Green Green Green Green Green Green Green
Green Red Red Red Green Purple Green Green Green Green Purple Green Green Green Green Green Green Green Green
Green Red Red Red Green Green Green Green Green Green Green Green Green Purple Green Green Green Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Red Red Red Green Green Green Green Purple Green Green Purple Green Purple Green Purple Green Green Purple
Green Red Red Red Green Green Green Green Green Green Green Green Green Green Purple Green Green Green Green
Purple Red Red Red Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Red Red Red Green Green Green Green Green Green Green Green Green Green Green Purple Green Green Green
Purple Red Red Red Green Green Green Green Green Green Green Green Purple Green Green Green Green Green Green
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Green Red Red Red Green Green Green Green Purple Green Purple Green Green Green Green Purple 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 Gray Gray Gray Gray Brown Black Yellow Blue
Row 2: Gray Pink Gray Gray Gray Purple Gray Gray Red
Row 3: Gray Purple Brown Black Yellow Gray Blue Gray Gray
Row 4: Gray Gray Purple Gray Black Gray Blue Orange Gray
Row 5: Pink Gray Gray Pink Gray Gray Gray Gray Gray
Output:
Row 1: Purple Gray Gray Gray Gray Brown Black Yellow Blue
Row 2: Gray Pink Gray Gray Gray Purple Gray Gray Red
Row 3: Gray Purple Brown Black Yellow Gray Blue Gray Gray
Row 4: Gray Gray Purple Gray Black Gray Blue Orange Gray
Row 5: Pink Gray Gray Pink Gray Gray Gray Gray Gray
Row 6: Pink Gray Gray Pink Gray Gray Gray Gray Gray
Row 7: Gray Gray Purple Gray Black Gray Blue Orange Gray
Row 8: Gray Purple Brown Black Yellow Gray Blue Gray Gray
Row 9: Gray Pink Gray Gray Gray Purple Gray Gray Red
Row 10: Purple Gray Gray Gray Gray Brown Black Yellow Blue
Example 2
Input:
Row 1: Pink Yellow Green Yellow Pink Green Yellow Yellow Green Green Gray Gray Gray Green Green Yellow Green Green Green Green Green Pink Pink Yellow Green Green
Row 2: Yellow Yellow Green Green Green Yellow Green Pink Pink Yellow Green Yellow Green Green Green Pink Green Gray Green Green Yellow Green Green Pink Yellow Pink
Row 3: Yellow Green Green Green Yellow Green Green Pink Green Yellow Pink Green Pink Green Pink Green Yellow Green Green Yellow Yellow Green Green Green Yellow Green
Row 4: Yellow Green Pink Green Gray Pink Yellow Yellow Green Green Green Green Green Yellow Green Yellow Green Yellow Yellow Yellow Green Yellow Green Green Pink Green
Row 5: Green Yellow Green Pink Pink Green Green Pink Green Pink Pink Gray Green Gray Green Yellow Green Green Yellow Yellow Green Yellow Green Yellow Pink Green
Row 6: Green Yellow Gray Gray Green Pink Green Green Green Green Green Yellow Gray Yellow Green Pink Yellow Green Green Green Green Yellow Gray Green Green Green
Row 7: Green Green Green Green Yellow Gray Green Pink Green Green Green Green Yellow Green Green Yellow Green Yellow Green Green Yellow Green Gray Pink Green Green
Row 8: Green Green Yellow Green Green Green Green Green Yellow Green Yellow Pink Gray Green Green Green Green Yellow Green Green Green Pink Green Green Yellow Green
Row 9: Green Green Green Yellow Gray Green Green Green Yellow Yellow Yellow Green Yellow Green Yellow Green Gray Green Green Yellow Green Green Yellow Green Green Green
Row 10: Yellow Green Yellow Green Green Green Yellow Yellow Yellow Green Green Green Yellow Green Green Green Yellow Yellow Green Pink Yellow Yellow Green Yellow Green Green
Row 11: Green Green Green Green Green Green Green Green Green Gray Pink Green Pink Pink Green Yellow Green Green Yellow Green Green Green Green Green Yellow Green
Row 12: Gray Green Green Pink Green Pink Green Yellow Green Green Green Gray Yellow Green Pink Green Green Green Green Green Green Green Green Green Green Yellow
Row 13: Yellow Pink Green Pink Green Green Green Pink Green Yellow Green Gray Green Yellow Pink Yellow Green Yellow Green Green Green Yellow Yellow Green Green Yellow
Row 14: Gray Yellow Green Green Green Green Green Pink Green Yellow Green Green Green Yellow Yellow Green Gray Pink Green Green Pink Pink Green Green Green Green
Row 15: Pink Green Green Green Green Green Yellow Green Green Green Green Yellow Pink Pink Yellow Yellow Gray Green Pink Yellow Pink Green Yellow Green Green Green
Output:
Row 1: Pink Yellow Green Yellow Pink Green Yellow Yellow Green Green Gray Gray Gray Green Green Yellow Green Green Green Green Green Pink Pink Yellow Green Green
Row 2: Yellow Yellow Green Green Green Yellow Green Pink Pink Yellow Green Yellow Green Green Green Pink Green Gray Green Green Yellow Green Green Pink Yellow Pink
Row 3: Yellow Green Green Green Yellow Green Green Pink Green Yellow Pink Green Pink Green Pink Green Yellow Green Green Yellow Yellow Green Green Green Yellow Green
Row 4: Yellow Green Pink Green Gray Pink Yellow Yellow Green Green Green Green Green Yellow Green Yellow Green Yellow Yellow Yellow Green Yellow Green Green Pink Green
Row 5: Green Yellow Green Pink Pink Green Green Pink Green Pink Pink Gray Green Gray Green Yellow Green Green Yellow Yellow Green Yellow Green Yellow Pink Green
Row 6: Green Yellow Gray Gray Green Pink Green Green Green Green Green Yellow Gray Yellow Green Pink Yellow Green Green Green Green Yellow Gray Green Green Green
Row 7: Green Green Green Green Yellow Gray Green Pink Green Green Green Green Yellow Green Green Yellow Green Yellow Green Green Yellow Green Gray Pink Green Green
Row 8: Green Green Yellow Green Green Green Green Green Yellow Green Yellow Pink Gray Green Green Green Green Yellow Green Green Green Pink Green Green Yellow Green
Row 9: Green Green Green Yellow Gray Green Green Green Yellow Yellow Yellow Green Yellow Green Yellow Green Gray Green Green Yellow Green Green Yellow Green Green Green
Row 10: Yellow Green Yellow Green Green Green Yellow Yellow Yellow Green Green Green Yellow Green Green Green Yellow Yellow Green Pink Yellow Yellow Green Yellow Green Green
Row 11: Green Green Green Green Green Green Green Green Green Gray Pink Green Pink Pink Green Yellow Green Green Yellow Green Green Green Green Green Yellow Green
Row 12: Gray Green Green Pink Green Pink Green Yellow Green Green Green Gray Yellow Green Pink Green Green Green Green Green Green Green Green Green Green Yellow
Row 13: Yellow Pink Green Pink Green Green Green Pink Green Yellow Green Gray Green Yellow Pink Yellow Green Yellow Green Green Green Yellow Yellow Green Green Yellow
Row 14: Gray Yellow Green Green Green Green Green Pink Green Yellow Green Green Green Yellow Yellow Green Gray Pink Green Green Pink Pink Green Green Green Green
Row 15: Pink Green Green Green Green Green Yellow Green Green Green Green Yellow Pink Pink Yellow Yellow Gray Green Pink Yellow Pink Green Yellow Green Green Green
Row 16: Pink Green Green Green Green Green Yellow Green Green Green Green Yellow Pink Pink Yellow Yellow Gray Green Pink Yellow Pink Green Yellow Green Green Green
Row 17: Gray Yellow Green Green Green Green Green Pink Green Yellow Green Green Green Yellow Yellow Green Gray Pink Green Green Pink Pink Green Green Green Green
Row 18: Yellow Pink Green Pink Green Green Green Pink Green Yellow Green Gray Green Yellow Pink Yellow Green Yellow Green Green Green Yellow Yellow Green Green Yellow
Row 19: Gray Green Green Pink Green Pink Green Yellow Green Green Green Gray Yellow Green Pink Green Green Green Green Green Green Green Green Green Green Yellow
Row 20: Green Green Green Green Green Green Green Green Green Gray Pink Green Pink Pink Green Yellow Green Green Yellow Green Green Green Green Green Yellow Green
Row 21: Yellow Green Yellow Green Green Green Yellow Yellow Yellow Green Green Green Yellow Green Green Green Yellow Yellow Green Pink Yellow Yellow Green Yellow Green Green
Row 22: Green Green Green Yellow Gray Green Green Green Yellow Yellow Yellow Green Yellow Green Yellow Green Gray Green Green Yellow Green Green Yellow Green Green Green
Row 23: Green Green Yellow Green Green Green Green Green Yellow Green Yellow Pink Gray Green Green Green Green Yellow Green Green Green Pink Green Green Yellow Green
Row 24: Green Green Green Green Yellow Gray Green Pink Green Green Green Green Yellow Green Green Yellow Green Yellow Green Green Yellow Green Gray Pink Green Green
Row 25: Green Yellow Gray Gray Green Pink Green Green Green Green Green Yellow Gray Yellow Green Pink Yellow Green Green Green Green Yellow Gray Green Green Green
Row 26: Green Yellow Green Pink Pink Green Green Pink Green Pink Pink Gray Green Gray Green Yellow Green Green Yellow Yellow Green Yellow Green Yellow Pink Green
Row 27: Yellow Green Pink Green Gray Pink Yellow Yellow Green Green Green Green Green Yellow Green Yellow Green Yellow Yellow Yellow Green Yellow Green Green Pink Green
Row 28: Yellow Green Green Green Yellow Green Green Pink Green Yellow Pink Green Pink Green Pink Green Yellow Green Green Yellow Yellow Green Green Green Yellow Green
Row 29: Yellow Yellow Green Green Green Yellow Green Pink Pink Yellow Green Yellow Green Green Green Pink Green Gray Green Green Yellow Green Green Pink Yellow Pink
Row 30: Pink Yellow Green Yellow Pink Green Yellow Yellow Green Green Gray Gray Gray Green Green Yellow Green Green Green Green Green Pink Pink Yellow Green Green
Example 3
Input:
Row 1: Brown Brown Purple Yellow Brown Yellow Brown Pink Black Brown Pink Brown Gray Green Pink Brown Pink Brown Orange Brown Purple Yellow Red Green Yellow Brown Green Brown
Row 2: Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Black Brown Red Brown
Row 3: Brown Purple Brown Brown Pink Red Brown Brown Yellow Black Brown Green Brown Brown Brown Purple Green Green Brown Green Pink Red Brown Purple Black Brown Black Brown
Row 4: Brown Brown Brown Yellow Brown Yellow Green Black Brown Brown Purple Brown Purple Yellow Brown Brown Green Brown Brown Brown Pink Brown Red Brown Brown Pink Purple Brown
Row 5: Black Brown Purple Brown Red Brown Brown Brown Purple Black Brown Brown Red Black Black Brown Black Black Brown Brown Brown Brown Brown Brown Black Brown Brown Pink
Output:
Row 1: Brown Brown Purple Yellow Brown Yellow Brown Pink Black Brown Pink Brown Gray Green Pink Brown Pink Brown Orange Brown Purple Yellow Red Green Yellow Brown Green Brown
Row 2: Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Black Brown Red Brown
Row 3: Brown Purple Brown Brown Pink Red Brown Brown Yellow Black Brown Green Brown Brown Brown Purple Green Green Brown Green Pink Red Brown Purple Black Brown Black Brown
Row 4: Brown Brown Brown Yellow Brown Yellow Green Black Brown Brown Purple Brown Purple Yellow Brown Brown Green Brown Brown Brown Pink Brown Red Brown Brown Pink Purple Brown
Row 5: Black Brown Purple Brown Red Brown Brown Brown Purple Black Brown Brown Red Black Black Brown Black Black Brown Brown Brown Brown Brown Brown Black Brown Brown Pink
Row 6: Black Brown Purple Brown Red Brown Brown Brown Purple Black Brown Brown Red Black Black Brown Black Black Brown Brown Brown Brown Brown Brown Black Brown Brown Pink
Row 7: Brown Brown Brown Yellow Brown Yellow Green Black Brown Brown Purple Brown Purple Yellow Brown Brown Green Brown Brown Brown Pink Brown Red Brown Brown Pink Purple Brown
Row 8: Brown Purple Brown Brown Pink Red Brown Brown Yellow Black Brown Green Brown Brown Brown Purple Green Green Brown Green Pink Red Brown Purple Black Brown Black Brown
Row 9: Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Black Brown Red Brown
Row 10: Brown Brown Purple Yellow Brown Yellow Brown Pink Black Brown Pink Brown Gray Green Pink Brown Pink Brown Orange Brown Purple Yellow Red Green Yellow Brown Green Brown
Here is the input grid for the test example:
Input:
Row 1: Orange Red Orange Purple Orange Orange Black
Row 2: Orange Pink Orange Black Black Orange Orange
Row 3: Red Orange Orange Orange Brown Orange Blue
Row 4: Red Orange Orange Green Blue Pink Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Orange Red Orange Purple Orange Orange Black
Orange Pink Orange Black Black Orange Orange
Red Orange Orange Orange Brown Orange Blue
Red Orange Orange Green Blue Pink Purple
Red Orange Orange Green Blue Pink Purple
Red Orange Orange Orange Brown Orange Blue
Orange Pink Orange Black Black Orange Orange
Orange Red Orange Purple Orange Orange Black |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: 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
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Green Green Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Green Green Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Green Green Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Green Green Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Green Green 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
Row 12: 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
Output:
Row 1: 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
Row 3: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 5: Green Green Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 6: Green Green Purple Purple Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 7: Green Green Purple Purple Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 8: Green Green Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Pink Pink Pink Pink Pink
Row 9: Green Green Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Green Green 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
Row 12: 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
Example 2
Input:
Row 1: Black Black Black Green Green Green Green Green Green 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 Pink Pink Pink Pink Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Black Green Green Green Green Green Green 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 Purple Purple Purple 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 Pink Pink Pink Pink Pink Black Black Black Black Black Black Black 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 Orange Orange Orange
Row 2: Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Brown Brown Brown Brown 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
Row 2: Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Brown Brown Brown Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Green Green Green 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
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
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
Row 6: Blue Blue Blue Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Green Green Green 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 Purple 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 Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow 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
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue 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: Blue Blue Blue Blue Blue Blue 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 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 Blue Blue
Row 4: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue
Row 5: Blue Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 6: Blue Pink Pink Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 7: Blue Pink Pink Yellow Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 8: Blue Pink Pink Yellow Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 9: Blue Pink Pink Yellow Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 10: Blue Pink Pink Yellow Red Gray Black Black Black Black Black Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 11: Blue Pink Pink Yellow Red Gray Black Black Black Black Black Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 12: Blue Pink Pink Yellow Red Gray Black Black Black Black Black Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 13: Blue Pink Pink Yellow Red Gray Black Black Black Black Black Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 14: Blue Pink Pink Yellow Red Gray Black Green Green Green Black Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 15: Blue Pink Pink Yellow Red Gray Black Black Black Black Black Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 16: Blue Pink Pink Yellow Red Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 17: Blue Pink Pink Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 18: Blue Pink Pink Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 19: Blue Pink Pink Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 20: Blue Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 21: Blue Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 22: Blue Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 23: Blue Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue Blue Blue Blue Blue Blue
Row 24: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue
Row 25: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue Blue Blue Blue Blue Blue
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 Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 3: Blue Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue
Row 4: Blue Pink Yellow Red Red Red Red Red Red Red Yellow Pink Blue
Row 5: Blue Pink Yellow Red Gray Gray Gray Gray Gray Red Yellow Pink Blue
Row 6: Blue Pink Yellow Red Gray Black Black Black Gray Red Yellow Pink Blue
Row 7: Blue Pink Yellow Red Gray Black Green Black Gray Red Yellow Pink Blue
Row 8: Blue Pink Yellow Red Gray Black Black Black Gray Red Yellow Pink Blue
Row 9: Blue Pink Yellow Red Gray Gray Gray Gray Gray Red Yellow Pink Blue
Row 10: Blue Pink Yellow Red Red Red Red Red Red Red Yellow Pink Blue
Row 11: Blue Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Pink Blue
Row 12: Blue Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Blue
Row 13: 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
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 Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Red Red Red Pink Pink Pink Pink Pink Pink Pink Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Red Red Red Red Red Red Red Red Red Red Red 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
Output:
Row 1: Orange Orange Orange Orange Orange
Row 2: Orange Red Red Red Orange
Row 3: Orange Red Pink Red Orange
Row 4: Orange Red Red Red Orange
Row 5: Orange Orange Orange Orange Orange
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green
Row 3: Green Green 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 Purple Green Green
Row 4: Green Green 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 Purple Green Green
Row 5: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 6: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 7: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Gray Gray Gray Gray Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 8: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Pink Pink Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 9: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Pink Pink Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 10: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Pink Pink Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 11: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Pink Pink Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 12: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Pink Pink Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 13: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Orange Orange Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 14: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Pink Pink Pink Pink Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 15: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Gray Gray Gray Gray Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 16: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Gray Gray Gray Gray Gray Gray Gray Gray Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 17: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 18: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 19: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 20: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Red Red Red Red Red Red Red Red Red Red Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 21: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 22: Green Green Purple Purple Purple Purple Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Purple Green Green
Row 23: Green Green 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 Purple Green Green
Row 24: Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green
Row 25: Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green
Row 26: Green Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green Green
Row 27: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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 Green Green Green Green Green
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 2: Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Row 3: Green Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Green
Row 4: Green Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Purple Green
Row 5: Green Purple Yellow Brown Red Red Red Red Red Red Red Brown Yellow Purple Green
Row 6: Green Purple Yellow Brown Red Gray Gray Gray Gray Gray Red Brown Yellow Purple Green
Row 7: Green Purple Yellow Brown Red Gray Pink Pink Pink Gray Red Brown Yellow Purple Green
Row 8: Green Purple Yellow Brown Red Gray Pink Orange Pink Gray Red Brown Yellow Purple Green
Row 9: Green Purple Yellow Brown Red Gray Pink Pink Pink Gray Red Brown Yellow Purple Green
Row 10: Green Purple Yellow Brown Red Gray Gray Gray Gray Gray Red Brown Yellow Purple Green
Row 11: Green Purple Yellow Brown Red Red Red Red Red Red Red Brown Yellow Purple Green
Row 12: Green Purple Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Purple Green
Row 13: Green Purple Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Purple Green
Row 14: Green Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Green
Row 15: 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray
Row 3: Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray
Row 4: Gray Gray Orange Brown Brown Brown Brown Brown Brown Brown Orange Orange Gray
Row 5: Gray Gray Orange Brown Brown Brown Purple Brown Brown Brown Orange Orange Gray
Row 6: Gray Gray Orange Brown Brown Brown Purple Brown Brown Brown Orange Orange Gray
Row 7: Gray Gray Orange Brown Brown Brown Purple Brown Brown Brown Orange Orange Gray
Row 8: Gray Gray Orange Brown Brown Brown Brown Brown Brown Brown Orange Orange Gray
Row 9: Gray Gray Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray
Row 10: 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
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 Orange Orange Orange Orange Orange Gray
Gray Orange Brown Brown Brown Orange Gray
Gray Orange Brown Purple Brown Orange Gray
Gray Orange Brown Brown Brown Orange Gray
Gray Orange Orange Orange Orange Orange 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: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: 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
Row 19: 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
Output:
Row 1: 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
Row 3: 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
Row 5: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 10: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Yellow Yellow Yellow Yellow Yellow Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: 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
Row 19: 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
Example 2
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Black Brown Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Black Black Black Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Green Green Green Green Green Green Green Green Green 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
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
Row 2: Brown Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Black Black Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Black Black Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Green Green Green Green Green Green Green Green Green 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
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 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 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 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 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow 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 Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Purple 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 Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 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
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 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 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 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 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow 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 Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Yellow Yellow Yellow Yellow 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple 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 Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 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 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
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 Green Green Green Green Pink Pink Pink Pink
Row 3: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Row 4: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Row 5: Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Row 6: Pink Pink Pink Pink Green Green Green Green Red Red Red Red
Row 7: Pink Pink Pink Pink Green Green Green Green Pink Pink Red Red
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 Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 20: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 21: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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 Green Green Green Green Pink Pink Pink Pink
Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Pink Pink Pink Pink Green Green Green Green Pink Pink Pink Pink
Pink Pink Pink Pink Green Green Green Green Red Red Pink Pink
Pink Pink Pink Pink Green Green Green Green Red Red Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
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: Red Red Orange Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Orange Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Orange Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Orange Red Green Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 13: 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 Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Green 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 Green Red Red Red Red Red Red
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 6: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 10: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 12: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 13: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 16: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Green Red Red Red Red Red Red
Example 2
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Black 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 Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
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
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Black 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 Orange Yellow Yellow Yellow Black 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 Orange Yellow Yellow Black 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: Black Black Black Black Black 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: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black 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 Black 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 Black 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 Black 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 Black 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: Purple Purple Purple Purple Purple Green Purple
Row 2: Purple Purple Purple Purple Purple Green Purple
Row 3: Purple Purple Gray Purple Purple Green Purple
Row 4: Purple Purple Purple Purple Purple Green Purple
Row 5: Purple Purple Purple Purple Purple Green Purple
Row 6: Purple Purple Purple Purple Purple Green Purple
Row 7: Purple Purple Purple Purple Purple Green Purple
Row 8: Purple Purple Purple Purple Purple Green Purple
Row 9: Green Green Green Green Green Green Green
Row 10: Purple Purple Purple Purple Purple Green Purple
Row 11: Purple Purple Purple Purple Purple Green Purple
Row 12: Purple Purple Purple Purple Purple Green Purple
Row 13: Purple Purple Purple Purple Purple Green Purple
Row 14: Purple Purple Purple Purple Purple Green Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Green
Row 2: Purple Purple Purple Purple Purple Purple Green
Row 3: Purple Purple Purple Purple Purple Purple Green
Row 4: Purple Purple Purple Purple Purple Purple Green
Row 5: Purple Purple Purple Purple Purple Purple Green
Row 6: Purple Purple Purple Purple Purple Purple Green
Row 7: Purple Purple Purple Purple Purple Purple Green
Row 8: Purple Purple Purple Purple Purple Purple Green
Row 9: Purple Purple Purple Purple Purple Purple Green
Row 10: Green Green Green Green Green Green Green
Row 11: Purple Purple Purple Purple Purple Purple Green
Row 12: Purple Purple Purple Purple Purple Purple Green
Row 13: Purple Purple Purple Purple Purple Purple Green
Row 14: Purple Purple Purple Purple Purple Purple Green
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Yellow Gray
Row 2: Gray Gray Gray Yellow Gray
Row 3: Gray Gray Gray Yellow Gray
Row 4: Gray Gray Gray Yellow Pink
Row 5: Gray Gray Gray Yellow Gray
Row 6: Gray Gray Gray Yellow Pink
Row 7: Gray Gray Gray Yellow Gray
Row 8: Gray Gray Gray Yellow Gray
Row 9: Gray Gray Gray Yellow Gray
Row 10: Gray Gray Gray Yellow Gray
Row 11: Gray Gray Gray Yellow Gray
Row 12: Gray Gray Gray Yellow Gray
Row 13: Gray Gray Gray Yellow Gray
Row 14: Yellow Yellow Yellow Yellow Yellow
Row 15: Gray Gray Gray Yellow Gray
Row 16: Gray Gray Gray Yellow Gray
Row 17: Gray Gray Gray Yellow Gray
Row 18: Gray Gray Gray Yellow Gray
Row 19: Gray Gray Gray Yellow Gray
Row 20: Gray Gray Gray Yellow Gray
Row 21: Gray Gray Gray Yellow Gray
Row 22: Gray Gray Gray Yellow Gray
Row 23: Gray Gray Gray Yellow Gray
Row 24: Gray Gray Gray Yellow Gray
Row 25: Gray Gray Gray Yellow Gray
Row 26: Gray Gray Gray Yellow Gray
Row 27: Gray Gray Gray Yellow Gray
Row 28: Gray Gray Gray Yellow Gray
Row 29: Gray Gray Gray Yellow Gray
Row 30: Gray Gray Gray Yellow Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Yellow Yellow Yellow Yellow Yellow
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow Gray Gray Gray
Gray Yellow 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: 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
Row 3: 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
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown 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
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown 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
Row 16: 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
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Red 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
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown 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
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Green Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Purple Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown 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
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown 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
Row 16: 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
Row 18: Brown Brown Brown Brown Green Brown Pink 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
Row 20: Brown Brown Brown Brown Purple Brown Orange Brown Brown Brown Brown Brown Brown Green Brown Pink Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Orange Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 2
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Blue Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray
Output:
Row 1: Gray Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Green Gray Pink Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Purple Gray Orange Gray Gray
Example 3
Input:
Row 1: Blue Blue Blue
Row 2: Blue Blue Blue
Row 3: Blue Black Blue
Row 4: Blue Blue Blue
Row 5: Blue Blue Blue
Row 6: Blue Blue Blue
Output:
Row 1: Blue Blue Blue
Row 2: Green Blue Pink
Row 3: Blue Blue Blue
Row 4: Purple Blue Orange
Row 5: Blue Blue Blue
Row 6: Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Brown 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
Row 2: Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown 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 Brown Blue Blue Blue Blue Blue Blue Brown 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 Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown 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 Brown Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown 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 Brown 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: Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown 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 Brown Blue Blue Blue Blue
Row 20: Blue Brown Blue Blue Blue Blue Brown 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 Brown 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 Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 24: Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown 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
Row 26: Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Brown 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
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 Brown Blue
Row 29: Blue Blue 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 30: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Brown 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 Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue
Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Orange Blue
Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Green Blue 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 Green Blue Pink Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Purple Blue Orange Blue Blue Blue Blue Purple Blue Orange Blue Blue
Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Blue
Blue Purple Blue Orange Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Green Blue Pink Blue Purple Blue Orange Blue Green Blue Pink Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue
Blue Purple Blue Orange Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Purple Blue Orange Blue
Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Pink Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue
Green Blue Pink Blue Blue Green Blue Pink Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue
Purple Blue Orange Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Pink Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Purple Blue Orange Green Blue Pink Green Blue Pink Blue Green Blue Pink Blue Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Blue Blue Purple Blue Orange Purple Blue Orange Blue Purple Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue 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 Blue Pink Blue Blue Blue Green Blue Pink Purple Blue Orange
Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue |
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 Red Red Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Brown Red Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Brown Red Brown Red Brown Brown Brown
Row 5: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Orange Brown Orange Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown 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
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: 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
Row 25: 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
Row 27: 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
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Red Red Green Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Red Red Green Green Green Green Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Red Red Green Red Green Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Red Green Red Green Red Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Red Green Red Green Red Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Red Red Green Red Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Red Red Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Red Red 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
Row 10: 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
Row 12: 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
Row 14: 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
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
Row 18: 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
Row 20: 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
Row 22: 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
Row 24: 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
Row 26: 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
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: 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 Blue Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Blue Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Blue Blue Orange Blue Blue Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Blue Orange Blue Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue 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 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
Row 14: Orange Orange Orange 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 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
Row 17: 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
Row 19: 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
Row 21: Orange 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 Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
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: Green Green Green Green Green Green Green Green Green Green Green Blue Green Green Green Green Green Green Blue Green Green
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Blue Blue Green Green Green
Row 4: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Blue Green Green Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Blue Green Blue Blue Green Blue Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Green Green Blue Blue Blue Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Blue Blue Blue Green Green Green Green Blue Blue Blue Green
Row 9: Green Green Green Green Green Green Green Green Green Green Blue Green Green Green Green Green Green Green Green Blue Green
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 14: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 15: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 16: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 18: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 19: 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
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 23: Green Green 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
Row 25: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: 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
Row 4: Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 5: Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Gray Gray Gray Gray Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Purple Purple Purple Purple 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 Brown Brown Brown Brown Brown Brown
Row 11: 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
Row 13: 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
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: 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 Gray Green Green Green Green Green Green Green Green Green Green
Row 4: Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 5: Gray Gray Gray Green Green Green Green Green Green Green Green Green Green
Row 6: Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green
Row 7: Gray Gray Gray Gray Green Green Green Green Green Green Green Green Green
Row 8: Gray Gray Gray Green Green Green Green Green Green Green Green Green Green
Row 9: Gray Gray Green Green Green Green Green Green Green Green Green Green Green
Row 10: Green Green Gray 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
Row 12: 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
Row 14: 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
Row 16: 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
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 Green Green Green Green Green Green Green Green
Row 22: 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 Black Black Purple Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Black Black Black Black Black Purple Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Black Black Black Black Black Black Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Black Purple Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Black Black Black Black Black Black Black Black Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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
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 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 Black Green Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Green Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Black Black Black Black Black Black Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Green Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Green Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Black Black Black Black Black Black Green Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Black Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Black Black Green Black Black Black Black Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Black Black Black Green Black Black Black 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 Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green 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: Red Red Red Orange Red Red Red Orange Red Red Red
Row 2: Red Red Red Orange Red Red Red Orange Red Red Red
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Green Red Red Orange Red Red Red Orange Red Red Red
Row 5: Red Red Red Orange Red Red Red Orange Red Red Blue
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Red Red Red Orange Red Red Red Orange Red Red Red
Row 8: Red Red Red Orange Red Red Red Orange Red Red Red
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Green Red Red Orange Red Red Red Orange Green Red Red
Row 11: Red Red Red Orange Red Red Red Orange Red Red Blue
Output:
Row 1: Red Red Red Orange Red Red Red Orange Red Red Red
Row 2: Red Red Red Orange Red Red Red Orange Red Red Red
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Green Red Red Orange Red Red Red Orange Red Red Red
Row 5: Red Red Red Orange Red Red Red Orange Red Red Blue
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Green Red Red Orange Red Red Red Orange Red Red Red
Row 8: Red Red Red Orange Red Red Red Orange Red Red Blue
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Green Red Red Orange Green Red Red Orange Green Red Red
Row 11: Red Red Red Orange Red Red Red Orange Red Red Blue
Example 2
Input:
Row 1: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 2: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 5: Pink Pink Yellow Orange Pink Pink Pink Orange Pink Pink Yellow Orange Purple Pink Pink Orange Pink Pink Pink
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 8: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 11: Pink Pink Yellow Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Gray Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 14: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 17: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 20: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 23: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Gray Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Gray Pink Pink
Row 26: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Output:
Row 1: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 2: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 4: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 5: Pink Pink Yellow Orange Pink Green Yellow Orange Pink Pink Yellow Orange Purple Pink Pink Orange Pink Pink Pink
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 7: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 8: Pink Pink Yellow Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Pink Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 11: Pink Pink Yellow Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Gray Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 14: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Gray Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 17: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 18: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 19: Gray Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 20: Pink Pink Pink Orange Pink Green Pink Orange Pink Pink Pink Orange Purple Pink Pink Orange Pink Pink Pink
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Gray Pink Pink Orange Pink Blue Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 23: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Gray Pink Pink Orange Gray Pink Pink Orange Gray Pink Pink Orange Gray Pink Pink Orange Gray Pink Pink
Row 26: Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink Orange Pink Pink Pink
Example 3
Input:
Row 1: Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Pink Black Black Orange Black Black Black Orange Pink Black Black Orange Black Black Black Orange Black Black Black
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Black Black Black Orange Black Yellow Black Orange Black Black Black Orange Black Black Black Orange Black Yellow Black
Output:
Row 1: Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black Orange Black Black Black
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 3: Pink Black Black Orange Pink Black Black Orange Pink Black Black Orange Black Black Black Orange Black Black Black
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Black Black Black Orange Black Yellow Black Orange Black Yellow Black Orange Black Yellow Black Orange Black Yellow Black
Here is the input grid for the test example:
Input:
Row 1: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 2: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 3: Green Green Green Gray Green Green Red Gray Green Green Green Gray Green Green Green
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 6: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 7: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 9: Green Green Green Gray Green Green Green Gray Green Purple Green Gray Green Green Green
Row 10: Green Green Green Gray Green Yellow Green Gray Green Green Green Gray Green Green Green
Row 11: Green Green Green Gray Green Green Red Gray Green Green Green Gray Green Green Red
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 13: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 14: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 15: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 16: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 17: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 18: Green Green Green Gray Green Yellow Green Gray Green Green Green Gray Green Green Green
Row 19: Green Green Green Gray Green Green Green Gray Green Brown Green Gray Green Green Green
Row 20: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 21: Green Purple Green Gray Green Green Green Gray Green Purple Green Gray Green Green Green
Row 22: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 23: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 24: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 25: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 26: Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Row 27: Green Green Green Gray Green Green Green Gray Green Brown Green Gray Green Green Green
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Red Gray Green Green Green Gray Green Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Red Gray Green Green Green Gray Green Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Green Green Green Gray Green Green Green Gray Green Purple Green Gray Green Green Green
Green Green Green Gray Green Yellow Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Red Gray Green Green Red Gray Green Green Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Green Green Green Gray Green Green Green Gray Green Purple Green Gray Green Green Green
Green Green Green Gray Green Yellow Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Green Green Green Gray Green Green Green Gray Green Purple Green Gray Green Green Green
Green Green Green Gray Green Yellow Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Brown Green Gray Green Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Green Purple Green Gray Green Purple Green Gray Green Purple Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Brown Green Gray Green Green Green
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Gray Green Brown Green Gray 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 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
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown Brown
Row 4: Brown Purple Purple Purple Brown Brown Brown Brown Brown Red Brown Brown Red Brown Brown
Row 5: Brown Purple Brown Brown Purple Brown Brown Brown Brown Brown Red Red Red Brown Brown
Row 6: Brown Brown Purple Brown Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Purple Purple Purple Brown Brown Purple Purple Purple Purple Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown
Row 10: Brown Brown Brown Red Red Red Red Brown Brown Brown Purple Purple Purple Purple Brown
Row 11: Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Red Red Red Red Brown Brown Brown Brown Brown Brown
Row 14: 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 Purple Purple Purple Purple Purple Purple Brown
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Brown Purple
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 18: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Purple Brown Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Purple Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Brown
Output:
Row 1: 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
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Red Red Red Brown Brown
Row 4: Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Red Brown Red Brown Brown
Row 5: Brown Brown Purple Brown Brown Purple Brown Brown Brown Brown Red Red Red Brown Brown
Row 6: Brown Brown Brown Purple Brown Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Purple Purple Purple Brown Brown Brown Purple Purple Purple Purple Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Purple Brown
Row 10: Brown Brown Brown Brown Red Red Red Red Brown Brown Purple Purple Purple Purple Brown
Row 11: Brown Brown Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Red Brown Brown Red Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Red Red Red Red Brown Brown Brown Brown Brown Brown
Row 14: 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 Purple Purple Purple Purple Purple Purple
Row 16: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Purple
Row 17: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Purple
Row 18: 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 Purple Purple Purple Purple Purple Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Purple Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Purple Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Purple Purple Purple Brown
Example 2
Input:
Row 1: Brown Brown Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown
Row 5: Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 6: Brown Brown Red Brown Brown Red Brown Brown Orange Orange Orange Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown
Row 7: Brown Brown Brown Red Brown Brown Red Brown Orange Brown Brown Orange Brown Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Red Red Red Brown Brown Orange Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange 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
Output:
Row 1: Brown Brown Brown Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown
Row 5: Brown Brown Brown Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Orange Brown Brown Brown Brown
Row 6: Brown Brown Brown Red Brown Brown Red Brown Brown Orange Orange Orange Brown Brown Brown Orange Brown Brown Brown Orange Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Red Brown Red Brown Brown Orange Brown Brown Orange Brown Brown Orange Orange Orange Orange Orange Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Red Red Red Brown Brown Brown Orange Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Orange Orange Orange 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
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown Brown
Row 2: Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Brown Pink Brown Brown
Row 3: Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown
Row 4: Brown Yellow Yellow Yellow Yellow 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 Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Brown Brown Yellow Brown Brown Brown Yellow 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 Yellow Brown Brown
Row 9: Brown Brown Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Brown
Row 10: Brown Brown Black Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow
Row 11: Brown Brown Brown Black Black Black Black Black Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Yellow Yellow Yellow Brown
Row 15: Brown Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Yellow Brown Brown Yellow
Row 16: Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow
Row 17: Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown Brown
Row 19: Brown Brown Brown Brown Pink Brown Brown Pink Brown Blue Blue Blue Blue Brown Brown Blue Brown Brown Brown Brown Blue Brown Brown
Row 20: Brown Brown Brown Brown Brown Pink Pink Pink Brown Blue Brown Brown Brown Blue Brown Brown Blue Brown Brown Brown Brown Blue Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Blue Blue Blue Blue Blue Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Output:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown
Row 2: Brown Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Brown Brown Brown Pink Brown Brown
Row 3: Brown Yellow Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Pink Pink Pink Brown Brown
Row 4: Brown Yellow Yellow Yellow Yellow 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 Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Brown
Row 9: Brown Brown Brown Black Black Black Black Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow
Row 10: Brown Brown Brown Black Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Yellow
Row 11: Brown Brown Brown Black Black Black Black Black Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Yellow Yellow Yellow Yellow
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Brown Brown Yellow Yellow Yellow
Row 15: Brown Brown Pink Pink Pink Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Brown Yellow
Row 16: Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Yellow
Row 17: Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Pink Brown Brown Pink Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Blue Brown Brown
Row 19: Brown Brown Brown Brown Brown Pink Brown Pink Brown Brown Blue Blue Blue Blue Brown Brown Blue Brown Brown Brown Brown Blue Brown
Row 20: Brown Brown Brown Brown Brown Pink Pink Pink Brown Brown Blue Brown Brown Blue Brown Brown Brown Blue Brown Brown Brown Blue Brown
Row 21: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue Brown Brown Brown Blue Blue Blue Blue Blue Brown
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Here is the input grid for the test example:
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue
Row 4: Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue
Row 5: Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Red Red Red Blue Blue
Row 6: Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Red Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Red Red Red Red Red Red Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Red Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 11: Blue Red Red Red Red Red Red 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 Red Red Red Red 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 Red Blue Blue Blue Blue Blue Blue Blue
Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue
Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Red Blue Blue Blue Blue Blue Blue
Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Blue Blue Red Red Red Blue
Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Red Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Red Red Red Blue
Blue Blue Blue Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Red Red Red Red Red Red Blue Blue Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Red Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Blue Red Red Red Red Red Red 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: Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Gray Blue Gray Pink Red Red Red Red Red Red
Row 3: Red Red Black Red Pink Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Orange Orange Orange Orange Red Red Red Red Red Red Red
Row 6: Red Orange Red Orange Red Red Red Red Red Red Red Red
Row 7: 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
Row 9: Red Red Red Red Orange Orange Orange Orange Red Red Red Red
Row 10: Red Red Red Red Orange Red Orange Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Orange Orange Orange Orange Red Red Red
Row 13: Red Red Red Red Red Orange Red Orange Red Red Red Red
Row 14: 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
Row 16: Red Red Orange Orange Orange Orange Red Red Red Red Red Red
Row 17: Red Red Orange Red Orange Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Orange Orange Orange Orange Red Red Red Red Red
Row 22: Red Red Red Orange Red Orange Red Red Red Red Red Red
Row 23: 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
Row 25: 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
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Gray Blue Gray Pink Red Red Red Red Red Red
Row 3: Red Red Black Red Pink Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Gray Blue Gray Pink Red Red Red Red Red Red Red
Row 6: Red Black Red Pink Red Red Red Red Red Red Red Red
Row 7: 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
Row 9: Red Red Red Red Gray Blue Gray Pink Red Red Red Red
Row 10: Red Red Red Red Black Red Pink Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Gray Blue Gray Pink Red Red Red
Row 13: Red Red Red Red Red Black Red Pink Red Red Red Red
Row 14: 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
Row 16: Red Red Gray Blue Gray Pink Red Red Red Red Red Red
Row 17: Red Red Black Red Pink Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Gray Blue Gray Pink Red Red Red Red Red
Row 22: Red Red Red Black Red Pink Red Red Red Red Red Red
Row 23: 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
Row 25: 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
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red
Example 2
Input:
Row 1: Black Black Pink Black Black Black Black Black Black Black
Row 2: Black Black Pink Pink Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Pink Black Black
Row 4: Black Black Black Black Pink Black Black Pink Pink Black
Row 5: Black Brown Black Black Pink Pink Black Black Black Black
Row 6: Black Green Purple Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black
Row 8: Pink Black Black Black Black Black Black Black Black Black
Row 9: Pink Pink Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Pink Black Black Black
Row 11: Black Black Black Pink Black Black Pink Pink Black Black
Row 12: Black Black Black Pink Pink Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Brown Black Black Black Black Black Black Black
Row 2: Black Black Green Purple Black Black Black Black Black Black
Row 3: Black Black Black Black Black Black Black Brown Black Black
Row 4: Black Black Black Black Brown Black Black Green Purple Black
Row 5: Black Brown Black Black Green Purple Black Black Black Black
Row 6: Black Green Purple Black Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Black Black Black Black
Row 8: Brown Black Black Black Black Black Black Black Black Black
Row 9: Green Purple Black Black Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black Brown Black Black Black
Row 11: Black Black Black Brown Black Black Green Purple Black Black
Row 12: Black Black Black Green Purple Black Black Black Black Black
Row 13: Black Black Black Black Black Black Black Black Black Black
Example 3
Input:
Row 1: Black Black Brown Black Black Black Black Black Gray Black Black Brown Black Black Black Black Black
Row 2: Black Brown Brown Black Black Brown Black Gray Purple Black Brown Brown Black Black Black Black Black
Row 3: Black Black Brown Black Brown Brown Black Black Yellow Black Black Brown Black Black Brown Black Black
Row 4: Black Brown Black Black Black Brown Black Black Black Black Black Black Black Brown Brown Black Black
Row 5: Brown Brown Black Black Black Black Brown Black Black Black Black Black Black Black Brown Black Black
Row 6: Black Brown Black Black Black Brown Brown Black Black Black Brown Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Brown Black Black Brown Brown Black Black Brown Black Black Black
Row 8: Black Black Brown Black Black Brown Black Black Black Black Brown Black Brown Brown Black Black Black
Row 9: Black Brown Brown Black Brown Brown Black Black Black Black Black Black Black Brown Black Black Black
Row 10: Black Black Brown Black Black Brown Black Black Black Brown Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Brown Brown Black Black Black Brown Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Brown Black Black Brown Brown Black Black Black
Row 13: Black Black Black Brown Black Black Brown Black Black Black Black Black Black Brown Black Black Black
Row 14: Black Black Brown Brown Black Brown Brown Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Brown Black Black Brown 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
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Output:
Row 1: Black Black Gray Black Black Black Black Black Gray Black Black Gray Black Black Black Black Black
Row 2: Black Gray Purple Black Black Gray Black Gray Purple Black Gray Purple Black Black Black Black Black
Row 3: Black Black Yellow Black Gray Purple Black Black Yellow Black Black Yellow Black Black Gray Black Black
Row 4: Black Gray Black Black Black Yellow Black Black Black Black Black Black Black Gray Purple Black Black
Row 5: Gray Purple Black Black Black Black Gray Black Black Black Black Black Black Black Yellow Black Black
Row 6: Black Yellow Black Black Black Gray Purple Black Black Black Gray Black Black Black Black Black Black
Row 7: Black Black Black Black Black Black Yellow Black Black Gray Purple Black Black Gray Black Black Black
Row 8: Black Black Gray Black Black Gray Black Black Black Black Yellow Black Gray Purple Black Black Black
Row 9: Black Gray Purple Black Gray Purple Black Black Black Black Black Black Black Yellow Black Black Black
Row 10: Black Black Yellow Black Black Yellow Black Black Black Gray Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Gray Purple Black Black Black Gray Black Black Black
Row 12: Black Black Black Black Black Black Black Black Black Yellow Black Black Gray Purple Black Black Black
Row 13: Black Black Black Gray Black Black Gray Black Black Black Black Black Black Yellow Black Black Black
Row 14: Black Black Gray Purple Black Gray Purple Black Black Black Black Black Black Black Black Black Black
Row 15: Black Black Black Yellow Black Black Yellow 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
Row 17: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Gray Gray Gray Gray Gray Gray
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Orange Orange Orange Gray Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Orange Orange Gray Gray Orange Gray Orange Gray Gray Gray Gray Gray Gray
Row 4: Gray Gray Gray Orange Orange Orange Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 5: Gray Gray Gray Orange Gray 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 Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Gray Gray Gray Gray Gray
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Black 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 Black Green Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Black Green Gray Gray Black Gray Black Gray Gray Gray Gray Gray Gray
Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Gray Gray Gray Black 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 Gray
Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Green Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Gray Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Black 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: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Brown Black Black
Row 2: Black Black Pink Black Purple Black Black Pink Black Purple Black Brown Black Black Purple Black Black Red Black
Row 3: Black Black Black Black Purple Black Black Black Black Purple Red Black Black Black Purple Black Black Black Pink
Row 4: Black Black Black Brown Purple Black Brown Red Black Purple Black Black Black Black Purple Black Black Black Black
Row 5: Black Black Red Black Purple Black Black Black Black Purple Black Black Pink Black Purple Black Black Black Black
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Black Black Black Black Purple Black Black Black Black Purple Black Black Pink Black Purple Black Black Black Black
Row 8: Black Black Black Black Purple Pink Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 9: Black Black Black Black Purple Black Red Black Black Purple Black Black Red Brown Purple Black Black Black Black
Row 10: Brown Black Black Red Purple Black Brown Black Black Purple Black Black Black Black Purple Black Brown Black Black
Row 11: Black Black Pink Black Purple Black Black Black Black Purple Black Black Black Black Purple Pink Black Black Red
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Black Black Red Brown Purple Black Brown Black Red Purple Black Black Black Black Purple Black Black Pink Black
Row 14: Black Black Black Black Purple Black Black Black Pink Purple Black Black Red Pink Purple Black Black Black Black
Row 15: Black Black Pink Black Purple Black Black Black Black Purple Black Brown Black Black Purple Black Black Brown Red
Row 16: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 17: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Black Brown Black Black Purple Black Red Black Black Purple Red Black Black Black Purple Pink Black Black Black
Row 20: Black Black Black Black Purple Brown Black Black Black Purple Black Black Black Black Purple Black Black Black Red
Row 21: Black Red Black Black Purple Black Black Black Black Purple Brown Black Black Black Purple Black Black Black Black
Row 22: Pink Black Black Black Purple Black Black Black Pink Purple Black Black Black Black Purple Black Black Brown Black
Row 23: Black Black Black Black Purple Black Black Black Black Purple Black Black Pink Black Purple Black Black Black Black
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Black Black Black Black Purple Brown Black Black Black Purple Black Pink Black Black Purple Black Black Red Black
Row 26: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 27: Pink Brown Black Black Purple Black Black Pink Black Purple Brown Red Black Black Purple Black Black Black Brown
Row 28: Black Black Black Red Purple Black Red Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 29: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Output:
Row 1: Black Black Black Black Purple Black Black Black Black Purple Red Red Red Red Purple Black Black Black Black
Row 2: Black Black Black Black Purple Black Black Black Black Purple Red Red Red Red Purple Black Black Black Black
Row 3: Black Black Black Black Purple Black Black Black Black Purple Red Red Red Red Purple Black Black Black Black
Row 4: Black Black Black Black Purple Black Black Black Black Purple Red Red Red Red Purple Black Black Black Black
Row 5: Black Black Black Black Purple Black Black Black Black Purple Red Red Red Red Purple Black Black Black Black
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 8: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 9: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 10: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 11: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Brown Brown Brown Brown
Row 14: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Brown Brown Brown Brown
Row 15: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Brown Brown Brown Brown
Row 16: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Brown Brown Brown Brown
Row 17: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Brown Brown Brown Brown
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 20: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 21: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 22: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 23: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 24: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 25: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 26: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 27: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 28: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Row 29: Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black Purple Black Black Black Black
Example 2
Input:
Row 1: Orange Orange Black Orange Brown
Row 2: Orange Orange Black Green Orange
Row 3: Orange Green Black Orange Orange
Row 4: Brown Purple Black Orange Gray
Row 5: Orange Orange Black Purple Orange
Row 6: Black Black Black Black Black
Row 7: Orange Gray Black Orange Orange
Row 8: Orange Green Black Orange Green
Row 9: Orange Orange Black Orange Brown
Row 10: Brown Purple Black Orange Purple
Row 11: Orange Orange Black Orange Gray
Row 12: Black Black Black Black Black
Row 13: Orange Orange Black Orange Orange
Row 14: Brown Purple Black Brown Orange
Row 15: Orange Orange Black Orange Green
Row 16: Orange Green Black Orange Gray
Row 17: Orange Gray Black Orange Purple
Row 18: Black Black Black Black Black
Row 19: Purple Orange Black Orange Brown
Row 20: Orange Orange Black Orange Orange
Row 21: Brown Orange Black Gray Green
Row 22: Green Orange Black Purple Orange
Row 23: Gray Orange Black Orange Orange
Row 24: Black Black Black Black Black
Row 25: Orange Purple Black Orange Orange
Row 26: Brown Orange Black Orange Gray
Row 27: Gray Orange Black Purple Orange
Row 28: Orange Green Black Orange Brown
Row 29: Orange Orange Black Orange Green
Output:
Row 1: Orange Orange Black Orange Orange
Row 2: Orange Orange Black Orange Orange
Row 3: Orange Orange Black Orange Orange
Row 4: Orange Orange Black Orange Orange
Row 5: Orange Orange Black Orange Orange
Row 6: Black Black Black Black Black
Row 7: Orange Orange Black Orange Orange
Row 8: Orange Orange Black Orange Orange
Row 9: Orange Orange Black Orange Orange
Row 10: Orange Orange Black Orange Orange
Row 11: Orange Orange Black Orange Orange
Row 12: Black Black Black Black Black
Row 13: Orange Orange Black Green Green
Row 14: Orange Orange Black Green Green
Row 15: Orange Orange Black Green Green
Row 16: Orange Orange Black Green Green
Row 17: Orange Orange Black Green Green
Row 18: Black Black Black Black Black
Row 19: Brown Brown Black Purple Purple
Row 20: Brown Brown Black Purple Purple
Row 21: Brown Brown Black Purple Purple
Row 22: Brown Brown Black Purple Purple
Row 23: Brown Brown Black Purple Purple
Row 24: Black Black Black Black Black
Row 25: Orange Orange Black Orange Orange
Row 26: Orange Orange Black Orange Orange
Row 27: Orange Orange Black Orange Orange
Row 28: Orange Orange Black Orange Orange
Row 29: Orange Orange Black Orange Orange
Example 3
Input:
Row 1: Blue Red Red Yellow Pink Orange Blue Red Red Red Yellow Orange Red Pink Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 2: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Yellow Red Red Orange Red Yellow Red Red Purple Orange Red Purple Red Red Red
Row 3: Red Red Red Purple Red Orange Red Red Purple Red Red Orange Red Blue Red Red Red Orange Red Pink Red Red Red Orange Yellow Blue Red Red Pink
Row 4: Red Red Black Red Red Orange Black Red Red Red Pink Orange Red Red Purple Black Red Orange Red Blue Red Black Red Orange Red Black Red Red Red
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
Row 6: Red Red Red Pink Red Orange Yellow Blue Red Red Pink Orange Red Red Red Red Yellow Orange Red Red Red Yellow Red Orange Red Yellow Blue Red Red
Row 7: Red Red Red Red Blue Orange Red Red Red Red Black Orange Red Red Red Red Red Orange Red Red Blue Red Purple Orange Red Red Red Red Red
Row 8: Red Red Purple Red Black Orange Red Purple Red Red Red Orange Red Pink Red Purple Red Orange Red Red Red Red Red Orange Red Red Purple Red Red
Row 9: Red Red Yellow Red Red Orange Red Red Red Red Red Orange Red Black Red Blue Red Orange Black Pink Red Red Red Orange Red Pink Red Red Black
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 Orange
Row 11: Red Blue Red Red Red Orange Red Pink Red Black Red Orange Red Red Red Black Blue Orange Red Red Red Red Red Orange Red Red Red Yellow Red
Row 12: Red Red Red Pink Red Orange Purple Red Red Red Red Orange Red Red Red Pink Red Orange Red Red Blue Red Purple Orange Red Red Black Red Red
Row 13: Purple Red Red Red Red Orange Red Red Blue Red Red Orange Red Red Red Red Red Orange Red Red Pink Red Red Orange Blue Red Red Pink Purple
Row 14: Red Yellow Red Black Red Orange Red Red Red Yellow Red Orange Red Yellow Purple Red Red Orange Red Red Red Yellow Red Orange Red Red Red Red Red
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Red Black Red Red Purple Orange Blue Red Pink Red Red Orange Red Red Red Red Red Orange Red Red Red Purple Red Orange Purple Red Red Red Red
Row 17: Red Red Red Red Red Orange Black Purple Yellow Red Red Orange Red Yellow Red Purple Red Orange Red Red Red Pink Red Orange Red Black Red Red Red
Row 18: Red Yellow Red Red Red Orange Red Red Red Red Red Orange Red Red Red Blue Red Orange Red Yellow Red Red Red Orange Red Red Red Yellow Pink
Row 19: Red Blue Red Red Pink Orange Red Red Red Red Red Orange Red Red Pink Black Red Orange Red Blue Red Red Black Orange Red Red Red Blue Red
Output:
Row 1: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 2: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 3: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 4: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red
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
Row 6: Red Red Red Red Red Orange Red Red Red Red Red Orange Blue Blue Blue Blue Blue Orange Red Red Red Red Red Orange Purple Purple Purple Purple Purple
Row 7: Red Red Red Red Red Orange Red Red Red Red Red Orange Blue Blue Blue Blue Blue Orange Red Red Red Red Red Orange Purple Purple Purple Purple Purple
Row 8: Red Red Red Red Red Orange Red Red Red Red Red Orange Blue Blue Blue Blue Blue Orange Red Red Red Red Red Orange Purple Purple Purple Purple Purple
Row 9: Red Red Red Red Red Orange Red Red Red Red Red Orange Blue Blue Blue Blue Blue Orange Red Red Red Red Red Orange Purple Purple Purple Purple Purple
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Red Red Red Red Red Orange Red Red Red Red Red Orange Pink Pink Pink Pink Pink Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 12: Red Red Red Red Red Orange Red Red Red Red Red Orange Pink Pink Pink Pink Pink Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 13: Red Red Red Red Red Orange Red Red Red Red Red Orange Pink Pink Pink Pink Pink Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 14: Red Red Red Red Red Orange Red Red Red Red Red Orange Pink Pink Pink Pink Pink Orange Red Red Red Red Red Orange Red Red Red Red Red
Row 15: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 16: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Yellow Yellow Yellow Yellow Yellow Orange Red Red Red Red Red
Row 17: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Yellow Yellow Yellow Yellow Yellow Orange Red Red Red Red Red
Row 18: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Yellow Yellow Yellow Yellow Yellow Orange Red Red Red Red Red
Row 19: Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red Red Red Orange Yellow Yellow Yellow Yellow Yellow Orange Red Red Red Red Red
Here is the input grid for the test example:
Input:
Row 1: Blue Orange Yellow Blue Brown
Row 2: Green Gray Yellow Green Gray
Row 3: Brown Blue Yellow Blue Blue
Row 4: Yellow Yellow Yellow Yellow Yellow
Row 5: Brown Orange Yellow Green Blue
Row 6: Blue Green Yellow Blue Brown
Row 7: Gray Blue Yellow Gray Orange
Row 8: Yellow Yellow Yellow Yellow Yellow
Row 9: Gray Green Yellow Blue Blue
Row 10: Brown Blue Yellow Green Orange
Row 11: Orange Blue Yellow Brown Gray
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Blue Blue Yellow Brown Brown
Blue Blue Yellow Brown Brown
Blue Blue Yellow Brown Brown
Yellow Yellow Yellow Yellow Yellow
Green Green Yellow Gray Gray
Green Green Yellow Gray Gray
Green Green Yellow Gray Gray
Yellow Yellow Yellow Yellow Yellow
Blue Blue Yellow Blue Blue
Blue Blue Yellow Blue Blue
Blue Blue Yellow 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: Orange Orange Orange Orange 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
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 Pink Orange Orange Orange Pink Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Brown Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Brown Orange Pink Orange Brown Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Brown Orange Brown Orange Brown 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 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 Green 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Blue Orange Green 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 Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Green Orange Orange Orange Orange Orange
Row 15: 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 Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: 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 Orange Orange Orange
Row 18: 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 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
Row 20: Orange Orange Orange Orange Orange Blue Orange Brown Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Brown Orange Green Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Blue Orange Pink Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Blue Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Blue Orange Brown Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue 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
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 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 Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Brown Orange Brown Orange Brown Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Brown Orange Pink Orange Brown Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Orange Orange Brown Orange Brown Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Brown Orange Brown Orange Brown 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 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 Green 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Blue Orange Green 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 Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange Orange Orange Green Orange Orange Orange Orange Orange
Row 15: 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 Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 17: 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 Orange Orange Orange
Row 18: 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 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
Row 20: Orange Orange Orange Orange Orange Blue Orange Brown Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 21: Orange Orange Orange Orange Orange Orange Blue Orange Blue Orange Orange Orange Blue Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 22: Orange Orange Orange Orange Orange Brown Orange Green Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Blue Orange Pink Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Blue Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Blue Orange Brown Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange Blue 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
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 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
Row 3: Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Yellow Blue Orange Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Orange Blue Black Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue Brown Blue Brown Blue Brown Blue
Row 7: Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Yellow Blue Blue Blue Yellow 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 Brown 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
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: Blue 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 Purple Blue Blue Blue Purple Blue Blue Yellow Blue Orange Blue Yellow Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue
Row 5: Blue Blue Blue Blue Blue Blue Black Blue Blue Blue Blue Orange Blue Black Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Orange Blue Blue Blue Blue Brown Blue Brown Blue Brown Blue
Row 7: Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Yellow Blue Orange Blue Yellow 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 Brown 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
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
Row 2: Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple 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 Purple Blue Blue Blue Purple Blue Blue Blue Brown Blue Blue Blue Brown 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
Row 10: Blue Blue Blue Blue Blue Green 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
Row 12: Blue Blue Blue Purple Blue Blue Blue Purple Blue Purple Blue Blue Blue Purple Blue Blue Brown Blue Brown Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Brown Blue Brown 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 Green Blue Blue Blue Blue Blue Purple Blue Blue Blue Purple 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 Green Blue Brown Blue Green Blue Brown Blue Blue Blue Brown Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Purple Blue Blue Blue Purple 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
Row 24: 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
Row 26: 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
Row 28: 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
Row 2: Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue
Row 5: Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 6: Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple 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 Purple Blue Blue Blue Purple Blue Blue Blue Brown Blue Blue Blue Brown 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
Row 10: Blue Blue Blue Blue Blue Green 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
Row 12: Blue Blue Blue Purple Blue Blue Blue Purple Blue Purple Blue Blue Blue Purple Blue Blue Brown Blue Brown Blue Blue Blue
Row 13: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue
Row 14: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Brown Blue Brown 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 Green Blue Blue Blue Blue Blue Purple Blue Blue Blue Purple 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 Green Blue Brown Blue Green Blue Brown Blue Blue Blue Brown Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 20: Blue Blue Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 22: Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Brown Blue Purple Blue Blue Blue Purple 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
Row 24: 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
Row 26: 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
Row 28: 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: 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 Gray Green Green Green Gray Green Green Green
Row 3: 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 Yellow 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
Row 6: Green Green Red Green Red Green Green Green Green Green Gray Green Green Green Gray Green Green Green
Row 7: Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Red Green Red 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
Row 10: 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
Row 12: Green Green Green Green Green Green Green Orange Green Green Green Green Green Green Green Green Green Green
Row 13: Green Green Green Green Green Green Brown Green Brown Green Green Brown Green Green Green Brown Green Green
Row 14: Green Green Green Green Green Orange Green Orange Green Orange Green Green Red Green Red Green Green Green
Row 15: Green Green Green Green Green Green Brown Green Brown Green Green Green Green Red Green Red Green Green
Row 16: Green Green Green Green Green Green Green Orange Green Green Green Green Red Green Red Green Green Green
Row 17: Green Green Green Green Green Green Green Green Green Green Green Brown Green Red Green Brown Green Green
Row 18: 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
Row 20: 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
Row 22: 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
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 Gray Green Green Green Gray Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Yellow Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Red Green Red Green Green Green Green Green Gray Green Green Green Gray Green Green Green
Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Red Green Red Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Green 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 Green Green Green Green Green Green
Green Green Green Green Green Green Brown Green Brown Green Green Brown Green Red Green Brown Green Green
Green Green Green Green Green Orange Green Orange Green Orange Green Green Red Green Red Green Green Green
Green Green Green Green Green Green Brown Green Brown Green Green Red Green Red Green Red Green Green
Green Green Green Green Green Green Green Orange Green Green Green Green Red Green Red Green Green Green
Green Green Green Green Green Green Green Green Green Green Green Brown Green Red Green 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 |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Gray Purple Green Green Gray Blue Purple Orange Gray Orange Purple Green Gray Green Black Black Gray
Row 2: Green Gray Green Gray Green Gray Purple Gray Pink Gray Green Gray Green Gray Green Gray Green
Row 3: Purple Black Gray Green Orange Black Gray Blue Black Green Gray Black Green Green Gray Green Black
Output:
Row 1: Gray Purple Green Green Gray Yellow Yellow Yellow Gray Orange Purple Green Gray Green Black Black Gray
Row 2: Yellow Gray Green Gray Green Gray Yellow Gray Pink Gray Green Gray Yellow Gray Green Gray Green
Row 3: Yellow Yellow Gray Green Orange Black Gray Blue Black Green Gray Yellow Yellow Yellow Gray Green Black
Example 2
Input:
Row 1: Blue Green Brown Orange Blue Brown Green Purple Blue Purple Brown Brown Blue Purple Green Purple Blue Orange Purple Purple Blue Orange Purple Orange Blue Purple Brown Orange Blue
Row 2: Brown Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple Blue Green Blue Purple Blue Green Blue Purple Blue Purple Blue Purple Blue Purple Blue Purple
Row 3: Orange Purple Blue Green Purple Brown Blue Purple Purple Purple Blue Purple Purple Purple Blue Orange Orange Purple Blue Orange Brown Purple Blue Purple Purple Brown Blue Purple Green
Output:
Row 1: Blue Green Brown Orange Blue Yellow Yellow Yellow Blue Purple Brown Brown Blue Purple Green Purple Blue Yellow Yellow Yellow Blue Orange Purple Orange Blue Purple Brown Orange Blue
Row 2: Yellow Blue Purple Blue Purple Blue Yellow Blue Purple Blue Purple Blue Yellow Blue Green Blue Purple Blue Yellow Blue Purple Blue Purple Blue Yellow Blue Purple Blue Purple
Row 3: Yellow Yellow Blue Green Purple Brown Blue Purple Purple Purple Blue Yellow Yellow Yellow Blue Orange Orange Purple Blue Orange Brown Purple Blue Yellow Yellow Yellow Blue Purple Green
Example 3
Input:
Row 1: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Gray Brown Gray Gray Gray Red Gray Gray Gray Gray Gray Blue
Row 2: Gray Blue Gray Gray Gray Pink Gray Gray Green Gray Red Blue Pink Blue Gray Gray Gray Gray Gray Gray Gray Gray Brown Blue Gray
Row 3: Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Green Blue Gray Gray Gray Gray Gray Green Gray Blue Gray Gray
Row 4: Gray Gray Red Blue Gray Gray Gray Pink Gray Blue Gray Red Pink Gray Gray Blue Gray Gray Gray Gray Brown Blue Gray Gray Gray
Row 5: Gray Gray Gray Gray Blue Gray Red Gray Blue Gray Brown Gray Gray Gray Gray Gray Blue Brown Red Brown Blue Gray Gray Gray Gray
Row 6: Gray Gray Brown Pink Gray Blue Gray Blue Gray Gray Gray Gray Gray Gray Pink Gray Gray Blue Gray Blue Gray Gray Gray Gray Gray
Row 7: Brown Gray Gray Gray Brown Gray Blue Gray Gray Gray Brown Gray Gray Pink Gray Gray Gray Brown Blue Gray Gray Gray Brown Gray Gray
Output:
Row 1: Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue
Row 2: Yellow Blue Gray Gray Gray Pink Gray Gray Green Gray Red Blue Pink Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Gray
Row 3: Yellow Yellow Blue Gray Gray Gray Gray Gray Gray Gray Blue Gray Gray Green Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Blue Gray Gray
Row 4: Yellow Yellow Yellow Blue Gray Gray Gray Pink Gray Blue Gray Red Pink Gray Gray Blue Yellow Yellow Yellow Yellow Yellow Blue Gray Gray Gray
Row 5: Yellow Yellow Yellow Yellow Blue Gray Red Gray Blue Gray Brown Gray Gray Gray Gray Gray Blue Yellow Yellow Yellow Blue Gray Gray Gray Gray
Row 6: Yellow Yellow Yellow Yellow Yellow Blue Gray Blue Gray Gray Gray Gray Gray Gray Pink Gray Gray Blue Yellow Blue Gray Gray Gray Gray Gray
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Blue Gray Gray Gray Brown Gray Gray Pink Gray Gray Gray Brown Blue Gray Gray Gray Brown Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Red Blue Blue Black Blue Green Red Blue Blue Blue Blue Blue Red Blue Pink Blue Green Blue Red Blue Orange Blue Green Blue Red Green
Row 2: Blue Red Blue Green Pink Red Blue Red Pink Blue Blue Red Green Red Blue Black Blue Red Blue Red Blue Orange Blue Red Blue Red
Row 3: Blue Orange Red Blue Red Blue Blue Blue Red Blue Red Blue Black Blue Red Blue Red Black Blue Blue Red Blue Red Black Blue Green
Row 4: Blue Black Green Red Orange Orange Blue Blue Blue Red Blue Blue Green Blue Blue Red Blue Blue Blue Brown Blue Red Blue Blue Black Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Red Blue Blue Black Blue Green Red Yellow Yellow Yellow Yellow Yellow Red Blue Pink Blue Green Blue Red Blue Orange Blue Green Blue Red Yellow
Yellow Red Blue Green Pink Red Blue Red Yellow Yellow Yellow Red Green Red Blue Black Blue Red Yellow Red Blue Orange Blue Red Blue Red
Yellow Yellow Red Blue Red Blue Blue Blue Red Yellow Red Blue Black Blue Red Blue Red Yellow Yellow Yellow Red Blue Red Black Blue Green
Yellow Yellow Yellow Red Orange Orange Blue Blue Blue Red Blue Blue Green Blue Blue Red Yellow Yellow Yellow Yellow Yellow Red Blue Blue 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: Orange Orange Orange Orange Orange Orange
Row 2: Pink Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Brown Orange
Row 5: Orange Orange Orange Gray Orange Orange
Row 6: Orange Orange Orange Orange Orange Blue
Row 7: Orange Orange Orange Orange Orange Orange
Row 8: Orange Blue Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Purple Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange
Row 2: Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 3: Orange Purple Orange Purple Orange Purple Orange Purple Orange Purple Orange Purple
Row 4: Orange Orange Purple Orange Brown Orange Orange Orange Purple Orange Brown Orange
Row 5: Orange Orange Orange Gray Purple Purple Purple Orange Orange Gray Purple Purple
Row 6: Orange Orange Purple Orange Purple Blue Orange Orange Purple Orange Purple Blue
Row 7: Purple Orange Purple Orange Purple Orange Purple Orange Purple Orange Purple Orange
Row 8: Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 9: Purple Orange Purple Orange Orange Orange Purple Orange Purple Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Purple Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange
Row 12: Pink Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange
Row 13: Orange Purple Orange Purple Orange Purple Orange Purple Orange Purple Orange Purple
Row 14: Orange Orange Purple Orange Brown Orange Orange Orange Purple Orange Brown Orange
Row 15: Orange Orange Orange Gray Purple Purple Purple Orange Orange Gray Purple Purple
Row 16: Orange Orange Purple Orange Purple Blue Orange Orange Purple Orange Purple Blue
Row 17: Purple Orange Purple Orange Purple Orange Purple Orange Purple Orange Purple Orange
Row 18: Orange Blue Orange Orange Orange Orange Orange Blue Orange Orange Orange Orange
Row 19: Purple Orange Purple Orange Orange Orange Purple Orange Purple Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 2
Input:
Row 1: Yellow Yellow Blue Yellow
Row 2: Yellow Yellow Yellow Yellow
Output:
Row 1: Yellow Yellow Blue Yellow Yellow Yellow Blue Yellow
Row 2: Yellow Purple Yellow Purple Yellow Purple Yellow Purple
Row 3: Yellow Yellow Blue Yellow Yellow Yellow Blue Yellow
Row 4: Yellow Purple Yellow Purple Yellow Purple Yellow Purple
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 Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange
Row 14: 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 Orange 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 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
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
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
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
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
Row 9: Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 11: Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple 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 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 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 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 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
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
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
Row 22: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 23: Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 24: Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 25: Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange
Row 27: Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Red Orange Orange Orange Orange Orange Orange
Row 28: Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Purple Orange Orange Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Orange Orange Orange Orange
Row 2: Orange Orange Pink Orange
Row 3: Orange Orange Orange Orange
Row 4: 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 Purple Orange Purple Orange Purple Orange Purple
Orange Orange Pink Orange Orange Orange Pink Orange
Orange Purple Orange Purple Orange Purple Orange Purple
Orange Orange Orange Orange Orange Orange Orange Orange
Orange Purple Orange Purple Orange Purple Orange Purple
Orange Orange Pink Orange Orange Orange Pink Orange
Orange Purple Orange Purple Orange Purple Orange Purple
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: Purple Purple Purple
Row 2: Green Green Green
Row 3: Green Green Green
Row 4: Blue Blue Blue
Row 5: Pink Pink Pink
Row 6: Brown Brown Brown
Row 7: Brown Brown Brown
Row 8: Orange Orange Orange
Row 9: Blue Blue Blue
Row 10: Blue Blue Blue
Row 11: Blue Blue Blue
Row 12: Blue Blue Blue
Row 13: Blue Blue Blue
Row 14: Blue Blue Blue
Row 15: Blue Blue Blue
Row 16: Pink Pink Pink
Row 17: Purple Purple Purple
Row 18: Purple Purple Purple
Row 19: Purple Purple Purple
Row 20: Red Red Red
Row 21: Orange Orange Orange
Output:
Row 1: Purple
Row 2: Green
Row 3: Blue
Row 4: Pink
Row 5: Brown
Row 6: Orange
Row 7: Blue
Row 8: Pink
Row 9: Purple
Row 10: Red
Row 11: Orange
Example 2
Input:
Row 1: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 2: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 3: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 4: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 5: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 6: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 7: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 8: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 9: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 10: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 11: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 12: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 13: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 14: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 15: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 16: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 17: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 18: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 19: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 20: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 21: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 22: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 23: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 24: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Row 25: Pink Purple Black Black Black Gray Gray Brown Green Green Purple Purple Purple Brown Pink Blue Blue Blue Red Red Red Red Red Red Red Gray Brown
Output:
Row 1: Pink Purple Black Gray Brown Green Purple Brown Pink Blue Red Gray Brown
Example 3
Input:
Row 1: Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown
Row 3: Gray Gray Gray Gray Gray
Row 4: Red Red Red Red Red
Row 5: Red Red Red Red Red
Row 6: Green Green Green Green Green
Row 7: Green Green Green Green Green
Row 8: Brown Brown Brown Brown Brown
Row 9: Orange Orange Orange Orange Orange
Row 10: Red Red Red Red Red
Row 11: Red Red Red Red Red
Row 12: Green Green Green Green Green
Row 13: Green Green Green Green Green
Row 14: Brown Brown Brown Brown Brown
Row 15: Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple
Row 17: Green Green Green Green Green
Row 18: Purple Purple Purple Purple Purple
Row 19: Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown
Row 21: Brown Brown Brown Brown Brown
Row 22: Purple Purple Purple Purple Purple
Row 23: Black Black Black Black Black
Output:
Row 1: Brown
Row 2: Gray
Row 3: Red
Row 4: Green
Row 5: Brown
Row 6: Orange
Row 7: Red
Row 8: Green
Row 9: Brown
Row 10: Purple
Row 11: Green
Row 12: Purple
Row 13: Brown
Row 14: Purple
Row 15: Black
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 5: Green Green Green Green Green Green Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green
Row 9: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 11: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 12: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 13: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 14: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 15: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 16: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 17: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 18: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 19: Pink Pink Pink Pink Pink Pink Pink Pink Pink
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: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 26: Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 27: Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 28: 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>
| Pink
Blue
Yellow
Green
Pink
Purple
Pink
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: Black Purple Black Blue Red Green Yellow Blue Black Green Orange Black Green Orange Gray Brown Yellow Gray Black Black Red Orange Purple Red Yellow Gray Black Yellow Red
Row 2: Black Purple Black Purple Black Green Brown Black Black Orange Black Green Orange Orange Green Yellow Black Black Green Blue Green Black Brown Yellow Black Black Yellow Yellow Red
Row 3: Black Purple Blue Orange Yellow Blue Blue Purple Black Brown Purple Black Black Orange Purple Blue Black Gray Orange Red Blue Yellow Blue Purple Black Black Blue Purple Purple
Row 4: Yellow Blue Red Orange Orange Green Green Black Brown Gray Red Black Red Gray Purple Orange Gray Blue Black Yellow Blue Gray Red Black Yellow Blue Yellow Black Blue
Row 5: Orange Black Gray Purple Orange Brown Green Purple Gray Red Black Gray Black Red Blue Blue Purple Yellow Blue Gray Orange Black Red Blue Gray Purple Brown Red Black
Row 6: Black Black Brown Gray Black Black Brown Blue Black Green Orange Orange Purple Purple Purple Black Black Blue Gray Brown Brown Black Purple Green Yellow Black Blue Gray Black
Row 7: Yellow Black Green Green Black Black Green Yellow Green Purple Red Brown Gray Orange Black Red Gray Purple Purple Black Green Black Orange Black Black Gray Orange Black Yellow
Row 8: Purple Gray Orange Gray Gray Blue Black Gray Yellow Black Red Purple Gray Red Yellow Blue Yellow Black Black Black Black Green Red Brown Purple Yellow Black Black Green
Output:
Row 1: Black Purple Black Blue Red Green Yellow Blue Black Green Orange Black Green Orange Gray Brown Yellow Gray Black Black Red Orange Purple Red Yellow Gray Black Yellow Red
Row 2: Black Purple Black Purple Black Green Brown Black Black Orange Black Green Orange Orange Green Yellow Black Black Green Blue Green Black Brown Yellow Pink Pink Yellow Yellow Red
Row 3: Black Purple Blue Orange Yellow Blue Blue Purple Black Brown Purple Black Black Orange Purple Blue Black Gray Orange Red Blue Yellow Blue Purple Pink Pink Blue Purple Purple
Row 4: Yellow Blue Red Orange Orange Green Green Black Brown Gray Red Black Red Gray Purple Orange Gray Blue Black Yellow Blue Gray Red Black Yellow Blue Yellow Black Blue
Row 5: Orange Black Gray Purple Orange Brown Green Purple Gray Red Black Gray Black Red Blue Blue Purple Yellow Blue Gray Orange Black Red Blue Gray Purple Brown Red Black
Row 6: Black Black Brown Gray Pink Pink Brown Blue Black Green Orange Orange Purple Purple Purple Black Black Blue Gray Brown Brown Black Purple Green Yellow Black Blue Gray Black
Row 7: Yellow Black Green Green Pink Pink Green Yellow Green Purple Red Brown Gray Orange Black Red Gray Purple Purple Black Green Black Orange Black Black Gray Orange Black Yellow
Row 8: Purple Gray Orange Gray Gray Blue Black Gray Yellow Black Red Purple Gray Red Yellow Blue Yellow Black Black Black Black Green Red Brown Purple Yellow Black Black Green
Example 2
Input:
Row 1: Black Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Black Yellow
Row 2: Yellow Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Black Yellow
Row 3: Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 4: Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Black Black Black Yellow Black Yellow Black Yellow Yellow Yellow Black
Row 5: Black Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Black Yellow Black Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Black Black Black
Output:
Row 1: Black Yellow Yellow Yellow Yellow Black Yellow Yellow Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Black Yellow
Row 2: Yellow Black Black Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Black Yellow
Row 3: Black Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Black
Row 4: Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Black Pink Pink Pink Yellow Black Yellow Black Yellow Yellow Yellow Black
Row 5: Black Yellow Black Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Black Yellow Pink Pink Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Yellow Yellow Yellow Yellow Black Black Black Black
Example 3
Input:
Row 1: Yellow Yellow Orange Orange
Row 2: Green Black Black Black
Row 3: Gray Black Black Black
Row 4: Red Black Black Blue
Row 5: Black Black Red Black
Row 6: Red Green Black Green
Row 7: Black Black Green Gray
Row 8: Blue Black Brown Purple
Row 9: Yellow Black Purple Gray
Row 10: Green Green Blue Black
Row 11: Red Black Green Red
Row 12: Black Red Blue Black
Row 13: Green Yellow Yellow Orange
Row 14: Black Black Red Black
Row 15: Blue Blue Gray Blue
Row 16: Yellow Black Green Purple
Row 17: Brown Blue Black Black
Row 18: Green Black Red Black
Row 19: Gray Black Yellow Black
Row 20: Blue Blue Purple Orange
Row 21: Gray Blue Black Black
Row 22: Brown Green Purple Red
Row 23: Brown Black Yellow Black
Row 24: Yellow Blue Black Black
Row 25: Orange Yellow Blue Black
Row 26: Blue Red Black Green
Output:
Row 1: Yellow Yellow Orange Orange
Row 2: Green Pink Pink Pink
Row 3: Gray Pink Pink Pink
Row 4: Red Pink Pink Blue
Row 5: Black Black Red Black
Row 6: Red Green Black Green
Row 7: Black Black Green Gray
Row 8: Blue Black Brown Purple
Row 9: Yellow Black Purple Gray
Row 10: Green Green Blue Black
Row 11: Red Black Green Red
Row 12: Black Red Blue Black
Row 13: Green Yellow Yellow Orange
Row 14: Black Black Red Black
Row 15: Blue Blue Gray Blue
Row 16: Yellow Black Green Purple
Row 17: Brown Blue Black Black
Row 18: Green Black Red Black
Row 19: Gray Black Yellow Black
Row 20: Blue Blue Purple Orange
Row 21: Gray Blue Black Black
Row 22: Brown Green Purple Red
Row 23: Brown Black Yellow Black
Row 24: Yellow Blue Black Black
Row 25: Orange Yellow Blue Black
Row 26: Blue Red Black Green
Here is the input grid for the test example:
Input:
Row 1: Black Red Gray Gray Purple Gray Black Red Black Black Black Black Black Black
Row 2: Black Red Black Black Yellow Black Gray Black Black Black Black Black Purple Red
Row 3: Yellow Brown Gray Blue Gray Yellow Orange Orange Purple Red Yellow Brown Orange Red
Row 4: Orange Yellow Brown Black Blue Yellow Black Blue Black Black Black Brown Green Blue
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Black Red Gray Gray Purple Gray Black Red Pink Pink Pink Pink Black Black
Black Red Black Black Yellow Black Gray Black Pink Pink Pink Pink Purple Red
Yellow Brown Gray Blue Gray Yellow Orange Orange Purple Red Yellow Brown Orange Red
Orange Yellow Brown Black Blue Yellow Black Blue Black Black Black Brown Green 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 Pink Purple
Row 2: Purple Gray Purple
Row 3: Brown Purple Purple
Row 4: Gray Green Purple
Row 5: Purple Purple Red
Row 6: Pink Purple Blue
Row 7: Purple Purple Gray
Row 8: Purple Purple Purple
Row 9: Purple Purple Brown
Row 10: Green Purple Brown
Row 11: Yellow Purple Yellow
Row 12: Purple Pink Green
Row 13: Yellow Purple Yellow
Output:
Row 1: Blue Pink Purple
Row 2: Purple Gray Purple
Row 3: Brown Purple Purple
Row 4: Gray Green Purple
Row 5: Purple Purple Red
Row 6: Pink Purple Blue
Row 7: Purple Purple Gray
Row 8: Purple Purple Purple
Row 9: Purple Purple Brown
Row 10: Green Purple Brown
Row 11: Yellow Purple Yellow
Row 12: Purple Pink Green
Row 13: Yellow Purple Yellow
Row 14: Yellow Purple Yellow
Row 15: Purple Pink Green
Row 16: Yellow Purple Yellow
Row 17: Green Purple Brown
Row 18: Purple Purple Brown
Row 19: Purple Purple Purple
Row 20: Purple Purple Gray
Row 21: Pink Purple Blue
Row 22: Purple Purple Red
Row 23: Gray Green Purple
Row 24: Brown Purple Purple
Row 25: Purple Gray Purple
Row 26: Blue Pink Purple
Example 2
Input:
Row 1: Gray Yellow Pink Pink Purple Yellow Purple Gray Pink Gray Gray Gray Purple Gray Pink Pink Pink Pink Gray Gray Gray Gray Pink Gray Pink Pink Pink Yellow Pink Gray
Row 2: Yellow Pink Purple Yellow Purple Gray Yellow Pink Pink Purple Gray Purple Yellow Pink Pink Yellow Gray Gray Yellow Pink Pink Purple Yellow Gray Gray Pink Gray Purple Pink Gray
Row 3: Gray Gray Gray Yellow Pink Purple Pink Gray Gray Pink Purple Pink Gray Pink Gray Gray Pink Yellow Gray Gray Yellow Pink Pink Gray Purple Gray Gray Gray Gray Yellow
Row 4: Pink Pink Purple Gray Gray Purple Pink Yellow Purple Gray Gray Pink Yellow Gray Yellow Pink Pink Purple Pink Pink Pink Purple Gray Purple Gray Gray Pink Gray Gray Pink
Row 5: Pink Yellow Gray Yellow Gray Purple Pink Gray Purple Purple Gray Purple Pink Pink Pink Purple Purple Gray Gray Gray Pink Gray Purple Yellow Gray Purple Gray Gray Purple Pink
Row 6: Purple Gray Gray Purple Gray Gray Pink Pink Pink Purple Pink Purple Purple Gray Purple Purple Gray Gray Pink Yellow Gray Purple Gray Gray Pink Purple Purple Yellow Gray Yellow
Row 7: Purple Pink Pink Gray Pink Pink Yellow Yellow Pink Gray Purple Gray Pink Purple Purple Purple Purple Yellow Yellow Gray Purple Gray Pink Pink Purple Gray Gray Pink Gray Gray
Output:
Row 1: Gray Yellow Pink Pink Purple Yellow Purple Gray Pink Gray Gray Gray Purple Gray Pink Pink Pink Pink Gray Gray Gray Gray Pink Gray Pink Pink Pink Yellow Pink Gray
Row 2: Yellow Pink Purple Yellow Purple Gray Yellow Pink Pink Purple Gray Purple Yellow Pink Pink Yellow Gray Gray Yellow Pink Pink Purple Yellow Gray Gray Pink Gray Purple Pink Gray
Row 3: Gray Gray Gray Yellow Pink Purple Pink Gray Gray Pink Purple Pink Gray Pink Gray Gray Pink Yellow Gray Gray Yellow Pink Pink Gray Purple Gray Gray Gray Gray Yellow
Row 4: Pink Pink Purple Gray Gray Purple Pink Yellow Purple Gray Gray Pink Yellow Gray Yellow Pink Pink Purple Pink Pink Pink Purple Gray Purple Gray Gray Pink Gray Gray Pink
Row 5: Pink Yellow Gray Yellow Gray Purple Pink Gray Purple Purple Gray Purple Pink Pink Pink Purple Purple Gray Gray Gray Pink Gray Purple Yellow Gray Purple Gray Gray Purple Pink
Row 6: Purple Gray Gray Purple Gray Gray Pink Pink Pink Purple Pink Purple Purple Gray Purple Purple Gray Gray Pink Yellow Gray Purple Gray Gray Pink Purple Purple Yellow Gray Yellow
Row 7: Purple Pink Pink Gray Pink Pink Yellow Yellow Pink Gray Purple Gray Pink Purple Purple Purple Purple Yellow Yellow Gray Purple Gray Pink Pink Purple Gray Gray Pink Gray Gray
Row 8: Purple Pink Pink Gray Pink Pink Yellow Yellow Pink Gray Purple Gray Pink Purple Purple Purple Purple Yellow Yellow Gray Purple Gray Pink Pink Purple Gray Gray Pink Gray Gray
Row 9: Purple Gray Gray Purple Gray Gray Pink Pink Pink Purple Pink Purple Purple Gray Purple Purple Gray Gray Pink Yellow Gray Purple Gray Gray Pink Purple Purple Yellow Gray Yellow
Row 10: Pink Yellow Gray Yellow Gray Purple Pink Gray Purple Purple Gray Purple Pink Pink Pink Purple Purple Gray Gray Gray Pink Gray Purple Yellow Gray Purple Gray Gray Purple Pink
Row 11: Pink Pink Purple Gray Gray Purple Pink Yellow Purple Gray Gray Pink Yellow Gray Yellow Pink Pink Purple Pink Pink Pink Purple Gray Purple Gray Gray Pink Gray Gray Pink
Row 12: Gray Gray Gray Yellow Pink Purple Pink Gray Gray Pink Purple Pink Gray Pink Gray Gray Pink Yellow Gray Gray Yellow Pink Pink Gray Purple Gray Gray Gray Gray Yellow
Row 13: Yellow Pink Purple Yellow Purple Gray Yellow Pink Pink Purple Gray Purple Yellow Pink Pink Yellow Gray Gray Yellow Pink Pink Purple Yellow Gray Gray Pink Gray Purple Pink Gray
Row 14: Gray Yellow Pink Pink Purple Yellow Purple Gray Pink Gray Gray Gray Purple Gray Pink Pink Pink Pink Gray Gray Gray Gray Pink Gray Pink Pink Pink Yellow Pink Gray
Example 3
Input:
Row 1: Gray Gray Black Black Purple Gray Gray Gray Gray Gray Gray Black Purple Gray Gray Purple Gray Gray Gray Black Gray Purple Gray Blue Purple
Row 2: Black Gray Blue Blue Black Gray Gray Gray Gray Purple Purple Gray Blue Blue Black Gray Gray Black Gray Purple Blue Black Black Purple Blue
Row 3: Black Gray Gray Black Blue Blue Gray Black Purple Purple Gray Gray Gray Gray Gray Blue Purple Gray Gray Gray Black Gray Blue Purple Black
Output:
Row 1: Gray Gray Black Black Purple Gray Gray Gray Gray Gray Gray Black Purple Gray Gray Purple Gray Gray Gray Black Gray Purple Gray Blue Purple
Row 2: Black Gray Blue Blue Black Gray Gray Gray Gray Purple Purple Gray Blue Blue Black Gray Gray Black Gray Purple Blue Black Black Purple Blue
Row 3: Black Gray Gray Black Blue Blue Gray Black Purple Purple Gray Gray Gray Gray Gray Blue Purple Gray Gray Gray Black Gray Blue Purple Black
Row 4: Black Gray Gray Black Blue Blue Gray Black Purple Purple Gray Gray Gray Gray Gray Blue Purple Gray Gray Gray Black Gray Blue Purple Black
Row 5: Black Gray Blue Blue Black Gray Gray Gray Gray Purple Purple Gray Blue Blue Black Gray Gray Black Gray Purple Blue Black Black Purple Blue
Row 6: Gray Gray Black Black Purple Gray Gray Gray Gray Gray Gray Black Purple Gray Gray Purple Gray Gray Gray Black Gray Purple Gray Blue Purple
Here is the input grid for the test example:
Input:
Row 1: Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Black Black Blue Purple Purple Purple Purple Purple Black Blue Blue Purple Purple
Row 2: Black Purple Purple Purple Black Black Purple Purple Black Black Purple Purple Blue Black Purple Red Black Purple Purple Purple Black Purple Purple
Row 3: Purple Purple Black Purple Purple Purple Purple Purple Red Purple Black Blue Black Black Purple Purple Blue Purple Purple Black Purple Purple Black
Row 4: Purple Purple Blue Purple Black Purple Purple Purple Blue Black Purple Purple Blue Blue Purple Black Purple Purple Black Black Purple Purple Purple
Row 5: Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Black Purple Purple Black Black Black Purple Purple Black Black Purple Black
Row 6: Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Blue Purple Purple Purple Purple Purple
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Black Black Blue Purple Purple Purple Purple Purple Black Blue Blue Purple Purple
Black Purple Purple Purple Black Black Purple Purple Black Black Purple Purple Blue Black Purple Red Black Purple Purple Purple Black Purple Purple
Purple Purple Black Purple Purple Purple Purple Purple Red Purple Black Blue Black Black Purple Purple Blue Purple Purple Black Purple Purple Black
Purple Purple Blue Purple Black Purple Purple Purple Blue Black Purple Purple Blue Blue Purple Black Purple Purple Black Black Purple Purple Purple
Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Black Purple Purple Black Black Black Purple Purple Black Black Purple Black
Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Blue Purple Purple Purple Purple Purple
Purple Purple Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Black Purple Black Purple Blue Purple Purple Purple Purple Purple
Purple Purple Purple Black Black Purple Purple Purple Purple Purple Purple Black Purple Purple Black Black Black Purple Purple Black Black Purple Black
Purple Purple Blue Purple Black Purple Purple Purple Blue Black Purple Purple Blue Blue Purple Black Purple Purple Black Black Purple Purple Purple
Purple Purple Black Purple Purple Purple Purple Purple Red Purple Black Blue Black Black Purple Purple Blue Purple Purple Black Purple Purple Black
Black Purple Purple Purple Black Black Purple Purple Black Black Purple Purple Blue Black Purple Red Black Purple Purple Purple Black Purple Purple
Purple Purple Purple Blue Purple Purple Purple Purple Purple Purple Black Black Blue Purple Purple Purple Purple Purple Black Blue Blue Purple Purple |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Purple Purple Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple
Row 2: Purple Orange Purple Purple Purple Orange Orange Orange Orange Purple Purple Orange Purple Orange Purple Purple
Row 3: Orange Orange Orange Orange Orange Orange Purple Orange Purple Purple Purple Orange Purple Orange Orange Purple
Row 4: Orange Orange Orange Orange Purple Orange Orange Purple Purple Orange Purple Orange Purple Orange Purple Orange
Row 5: Orange Orange Orange Orange Purple Orange Purple Yellow Orange Orange Orange Orange Orange Orange Purple Purple
Row 6: Orange Orange Orange Orange Orange Purple Purple Purple Yellow Orange Purple Orange Orange Purple Purple Orange
Row 7: Orange Purple Purple Orange Orange Purple Orange Purple Yellow Yellow Purple Orange Orange Orange Purple Purple
Row 8: Orange Orange Orange Purple Orange Orange Orange Purple Orange Yellow Yellow Orange Purple Purple Purple Orange
Row 9: Purple Orange Orange Purple Orange Purple Orange Orange Yellow Yellow Purple Purple Purple Orange Orange Orange
Row 10: Purple Purple Orange Purple Purple Orange Orange Orange Yellow Orange Orange Purple Purple Purple Orange Purple
Row 11: Orange Orange Purple Orange Orange Orange Orange Yellow Orange Orange Purple Orange Orange Orange Orange Orange
Row 12: Orange Orange Purple Purple Orange Purple Orange Orange Purple Orange Purple Purple Purple Purple Orange Orange
Row 13: Purple Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Purple Orange Purple Purple Orange
Output:
Row 1: Purple Purple Purple Orange Orange Orange Orange Orange Purple Purple Purple Purple Orange Orange Purple Purple
Row 2: Purple Orange Purple Purple Purple Orange Orange Orange Orange Purple Purple Orange Purple Orange Purple Purple
Row 3: Orange Orange Orange Orange Orange Orange Purple Orange Purple Purple Purple Orange Purple Orange Orange Purple
Row 4: Orange Orange Orange Orange Purple Orange Orange Purple Purple Orange Purple Orange Purple Orange Purple Orange
Row 5: Purple Purple Purple Purple Purple Purple Purple Yellow Orange Orange Orange Orange Orange Orange Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Yellow Orange Purple Orange Orange Purple Purple Orange
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Purple Orange Orange Orange Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Orange Purple Purple Purple Orange
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Yellow Yellow Purple Purple Purple Orange Orange Orange
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Yellow Orange Orange Purple Purple Purple Orange Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Yellow Orange Orange Purple Orange Orange Orange Orange Orange
Row 12: Orange Orange Purple Purple Orange Purple Orange Orange Purple Orange Purple Purple Purple Purple Orange Orange
Row 13: Purple Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Purple Orange Purple Purple Orange
Example 2
Input:
Row 1: Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Orange Blue Blue Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 4: Orange Orange Blue Blue Red Red Blue Red Red Blue Blue Blue Blue Blue Blue
Row 5: Blue Orange Blue Red Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Orange Blue
Row 7: Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue Orange Blue Blue Blue Orange Blue Blue Orange Blue Blue Orange
Row 11: Orange 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 Orange
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 Orange Blue Blue Blue Blue Blue Blue
Row 15: Orange Blue Blue Blue Blue Orange Blue Blue Blue Orange Blue Orange Blue Blue Blue
Row 16: Blue Blue Orange Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Orange 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 Orange Blue Blue
Row 20: Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Blue Blue Blue Orange Orange Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Orange Blue Blue Red Red Red Blue Blue Blue Blue Blue Blue Blue
Row 4: Orange Orange Blue Blue Red Red Orange Red Red Blue Blue Blue Blue Blue Blue
Row 5: Blue Orange Blue Red Orange Orange Orange Orange Orange Red Blue Blue Blue Blue Blue
Row 6: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Orange Blue
Row 7: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 8: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 9: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 10: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Orange Blue Blue Orange
Row 11: Orange Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Orange
Row 13: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 14: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 15: Orange Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Orange Blue Blue Blue
Row 16: Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 17: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 18: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Orange Blue Blue
Row 20: Blue Orange Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Row 21: Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Orange Pink Pink Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Pink Pink Pink Pink Orange
Row 2: Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Pink Pink Orange Orange Pink Pink Orange Orange Orange Orange Orange Pink Orange Orange Pink Orange Pink
Row 3: Orange Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Pink Pink Pink Pink Pink Orange Pink Orange Pink Orange Pink Pink Pink Pink Orange
Row 4: Orange Orange Orange Orange Pink Pink Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Pink Orange Orange Pink Pink Pink Orange Pink Orange Pink Orange Pink
Row 5: Pink Orange Orange Pink Orange Orange Pink Orange Pink Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Pink Orange Orange Pink Pink Pink Orange
Row 6: Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Orange Gray Pink Orange Pink Pink Orange Gray Orange Pink Pink
Row 7: Pink Pink Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Orange Orange Pink Orange Pink Pink Pink Pink Pink Gray Gray Orange Gray Gray Pink Pink Pink Orange
Row 8: Orange Pink Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange Pink Pink Pink Orange Orange Orange Pink Orange Orange Orange Gray Gray Gray Orange Pink Orange Pink Orange
Row 9: Orange Pink Orange Pink Pink Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Orange Pink Pink Pink Orange Pink Gray Pink Orange Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink
Row 11: Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Orange Orange Orange Pink Pink Pink Orange Pink Pink Pink Orange Orange Orange Pink Orange
Row 12: Orange Orange Orange Orange Pink Orange Orange Pink Orange Pink Pink Orange Orange Pink Orange Orange Pink Pink Pink Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Pink
Row 13: Pink Orange Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Pink Orange Orange Pink Pink Orange Orange Pink Pink Orange Orange Pink
Row 14: Pink Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Pink Pink Pink Orange Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Orange Pink
Row 15: Orange Pink Pink Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Row 16: Pink Orange Orange Orange Pink Pink Pink Orange Orange Pink Orange Pink Pink Orange Orange Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Orange Orange
Row 17: Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Pink Pink Pink Pink Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange
Row 18: Pink Orange Orange Pink Orange Pink Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Orange Pink Pink
Row 19: Orange Pink Orange Pink Pink Pink Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Pink Orange Pink Pink
Output:
Row 1: Orange Pink Pink Pink Orange Orange Orange Orange Pink Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 2: Orange Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Pink Pink Orange Orange Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink
Row 3: Orange Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 4: Orange Orange Orange Orange Pink Pink Orange Pink Orange Orange Pink Orange Orange Orange Pink Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Orange Pink
Row 5: Pink Orange Orange Pink Orange Orange Pink Orange Pink Pink Pink Pink Pink Orange Pink Orange Orange Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Orange
Row 6: Pink Orange Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Orange Gray Pink Pink Pink Pink Pink Gray Orange Pink Pink
Row 7: Pink Pink Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink Orange Orange Pink Orange Pink Pink Pink Pink Pink Gray Gray Pink Gray Gray Pink Pink Pink Orange
Row 8: Orange Pink Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange Pink Pink Pink Orange Orange Orange Pink Orange Orange Orange Gray Gray Gray Orange Pink Orange Pink Orange
Row 9: Orange Pink Orange Pink Pink Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink Orange Orange Orange Pink Pink Pink Orange Pink Gray Pink Orange Pink Pink Pink Pink
Row 10: Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Pink Orange Orange Orange Orange Pink
Row 11: Orange Orange Orange Orange Pink Orange Pink Pink Orange Pink Pink Orange Pink Pink Orange Orange Orange Orange Pink Pink Pink Orange Pink Pink Pink Orange Orange Orange Pink Orange
Row 12: Orange Orange Orange Orange Pink Orange Orange Pink Orange Pink Pink Orange Orange Pink Orange Orange Pink Pink Pink Orange Orange Orange Pink Pink Pink Orange Orange Orange Orange Pink
Row 13: Pink Orange Orange Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Pink Orange Orange Orange Pink Orange Orange Pink Pink Orange Orange Pink Pink Orange Orange Pink
Row 14: Pink Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Pink Pink Pink Orange Pink Pink Pink Pink Orange Pink Pink Pink Pink Pink Pink Pink Orange Pink
Row 15: Orange Pink Pink Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange Orange Pink Pink Pink Pink Pink Pink Orange Orange Orange Orange Orange Orange Pink Pink Pink Orange
Row 16: Pink Orange Orange Orange Pink Pink Pink Orange Orange Pink Orange Pink Pink Orange Orange Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Orange Orange Orange Orange Orange
Row 17: Pink Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange Orange Pink Orange Orange Pink Pink Pink Pink Orange Orange Orange Pink Orange Orange Orange Pink Orange Orange
Row 18: Pink Orange Orange Pink Orange Pink Pink Orange Pink Orange Pink Orange Pink Pink Orange Orange Pink Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Orange Pink Pink
Row 19: Orange Pink Orange Pink Pink Pink Pink Orange Orange Orange Orange Pink Orange Orange Orange Pink Orange Pink Orange Orange Pink Pink Pink Pink Orange Pink Pink Orange Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray
Row 2: Gray Pink Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Row 3: Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Pink Gray Gray
Row 4: Gray Gray Gray Gray Gray Gray Black Black Gray Pink Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Gray Gray
Row 7: Gray Gray Gray Gray Pink Gray Gray Black Gray Gray Gray Gray Gray Gray
Row 8: Pink Gray Gray Gray Gray Gray Gray Gray Black 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 Pink Gray Gray Gray Gray Gray
Gray Pink Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray
Gray Gray Gray Gray Gray Gray Gray Black Pink Pink Pink Pink Pink Pink
Gray Gray Gray Gray Gray Gray Black Black Pink Pink Pink Pink Pink Pink
Gray Gray Gray Gray Gray Black Black 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 Pink Gray Gray Black Gray Gray Gray Gray Gray Gray
Pink Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray Gray |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Pink Black Black Pink Black Black Black Black Black Black Black Black
Row 3: Black Brown Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 5: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 6: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 7: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 8: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 9: Black Black Black Black Black Black Black Black Black Black Pink Black Black
Row 10: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 11: Black Black Black Black Black Black Black Black Orange Red 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 Red Black Black Black
Row 14: Black Black Black Black Black Black Black Black Orange Red Black Black Black
Row 15: Black Black Black Black Black Black Black Black Black Red Black Black Black
Row 16: Black Black Black Orange Black Black Black Black Black Red Pink Black Black
Row 17: Black Black Black Black Black Black Green Black Orange Black Black Black Black
Row 18: Black Pink Black Black Black Black Pink Black Black Red Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Gray 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 Pink Black Black Pink Black Black Black Black Black Black Black Black
Row 3: Black Brown Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 5: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 6: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 7: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 8: Black Black Black Black Black Black Black Yellow Yellow Yellow Yellow Yellow Black
Row 9: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 10: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 11: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 12: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 13: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 14: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 15: Black Black Black Black Black Black Black Black Orange Red Pink Black Black
Row 16: Black Black Black Orange Black Black Black Black Orange Red Pink Black Black
Row 17: Black Black Black Black Black Black Green Black Orange Red Black Black Black
Row 18: Black Pink Black Black Black Black Pink Black Black Red Black Black Black
Row 19: Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 20: Black Black Black Black Black Black Gray Black Black Black Black Black Black
Example 2
Input:
Row 1: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Brown Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Black Blue Red Red Red Red Red Red Red Blue Orange Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Brown Blue Red Red Red Red Red Red Red Blue Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Brown Blue Brown Blue
Row 5: Green Blue Blue Green Green Green Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Brown Brown Blue Blue Blue Blue Brown Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Black Black Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Blue Blue Blue Blue Blue Blue Brown Blue Blue Brown Blue Blue Blue Blue Blue Brown
Row 8: Blue Blue Blue Green Blue Blue Red Red Red Red Red Red Red Black Blue Blue Blue Blue Black Blue Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Green Blue Blue Blue Red Red Red Red Red Red Red Blue Blue Blue Orange Blue Orange Orange Blue Blue Blue Orange Orange Blue Blue Blue Orange
Row 10: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Orange Blue Blue Blue Blue Blue Green Blue Brown Green Blue Blue Blue Brown Blue Blue Blue
Row 11: Brown Blue Blue Blue Blue Blue Blue Blue Black Green Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Orange Blue Blue Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Black Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Blue Orange Black Blue Blue Black Blue Blue
Row 14: Blue Black Blue Green Brown Blue Blue Blue Blue Green Blue Blue Orange Blue Brown Black Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Brown Blue Blue Blue Green Blue
Row 16: Blue Blue Blue Blue Blue Blue Blue Black Blue Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Brown Blue Green Blue
Row 17: Brown Blue Black Black Blue Blue Orange Black Blue Green Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Brown Orange Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Black Blue Blue
Row 20: Blue Blue Blue Blue Green Blue Blue Black Blue Blue Orange Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Black Blue Blue Blue Blue Blue Green Blue
Row 21: Blue Blue Brown Blue Orange Blue Orange Blue Blue Blue Orange Blue Orange Green Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue Blue
Row 2: Blue Blue Blue Blue Black Black Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 3: Blue Blue Blue Blue Brown Brown Red Red Red Red Red Red Red Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue
Row 5: Green Green Green Green Green Green Red Red Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue
Row 6: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Black Black Black Black Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Red Red Red Red Red Red Red Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Blue Blue Blue Green Green Green Red Red Red Red Red Red Red Black Black Black Black Black Black Black Black Blue Blue Blue Blue Blue Blue Blue Blue
Row 9: Blue Blue Green Green Green Green Red Red Red Red Red Red Red Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Blue Blue Blue Blue Blue Blue Orange Black Black Green Orange Blue Orange Blue Blue Blue Blue Blue Green Blue Brown Green Blue Blue Blue Brown Blue Blue Blue
Row 11: Brown Blue Blue Blue Blue Blue Orange Black Black Green Orange Blue Orange Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue Orange Blue Orange Black Black Green Orange Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 13: Blue Black Blue Green Blue Blue Orange Black Blue Green Orange Blue Orange Blue Blue Blue Blue Blue Blue Blue Brown Blue Orange Black Blue Blue Black Blue Blue
Row 14: Blue Black Blue Green Brown Blue Orange Black Blue Green Orange Blue Orange Blue Brown Black Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 15: Orange Blue Blue Blue Blue Blue Orange Black Blue Green Orange Blue Orange Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Brown Blue Blue Blue Green Blue
Row 16: Blue Blue Blue Blue Blue Blue Orange Black Blue Green Orange Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Brown Blue Green Blue
Row 17: Brown Blue Black Black Blue Blue Orange Black Blue Green Orange Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue
Row 18: Blue Blue Blue Blue Blue Orange Orange Black Blue Blue Orange Blue Orange Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 19: Blue Blue Blue Blue Brown Orange Orange Black Blue Blue Orange Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Black Blue Blue
Row 20: Blue Blue Blue Blue Green Blue Orange Black Blue Blue Orange Blue Orange Blue Blue Blue Blue Green Blue Blue Blue Black Blue Blue Blue Blue Blue Green Blue
Row 21: Blue Blue Brown Blue Orange Blue Orange Blue Blue Blue Orange Blue Orange Green Blue Blue Blue Blue Blue Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue
Example 3
Input:
Row 1: Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 2: Blue Blue Blue Purple Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue
Row 3: Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple Blue Blue Purple Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Purple Purple Blue Purple Blue Blue Blue Purple Purple Purple Purple
Row 5: Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple
Row 6: Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Blue Purple Blue Purple Purple Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 8: Blue Purple Blue Blue Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Blue Blue Blue Purple Purple
Row 9: Blue Blue Blue Purple Blue Purple Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Purple Blue Blue Blue Blue Blue
Row 10: Purple Blue Blue Blue Blue Purple Purple Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Purple Blue Blue Blue Purple
Row 11: Blue Blue Blue Purple Blue Blue Blue Blue Orange Orange Orange Orange Orange Orange Orange Orange Blue Blue Purple Blue Purple Blue Blue
Row 12: Purple Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple
Row 13: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 14: Blue Blue Purple Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 2: Blue Blue Blue Purple Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Purple Blue Blue Blue Blue
Row 3: Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple Blue Blue Purple Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue
Row 4: Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Purple Purple Purple Purple Blue Blue Blue Purple Purple Purple Purple
Row 5: Blue Blue Blue Blue Purple Blue Blue Blue Blue Purple Blue Blue Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue Purple
Row 6: Blue Blue Blue Blue Blue Blue Blue Purple Purple Purple Blue Blue Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Blue
Row 7: Blue Blue Blue Blue Blue Blue Purple Blue Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Blue Blue Purple Blue
Row 8: Blue Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 9: Blue Blue Blue Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Blue Blue Blue Blue Blue
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple
Row 11: Blue Blue Blue Purple Purple Purple Purple Purple Orange Orange Orange Orange Orange Orange Orange Orange Purple Purple Purple Purple Purple Blue Blue
Row 12: Purple Blue Purple Blue Purple Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Purple
Row 13: Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue
Row 14: Blue Blue Purple Blue Purple Purple Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Red Red Red Red Red Red Red Red Gray Red Red Red Purple Gray Red Red Red Red Red Red Red Pink Red Red
Row 2: Red Red Red Yellow 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 Purple Red Red Blue 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 Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Pink 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
Row 11: Red Red Red Red Orange 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 Yellow Purple Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Red Red Red Red Gray Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Yellow Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Red Red Red Red Red Red Red Red Red Black Black Red Yellow Red Red Yellow Red Red Red Red Red Red Red Red
Row 18: Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Yellow Red
Row 20: Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Purple Red Red Red Red Purple
Row 21: Red Gray Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Orange Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Gray Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Orange Red Red Red Red Red Red Red Red Gray Blue Red Red Red Red Red Red Brown Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
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 Gray Red Red Red Purple Gray Red Red Red Red Red Red Red Pink Red Red
Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Purple Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red 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 Yellow Purple Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Gray Gray Gray Gray Gray Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Yellow Yellow Yellow Yellow Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Black Black Yellow Yellow Yellow Yellow Yellow Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Black Black Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Red
Red Red Red Red Red Red Red Red Red Black Black Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Red Gray Gray Gray Gray Gray Gray Gray Gray Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Orange Orange Orange Black Black Red Red Red Red Red Red Red Red Red Red Red Red Red
Gray Red Red Red Blue Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Red Red Orange Red Red Red Red Red Red Red Red Gray Blue Red Red Red Red Red Red Brown Red Red Red Red
Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red 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: Black Black Brown Black Black Gray Black Yellow Black
Row 2: Black Black Brown Black Black Gray Black Yellow Black
Row 3: Black Black Brown Black Black Gray Black Yellow Black
Row 4: Black Black Brown Black Black Gray Black Yellow Black
Row 5: Black Black Brown Black Black Gray Black Yellow Black
Row 6: Black Black Brown Black Black Gray Black Yellow Black
Row 7: Gray Gray Brown Gray Gray Gray Gray Yellow Gray
Row 8: Black Black Brown Black Black Gray Black Yellow Black
Row 9: Black Black Brown Black Black Gray Black Yellow Black
Row 10: Black Black Brown Black Black Gray Black Yellow Black
Row 11: Red Red Brown Red Red Gray Red Yellow Red
Row 12: Black Black Brown Black Black Gray Black Yellow Black
Row 13: Black Black Brown Black Black Gray Black Yellow Black
Row 14: Brown Brown Brown Brown Brown Gray Brown Yellow Brown
Row 15: Black Black Brown Black Black Gray Black Yellow Black
Row 16: Black Black Brown Black Black Gray Black Yellow Black
Row 17: Black Black Brown Black Black Gray Black Yellow Black
Row 18: Black Black Brown Black Black Gray Black Yellow Black
Row 19: Black Black Brown Black Black Gray Black Yellow Black
Row 20: Black Black Brown Black Black Gray Black Yellow Black
Row 21: Black Black Brown Black Black Gray Black Yellow Black
Row 22: Brown Brown Brown Brown Brown Gray Brown Yellow Brown
Row 23: Black Black Brown Black Black Gray Black Yellow Black
Row 24: Yellow Yellow Brown Yellow Yellow Gray Yellow Yellow Yellow
Row 25: Black Black Brown Black Black Gray Black Yellow Black
Row 26: Red Red Brown Red Red Gray Red Yellow Red
Row 27: Black Black Brown Black Black Gray Black Yellow Black
Row 28: Black Black Brown Black Black Gray Black Yellow Black
Output:
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 Black Black Black
Row 6: Black Black Black Black
Row 7: Black Black Black Black
Example 2
Input:
Row 1: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 8: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 12: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 13: Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 14: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 15: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 16: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 17: Gray Gray Gray Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 18: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 19: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 20: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 21: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 24: Brown Brown Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Green Green Green Green Green Yellow Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 29: Red Red Red Red Red Yellow Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Output:
Row 1: Red Red
Row 2: Red Red
Row 3: Red Red
Row 4: Red Red
Row 5: Red Red
Example 3
Input:
Row 1: Gray Red Gray Gray Gray
Row 2: Gray Red Gray Gray Gray
Row 3: Gray Red Gray Gray Gray
Row 4: Gray Red Gray Gray Gray
Row 5: Gray Red Gray Gray Gray
Row 6: Purple Red Purple Purple Purple
Row 7: Gray Red Gray Gray Gray
Row 8: Gray Red Gray Gray Gray
Row 9: Gray Red Gray Gray Gray
Row 10: Red Red Red Red Red
Row 11: Gray Red Gray Gray Gray
Row 12: Gray Red Gray Gray Gray
Row 13: Purple Red Purple Purple Purple
Row 14: Gray Red Gray Gray Gray
Row 15: Purple Red Purple Purple Purple
Row 16: Gray Red Gray Gray Gray
Row 17: Gray Red Gray Gray Gray
Row 18: Brown Red Brown Brown Brown
Row 19: Gray Red Gray Gray Gray
Row 20: Gray Red Gray Gray Gray
Output:
Row 1: Gray Gray
Row 2: Gray Gray
Row 3: Gray Gray
Row 4: Gray Gray
Row 5: Gray Gray
Row 6: Gray Gray
Here is the input grid for the test example:
Input:
Row 1: Red Pink Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 2: Black Pink Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Red Pink Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Pink Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Pink Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 6: Red Pink Red Red Red Black Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 7: Red Pink Red Red Red Black 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 |
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 Green Green Blue Orange Green Orange Yellow Orange
Row 2: Orange Orange Orange Orange Red Orange Orange Red Orange Orange Orange Orange Orange Yellow Orange
Row 3: Purple Orange Orange Orange Orange Orange Orange Orange Red Orange Purple Orange Blue Orange Orange
Row 4: Orange Orange Orange Orange Blue Orange Orange Orange Orange Brown Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Purple Orange Orange Gray Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Brown Brown Orange Orange Orange Red Orange Orange Orange Orange Orange
Row 7: Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Green
Row 8: Green Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink Orange Orange Gray Green
Row 9: Orange Orange Orange Orange Red Orange Orange Orange Purple Orange Red Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Blue Orange Pink Orange Orange Orange Orange Orange Orange Orange
Row 11: Pink Purple Orange Orange Gray Orange Orange Orange Orange Orange Orange Pink Orange Orange Orange
Row 12: Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 13: Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Red Orange Black Orange
Row 14: Orange Pink Orange Gray Yellow Yellow Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Black Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 16: Orange Orange Orange Orange Orange Orange Pink Orange Pink Orange Brown Orange Red Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange Orange Orange Orange Orange
Row 18: Orange Orange Orange Red Orange Red Orange Orange Orange Orange Orange Orange Orange Gray Orange
Row 19: Orange Black Orange Orange Orange Orange Orange Gray Orange Orange Blue Orange Black Orange Red
Row 20: Orange Orange Blue Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange
Row 21: Green Orange Orange Black Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Green
Row 22: Yellow Blue Black Orange Orange Orange Yellow Orange Orange Orange Orange Pink Red Orange Orange
Row 23: Orange Orange Orange Black Purple Gray Pink Yellow Orange Orange Orange Blue Orange Red Black
Row 24: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 26: Green Orange Pink Orange Gray Orange Orange Pink Orange Pink Orange Orange Yellow Orange Green
Row 27: Orange Orange Orange Orange Purple Orange Brown Orange Orange Orange Orange Orange Black Orange Orange
Row 28: Green Orange Brown Orange Orange Brown Orange Orange Orange Orange Orange Red Gray Orange Green
Row 29: Orange Orange Orange Orange Orange Orange Pink Green Green Orange Orange Green Orange Orange Black
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 9: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 13: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 17: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 18: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 19: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 20: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 21: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 22: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 23: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 24: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 25: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 26: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 27: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Row 28: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green
Row 29: Orange Orange Orange Orange Orange Orange Orange Green Green Orange Orange Green Orange Orange Orange
Example 2
Input:
Row 1: Green Gray Blue Black Gray Green Green Green Yellow Yellow Green Red Red Red Purple Green Red Green Green Green
Row 2: Green Green Green Green Green Gray Green Green Gray Green Green Green Green Orange Green Green Green Green Green Green
Row 3: Red Green Green Green Green Black Green Yellow Green Black Green Gray Yellow Green Green Black Blue Green Green Red
Row 4: Green Green Green Green Green Green Green Purple Green Green Orange Green Green Green Purple Green Black Green Green Green
Row 5: Green Blue Black Blue Orange Pink Black Yellow Yellow Green Green Green Purple Green Green Green Green Gray Green Green
Row 6: Orange Yellow Green Green Green Green Black Green Green Green Orange Green Green Pink Yellow Green Green Green Blue Green
Row 7: Green Green Green Blue Green Gray Green Orange Green Green Green Black Green Green Black Gray Green Blue Green Green
Row 8: Green Brown Green Green Orange Green Purple Green Green Green Black Red Red Red Green Black Red Green Green Blue
Output:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Row 2: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Row 3: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Row 5: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Row 6: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Row 7: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Row 8: Green Green Green Green Green Green Green Green Green Green Green Red Red Red Green Green Red Green Green Green
Example 3
Input:
Row 1: Blue Black Yellow Blue Purple Purple Blue Blue Blue Green Blue Blue Blue Blue Green Purple Blue Green Green Blue Green Blue Blue Green Blue
Row 2: Blue Blue Yellow Blue Blue Blue Blue Blue Blue Gray Blue Blue Blue Blue Black Blue Black Blue Blue Blue Blue Blue Blue Gray Black
Row 3: Blue Blue Blue Blue Purple Blue Blue Blue Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Blue Red Purple Brown
Row 4: Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Orange Yellow Pink Red Blue Yellow Brown Brown Pink Blue Gray Blue Blue Blue Green
Row 5: Blue Blue Blue Gray Blue Purple Orange Purple Pink Blue Black Blue Blue Blue Pink Blue Blue Gray Red Blue Blue Pink Blue Yellow Blue
Row 6: Blue Blue Yellow Blue Blue Brown Blue Blue Blue Blue Blue Blue Blue Blue Purple Blue Red Blue Gray Gray Blue Gray Blue Blue Red
Row 7: Red Blue Blue Blue Blue Blue Yellow Pink Blue Orange Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Row 8: Blue Yellow Blue Blue Blue Red Yellow Blue Blue Blue Blue Blue Blue Orange Blue Blue Blue Black Blue Orange Blue Blue Blue Brown Orange
Row 9: Blue Blue Blue Blue Brown Orange Blue Blue Orange Green Blue Blue Blue Blue Green Black Blue Green Green Blue Green Blue Blue Green Blue
Output:
Row 1: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Row 2: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Row 3: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
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: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Row 6: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Row 7: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Row 8: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Row 9: Blue Blue Blue Blue Blue Blue Blue Blue Blue Green Blue Blue Blue Blue Green Blue Blue Green Green Blue Green Blue Blue Green Blue
Here is the input grid for the test example:
Input:
Row 1: Yellow Red Red Red Red Pink Red Brown Red Red Red Red Black Red Pink Red Red Purple Red
Row 2: Pink Red Red Red Red Red Red Red Brown Green Red Red Red Red Red Red Black Blue Pink
Row 3: Red Red Red Red Yellow Red Gray Red Red Brown Red Red Blue Red Red Red Red Yellow Gray
Row 4: Gray Red Red Red Red Red Red Red Red Red Yellow Gray Red Red Red Red Gray Orange Black
Row 5: Red Red Red Red Red Green Red Red Red Red Red Red Orange Red Red Red Red Red Brown
Row 6: Pink Red Blue Purple Red Red Red Orange Red Red Yellow Red Brown Brown Red Red Red Red Pink
Row 7: Red Red Red Red Brown Red Red Blue Red Blue Red Red Red Red Red Red Red Red Purple
Row 8: Blue Red Red Black Red Red Red Red Brown Gray Red Purple Red Red Red Red Orange Red Red
Row 9: Red Red Orange Red Red Red Yellow Red Gray Red Orange Red Red Red Black Red Red Red Red
Row 10: Red Orange Purple Orange Red Red Red Blue Red Red Red Brown Red Red Red Red Black Red Red
Row 11: Red Red Red Red Red Red Red Red Red Black Red Yellow Yellow Red Red Red Red Red Red
Row 12: Pink Red Yellow Red Blue Red Red Blue Red Green Gray Red Red Red Red Red Orange Red Pink
Row 13: Red Orange Orange Red Red Yellow Red Red Red Red Red Red Red Red Green Red Red Purple Red
Row 14: Red Black Green Red Red Red Orange Brown Purple Red Red Purple Red Gray Gray Red Yellow Red Yellow
Row 15: Orange Red Red Red Gray Red Red Gray Red Red Red Red Red Red Yellow Red Black Green Red
Row 16: Red Purple Red Red Yellow Red Red Blue Red Red Red Red Purple Red Red Red Red Red Brown
Row 17: Orange Orange Red Brown Red Red Red Green Red Red Red Red Red Red Red Red Red Purple Orange
Row 18: Red Red Blue Red Red Red Red Gray Red Red Red Yellow Red Red Red Red Gray Red Gray
Row 19: Pink Red Red Red Gray Red Red Green Red Red Gray Orange Blue Blue Red Green Red Red Pink
Row 20: Gray Red Red Black Red Red Orange Purple Red Red Red Red Red Red Red Orange Purple Red Gray
Row 21: Red Red Red Black Red Pink Red Red Orange Red Red Yellow Gray Red Pink Red Gray Blue 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 Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink Red Red Red Red
Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Pink 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: 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 Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple
Row 12: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Orange Purple Purple Orange Blue Purple Purple Purple Purple
Row 14: Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 20: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Orange Purple Purple Orange Blue Purple Purple Purple Purple
Row 2: Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple
Row 4: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Orange Purple Purple Orange Blue Purple Purple Purple Purple
Row 6: Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple
Row 8: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Orange Purple Purple Orange Blue Purple Purple Purple Purple
Row 10: Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple
Row 12: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Orange Purple Purple Orange Blue Purple Purple Purple Purple
Row 14: Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple
Row 16: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Orange Purple Purple Orange Blue Purple Purple Purple Purple
Row 18: Purple Purple Blue Purple Green Purple Purple Purple Purple Purple Purple
Row 19: Purple Purple Purple Purple Orange Blue Purple Purple Purple Purple Purple
Row 20: Purple Purple Green Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange
Row 7: Orange Orange Orange Orange Orange Orange Orange
Row 8: Orange Orange Orange Orange Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange
Row 11: Black Orange Orange Orange Orange Orange Orange
Row 12: Orange Green Orange Orange Orange Orange Orange
Row 13: Orange Brown Orange Orange Orange Orange Orange
Row 14: Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Orange Brown Orange Orange Orange Orange Orange
Row 2: Black Orange Orange Orange Orange Orange Orange
Row 3: Orange Green Orange Orange Orange Orange Orange
Row 4: Orange Brown Orange Orange Orange Orange Orange
Row 5: Black Orange Orange Orange Orange Orange Orange
Row 6: Orange Green Orange Orange Orange Orange Orange
Row 7: Orange Brown Orange Orange Orange Orange Orange
Row 8: Black Orange Orange Orange Orange Orange Orange
Row 9: Orange Green Orange Orange Orange Orange Orange
Row 10: Orange Brown Orange Orange Orange Orange Orange
Row 11: Black Orange Orange Orange Orange Orange Orange
Row 12: Orange Green Orange Orange Orange Orange Orange
Row 13: Orange Brown Orange Orange Orange Orange Orange
Row 14: Black Orange Orange Orange Orange Orange Orange
Row 15: Orange Green 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
Row 2: Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Yellow Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Yellow 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
Row 6: Black Black Black Black Black Black Gray 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
Row 8: 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
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 Black
Row 16: 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
Row 18: 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
Row 20: 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
Row 22: 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 Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 2: Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 3: Yellow Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Black Black Black Black Black Black Black Yellow 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
Row 6: Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 7: Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 8: Yellow Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black Black Yellow 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 Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 12: Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 13: Yellow Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 14: Black Black Black Black Black Black Black Yellow 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
Row 16: Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 17: Black Yellow Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 18: Yellow Black Black Black Black Black Black Black Orange Black Black Black Black Black Black Black Black Black Black Black Black
Row 19: Black Black Black Black Black Black Black Yellow 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
Row 21: Black Black Black Black Black Black Gray Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 22: Black Yellow 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: 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 Orange Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 6: Yellow Yellow Yellow Yellow Yellow Black Black Orange Purple Yellow Purple Black Yellow Yellow Yellow Yellow Yellow Yellow
Row 7: Yellow Yellow Yellow Orange Yellow Purple Green Yellow Yellow Yellow Yellow Yellow Green Green 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
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 Orange Yellow Purple Green Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Orange Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Black Black Orange Purple Yellow Purple Black Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Orange Yellow Purple Green Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Orange Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Black Black Orange Purple Yellow Purple Black Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Orange Yellow Purple Green Yellow Yellow Yellow Yellow Yellow Green Green Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Orange Yellow Yellow Yellow Pink Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Yellow Yellow Yellow Yellow Yellow Black Black Orange Purple Yellow Purple Black 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: Yellow Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Pink
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Green Brown Blue Green Blue Blue Blue Green Green Blue Green Green Green Green Blue Green Green Blue Green Green Blue Green Brown Green
Row 4: Green Brown Green Blue Green Green Green Blue Blue Green Green Green Blue Blue Green Green Blue Blue Blue Green Green Blue Brown Green
Row 5: Green Brown Blue Green Blue Blue Green Green Green Green Blue Blue Green Green Green Blue Blue Blue Blue Green Blue Green Brown Green
Row 6: Green Brown Blue Blue Green Blue Blue Green Blue Blue Blue Blue Blue Green Green Blue Blue Blue Blue Blue Green Green Brown Green
Row 7: Green Brown Green Green Green Green Blue Blue Green Green Blue Green Green Green Green Blue Blue Green Blue Blue Green Green Brown Green
Row 8: Green Brown Blue Green Blue Blue Blue Blue Blue Green Green Green Green Green Blue Blue Blue Green Blue Blue Green Green Brown Green
Row 9: Green Brown Green Blue Green Green Blue Blue Green Blue Blue Blue Blue Green Green Blue Green Green Green Blue Blue Blue Brown Green
Row 10: Green Brown Green Blue Green Green Green Blue Green Blue Blue Blue Green Green Green Blue Blue Green Blue Green Green Blue Brown Green
Row 11: Green Brown Blue Green Green Green Green Green Green Green Blue Green Blue Blue Blue Blue Blue Green Blue Blue Blue Green Brown Green
Row 12: Green Brown Blue Blue Green Blue Green Green Green Green Blue Blue Green Green Green Green Green Green Blue Green Green Green Brown Green
Row 13: Green Brown Green Green Blue Blue Green Green Blue Blue Green Blue Blue Green Blue Green Green Blue Blue Green Green Blue Brown Green
Row 14: Green Brown Green Green Green Green Green Green Green Green Blue Green Green Blue Blue Blue Blue Green Green Blue Blue Green Brown Green
Row 15: Green Brown Blue Green Blue Green Blue Blue Green Green Green Green Green Blue Green Green Blue Blue Green Blue Green Blue Brown Green
Row 16: Green Brown Green Green Green Green Blue Green Green Green Blue Blue Blue Green Blue Green Green Green Green Blue Blue Green Brown Green
Row 17: Green Brown Green Blue Blue Green Green Blue Blue Green Green Blue Green Blue Green Green Green Blue Green Blue Green Green Brown Green
Row 18: Green Brown Green Green Blue Blue Blue Blue Green Green Blue Blue Blue Blue Green Blue Green Green Blue Green Green Green Brown Green
Row 19: Green Brown Blue Green Green Green Green Blue Green Green Blue Green Green Blue Green Blue Green Green Blue Blue Green Green Brown Green
Row 20: Green Brown Blue Green Green Green Green Blue Blue Green Green Green Blue Blue Blue Blue Green Green Blue Blue Blue Blue Brown Green
Row 21: Green Brown Green Blue Blue Green Green Blue Green Green Blue Green Blue Blue Blue Green Blue Green Green Green Blue Green Brown Green
Row 22: Green Brown Green Green Green Green Green Green Green Green Blue Green Blue Blue Blue Green Blue Blue Blue Green Blue Blue Brown Green
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Purple Brown Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Black
Output:
Row 1: Yellow Green Yellow Yellow Yellow Green Green Yellow Green Green Green Green Pink Green Green Pink Green Green Pink Green
Row 2: Green Yellow Green Green Green Yellow Yellow Green Green Green Pink Pink Green Green Pink Pink Pink Green Green Pink
Row 3: Yellow Green Yellow Yellow Green Green Green Green Yellow Yellow Green Green Green Pink Pink Pink Pink Green Pink Green
Row 4: Yellow Yellow Green Yellow Yellow Green Yellow Yellow Yellow Yellow Pink Green Green Pink Pink Pink Pink Pink Green Green
Row 5: Green Green Green Green Yellow Yellow Green Green Yellow Green Green Green Green Pink Pink Green Pink Pink Green Green
Row 6: Yellow Green Yellow Yellow Yellow Yellow Yellow Green Green Green Green Green Pink Pink Pink Green Pink Pink Green Green
Row 7: Green Yellow Green Green Yellow Yellow Green Yellow Yellow Yellow Pink Green Green Pink Green Green Green Pink Pink Pink
Row 8: Green Yellow Green Green Green Yellow Green Yellow Yellow Yellow Green Green Green Pink Pink Green Pink Green Green Pink
Row 9: Yellow Green Green Green Green Green Green Green Yellow Green Pink Pink Pink Pink Pink Green Pink Pink Pink Green
Row 10: Yellow Yellow Green Yellow Green Green Green Green Yellow Yellow Green Green Green Green Green Green Pink Green Green Green
Row 11: Green Green Purple Purple Green Green Purple Purple Green Purple Black Green Black Green Green Black Black Green Green Black
Row 12: Green Green Green Green Green Green Green Green Purple Green Green Black Black Black Black Green Green Black Black Green
Row 13: Purple Green Purple Green Purple Purple Green Green Green Green Green Black Green Green Black Black Green Black Green Black
Row 14: Green Green Green Green Purple Green Green Green Purple Purple Black Green Black Green Green Green Green Black Black Green
Row 15: Green Purple Purple Green Green Purple Purple Green Green Purple Green Black Green Green Green Black Green Black Green Green
Row 16: Green Green Purple Purple Purple Purple Green Green Purple Purple Black Black Green Black Green Green Black Green Green Green
Row 17: Purple Green Green Green Green Purple Green Green Purple Green Green Black Green Black Green Green Black Black Green Green
Row 18: Purple Green Green Green Green Purple Purple Green Green Green Black Black Black Black Green Green Black Black Black Black
Row 19: Green Purple Purple Green Green Purple Green Green Purple Green Black Black Black Green Black Green Green Green Black Green
Row 20: Green Green Green Green Green Green Green Green Purple Green Black Black Black Green Black Black Black Green Black Black
Example 2
Input:
Row 1: Orange Red Green Green Green Green Green Green Green Green Red Brown
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Green Red Green Purple Green Purple Purple Purple Purple Purple Red Green
Row 4: Green Red Purple Green Purple Purple Purple Green Purple Green Red Green
Row 5: Green Red Purple Purple Purple Purple Green Purple Green Purple Red Green
Row 6: Green Red Green Green Purple Purple Green Green Green Purple Red Green
Row 7: Green Red Green Purple Purple Purple Purple Purple Purple Purple Red Green
Row 8: Green Red Purple Purple Purple Green Purple Green Green Purple Red Green
Row 9: Green Red Purple Purple Purple Green Green Purple Green Green Red Green
Row 10: Green Red Green Green Green Green Green Purple Green Purple Red Green
Row 11: Green Red Green Green Green Green Green Green Purple Green Red Green
Row 12: Green Red Green Purple Green Green Purple Green Green Purple Red Green
Row 13: Green Red Green Green Green Green Green Purple Green Green Red Green
Row 14: Green Red Purple Green Green Purple Green Green Purple Green Red Green
Row 15: Green Red Green Green Green Green Green Green Purple Green Red Green
Row 16: Green Red Green Green Green Green Green Green Green Green Red Green
Row 17: Red Red Red Red Red Red Red Red Red Red Red Red
Row 18: Pink Red Green Green Green Green Green Green Green Green Red Gray
Output:
Row 1: Green Orange Green Orange Brown Brown Brown Brown
Row 2: Orange Green Orange Orange Brown Green Brown Green
Row 3: Orange Orange Orange Orange Green Brown Green Brown
Row 4: Green Green Orange Orange Green Green Green Brown
Row 5: Green Orange Orange Orange Brown Brown Brown Brown
Row 6: Orange Orange Orange Green Brown Green Green Brown
Row 7: Orange Orange Orange Green Green Brown Green Green
Row 8: Green Green Green Green Green Gray Green Gray
Row 9: Green Green Green Green Green Green Gray Green
Row 10: Green Pink Green Green Gray Green Green Gray
Row 11: Green Green Green Green Green Gray Green Green
Row 12: Pink Green Green Pink Green Green Gray Green
Row 13: Green Green Green Green Green Green Gray Green
Row 14: Green Green Green Green Green Green Green Green
Example 3
Input:
Row 1: Black Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Blue
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Orange Brown Green Green Green Orange Green Green Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange
Row 4: Orange Brown Green Orange Orange Green Orange Green Green Green Orange Orange Orange Orange Orange Orange Green Orange Brown Orange
Row 5: Orange Brown Green Green Green Orange Orange Green Green Green Orange Orange Orange Green Orange Orange Orange Orange Brown Orange
Row 6: Orange Brown Green Orange Orange Green Green Green Green Green Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange
Row 7: Orange Brown Green Green Green Orange Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange
Row 8: Orange Brown Green Green Green Green Green Green Green Green Orange Orange Orange Green Orange Orange Orange Orange Brown Orange
Row 9: Orange Brown Green Green Orange Orange Green Green Orange Green Orange Orange Orange Orange Green Orange Orange Orange Brown Orange
Row 10: Orange Brown Orange Green Green Green Green Green Green Orange Orange Orange Green Orange Orange Orange Orange Orange Brown Orange
Row 11: Orange Brown Orange Green Orange Green Green Green Orange Orange Orange Green Orange Orange Orange Orange Orange Orange Brown Orange
Row 12: Orange Brown Green Green Green Green Green Green Orange Green Orange Orange Green Orange Orange Orange Green Orange Brown Orange
Row 13: Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Green Green Orange Green Orange Brown Orange
Row 14: Orange Brown Green Orange Orange Green Green Orange Orange Green Orange Green Green Green Green Green Green Green Brown Orange
Row 15: Orange Brown Orange Orange Orange Orange Orange Green Green Orange Green Green Green Green Orange Green Green Green Brown Orange
Row 16: Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Green Orange Green Green Green Green Green Green Brown Orange
Row 17: Orange Brown Orange Orange Orange Orange Green Orange Orange Orange Green Orange Orange Orange Green Green Orange Orange Brown Orange
Row 18: Orange Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green Green Green Green Green Green Brown Orange
Row 19: Orange Brown Orange Green Orange Green Orange Orange Orange Orange Green Orange Green Green Green Green Orange Orange Brown Orange
Row 20: Orange Brown Green Green Orange Orange Green Orange Orange Orange Green Green Orange Orange Green Green Green Green Brown Orange
Row 21: Orange Brown Orange Green Orange Orange Orange Green Orange Orange Green Green Orange Green Green Green Green Green Brown Orange
Row 22: Orange Brown Green Orange Green Orange Orange Green Orange Orange Green Green Orange Orange Green Orange Orange Orange Brown Orange
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Pink Brown Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Yellow
Output:
Row 1: Black Black Black Orange Black Black Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 2: Black Orange Orange Black Orange Black Black Black Orange Orange Orange Orange Orange Orange Blue Orange
Row 3: Black Black Black Orange Orange Black Black Black Orange Orange Orange Blue Orange Orange Orange Orange
Row 4: Black Orange Orange Black Black Black Black Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 5: Black Black Black Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange Orange Orange
Row 6: Black Black Black Black Black Black Black Black Orange Orange Orange Blue Orange Orange Orange Orange
Row 7: Black Black Orange Orange Black Black Orange Black Orange Orange Orange Orange Blue Orange Orange Orange
Row 8: Orange Black Black Black Black Black Black Orange Orange Orange Blue Orange Orange Orange Orange Orange
Row 9: Orange Black Orange Black Black Black Orange Orange Orange Blue Orange Orange Orange Orange Orange Orange
Row 10: Black Black Black Black Black Black Orange Black Orange Orange Blue Orange Orange Orange Blue Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Yellow Yellow Orange Yellow Orange
Row 12: Pink Orange Orange Pink Pink Orange Orange Pink Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Orange Orange Orange Orange Orange Pink Pink Orange Yellow Yellow Yellow Yellow Orange Yellow Yellow Yellow
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Yellow Orange Yellow Yellow Yellow Yellow Yellow Yellow
Row 15: Orange Orange Orange Orange Pink Orange Orange Orange Yellow Orange Orange Orange Yellow Yellow Orange Orange
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Yellow Yellow Yellow Yellow Yellow Yellow
Row 17: Orange Pink Orange Pink Orange Orange Orange Orange Yellow Orange Yellow Yellow Yellow Yellow Orange Orange
Row 18: Pink Pink Orange Orange Pink Orange Orange Orange Yellow Yellow Orange Orange Yellow Yellow Yellow Yellow
Row 19: Orange Pink Orange Orange Orange Pink Orange Orange Yellow Yellow Orange Yellow Yellow Yellow Yellow Yellow
Row 20: Pink Orange Pink Orange Orange Pink Orange Orange Yellow Yellow Orange Orange Yellow Orange Orange Orange
Here is the input grid for the test example:
Input:
Row 1: Brown Red Black Black Black Black Black Black Black Black Red Gray
Row 2: Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Black Red Blue Blue Blue Blue Blue Black Black Blue Red Black
Row 4: Black Red Blue Blue Black Blue Black Black Black Blue Red Black
Row 5: Black Red Blue Blue Blue Blue Black Black Black Black Red Black
Row 6: Black Red Blue Blue Blue Blue Blue Blue Blue Blue Red Black
Row 7: Black Red Blue Blue Blue Blue Blue Blue Black Blue Red Black
Row 8: Black Red Blue Blue Blue Blue Blue Blue Black Blue Red Black
Row 9: Red Red Red Red Red Red Red Red Red Red Red Red
Row 10: Orange Red Black Black Black Black Black Black Black Black Red Pink
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 Gray Black Black Gray
Brown Brown Black Brown Black Black Black Gray
Brown Brown Brown Brown Black Black Black Black
Orange Orange Orange Orange Pink Pink Pink Pink
Orange Orange Orange Orange Pink Pink Black Pink
Orange Orange Orange Orange Pink Pink 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: 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple
Row 3: Purple Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Purple
Row 4: Purple Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Purple
Row 5: Purple Orange Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Orange Purple
Row 6: Purple Orange Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Orange Purple
Row 7: Purple Orange Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Orange Purple
Row 8: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Brown Yellow Yellow Orange Purple
Row 9: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Brown Yellow Yellow Orange Purple
Row 10: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Gray Gray Gray Gray Gray Black Brown Yellow Yellow Orange Purple
Row 11: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 12: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 13: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 14: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Red Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 15: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Red Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 16: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 17: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 18: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 19: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 20: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Green Green Green Green Gray Black Brown Yellow Yellow Orange Purple
Row 21: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Gray Gray Gray Gray Gray Black Brown Yellow Yellow Orange Purple
Row 22: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Gray Gray Gray Gray Gray Gray Black Brown Yellow Yellow Orange Purple
Row 23: Purple Orange Yellow Yellow Brown Brown Brown Brown Black Black Black Black Black Black Black Black Black Black Brown Yellow Yellow Orange Purple
Row 24: Purple Orange Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Orange Purple
Row 25: Purple Orange Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Orange Purple
Row 26: Purple Orange Yellow Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Yellow Orange Purple
Row 27: Purple Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Purple
Row 28: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple
Row 29: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple
Row 30: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple
Row 3: Purple Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Purple
Row 4: Purple Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Orange Purple
Row 5: Purple Orange Yellow Brown Black Black Black Black Black Black Black Brown Yellow Orange Purple
Row 6: Purple Orange Yellow Brown Black Gray Gray Gray Gray Gray Black Brown Yellow Orange Purple
Row 7: Purple Orange Yellow Brown Black Gray Green Green Green Gray Black Brown Yellow Orange Purple
Row 8: Purple Orange Yellow Brown Black Gray Green Red Green Gray Black Brown Yellow Orange Purple
Row 9: Purple Orange Yellow Brown Black Gray Green Green Green Gray Black Brown Yellow Orange Purple
Row 10: Purple Orange Yellow Brown Black Gray Gray Gray Gray Gray Black Brown Yellow Orange Purple
Row 11: Purple Orange Yellow Brown Black Black Black Black Black Black Black Brown Yellow Orange Purple
Row 12: Purple Orange Yellow Brown Brown Brown Brown Brown Brown Brown Brown Brown Yellow Orange Purple
Row 13: Purple Orange Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Orange Purple
Row 14: Purple Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Example 2
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 3: Pink Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink
Row 4: Pink Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink
Row 5: Pink Orange Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Orange Pink
Row 6: Pink Orange Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Red Orange Pink
Row 7: Pink Orange Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Red Orange Pink
Row 8: Pink Orange Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Red Orange Pink
Row 9: Pink Orange Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Red Orange Pink
Row 10: Pink Orange Orange Red Purple Brown Brown Black Black Black Black Black Black Black Black Black Black Black Brown Purple Purple Red Orange Pink
Row 11: Pink Orange Orange Red Purple Brown Brown Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Brown Purple Purple Red Orange Pink
Row 12: Pink Orange Orange Red Purple Brown Brown Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Brown Purple Purple Red Orange Pink
Row 13: Pink Orange Orange Red Purple Brown Brown Black Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Black Brown Purple Purple Red Orange Pink
Row 14: Pink Orange Orange Red Purple Brown Brown Black Blue Yellow Gray Gray Gray Yellow Yellow Blue Blue Black Brown Purple Purple Red Orange Pink
Row 15: Pink Orange Orange Red Purple Brown Brown Black Blue Yellow Yellow Yellow Yellow Yellow Yellow Blue Blue Black Brown Purple Purple Red Orange Pink
Row 16: Pink Orange Orange Red Purple Brown Brown Black Blue Blue Blue Blue Blue Blue Blue Blue Blue Black Brown Purple Purple Red Orange Pink
Row 17: Pink Orange Orange Red Purple Brown Brown Black Black Black Black Black Black Black Black Black Black Black Brown Purple Purple Red Orange Pink
Row 18: Pink Orange Orange Red Purple Brown Brown Black Black Black Black Black Black Black Black Black Black Black Brown Purple Purple Red Orange Pink
Row 19: Pink Orange Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Purple Red Orange Pink
Row 20: Pink Orange Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Orange Pink
Row 21: Pink Orange Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Orange Pink
Row 22: Pink Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink
Row 23: Pink Orange Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink
Row 24: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange 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
Output:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink
Row 2: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 3: Pink Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink
Row 4: Pink Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Orange Pink
Row 5: Pink Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Red Orange Pink
Row 6: Pink Orange Red Purple Brown Black Black Black Black Black Black Black Brown Purple Red Orange Pink
Row 7: Pink Orange Red Purple Brown Black Blue Blue Blue Blue Blue Black Brown Purple Red Orange Pink
Row 8: Pink Orange Red Purple Brown Black Blue Yellow Yellow Yellow Blue Black Brown Purple Red Orange Pink
Row 9: Pink Orange Red Purple Brown Black Blue Yellow Gray Yellow Blue Black Brown Purple Red Orange Pink
Row 10: Pink Orange Red Purple Brown Black Blue Yellow Yellow Yellow Blue Black Brown Purple Red Orange Pink
Row 11: Pink Orange Red Purple Brown Black Blue Blue Blue Blue Blue Black Brown Purple Red Orange Pink
Row 12: Pink Orange Red Purple Brown Black Black Black Black Black Black Black Brown Purple Red Orange Pink
Row 13: Pink Orange Red Purple Brown Brown Brown Brown Brown Brown Brown Brown Brown Purple Red Orange Pink
Row 14: Pink Orange Red Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Red Orange Pink
Row 15: Pink Orange Red Red Red Red Red Red Red Red Red Red Red Red Red Orange Pink
Row 16: Pink Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Pink
Row 17: 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 Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 3: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 4: Blue Brown Brown Black Black Black Black Black Brown Blue Blue Blue
Row 5: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 6: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 7: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 8: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 9: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 10: Blue Brown Brown Brown Brown Brown Brown Brown Brown Blue Blue Blue
Row 11: Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue
Output:
Row 1: Blue Blue Blue Blue Blue
Row 2: Blue Brown Brown Brown Blue
Row 3: Blue Brown Black Brown Blue
Row 4: Blue Brown Brown Brown Blue
Row 5: Blue Blue Blue Blue Blue
Here is the input grid for the test example:
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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: 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown Brown
Row 5: Brown Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Brown Brown
Row 6: Brown Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 7: Brown Purple Gray Blue Red Red Red Red Red Red Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 8: Brown Purple Gray Blue Red Orange Orange Orange Red Red Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 9: Brown Purple Gray Blue Red Orange Yellow Orange Red Red Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 10: Brown Purple Gray Blue Red Orange Orange Orange Red Red Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 11: Brown Purple Gray Blue Red Orange Orange Orange Red Red Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 12: Brown Purple Gray Blue Red Red Red Red Red Red Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 13: Brown Purple Gray Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Gray Gray Gray Purple Purple Brown Brown
Row 14: Brown Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Purple Brown Brown
Row 15: Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple 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
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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Brown Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Brown
Brown Purple Gray Blue Blue Blue Blue Blue Blue Blue Gray Purple Brown
Brown Purple Gray Blue Red Red Red Red Red Blue Gray Purple Brown
Brown Purple Gray Blue Red Orange Orange Orange Red Blue Gray Purple Brown
Brown Purple Gray Blue Red Orange Yellow Orange Red Blue Gray Purple Brown
Brown Purple Gray Blue Red Orange Orange Orange Red Blue Gray Purple Brown
Brown Purple Gray Blue Red Red Red Red Red Blue Gray Purple Brown
Brown Purple Gray Blue Blue Blue Blue Blue Blue Blue Gray Purple Brown
Brown Purple Gray Gray Gray Gray Gray Gray Gray Gray Gray Purple Brown
Brown Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Brown
Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown |
You will be given multiple input-output grid pairs as reference examples. Each grid is a 2D array represented as a string, where cells (colors) are separated by spaces and rows by newlines. The output grid is derived from the input grid by applying a consistent transformation rule.
Your task:
1. Identify the underlying transformation rule that maps input grids to their corresponding output grids.
2. Generalize the rule to apply it to new test inputs.
3. Produce the correct output grid for each given test input.
Guidelines:
- Analyze patterns systematically.
- Explain the transformation logic step-by-step before generating the final output.
Example 1
Input:
Row 1: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Black Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Brown Brown Brown Brown Brown Brown Brown Black 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
Row 6: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 7: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 8: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 9: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 10: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 11: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 12: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 13: Brown Brown Brown Brown Brown Brown Green Brown Brown Brown Green Brown Brown Brown Brown Brown Brown Brown
Row 14: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 15: Brown Brown Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 16: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 17: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 18: Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 19: Brown Brown Brown Brown Brown Brown Orange Brown Brown Brown Brown Brown 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
Output:
Row 1: Green Brown Brown Orange Green
Row 2: Orange Brown Brown Brown Black
Row 3: Orange Brown Brown Brown Brown
Row 4: Orange Brown Brown Brown Black
Row 5: Green Orange Brown Black Green
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 Green Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 3: Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 4: Red Red Red Green Red Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red
Row 5: Red Red Red Red Red Red Pink Pink 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 Pink 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 Green Pink Red Red Red Red Green Red Red Red Red Red Red Red Red Red Red Red Red
Row 9: Red Red Red Green Pink Red Red Red Red Green Pink Red Red Red Red Red Red Red Red Red Red Red
Row 10: Red Red Red Green Pink Red Red Red Red Red Pink Red Red Red Red Red Red Red Red Red Red Red
Row 11: Red Red Red Red Red Red Red Red Green 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 Pink Red Red Red Red Red Red Red Red Red Red Red
Row 14: Red Red Red Red Red Pink Red Pink Red Red Red Red Orange Red Red Red Red Red Orange 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
Row 17: 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
Row 19: 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
Row 21: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 22: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 23: Red Red Red Red Red Red Red Red Red Red Red Red Orange Red Red Red Red Red Orange Red Red Red
Row 24: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 25: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 26: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 27: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 28: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 29: Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red
Row 30: 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: Orange Green Pink Pink Green Red Orange
Row 2: Green Red Red Red Red Red Pink
Row 3: Green Red Red Red Red Red Green
Row 4: Pink Red Red Red Red Red Red
Row 5: Pink Red Red Red Red Red Pink
Row 6: Pink Red Red Red Red Red Pink
Row 7: Green Red Red Red Red Red Green
Row 8: Green Red Red Red Red Red Green
Row 9: Green Red Red Red Red Red Pink
Row 10: Orange Pink Red Pink Red Green Orange
Example 3
Input:
Row 1: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 2: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow Yellow
Row 3: 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 Green Yellow Yellow Yellow
Row 5: 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
Row 7: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Green Yellow Yellow Yellow Yellow
Row 8: 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
Row 10: 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
Row 12: Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 13: Yellow Yellow Yellow Yellow Yellow Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 14: 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
Row 16: 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
Row 18: Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 19: Yellow Yellow Yellow Blue 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
Row 21: 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
Row 23: Yellow Yellow 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 Yellow Yellow
Row 25: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 26: Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Output:
Row 1: Brown Blue Brown
Row 2: Yellow Yellow Blue
Row 3: Yellow Yellow Yellow
Row 4: Green Yellow Yellow
Row 5: Yellow Yellow Yellow
Row 6: Yellow Yellow Green
Row 7: Yellow Yellow Yellow
Row 8: Blue Yellow Yellow
Row 9: Brown Green 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 Black 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 Black 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 Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Black Gray Gray Gray Gray
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Yellow Gray Gray Yellow Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray
Row 6: Gray Gray Gray Gray Gray Yellow 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
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray Green 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
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Pink Gray
Row 11: Gray Gray Gray Gray Gray Blue Blue 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
Row 13: Gray Gray Gray Gray Gray Red 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 Green Gray Gray Gray Gray Gray Gray Green Gray Gray Gray Gray Gray Gray
Row 15: Gray Gray Gray Gray Blue Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Pink Purple 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
Row 17: Gray Gray Gray Gray Gray Red 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 Purple Gray Purple 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
Reason step by step and finalize your response with the output grid for the new test input in format:
<answer>
{answer}
</answer>
| Green Blue Blue Yellow Pink Pink Yellow Green
Yellow Gray Gray Gray Gray Gray Gray Red
Gray Gray Gray Gray Gray Gray Gray Gray
Black Gray Gray Gray Gray Gray Gray Purple
Blue Gray Gray Gray Gray Gray Gray Black
Pink Gray Gray Gray Gray Gray Gray Red
Green Gray Purple Red Purple Gray 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: Blue Blue Blue Purple
Row 2: Blue Blue Blue Purple
Row 3: Blue Blue Blue Brown
Row 4: Blue Brown Blue Blue
Row 5: Blue Blue Blue Blue
Row 6: Blue Brown Blue Blue
Row 7: Blue Blue Blue Blue
Row 8: Blue Blue Blue Black
Row 9: Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue
Row 13: Brown Blue Blue Blue
Row 14: Blue Blue Brown Blue
Row 15: Blue Blue Blue Blue
Row 16: Blue Blue Blue Orange
Row 17: Blue Purple Blue Blue
Row 18: Yellow Blue Blue Blue
Row 19: Blue Blue Blue Blue
Row 20: Blue Blue Blue Orange
Row 21: Pink Blue Blue Blue
Row 22: Blue Blue Blue Pink
Row 23: Blue Pink Blue Blue
Row 24: Yellow Blue Blue Blue
Row 25: Blue Blue Blue Purple
Row 26: Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue
Row 28: Blue Blue Black Blue
Row 29: Yellow Blue Blue Blue
Output:
Row 1: Blue Blue Blue Purple
Row 2: Blue Blue Blue Purple
Row 3: Blue Blue Blue Brown
Row 4: Blue Brown Gray Brown
Row 5: Blue Blue Blue Blue
Row 6: Blue Brown Gray Brown
Row 7: Blue Blue Blue Blue
Row 8: Blue Blue Blue Black
Row 9: Blue Blue Blue Blue
Row 10: Blue Blue Blue Blue
Row 11: Blue Blue Blue Blue
Row 12: Blue Blue Blue Blue
Row 13: Brown Gray Brown Gray
Row 14: Blue Blue Brown Gray
Row 15: Blue Blue Blue Blue
Row 16: Blue Blue Blue Orange
Row 17: Blue Purple Gray Purple
Row 18: Yellow Gray Yellow Gray
Row 19: Blue Blue Blue Blue
Row 20: Blue Blue Blue Orange
Row 21: Pink Gray Pink Gray
Row 22: Blue Blue Blue Pink
Row 23: Blue Pink Gray Pink
Row 24: Yellow Gray Yellow Gray
Row 25: Blue Blue Blue Purple
Row 26: Blue Blue Blue Blue
Row 27: Blue Blue Blue Blue
Row 28: Blue Blue Black Gray
Row 29: Yellow Gray Yellow Gray
Example 2
Input:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange Orange
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Orange Orange
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange Orange Orange Orange
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange Orange
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange Orange Orange Orange Orange
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Orange Orange Orange
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Orange Orange Orange
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Orange
Row 13: Orange Orange Orange Orange Orange Orange Black 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
Row 15: Orange Orange Blue 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 Purple
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Black 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
Row 20: Blue 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
Output:
Row 1: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Gray Brown Gray
Row 2: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown Gray Brown
Row 3: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Gray Black Gray Black Gray Black
Row 4: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Purple Gray Purple Gray Purple
Row 5: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray Purple Gray Purple Gray
Row 6: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Brown
Row 7: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Green
Row 8: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Blue Gray Blue Gray
Row 9: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black Gray Black Gray
Row 11: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 12: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple Gray
Row 13: Orange Orange Orange Orange Orange Orange Black Gray Black Gray Black Gray Black Gray Black Gray Black
Row 14: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 15: Orange Orange Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue
Row 16: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Purple
Row 17: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 18: Black Gray Black Gray Black Gray Black Gray Black Gray Black Gray Black Gray Black Gray Black
Row 19: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Row 20: Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue Gray Blue
Row 21: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Example 3
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 Purple 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 Brown 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
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 Purple Gray Purple Gray Purple Gray Purple Gray Purple
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 Brown Gray Brown Gray
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
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
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
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
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
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 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 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
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 Black
Row 9: 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 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 Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Yellow Gray Yellow Gray Yellow Gray Yellow Gray Yellow 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: Blue Blue Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Blue Blue Brown Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 4: Purple Purple Brown Purple Gray Purple Gray Gray Purple Gray Gray
Row 5: Purple Purple Brown Gray Purple Gray Gray Purple Gray Gray Gray
Row 6: Purple Purple Brown Purple Purple Purple Gray Purple Purple Purple Gray
Row 7: Purple Purple Brown Gray Gray Gray Gray Gray Purple Purple Gray
Row 8: Purple Purple Brown Purple Gray Gray Gray Gray Gray Purple Gray
Row 9: Purple Purple Brown Gray Purple Purple Gray Gray Purple Purple Gray
Row 10: Purple Purple Brown Purple Purple Gray Gray Gray Purple Purple Gray
Row 11: Purple Purple Brown Purple Purple Gray Purple Purple Purple Purple Gray
Row 12: Purple Purple Brown Purple Purple Purple Purple Gray Purple Purple Purple
Row 13: Purple Purple Brown Gray Purple Gray Gray Gray Purple Purple Purple
Row 14: Purple Purple Brown Gray Purple Gray Gray Gray Purple Purple Purple
Row 15: Purple Purple Brown Purple Gray Purple Purple Gray Gray Purple Purple
Output:
Row 1: Purple Blue Purple Blue Blue Purple Blue Blue
Row 2: Blue Purple Blue Blue Purple Blue Blue Blue
Row 3: Purple Purple Purple Blue Purple Purple Purple Blue
Row 4: Blue Blue Blue Blue Blue Purple Purple Blue
Row 5: Purple Blue Blue Blue Blue Blue Purple Blue
Row 6: Blue Purple Purple Blue Blue Purple Purple Blue
Row 7: Purple Purple Blue Blue Blue Purple Purple Blue
Row 8: Purple Purple Blue Purple Purple Purple Purple Blue
Row 9: Purple Purple Purple Purple Blue Purple Purple Purple
Row 10: Blue Purple Blue Blue Blue Purple Purple Purple
Row 11: Blue Purple Blue Blue Blue Purple Purple Purple
Row 12: Purple Blue Purple Purple Blue Blue Purple Purple
Example 2
Input:
Row 1: Black Black Pink Black Black Black Yellow Black Black
Row 2: Black Black Black Black Black Black Yellow Black Black
Row 3: Black Black Black Pink Black Black Yellow Black Black
Row 4: Pink Black Black Black Black Black Yellow Black Black
Row 5: Black Black Black Black Black Black Yellow Black Black
Row 6: Black Black Black Pink Black Black Yellow Black Black
Row 7: Black Black Black Black Black Black Yellow Black Black
Row 8: Black Black Black Black Black Black Yellow Black Black
Row 9: Black Black Black Black Black Black Yellow Black Black
Row 10: Black Black Black Black Black Black Yellow Black Black
Row 11: Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Row 12: Black Black Black Black Black Black Yellow Gray Gray
Row 13: Black Black Black Black Black Black Yellow Gray Gray
Output:
Row 1: Black Black Gray Black Black Black
Row 2: Black Black Black Black Black Black
Row 3: Black Black Black Gray Black Black
Row 4: Gray Black Black Black Black Black
Row 5: Black Black Black Black Black Black
Row 6: Black Black Black Gray Black Black
Row 7: Black Black Black Black Black Black
Row 8: Black Black Black Black Black Black
Row 9: Black Black Black Black Black Black
Row 10: Black Black Black Black Black Black
Example 3
Input:
Row 1: Yellow Yellow Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 2: Pink Pink Black Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 3: Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black Black
Row 4: Brown Brown Black Red Brown Brown Red Brown Brown Brown Red Brown Brown Brown Red Brown Red Red Red Brown Red Red Brown Brown Brown
Row 5: Brown Brown Black Red Brown Brown Red Red Red Red Brown Brown Red Red Red Red Red Red Brown Brown Brown Brown Brown Red Red
Row 6: Brown Brown Black Brown Brown Brown Red Brown Brown Red Red Brown Red Brown Red Brown Red Red Red Red Red Red Brown Red Red
Row 7: Brown Brown Black Brown Brown Brown Brown Red Red Brown Brown Brown Red Brown Brown Brown Red Brown Red Red Red Brown Brown Red Red
Row 8: Brown Brown Black Brown Brown Brown Brown Red Brown Red Brown Brown Red Red Brown Red Red Brown Brown Red Red Red Brown Brown Red
Row 9: Brown Brown Black Red Red Brown Brown Red Brown Red Red Red Red Red Red Red Brown Red Brown Brown Brown Brown Red Brown Brown
Row 10: Brown Brown Black Red Brown Red Red Brown Brown Red Red Red Red Red Red Brown Brown Brown Red Red Red Brown Red Red Red
Row 11: Brown Brown Black Brown Red Red Red Brown Brown Red Brown Brown Brown Red Brown Brown Brown Brown Brown Brown Red Red Brown Red Red
Row 12: Brown Brown Black Red Brown Brown Red Red Red Brown Brown Red Red Brown Red Red Red Brown Red Brown Red Red Brown Brown Brown
Row 13: Brown Brown Black Red Brown Red Brown Red Brown Brown Red Brown Brown Red Red Red Brown Red Red Brown Red Brown Brown Brown Red
Row 14: Brown Brown Black Brown Red Brown Brown Red Red Red Brown Brown Brown Brown Red Brown Brown Brown Red Red Brown Brown Brown Brown Brown
Row 15: Brown Brown Black Red Red Brown Red Red Brown Red Brown Red Brown Brown Brown Red Red Red Red Red Brown Brown Brown Red Red
Row 16: Brown Brown Black Red Brown Brown Brown Red Red Brown Brown Red Red Red Red Brown Brown Red Red Red Red Brown Brown Brown Brown
Row 17: Brown Brown Black Red Red Brown Red Red Red Brown Brown Red Red Brown Brown Red Brown Red Red Brown Red Red Red Red Red
Row 18: Brown Brown Black Red Brown Brown Brown Red Red Brown Brown Brown Brown Brown Red Red Brown Red Red Red Red Brown Red Brown Red
Row 19: Brown Brown Black Red Brown Red Brown Red Brown Brown Red Brown Red Brown Brown Red Brown Red Brown Brown Brown Red Brown Red Red
Row 20: Brown Brown Black Red Brown Brown Red Brown Brown Red Brown Brown Red Red Brown Brown Brown Red Red Red Red Red Brown Brown Brown
Row 21: Brown Brown Black Brown Brown Red Red Red Red Red Red Red Red Brown Brown Red Red Red Brown Brown Red Red Brown Red Red
Output:
Row 1: Yellow Brown Brown Yellow Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Yellow Yellow Yellow Brown Yellow Yellow Brown Brown Brown
Row 2: Yellow Brown Brown Yellow Yellow Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Brown Brown Yellow Yellow
Row 3: Brown Brown Brown Yellow Brown Brown Yellow Yellow Brown Yellow Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Yellow
Row 4: Brown Brown Brown Brown Yellow Yellow Brown Brown Brown Yellow Brown Brown Brown Yellow Brown Yellow Yellow Yellow Brown Brown Yellow Yellow
Row 5: Brown Brown Brown Brown Yellow Brown Yellow Brown Brown Yellow Yellow Brown Yellow Yellow Brown Brown Yellow Yellow Yellow Brown Brown Yellow
Row 6: Yellow Yellow Brown Brown Yellow Brown Yellow Yellow Yellow Yellow Yellow Yellow Yellow Brown Yellow Brown Brown Brown Brown Yellow Brown Brown
Row 7: Yellow Brown Yellow Yellow Brown Brown Yellow Yellow Yellow Yellow Yellow Yellow Brown Brown Brown Yellow Yellow Yellow Brown Yellow Yellow Yellow
Row 8: Brown Yellow Yellow Yellow Brown Brown Yellow Brown Brown Brown Yellow Brown Brown Brown Brown Brown Brown Yellow Yellow Brown Yellow Yellow
Row 9: Yellow Brown Brown Yellow Yellow Yellow Brown Brown Yellow Yellow Brown Yellow Yellow Yellow Brown Yellow Brown Yellow Yellow Brown Brown Brown
Row 10: Pink Brown Pink Brown Pink Brown Brown Pink Brown Brown Pink Pink Pink Brown Pink Pink Brown Pink Brown Brown Brown Pink
Row 11: Brown Pink Brown Brown Pink Pink Pink Brown Brown Brown Brown Pink Brown Brown Brown Pink Pink Brown Brown Brown Brown Brown
Row 12: Pink Pink Brown Pink Pink Brown Pink Brown Pink Brown Brown Brown Pink Pink Pink Pink Pink Brown Brown Brown Pink Pink
Row 13: Pink Brown Brown Brown Pink Pink Brown Brown Pink Pink Pink Pink Brown Brown Pink Pink Pink Pink Brown Brown Brown Brown
Row 14: Pink Pink Brown Pink Pink Pink Brown Brown Pink Pink Brown Brown Pink Brown Pink Pink Brown Pink Pink Pink Pink Pink
Row 15: Pink Brown Brown Brown Pink Pink Brown Brown Brown Brown Brown Pink Pink Brown Pink Pink Pink Pink Brown Pink Brown Pink
Row 16: Pink Brown Pink Brown Pink Brown Brown Pink Brown Pink Brown Brown Pink Brown Pink Brown Brown Brown Pink Brown Pink Pink
Row 17: Pink Brown Brown Pink Brown Brown Pink Brown Brown Pink Pink Brown Brown Brown Pink Pink Pink Pink Pink Brown Brown Brown
Row 18: Brown Brown Pink Pink Pink Pink Pink Pink Pink Pink Brown Brown Pink Pink Pink Brown Brown Pink Pink Brown Pink Pink
Here is the input grid for the test example:
Input:
Row 1: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Red Green
Row 2: Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Pink Purple Red Red
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Gray Gray Pink Gray Pink Gray Gray Pink Gray Pink Gray Pink Pink Pink Gray Gray Pink Pink Purple Pink Pink
Row 5: Gray Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Gray Pink Pink Pink Gray Gray Purple Pink Pink
Row 6: Gray Pink Gray Pink Gray Pink Gray Pink Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray Purple Pink Pink
Row 7: Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Pink Pink Gray Pink Gray Gray Pink Purple Pink Pink
Row 8: Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Gray Purple Pink Pink
Row 9: Gray Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Gray Gray Pink Gray Gray Gray Purple Pink Pink
Row 10: Pink Gray Gray Pink Pink Gray Gray Pink Pink Gray Gray Gray Gray Gray Gray Gray Pink Gray Purple Pink Pink
Row 11: Pink Gray Pink Pink Pink Pink Pink Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Purple Pink Pink
Row 12: Gray Gray Gray Gray Pink Gray Gray Pink Gray Pink Gray Gray Pink Gray Gray Pink Pink Pink Purple Pink Pink
Row 13: Gray Gray Pink Gray Gray Pink Pink Pink Pink Gray Gray Gray Gray Pink Gray Gray Gray Pink Purple Pink Pink
Row 14: Pink Gray Pink Pink Pink Pink Gray Gray Gray Gray Pink Gray Pink Pink Gray Pink Gray Pink Purple Pink Pink
Row 15: Gray Pink Pink Gray Gray Pink Pink Gray Gray Gray Pink Pink Gray Pink Gray Gray Gray Pink Purple Pink Pink
Row 16: Gray Gray Pink Pink Pink Pink Pink Gray Pink Pink Pink Pink Pink Gray Gray Gray Gray Pink Purple Pink Pink
Row 17: Pink Pink Gray Gray Pink Pink Pink Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Pink Purple Pink Pink
Row 18: Gray Pink Gray Pink Pink Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Pink Gray Purple Pink Pink
Row 19: Pink Pink Gray Gray Pink Pink Pink Gray Pink Pink Gray Pink Gray Gray Gray Pink Gray Gray Purple Pink Pink
Row 20: Pink Pink Gray Gray Pink Gray Pink Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Gray Purple Pink Pink
Row 21: Gray Pink Pink Gray Gray Gray Gray Gray Pink Pink Gray Gray Gray Gray Pink Pink Pink Gray Purple Pink Pink
Row 22: Pink Gray Gray Pink Gray Gray Pink Gray Pink Pink Gray Gray Pink Pink Gray Pink Gray Pink Purple Pink Pink
Row 23: Gray Pink Gray Gray Gray Gray Pink Gray Gray Gray Pink Gray Gray Gray Gray Gray Gray Pink Purple Pink Pink
Row 24: Pink Gray Pink Pink Gray Pink Gray Gray Gray Pink Gray Pink Pink Pink Pink Gray Pink Gray Purple Pink Pink
Row 25: Gray Pink Pink Pink Gray Pink Gray Pink Gray Pink Pink Gray Pink Gray Pink Pink Gray Gray Purple Pink Pink
Row 26: Gray Gray Gray Gray Gray Pink Gray Pink Gray Gray Gray Gray Gray Gray Gray Gray Pink Gray Purple Pink Pink
Row 27: Gray Gray Pink Gray Pink Gray Pink Pink Gray Gray Gray Gray Gray Pink Pink Pink Gray Pink Purple Pink Pink
Row 28: Gray Pink Pink Pink Pink Gray Gray Gray Gray Gray Gray Pink Gray Pink Gray Pink Gray Gray Purple Pink Pink
Row 29: Gray Gray Gray Gray Gray Gray Pink Gray Gray Pink Gray Gray Gray Gray Pink Gray Pink Gray Purple 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 Pink Red Pink Red Red Pink Red Pink Green Pink Pink Pink Green Green Pink Pink
Red Pink Red Red Pink Red Red Pink Red Green Green Pink Green Pink Pink Pink Green Green
Red Pink Red Pink Red Pink Red Pink Pink Green Green Pink Green Green Pink Green Green Green
Red Red Red Red Red Pink Red Red Red Green Green Pink Pink Green Pink Green Green Pink
Red Red Pink Red Red Red Red Red Red Green Pink Green Green Green Green Green Green Green
Red Red Red Pink Red Pink Red Red Pink Green Green Pink Green Green Pink Green Green Green
Pink Red Red Pink Pink Red Red Pink Pink Green Green Green Green Green Green Green Pink Green
Pink Red Pink Pink Pink Pink Pink Red Red Green Pink Green Green Green Pink Green Green Green
Red Red Red Red Pink Red Red Pink Red Pink Green Green Pink Green Green Pink Pink Pink
Red Red Pink Red Red Pink Pink Pink Pink Green Green Green Green Pink Green Green Green Pink
Pink Red Pink Pink Pink Pink Red Red Red Green Pink Green Pink Pink Green Pink Green Pink
Red Pink Pink Red Red Pink Pink Red Red Green Pink Pink Green Pink Green Green Green Pink
Red Red Pink Pink Pink Pink Pink Red Pink Pink Pink Pink Pink Green Green Green Green Pink
Pink Pink Red Red Pink Pink Pink Red Red Red Pink Red Red Pink Red Red Red Pink
Red Pink Red Pink Pink Red Red Red Red Red Red Pink Red Pink Red Red Pink Red
Pink Pink Red Red Pink Pink Pink Red Pink Pink Red Pink Red Red Red Pink Red Red
Pink Pink Red Red Pink Red Pink Red Red Red Red Pink Pink Red Red Red Red Red
Red Pink Pink Red Red Red Red Red Pink Pink Red Red Red Red Pink Pink Pink Red
Pink Red Red Pink Red Red Pink Red Pink Pink Red Red Pink Pink Red Pink Red Pink
Red Pink Red Red Red Red Pink Red Red Red Pink Red Red Red Red Red Red Pink
Pink Red Pink Pink Red Pink Red Red Red Pink Red Pink Pink Pink Pink Red Pink Red
Red Pink Pink Pink Red Pink Red Pink Red Pink Pink Red Pink Red Pink Pink Red Red
Red Red Red Red Red Pink Red Pink Red Red Red Red Red Red Red Red Pink Red
Red Red Pink Red Pink Red Pink Pink Red Red Red Red Red Pink Pink Pink Red Pink
Red Pink Pink Pink Pink Red Red Red Red Red Red Pink Red Pink Red Pink Red Red
Red Red Red Red Red Red Pink Red Red Pink Red Red Red Red Pink Red Pink 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 Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Orange Orange Orange Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
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 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
Row 8: 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 Black Black Black Orange Orange Orange
Row 10: Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Black 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 Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange Orange
Output:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Orange Orange Orange Blue 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 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
Row 8: 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
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 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
Example 2
Input:
Row 1: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 2: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 3: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Gray Gray Gray Purple
Row 15: Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Gray Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 19: Brown Brown Brown Brown Brown Brown Brown Purple Brown Brown Brown Brown Purple Purple Purple Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Purple 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
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
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 Purple Purple Purple Purple Purple Purple Purple
Row 4: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 5: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 6: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 7: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 8: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 9: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 10: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 11: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 12: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 13: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 14: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 15: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 16: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 17: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple
Row 18: Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Purple Blue Blue Blue Purple Purple Purple Purple Purple Purple Purple
Row 19: Brown Brown Brown Brown Brown Brown Brown Blue Brown Brown Brown Brown Blue Blue Blue Brown Brown Brown Brown Brown Brown Brown
Row 20: Brown Brown Brown Brown Brown Brown Brown Blue 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
Row 22: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 23: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 24: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Row 25: Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown Brown
Example 3
Input:
Row 1: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown
Row 2: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown
Row 3: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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 Brown Brown Brown
Row 5: Green Green Green Green Green Green Gray Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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 Brown Brown Brown Brown
Row 9: Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Green Brown Brown Brown
Row 10: Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Brown Brown Brown Brown
Row 11: Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green Brown Brown Brown Brown
Row 12: Green Green Green Green Green Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Green Green Green 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 Brown Brown Brown Brown
Row 2: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown
Row 3: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown
Row 4: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown
Row 5: Green Green Green Green Green Green Green Green Green Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Brown Brown Brown
Row 6: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown
Row 7: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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 Brown Brown Brown Brown
Row 9: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Blue Brown Brown Brown
Row 10: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown
Row 11: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Brown Brown Brown Brown
Row 12: Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green Green 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 Red Red Red Red Red Red
Row 2: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red
Row 3: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 4: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 5: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 6: Gray Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Red Red Red Red Red Red
Row 7: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 8: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 9: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Row 10: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red
Row 11: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red
Row 12: Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red
Row 13: Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray Red Red Red Red Red Red
Row 14: Gray Gray Gray Gray Gray Gray Black Black Gray Gray Gray Gray Red Red Red Red Red Red
Row 15: Gray Gray Gray Gray Gray Black Black Black Gray Gray Gray Gray 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>
| Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Blue Blue Blue Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red
Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Gray Red Red Red Red Red Red |
Subsets and Splits