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LLMcompe-Team-Watanabe
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ARC_data_preprocess

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pandas
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Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 2x2): ``` 7 9 4 3 ``` - Output (shape: 6x6): ``` 7 9 7 9 7 9 4 3 4 3 4 3 9 7 9 7 9 7 3 4 3 4 3 4 7 9 7 9 7 9 4 3 4 3 4 3 ``` ### Training Pair 2 - Input (shape: 2x2): ``` 8 6 6 4 ``` - Output (shape: 6x6): ``` 8 6 8 6 8 6 6 4 6 4 6 4 6 8 6 8 6 8 4 6 4 6 4 6 8 6 8 6 8 6 6 4 6 4 6 4 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 2x2): ``` 3 2 7 8 ```
``` 3 2 3 2 3 2 7 8 7 8 7 8 2 3 2 3 2 3 8 7 8 7 8 7 3 2 3 2 3 2 7 8 7 8 7 8 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 5 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 3x3): ``` 6 6 0 6 0 0 0 6 6 ``` - Output (shape: 9x9): ``` 6 6 0 6 6 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 6 0 6 6 0 0 0 6 6 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 6 6 0 6 6 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 6 0 6 6 ``` ### Training Pair 2 - Input (shape: 3x3): ``` 4 0 4 0 0 0 0 4 0 ``` - Output (shape: 9x9): ``` 4 0 4 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 3x3): ``` 0 0 0 0 0 2 2 0 2 ``` - Output (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 2 0 2 0 0 0 2 0 2 ``` ### Training Pair 4 - Input (shape: 3x3): ``` 2 2 2 0 0 0 0 2 2 ``` - Output (shape: 9x9): ``` 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 ``` ### Training Pair 5 - Input (shape: 3x3): ``` 0 7 7 7 7 7 0 7 7 ``` - Output (shape: 9x9): ``` 0 0 0 0 7 7 0 7 7 0 0 0 7 7 7 7 7 7 0 0 0 0 7 7 0 7 7 0 7 7 0 7 7 0 7 7 7 7 7 7 7 7 7 7 7 0 7 7 0 7 7 0 7 7 0 0 0 0 7 7 0 7 7 0 0 0 7 7 7 7 7 7 0 0 0 0 7 7 0 7 7 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 3x3): ``` 7 0 7 7 0 7 7 7 0 ```
``` 7 0 7 0 0 0 7 0 7 7 0 7 0 0 0 7 0 7 7 7 0 0 0 0 7 7 0 7 0 7 0 0 0 7 0 7 7 0 7 0 0 0 7 0 7 7 7 0 0 0 0 7 7 0 7 0 7 7 0 7 0 0 0 7 0 7 7 0 7 0 0 0 7 7 0 7 7 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 5 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 14x14): ``` 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 0 0 0 0 0 8 8 8 8 0 8 8 8 0 0 0 0 0 8 8 0 0 8 8 8 0 8 8 0 0 0 0 0 0 0 8 8 0 0 0 8 0 0 0 0 0 0 0 8 8 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x14): ``` 0 0 0 0 0 0 0 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 7 0 0 0 0 0 0 7 7 7 7 0 7 7 7 0 0 0 0 0 7 7 0 0 7 7 7 0 7 7 0 0 0 0 0 0 0 7 7 0 0 0 7 0 0 0 0 0 0 0 7 7 0 0 0 7 7 0 0 0 0 0 0 0 0 0 0 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 8 0 8 8 0 0 0 0 0 0 0 8 0 8 0 8 0 8 0 0 0 0 0 0 0 8 8 0 8 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 3 3 0 0 0 0 0 0 0 3 0 3 0 3 0 3 0 0 0 0 0 0 0 3 3 0 3 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 14x14): ``` 0 0 0 8 0 0 0 8 0 0 0 0 0 0 0 8 0 8 0 8 0 8 0 8 0 0 0 0 0 8 8 8 8 8 8 8 8 8 0 0 0 0 0 8 0 8 0 8 0 8 0 8 0 0 0 0 0 8 0 0 0 8 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x14): ``` 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 4 - Input (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 8 8 8 0 8 8 0 0 0 0 0 0 0 0 0 8 0 8 8 0 0 0 0 0 0 0 0 0 0 0 8 0 0 8 8 0 0 0 0 0 0 0 0 0 0 8 8 0 8 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 3 3 0 3 3 0 0 0 0 0 0 0 0 0 3 0 3 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 3 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 5 - Input (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 8 8 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 8 8 0 8 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 0 0 0 0 0 0 0 0 8 8 8 0 8 8 8 0 0 0 0 0 0 0 8 0 0 0 0 0 8 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 2 2 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 0 0 0 0 0 8 0 0 0 8 0 8 0 8 0 0 0 0 0 8 0 8 0 8 0 0 0 8 0 0 0 0 0 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 7 7 7 7 7 7 7 0 0 0 0 0 7 0 0 0 7 0 7 0 7 0 0 0 0 0 7 0 7 0 7 0 0 0 7 0 0 0 0 0 7 7 7 7 7 7 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 5 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 3 0 0 3 0 3 0 0 0 0 3 3 3 3 3 3 3 0 0 0 0 3 0 0 0 0 3 0 0 0 0 3 0 0 0 3 3 0 0 0 0 3 3 0 0 3 0 3 0 0 0 3 0 3 0 0 3 0 0 0 0 0 3 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 0 3 4 4 3 0 0 0 0 0 0 3 4 4 3 0 3 0 0 0 0 3 3 3 3 3 3 3 0 0 0 0 3 0 0 0 0 3 0 0 0 0 3 0 0 0 3 3 0 0 0 0 3 3 0 0 3 4 3 0 0 0 3 4 3 0 0 3 0 0 0 0 0 3 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 3 0 3 3 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 3 0 3 3 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 10x10): ``` 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 3 0 3 3 0 3 0 0 3 0 0 3 0 0 3 0 3 0 0 0 0 3 0 0 3 3 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 0 3 3 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 3 0 3 3 0 3 0 0 3 0 0 3 4 4 3 4 3 0 0 0 0 3 4 4 3 3 0 0 0 0 0 3 4 4 3 0 0 0 0 0 0 3 4 4 3 0 0 0 0 0 0 0 3 3 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 4 - Input (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 3 3 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 3 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 3 3 3 3 0 3 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 4 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 4 4 4 3 0 0 0 0 0 0 0 0 3 0 0 0 3 4 4 4 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 4 4 4 3 0 0 0 0 0 0 3 0 0 0 0 0 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 3 3 4 4 3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 3 3 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 3 3 3 3 0 3 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 5 - Input (shape: 6x6): ``` 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 3 0 0 0 0 3 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 ``` - Output (shape: 6x6): ``` 0 0 0 0 0 0 0 0 3 0 0 0 0 3 4 3 0 0 0 0 3 4 3 0 0 0 0 3 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 3 3 3 3 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 3 0 0 0 0 0 0 0 0 3 3 0 3 0 0 0 3 3 3 3 3 0 0 0 0 3 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 3 3 3 3 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 4 3 4 4 3 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 3 4 4 4 3 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 4 4 4 3 0 0 0 0 0 0 0 0 3 3 4 3 0 0 0 3 3 3 3 3 0 0 0 0 3 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 15x15): ``` 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 2 3 3 3 2 3 3 3 2 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 8 8 8 2 0 0 0 0 0 0 0 0 0 0 2 8 2 8 2 0 0 0 0 0 0 0 0 0 0 2 8 8 8 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 9x9): ``` 2 2 2 2 2 2 2 0 0 2 0 0 0 0 0 2 0 0 2 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 0 0 0 0 2 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 9x9): ``` 2 2 2 2 2 2 2 0 0 2 4 4 4 4 4 2 0 0 2 4 4 4 4 4 2 0 0 2 4 4 2 4 4 2 0 0 2 4 4 4 4 4 2 0 0 2 4 4 4 4 4 2 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 13x13): ``` 0 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 2 0 ``` - Output (shape: 13x13): ``` 0 2 2 2 2 2 0 0 0 0 0 0 0 0 2 8 8 8 2 0 0 0 0 0 0 0 0 2 8 2 8 2 0 0 0 0 0 0 0 0 2 8 8 8 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 2 4 4 2 4 4 2 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 2 2 2 2 2 2 2 0 ``` ### Training Pair 4 - Input (shape: 7x7): ``` 2 2 2 2 2 0 0 2 0 0 0 2 0 0 2 0 2 0 2 0 0 2 0 0 0 2 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 7x7): ``` 2 2 2 2 2 0 0 2 8 8 8 2 0 0 2 8 2 8 2 0 0 2 8 8 8 2 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 2 8 8 8 2 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 2 8 2 8 2 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 2 8 8 8 2 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 2 2 2 2 2 0 0 0 0 0 2 3 3 3 2 3 3 3 2 0 0 0 0 0 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 0 0 0 0 0 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 2 2 2 2 2 0 0 0 2 3 3 3 3 3 3 3 2 0 0 0 2 8 8 8 2 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 2 8 2 8 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 8 8 8 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 2 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 4 4 4 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 6x3): ``` 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ``` - Output (shape: 9x3): ``` 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 ``` ### Training Pair 2 - Input (shape: 6x3): ``` 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 ``` - Output (shape: 9x3): ``` 0 2 0 2 2 0 0 2 0 0 2 2 0 2 0 2 2 0 0 2 0 0 2 2 0 2 0 ``` ### Training Pair 3 - Input (shape: 6x3): ``` 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 ``` - Output (shape: 9x3): ``` 0 2 0 2 2 0 0 2 0 0 2 0 2 2 0 0 2 0 0 2 0 2 2 0 0 2 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 6x3): ``` 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 ```
``` 2 2 2 0 2 0 0 2 0 2 2 2 0 2 0 0 2 0 2 2 2 0 2 0 0 2 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 8x9): ``` 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 8x9): ``` 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 0 8 0 0 0 8 0 0 0 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 14x9): ``` 0 0 0 0 0 0 0 0 0 0 6 6 6 0 0 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x9): ``` 0 0 0 0 0 0 0 0 0 0 0 6 6 6 0 0 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 0 0 6 0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 4 0 0 0 0 4 0 0 0 0 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 8 8 8 0 7 7 0 2 2 2 8 8 8 0 7 7 0 2 2 2 ``` - Output (shape: 10x10): ``` 8 8 8 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 8 8 7 7 0 0 0 0 0 0 0 0 7 2 2 2 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 1 0 0 0 0 0 0 0 4 1 1 0 2 2 0 3 3 0 4 1 1 0 2 2 0 3 3 0 4 ``` - Output (shape: 10x10): ``` 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 0 2 3 3 0 0 0 0 0 0 0 0 3 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 3 3 3 4 4 4 4 0 2 0 3 3 3 4 4 4 4 0 2 0 3 3 3 ``` - Output (shape: 10x10): ``` 4 4 4 4 0 0 0 0 0 0 4 4 4 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 7 0 8 8 0 6 0 0 0 0 7 0 8 8 0 6 0 3 3 0 7 0 8 8 0 6 0 3 3 0 ```
``` 7 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 8 6 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 1 1 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 1 0 0 0 4 0 0 0 4 2 2 0 2 2 2 0 2 2 2 0 1 1 1 0 4 4 4 0 4 4 2 0 0 0 2 0 0 0 2 0 0 0 1 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 3 3 3 0 3 3 3 0 3 3 3 0 0 0 0 0 0 8 0 8 0 3 0 3 0 3 0 3 0 3 0 3 0 0 0 0 0 0 8 8 8 0 3 3 3 0 3 3 3 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 21x21): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 2 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 0 8 0 8 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 8 0 8 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 3x7): ``` 1 1 0 5 0 1 0 0 0 1 5 1 1 1 1 1 0 5 0 1 0 ``` - Output (shape: 3x3): ``` 0 2 0 0 0 2 0 2 0 ``` ### Training Pair 2 - Input (shape: 3x7): ``` 1 0 0 5 0 1 0 0 1 0 5 1 1 1 1 0 0 5 0 0 0 ``` - Output (shape: 3x3): ``` 0 0 0 0 2 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 3x7): ``` 0 0 1 5 0 0 0 1 1 0 5 1 0 1 0 1 1 5 1 0 1 ``` - Output (shape: 3x3): ``` 0 0 0 2 0 0 0 0 2 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 3x7): ``` 1 0 1 5 1 0 1 0 1 0 5 1 0 1 1 0 1 5 0 1 0 ```
``` 2 0 2 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 7x7): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 2 0 0 0 0 1 2 4 0 0 0 1 2 4 0 0 0 1 2 4 0 0 ``` - Output (shape: 7x7): ``` 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 ``` ### Training Pair 2 - Input (shape: 7x7): ``` 2 8 3 0 0 0 0 8 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 7x7): ``` 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 8 3 2 ``` ### Training Pair 3 - Input (shape: 7x7): ``` 0 0 0 0 8 3 0 0 0 0 8 3 0 0 0 0 8 3 0 0 0 0 8 3 0 0 0 4 8 3 0 0 0 4 0 3 0 0 0 4 0 0 0 0 0 4 0 0 0 ``` - Output (shape: 7x7): ``` 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 8 3 4 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 7x7): ``` 0 1 0 0 0 0 2 1 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 4 2 0 0 0 0 4 0 ```
``` 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 3 3 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 0 0 3 3 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 3 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 0 0 3 4 4 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 0 0 0 0 3 3 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 0 0 0 0 0 3 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 2 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 3 3 4 4 4 4 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 2 2 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 0 0 2 2 0 0 2 0 2 0 0 2 2 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - 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Input (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 2 0 2 2 2 0 2 0 2 2 0 2 0 2 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 3 3 3 3 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 3 3 3 3 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 4 4 4 4 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 4 4 4 4 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 4 4 4 4 4 0 0 0 0 0 4 4 4 4 0 0 0 0 0 4 4 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 2 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 2 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 2 2 0 2 8 8 8 8 8 0 2 0 2 2 8 8 8 8 2 2 0 2 0 8 8 0 0 0 2 2 2 2 2 2 8 8 8 8 8 2 2 2 2 2 8 8 8 8 2 2 2 2 2 8 8 2 2 2 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 8 2 2 8 0 0 0 0 0 8 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 8 2 2 2 8 0 0 0 0 0 2 8 8 8 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 8 2 8 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 2 2 2 0 0 0 0 0 2 2 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 8 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 8 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 3 3 0 0 0 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 3 3 0 0 0 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 3 0 0 0 0 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 3 0 0 0 0 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 3 0 0 0 0 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 3 0 0 0 0 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 0 0 0 0 0 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 0 0 0 0 0 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 0 0 0 0 0 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 0 0 0 0 0 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 4 4 4 4 3 2 2 2 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 4 4 4 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 9x10): ``` 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 2 0 0 0 8 8 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 9x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 2 8 8 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 14x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 2 2 0 2 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 11x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 11x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 11x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 8 8 0 0 2 2 0 0 0 0 8 8 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 8 8 2 2 0 0 0 0 0 0 8 8 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 21x22): ``` 0 3 0 0 0 3 3 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 1 1 1 2 3 3 0 3 0 0 0 1 1 3 3 3 0 1 1 2 3 3 0 1 1 2 3 3 3 0 3 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 1 3 3 0 0 0 3 0 1 3 3 3 1 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 3 3 3 0 3 1 2 3 3 0 1 1 2 3 3 0 0 3 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 3 2 1 3 0 1 1 2 3 3 0 0 0 0 1 1 1 2 3 3 0 1 1 2 3 3 3 1 3 2 3 3 0 0 0 0 0 8 1 8 8 3 0 8 8 8 8 8 0 1 8 8 8 8 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 3 0 0 1 1 3 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 1 3 3 0 1 1 2 3 1 0 0 0 0 1 1 1 2 3 3 0 1 1 2 3 1 0 1 1 2 3 3 0 0 0 0 3 8 8 8 3 3 1 8 8 8 8 8 0 8 8 8 8 8 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 3 0 3 0 1 1 0 3 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 21x22): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 1 1 2 3 3 0 1 1 2 3 3 0 1 1 2 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 23x22): ``` 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 6 6 6 6 6 6 0 0 6 6 6 6 3 6 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 3 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 3 0 0 0 0 3 8 8 3 3 8 8 0 0 8 8 3 3 8 3 0 0 0 3 0 0 0 3 8 8 3 3 8 8 0 0 8 8 3 3 8 8 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 6 6 6 6 0 0 6 6 3 6 6 6 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 3 8 3 3 8 3 0 3 0 0 0 3 0 0 8 8 3 3 3 8 0 0 3 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 3 3 3 3 8 0 0 0 0 0 0 3 3 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 6 6 3 6 6 6 0 3 6 6 6 3 6 6 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 3 0 0 0 8 3 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 23x22): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 6 6 6 6 0 0 6 6 6 6 6 6 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 6 6 6 6 0 0 6 6 6 6 6 6 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 6 6 6 6 0 0 6 6 6 6 6 6 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 8 8 3 3 8 8 0 0 8 8 3 3 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 22x22): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2 2 2 2 2 0 2 2 2 2 0 0 2 2 2 2 0 0 0 0 3 0 3 2 2 3 0 0 3 2 2 3 0 3 3 2 2 3 0 0 3 0 0 0 2 3 3 3 0 0 3 3 3 3 0 0 3 3 3 3 0 0 0 0 0 0 2 3 1 3 0 0 2 2 1 2 0 0 3 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 2 2 2 2 3 0 2 2 2 2 0 0 2 2 2 2 2 0 0 0 0 0 3 2 2 3 0 0 3 2 2 3 0 3 3 2 2 3 2 0 0 0 0 0 3 3 3 3 0 0 3 3 3 3 0 0 3 3 3 3 0 0 0 0 0 0 3 3 1 3 0 0 3 1 1 3 0 0 3 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 3 2 3 2 0 0 2 3 2 2 0 0 0 0 0 0 3 2 2 3 0 0 3 2 3 3 0 0 3 2 3 3 0 0 0 0 0 3 3 3 3 3 0 0 3 3 3 3 0 0 3 2 3 3 0 0 2 0 0 0 3 1 1 3 0 3 3 1 1 3 0 0 3 1 1 3 0 0 0 0 0 0 2 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 3 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 22x22): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 3 2 2 3 0 0 3 2 2 3 0 0 3 2 2 3 0 0 0 0 0 0 3 3 3 3 0 0 3 3 3 3 0 0 3 3 3 3 0 0 0 0 0 0 3 1 1 3 0 0 3 1 1 3 0 0 3 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 3 2 2 3 0 0 3 2 2 3 0 0 3 2 2 3 0 0 0 0 0 0 3 3 3 3 0 0 3 3 3 3 0 0 3 3 3 3 0 0 0 0 0 0 3 1 1 3 0 0 3 1 1 3 0 0 3 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 3 2 2 3 0 0 3 2 2 3 0 0 3 2 2 3 0 0 0 0 0 0 3 3 3 3 0 0 3 3 3 3 0 0 3 3 3 3 0 0 0 0 0 0 3 1 1 3 0 0 3 1 1 3 0 0 3 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 24x22): ``` 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 2 2 8 3 2 0 2 2 8 2 2 0 3 2 8 2 2 0 0 0 3 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 3 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 3 8 8 3 3 8 0 8 8 8 8 8 0 8 8 3 8 8 0 0 0 0 0 8 8 8 8 3 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 3 0 0 0 0 0 2 3 8 2 2 0 2 2 3 2 3 0 2 2 8 2 2 0 0 0 3 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 3 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 8 8 8 8 8 3 8 8 8 8 3 0 8 8 8 3 8 0 0 0 0 0 8 8 8 3 8 0 8 3 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 3 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 2 2 8 2 2 0 2 2 8 2 2 0 2 2 8 2 2 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 3 0 0 3 3 3 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 3 8 8 8 8 0 8 8 3 3 8 0 8 8 3 8 8 0 3 0 0 0 8 8 8 8 8 0 8 8 3 8 8 0 3 8 8 8 8 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 3 0 0 3 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 8 2 2 0 2 2 8 2 2 0 2 2 8 2 2 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 8 2 2 0 2 2 8 2 2 0 2 2 8 2 2 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 8 2 2 0 2 2 8 2 2 0 2 2 8 2 2 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 3 3 8 3 3 0 3 3 8 3 3 0 3 3 8 3 3 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 8 8 8 8 8 0 8 8 8 8 8 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 3x3): ``` 0 0 6 0 6 0 6 0 0 ``` - Output (shape: 9x9): ``` 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 6 6 0 0 0 6 6 0 0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 6 6 0 0 0 6 6 0 0 0 0 0 0 0 6 0 6 0 0 0 0 0 0 0 6 6 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 3x3): ``` 0 7 0 7 7 7 0 7 0 ``` - Output (shape: 9x9): ``` 0 0 0 7 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 7 0 0 0 7 0 7 7 0 7 7 0 7 0 0 0 0 0 0 0 0 0 7 0 7 7 0 7 7 0 7 0 0 0 7 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 7 0 0 0 ``` ### Training Pair 3 - Input (shape: 3x3): ``` 4 4 0 0 0 4 0 0 4 ``` - Output (shape: 9x9): ``` 0 0 4 0 0 4 0 0 0 4 4 0 4 4 0 0 0 0 4 4 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 4 4 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 3x3): ``` 0 0 3 3 3 0 0 3 0 ```
``` 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 3 3 3 0 3 3 0 0 0 0 0 0 3 0 0 3 0 0 0 3 0 3 3 0 3 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 3 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 23x23): ``` 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 0 0 1 4 4 1 0 0 1 0 0 1 0 0 0 0 1 2 2 1 0 0 1 0 0 1 4 4 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 9 9 1 0 0 1 0 0 1 0 0 1 9 9 0 0 1 0 0 1 0 0 1 9 9 1 0 0 1 0 0 1 0 0 1 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 1 0 0 1 8 8 1 0 0 0 0 1 0 0 1 0 0 1 8 8 1 0 0 1 0 0 1 8 8 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 ``` - Output (shape: 23x23): ``` 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 0 0 1 4 4 1 0 0 1 0 0 1 0 0 0 0 1 2 2 1 0 0 1 0 0 1 4 4 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 9 9 1 9 9 1 9 9 1 9 9 1 9 9 0 0 1 2 2 1 0 0 1 9 9 1 9 9 1 9 9 1 9 9 1 9 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 0 0 1 2 2 1 0 0 1 0 0 1 0 0 1 0 0 1 8 8 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 8 8 1 8 8 1 8 8 1 8 8 1 0 0 0 0 1 0 0 1 0 0 1 8 8 1 8 8 1 8 8 1 8 8 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 ``` ### Training Pair 2 - Input (shape: 20x20): ``` 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 2 2 8 0 0 8 0 0 8 0 0 8 2 2 8 0 0 0 0 8 2 2 8 0 0 8 0 0 8 0 0 8 2 2 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 1 1 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 1 1 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 2 2 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 2 2 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 3 3 8 0 0 8 3 3 8 0 0 8 0 0 8 0 0 0 0 8 3 3 8 0 0 8 3 3 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 ``` - Output (shape: 20x20): ``` 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 2 2 8 2 2 8 2 2 8 2 2 8 2 2 8 0 0 0 0 8 2 2 8 2 2 8 2 2 8 2 2 8 2 2 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 1 1 8 0 0 8 2 2 8 0 0 0 0 8 0 0 8 0 0 8 1 1 8 0 0 8 2 2 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 2 2 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 2 2 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 3 3 8 3 3 8 3 3 8 0 0 8 0 0 8 0 0 0 0 8 3 3 8 3 3 8 3 3 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 8 0 0 ``` ### Training Pair 3 - Input (shape: 23x23): ``` 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 2 2 4 0 0 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 2 2 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 3 3 4 0 0 4 0 0 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 3 3 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 ``` - Output (shape: 23x23): ``` 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 2 2 4 2 2 4 2 2 4 2 2 4 0 0 0 0 4 3 3 4 0 0 4 2 2 4 2 2 4 2 2 4 2 2 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 3 3 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 0 0 4 0 0 0 0 4 3 3 4 3 3 4 3 3 4 3 3 4 3 3 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 26x26): ``` 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 3 3 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 3 3 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 ```
``` 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 3 3 4 0 0 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 3 3 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 8 8 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 0 0 4 0 0 4 0 0 0 0 4 2 2 4 2 2 4 2 2 4 2 2 4 2 2 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 4 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 20x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 20x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 3 4 3 3 3 3 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 7 4 7 7 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 8 8 8 8 9 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 30x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 30x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 2 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 6 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 2 2 3 2 2 2 2 2 5 2 2 2 2 2 2 2 0 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 7 7 5 7 7 7 7 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 5 0 0 0 0 5 0 0 0 5 0 0 0 0 5 0 5 0 5 0 0 0 0 5 0 5 0 5 0 0 5 0 5 0 5 0 5 0 0 5 0 5 0 5 0 5 0 ``` - Output (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 0 0 0 0 2 0 3 0 1 0 0 0 0 2 0 3 0 1 0 0 4 0 2 0 3 0 1 0 0 4 0 2 0 3 0 1 0 ``` ### Training Pair 2 - Input (shape: 9x9): ``` 0 0 0 0 0 5 0 0 0 0 5 0 0 0 5 0 0 0 0 5 0 0 0 5 0 0 0 0 5 0 5 0 5 0 0 0 0 5 0 5 0 5 0 0 0 0 5 0 5 0 5 0 0 0 0 5 0 5 0 5 0 5 0 0 5 0 5 0 5 0 5 0 0 5 0 5 0 5 0 5 0 ``` - Output (shape: 9x9): ``` 0 0 0 0 0 1 0 0 0 0 2 0 0 0 1 0 0 0 0 2 0 0 0 1 0 0 0 0 2 0 3 0 1 0 0 0 0 2 0 3 0 1 0 0 0 0 2 0 3 0 1 0 0 0 0 2 0 3 0 1 0 4 0 0 2 0 3 0 1 0 4 0 0 2 0 3 0 1 0 4 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 5 0 0 0 5 0 0 0 0 5 0 0 0 5 0 0 0 0 5 0 0 0 5 0 5 0 0 5 0 0 0 5 0 5 0 0 5 0 5 0 5 0 5 0 0 5 0 5 0 5 0 5 0 0 5 0 5 0 5 0 5 0 ```
``` 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 1 0 0 0 2 0 0 0 0 1 0 0 0 2 0 3 0 0 1 0 0 0 2 0 3 0 0 1 0 4 0 2 0 3 0 0 1 0 4 0 2 0 3 0 0 1 0 4 0 2 0 3 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 11x11): ``` 0 3 0 5 0 6 3 5 0 6 2 6 0 4 5 2 8 0 5 0 0 8 0 2 8 5 0 4 0 5 3 0 4 5 5 5 5 5 5 5 5 5 5 5 0 2 0 5 4 0 3 5 3 4 0 4 0 8 5 2 0 6 5 0 0 2 3 6 0 5 0 8 0 5 8 6 0 5 5 5 5 5 5 5 5 5 5 5 6 3 0 5 0 3 0 5 0 0 3 0 0 2 5 0 6 4 5 2 8 0 8 4 0 5 2 0 0 5 4 0 6 ``` - Output (shape: 11x11): ``` 0 0 0 5 3 3 3 5 0 0 0 0 0 0 5 3 3 3 5 0 0 0 0 0 0 5 3 3 3 5 0 0 0 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 6 6 6 5 4 4 4 0 0 0 5 6 6 6 5 4 4 4 0 0 0 5 6 6 6 5 4 4 4 5 5 5 5 5 5 5 5 5 5 5 2 2 2 5 0 0 0 5 0 0 0 2 2 2 5 0 0 0 5 0 0 0 2 2 2 5 0 0 0 5 0 0 0 ``` ### Training Pair 2 - Input (shape: 11x11): ``` 2 0 3 5 4 6 0 5 0 6 0 0 0 8 5 0 0 2 5 4 0 3 4 6 0 5 3 8 0 5 2 0 8 5 5 5 5 5 5 5 5 5 5 5 4 0 8 5 0 0 2 5 0 6 4 0 0 2 5 0 3 0 5 3 0 0 3 0 6 5 4 0 6 5 8 0 2 5 5 5 5 5 5 5 5 5 5 5 3 6 0 5 0 8 4 5 2 0 0 0 8 4 5 2 0 0 5 8 0 3 2 0 0 5 0 3 6 5 6 4 0 ``` - Output (shape: 11x11): ``` 0 0 0 5 0 0 0 5 2 2 2 0 0 0 5 0 0 0 5 2 2 2 0 0 0 5 0 0 0 5 2 2 2 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 3 3 3 5 0 0 0 0 0 0 5 3 3 3 5 0 0 0 0 0 0 5 3 3 3 5 0 0 0 5 5 5 5 5 5 5 5 5 5 5 4 4 4 5 0 0 0 5 6 6 6 4 4 4 5 0 0 0 5 6 6 6 4 4 4 5 0 0 0 5 6 6 6 ``` ### Training Pair 3 - Input (shape: 11x11): ``` 3 8 4 5 4 6 0 5 2 0 8 0 0 0 5 8 0 3 5 6 0 3 6 2 0 5 0 2 0 5 4 0 0 5 5 5 5 5 5 5 5 5 5 5 0 4 2 5 8 0 3 5 0 4 0 0 8 6 5 0 0 4 5 0 2 6 0 3 0 5 2 6 0 5 0 3 0 5 5 5 5 5 5 5 5 5 5 5 0 6 0 5 6 2 0 5 3 6 0 3 0 8 5 0 8 3 5 0 0 4 4 2 0 5 0 0 4 5 2 0 8 ``` - Output (shape: 11x11): ``` 0 0 0 5 4 4 4 5 0 0 0 0 0 0 5 4 4 4 5 0 0 0 0 0 0 5 4 4 4 5 0 0 0 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 2 2 2 5 6 6 6 0 0 0 5 2 2 2 5 6 6 6 0 0 0 5 2 2 2 5 6 6 6 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 3 3 3 5 0 0 0 0 0 0 5 3 3 3 5 0 0 0 0 0 0 5 3 3 3 5 0 0 0 ``` ### Training Pair 4 - Input (shape: 11x11): ``` 2 0 0 5 0 6 2 5 0 0 4 0 4 3 5 4 0 8 5 3 0 6 6 0 0 5 3 0 0 5 8 0 2 5 5 5 5 5 5 5 5 5 5 5 3 8 0 5 6 2 0 5 0 4 8 0 0 4 5 0 0 4 5 6 0 0 6 2 0 5 3 8 0 5 0 3 2 5 5 5 5 5 5 5 5 5 5 5 0 3 6 5 0 2 0 5 0 6 0 2 0 0 5 4 0 8 5 0 0 8 8 0 4 5 6 3 0 5 2 3 4 ``` - Output (shape: 11x11): ``` 2 2 2 5 0 0 0 5 0 0 0 2 2 2 5 0 0 0 5 0 0 0 2 2 2 5 0 0 0 5 0 0 0 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 4 4 4 5 3 3 3 0 0 0 5 4 4 4 5 3 3 3 0 0 0 5 4 4 4 5 3 3 3 5 5 5 5 5 5 5 5 5 5 5 6 6 6 5 0 0 0 5 0 0 0 6 6 6 5 0 0 0 5 0 0 0 6 6 6 5 0 0 0 5 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 11x11): ``` 6 4 0 5 0 3 0 5 0 4 0 0 0 3 5 2 8 6 5 8 0 2 2 0 8 5 4 0 0 5 6 3 0 5 5 5 5 5 5 5 5 5 5 5 2 0 0 5 0 3 0 5 3 6 2 3 4 6 5 8 4 2 5 0 0 4 0 8 0 5 0 0 6 5 8 0 0 5 5 5 5 5 5 5 5 5 5 5 0 2 4 5 0 6 4 5 0 2 8 0 6 3 5 0 0 3 5 4 0 6 0 0 0 5 2 0 8 5 3 0 0 ```
``` 0 0 0 5 2 2 2 5 4 4 4 0 0 0 5 2 2 2 5 4 4 4 0 0 0 5 2 2 2 5 4 4 4 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 6 6 6 5 3 3 3 0 0 0 5 6 6 6 5 3 3 3 0 0 0 5 6 6 6 5 3 3 3 5 5 5 5 5 5 5 5 5 5 5 0 0 0 5 0 0 0 5 0 0 0 0 0 0 5 0 0 0 5 0 0 0 0 0 0 5 0 0 0 5 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 12x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 8 6 8 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 8 6 8 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 12x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 8 0 6 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 8 8 6 8 8 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 6 0 8 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 8 0 6 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 8 8 6 8 8 0 0 0 0 0 0 0 0 6 8 6 0 0 0 0 0 0 0 0 6 0 8 0 6 0 ``` ### Training Pair 2 - Input (shape: 12x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 7 2 7 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 7 2 7 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 12x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 2 0 7 0 2 0 0 0 0 0 0 0 0 2 7 2 0 0 0 0 0 0 0 0 7 7 2 7 7 0 0 0 0 0 0 0 0 2 7 2 0 0 0 0 0 0 0 0 2 0 7 0 2 0 2 0 7 0 2 0 0 0 0 0 0 0 0 2 7 2 0 0 0 0 0 0 0 0 7 7 2 7 7 0 0 0 0 0 0 0 0 2 7 2 0 0 0 0 0 0 0 0 2 0 7 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 12x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 4 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 4 0 3 0 4 0 0 0 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 0 3 3 4 3 3 0 0 0 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 0 4 0 3 0 4 0 4 0 3 0 4 0 0 0 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 0 3 3 4 3 3 0 0 0 0 0 0 0 0 4 3 4 0 0 0 0 0 0 0 0 4 0 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 3 1 1 0 0 0 0 0 0 0 0 1 1 4 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 2 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 20x20): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 3 3 1 0 0 0 0 0 0 0 0 1 4 4 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 4 4 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 3 3 3 3 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 3 3 3 3 1 1 1 3 1 0 0 0 1 4 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 2 1 1 1 1 2 1 0 0 0 0 0 0 1 1 1 0 0 1 2 2 1 0 0 1 1 1 0 0 0 0 0 0 1 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 3 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 ``` - Output (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 2 2 2 1 0 0 0 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 1 2 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 2 2 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 2 2 2 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 2 2 2 2 2 2 2 1 1 1 1 2 2 1 1 1 1 2 1 0 0 0 0 0 1 2 1 1 1 1 2 2 2 2 2 2 2 1 0 0 1 2 2 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 2 2 2 2 2 2 2 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 2 2 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 2 2 1 0 1 3 1 1 1 3 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 3 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 3 1 1 1 1 3 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 3 3 3 1 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 3 1 1 1 1 3 3 3 3 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 3 3 3 3 1 1 1 1 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 3 3 3 1 0 0 0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 18x18): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 4 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 3 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 6 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 ``` - Output (shape: 18x18): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 4 4 1 1 1 1 4 4 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 4 4 1 1 1 1 4 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 4 4 1 0 0 1 3 1 1 1 3 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 6 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 6 6 1 0 0 1 0 0 0 0 0 1 6 6 1 0 0 1 6 6 1 0 1 1 1 0 0 0 0 1 6 6 1 1 1 1 6 6 1 1 1 6 1 0 0 0 0 1 1 1 1 0 0 1 6 6 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 30x30): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 4 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 8 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 6 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 4 4 4 1 0 0 1 1 1 1 1 1 0 0 1 4 4 4 4 1 0 0 0 1 4 4 1 1 1 1 4 4 4 1 1 1 1 4 4 4 4 1 1 1 1 4 4 4 4 1 0 0 0 1 4 4 1 0 0 1 4 4 4 1 0 0 1 4 4 4 4 1 0 0 1 4 4 4 4 1 0 0 0 1 1 1 1 0 0 1 4 4 4 1 0 0 1 1 1 1 1 1 0 0 1 4 4 4 4 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 4 4 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 4 4 1 1 1 4 1 0 0 0 0 1 1 1 1 0 0 0 0 1 4 4 1 0 0 0 0 0 0 1 1 1 1 0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 1 4 4 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 8 8 8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 8 8 8 1 1 1 8 8 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 1 0 0 0 1 8 8 8 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 8 8 8 8 8 8 8 8 8 8 1 0 0 0 0 1 1 1 1 0 0 1 8 1 1 1 8 1 0 1 8 8 8 8 8 8 8 8 8 8 1 0 0 0 0 1 6 6 1 0 0 1 1 1 0 1 8 1 1 1 8 8 8 8 8 8 8 8 8 8 1 0 0 0 0 1 6 6 1 0 0 0 0 0 0 1 1 1 0 1 8 8 8 8 8 8 8 8 8 8 1 0 0 0 0 1 6 6 1 0 0 0 0 0 0 0 0 0 0 1 8 8 8 8 8 8 8 8 8 8 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 6 6 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 6 6 1 0 0 0 1 6 6 1 1 1 1 6 6 1 1 1 1 1 6 6 1 1 1 1 1 1 1 1 6 6 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 30x30): ``` 0 2 0 0 0 2 0 8 0 0 0 2 0 2 0 2 0 0 2 8 0 0 2 0 8 0 0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 1 1 1 1 1 1 1 1 2 8 8 2 0 0 0 0 0 0 8 0 2 3 3 3 3 3 3 0 0 2 1 1 1 1 1 1 1 1 0 0 0 9 9 9 9 9 0 0 8 0 8 3 3 3 3 3 3 2 2 2 1 1 1 1 1 1 1 1 8 0 8 9 9 9 9 9 8 8 2 8 0 3 3 3 3 3 3 8 8 0 1 1 1 1 1 1 1 1 0 0 2 9 9 9 9 9 0 0 8 0 0 3 3 3 3 3 3 0 0 2 2 2 8 8 8 8 0 2 8 2 0 9 9 9 9 9 0 0 0 0 0 8 0 0 8 0 0 2 8 2 0 0 2 0 0 0 0 0 0 8 0 9 9 9 9 9 8 8 0 8 8 8 0 0 2 0 8 0 0 0 2 8 8 0 0 0 8 0 2 0 2 0 8 0 0 8 8 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 2 8 8 2 0 0 2 0 0 2 0 0 8 2 8 0 8 0 0 0 0 0 8 2 8 2 8 0 0 0 0 0 0 2 8 2 0 0 0 0 0 8 0 0 0 0 0 0 2 6 6 6 6 0 8 0 0 4 4 4 4 4 4 2 0 0 0 8 0 0 2 0 0 0 2 0 8 0 8 6 6 6 6 0 8 0 8 4 4 4 4 4 4 2 0 2 2 2 0 1 1 1 1 1 8 0 0 2 0 6 6 6 6 8 0 2 2 4 4 4 4 4 4 8 0 8 0 0 0 1 1 1 1 1 0 2 0 2 8 6 6 6 6 8 0 8 0 4 4 4 4 4 4 0 8 2 2 0 2 1 1 1 1 1 0 8 0 0 2 6 6 6 6 0 0 0 2 4 4 4 4 4 4 0 0 8 0 8 8 1 1 1 1 1 8 0 0 0 0 6 6 6 6 0 0 2 8 0 8 8 2 8 0 8 0 0 0 0 0 1 1 1 1 1 0 2 2 8 0 6 6 6 6 0 2 0 0 0 0 2 8 0 0 0 2 8 0 0 2 0 0 0 0 0 0 0 0 0 8 0 2 0 0 0 0 0 8 0 0 0 2 8 0 0 0 0 0 0 0 0 8 2 0 0 0 2 0 0 2 0 8 0 0 0 2 8 0 8 0 0 0 8 0 8 8 8 0 8 0 0 8 0 2 2 0 2 8 0 0 0 0 0 8 8 2 2 8 0 8 2 2 8 0 0 0 0 8 0 2 0 8 0 0 0 8 2 2 2 0 0 0 0 2 8 0 8 0 0 2 2 8 0 0 2 0 0 0 2 2 2 0 0 0 2 2 8 0 8 8 0 0 8 8 0 8 0 8 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 8 2 0 0 0 0 2 8 2 0 2 0 0 8 0 0 0 2 0 8 0 0 0 2 8 8 0 8 0 2 0 0 0 8 2 0 0 0 0 0 0 0 8 8 0 2 0 8 0 0 0 0 0 0 2 2 0 0 2 0 0 8 8 0 8 2 0 0 0 8 0 8 0 8 2 0 0 0 8 0 0 8 0 2 0 0 8 0 2 2 8 0 0 0 0 8 0 2 2 8 2 8 0 2 2 0 0 0 2 2 2 2 2 2 0 0 0 8 0 8 0 0 8 2 0 0 2 8 2 8 0 0 0 0 0 0 0 0 8 0 0 2 0 2 2 0 0 8 0 2 0 0 8 8 0 0 0 0 8 0 0 0 8 0 2 8 0 0 0 0 0 0 0 0 0 0 2 8 2 8 0 0 8 0 8 2 0 2 8 8 0 0 0 2 0 0 0 8 8 0 8 0 0 0 8 2 8 8 0 2 8 2 2 2 2 0 8 8 0 0 0 8 0 0 8 0 8 0 0 0 8 0 2 0 0 8 0 8 0 0 2 8 0 0 ``` - Output (shape: 2x3): ``` 3 1 9 6 4 1 ``` ### Training Pair 2 - Input (shape: 30x30): ``` 0 2 0 0 0 2 5 2 2 0 5 2 5 5 0 2 2 5 2 2 5 5 0 2 0 0 2 0 0 0 5 0 0 5 2 2 5 2 5 0 0 2 2 5 5 2 2 5 0 5 2 0 0 0 5 0 5 5 0 2 5 0 2 2 8 8 8 8 8 8 8 5 0 2 4 4 4 4 5 0 0 2 3 3 3 3 3 0 0 2 0 5 0 5 8 8 8 8 8 8 8 2 0 0 4 4 4 4 0 0 2 0 3 3 3 3 3 0 2 0 5 0 5 0 8 8 8 8 8 8 8 2 2 0 4 4 4 4 2 2 0 2 3 3 3 3 3 5 0 5 0 0 0 5 8 8 8 8 8 8 8 2 0 0 4 4 4 4 0 0 2 2 3 3 3 3 3 0 0 2 0 0 0 2 5 5 5 2 2 0 0 0 2 5 0 5 2 0 2 0 5 0 5 2 0 2 0 5 5 2 0 0 2 2 5 5 0 0 2 0 5 0 5 0 0 0 2 2 0 0 2 0 0 0 2 0 2 0 0 0 0 2 0 2 0 0 0 0 2 0 2 0 2 0 5 2 0 0 0 5 2 0 5 2 0 0 5 2 0 0 0 2 0 2 0 0 2 0 0 0 2 5 2 0 0 2 0 0 2 0 2 0 0 0 2 0 5 0 5 0 0 2 2 2 1 1 1 1 1 2 2 2 3 3 3 3 3 3 3 0 0 7 7 7 7 7 0 0 5 0 0 0 0 2 1 1 1 1 1 0 5 0 3 3 3 3 3 3 3 2 0 7 7 7 7 7 2 5 5 5 0 0 5 2 1 1 1 1 1 5 2 0 3 3 3 3 3 3 3 0 2 7 7 7 7 7 0 2 5 2 2 5 0 2 1 1 1 1 1 2 0 0 3 3 3 3 3 3 3 2 5 7 7 7 7 7 0 0 0 0 0 0 0 2 0 0 5 0 2 2 2 0 3 3 3 3 3 3 3 0 0 7 7 7 7 7 2 0 2 2 0 0 2 0 0 5 0 2 0 2 0 5 5 0 0 2 0 5 2 2 2 2 0 5 2 0 0 2 2 0 0 0 5 2 0 0 2 0 5 0 0 0 0 5 0 0 0 2 2 0 0 0 0 5 5 0 2 0 0 5 0 2 2 0 8 8 8 8 8 0 2 0 5 4 4 4 4 4 2 0 0 2 0 0 5 0 0 0 2 0 0 0 2 0 8 8 8 8 8 2 2 5 0 4 4 4 4 4 0 2 5 0 1 1 1 1 1 2 0 2 2 2 0 0 8 8 8 8 8 5 0 0 0 4 4 4 4 4 0 0 5 5 1 1 1 1 1 5 0 0 2 5 5 0 8 8 8 8 8 0 5 0 5 4 4 4 4 4 0 5 0 2 1 1 1 1 1 0 0 0 2 0 0 0 8 8 8 8 8 0 0 0 5 2 5 0 0 2 5 0 2 2 1 1 1 1 1 0 0 0 0 5 2 5 5 2 2 0 2 0 0 2 5 0 5 0 0 5 0 0 0 0 1 1 1 1 1 0 0 0 2 0 0 0 2 5 0 0 5 5 2 0 2 2 0 0 5 5 0 0 0 5 0 2 0 5 0 0 2 5 0 0 5 0 0 0 0 2 0 5 5 0 2 5 0 0 0 2 0 2 0 0 5 0 0 0 0 0 0 5 0 2 0 2 0 5 2 5 0 5 2 0 0 0 0 0 0 5 2 2 5 2 0 0 0 0 0 5 5 0 0 0 0 5 5 0 2 2 2 0 0 2 0 2 0 0 5 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 2 2 0 0 0 0 5 2 2 2 0 0 0 5 2 2 2 0 0 0 0 2 0 5 5 0 0 0 5 0 2 0 5 0 0 0 5 0 2 0 2 2 2 5 5 0 0 2 2 5 2 2 0 0 0 0 2 5 0 2 0 5 0 0 5 5 5 0 0 2 0 0 0 5 ``` - Output (shape: 3x3): ``` 8 4 3 1 3 7 8 4 1 ``` ### Training Pair 3 - Input (shape: 30x30): ``` 1 0 0 0 9 1 1 0 1 9 1 0 9 0 0 1 0 1 0 0 0 0 1 9 0 1 1 9 9 9 0 0 0 0 9 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 9 9 0 0 1 1 1 1 9 0 1 1 1 0 0 1 1 9 1 0 1 0 4 4 4 4 4 4 1 1 0 0 1 0 1 0 0 0 1 9 0 1 9 0 0 0 0 1 0 0 1 1 4 4 4 4 4 4 0 9 0 0 8 8 8 8 1 0 1 0 0 0 1 1 0 9 0 9 0 0 0 9 4 4 4 4 4 4 9 0 1 1 8 8 8 8 0 1 9 0 1 1 0 8 8 8 8 8 8 1 0 0 4 4 4 4 4 4 1 0 0 0 8 8 8 8 1 0 9 0 1 0 9 8 8 8 8 8 8 0 0 9 4 4 4 4 4 4 0 0 1 9 8 8 8 8 1 0 1 0 9 0 0 8 8 8 8 8 8 0 0 0 0 0 0 9 9 0 9 0 0 1 0 1 9 1 0 0 9 1 0 9 1 1 0 1 9 1 0 1 0 9 1 0 0 0 9 9 1 0 1 1 0 0 0 0 0 9 0 1 1 1 0 9 9 0 0 9 0 0 0 0 7 7 7 7 1 1 1 0 1 0 3 3 3 3 3 0 1 0 0 1 0 0 3 3 3 1 9 1 0 0 7 7 7 7 0 1 0 9 0 0 3 3 3 3 3 1 1 9 1 0 1 1 3 3 3 1 0 0 1 0 7 7 7 7 0 0 9 0 0 0 3 3 3 3 3 0 1 0 0 1 1 0 3 3 3 9 0 1 0 9 1 1 0 0 0 1 9 1 1 1 3 3 3 3 3 0 0 9 0 0 0 1 0 9 9 9 0 9 9 1 9 9 0 0 1 0 1 0 0 9 0 0 0 0 9 0 9 0 0 1 0 1 0 9 1 0 1 9 1 9 0 0 1 0 0 0 0 0 0 9 9 9 9 0 9 9 1 0 1 0 9 0 1 9 0 0 0 0 9 9 1 1 1 9 0 1 9 1 4 4 4 4 4 9 0 1 0 0 9 0 0 0 9 0 9 0 0 9 0 0 9 0 0 0 1 0 0 9 4 4 4 4 4 0 1 0 0 0 9 0 9 2 2 2 2 2 9 9 1 9 8 8 8 8 0 9 0 9 4 4 4 4 4 0 0 0 0 1 0 0 1 2 2 2 2 2 1 0 1 0 8 8 8 8 1 9 9 1 4 4 4 4 4 1 0 9 9 0 0 1 0 2 2 2 2 2 0 1 0 1 8 8 8 8 0 9 1 0 4 4 4 4 4 0 1 1 1 1 1 0 0 2 2 2 2 2 0 0 1 0 8 8 8 8 0 9 0 0 1 1 0 0 1 1 1 1 0 0 9 1 9 0 9 0 9 9 1 9 9 9 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 9 0 9 0 0 1 0 0 9 1 1 9 9 1 0 9 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 9 1 1 1 1 0 0 9 1 0 1 1 1 9 1 9 0 9 1 1 1 1 0 0 0 1 0 0 0 1 9 9 1 1 0 1 0 0 9 0 0 1 0 0 0 0 0 0 0 0 9 0 9 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 9 9 9 1 1 1 0 0 0 0 0 0 9 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 9 9 0 1 0 1 1 0 1 0 0 0 9 0 1 9 1 1 1 1 0 9 9 0 0 0 0 0 0 9 0 1 0 0 0 0 9 0 1 1 0 1 9 0 9 0 0 0 0 9 1 0 0 0 0 9 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 9 9 0 1 0 9 0 9 0 1 1 1 0 0 1 0 0 9 0 1 0 9 9 9 1 ``` - Output (shape: 3x3): ``` 8 4 8 3 7 3 2 8 4 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 30x30): ``` 5 5 0 0 0 8 5 0 0 8 8 8 0 8 0 0 5 5 0 5 0 5 8 0 0 0 0 0 0 8 8 8 5 5 0 8 0 0 5 8 0 0 5 8 0 8 0 8 0 8 0 0 5 0 8 8 0 0 0 0 0 5 5 5 0 5 8 0 5 8 0 0 0 5 0 5 8 8 5 8 5 0 5 0 0 0 0 0 5 5 0 0 0 5 5 5 8 8 0 0 0 5 8 3 3 3 3 3 5 0 8 0 8 8 0 8 8 0 0 5 0 5 0 5 2 2 2 2 2 2 0 5 8 3 3 3 3 3 8 8 8 3 3 3 3 3 3 0 0 5 8 8 0 0 2 2 2 2 2 2 0 0 0 3 3 3 3 3 5 8 0 3 3 3 3 3 3 0 8 0 8 5 0 0 2 2 2 2 2 2 0 0 8 3 3 3 3 3 0 0 0 3 3 3 3 3 3 5 0 0 5 0 8 8 2 2 2 2 2 2 8 0 0 3 3 3 3 3 0 0 0 0 5 5 0 0 0 0 0 5 0 0 0 5 0 8 0 5 5 0 0 0 0 0 0 5 5 5 0 0 0 0 0 0 0 0 0 8 8 0 0 0 5 0 5 5 0 8 0 8 8 0 0 5 8 0 0 0 0 5 0 0 1 1 1 1 1 5 5 5 8 0 8 4 4 4 4 4 5 0 5 8 7 7 7 7 7 0 0 8 5 0 1 1 1 1 1 0 5 0 8 5 0 4 4 4 4 4 0 0 0 0 7 7 7 7 7 0 0 5 0 0 1 1 1 1 1 0 5 0 0 8 0 4 4 4 4 4 0 0 0 0 7 7 7 7 7 5 0 0 5 8 1 1 1 1 1 5 5 0 0 8 5 4 4 4 4 4 0 0 0 0 7 7 7 7 7 0 8 0 8 0 1 1 1 1 1 5 5 0 0 5 8 4 4 4 4 4 0 0 8 0 8 0 0 0 0 0 5 0 0 0 5 0 0 0 5 0 5 8 8 8 0 0 0 0 8 0 8 0 0 0 0 0 0 5 0 0 5 5 8 0 5 0 5 8 0 0 0 5 0 8 0 5 0 0 0 5 5 8 5 5 3 3 3 3 3 3 3 8 0 5 0 7 7 7 7 5 0 5 0 0 5 5 0 5 1 1 1 1 0 0 3 3 3 3 3 3 3 0 8 8 8 7 7 7 7 8 0 8 0 0 0 0 0 0 1 1 1 1 5 8 3 3 3 3 3 3 3 8 5 0 8 7 7 7 7 0 5 5 0 5 0 8 0 5 1 1 1 1 5 0 3 3 3 3 3 3 3 5 0 5 0 7 7 7 7 5 0 0 0 0 5 0 0 8 1 1 1 1 0 0 5 8 0 0 5 8 8 0 0 8 0 7 7 7 7 8 0 0 5 0 5 8 0 0 8 0 5 0 0 0 0 0 5 8 0 0 5 8 0 0 5 0 8 8 8 0 0 5 0 5 0 5 5 4 4 4 5 0 5 0 6 6 6 6 6 6 0 0 2 2 2 2 2 2 0 0 5 5 0 8 0 5 5 4 4 4 0 8 5 0 6 6 6 6 6 6 0 0 2 2 2 2 2 2 5 0 8 5 8 0 0 0 0 4 4 4 5 0 8 0 6 6 6 6 6 6 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 4 4 4 5 5 0 8 6 6 6 6 6 6 5 0 2 2 2 2 2 2 0 0 8 0 5 5 0 0 0 5 5 8 5 8 0 0 6 6 6 6 6 6 8 5 8 0 0 8 5 0 8 5 0 0 0 5 8 5 0 8 5 5 5 0 8 8 0 0 5 0 8 5 5 0 0 0 5 8 0 0 0 0 8 5 0 0 0 0 8 0 0 5 8 8 8 5 0 0 0 5 0 5 0 0 0 5 0 8 0 5 5 0 0 8 8 0 5 0 0 0 0 0 5 8 8 8 0 0 5 5 5 5 8 5 0 0 5 8 5 8 5 5 0 5 ```
``` 2 3 3 4 7 1 1 3 7 4 6 2 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 8 8 8 8 8 0 0 8 0 8 0 0 0 0 8 0 0 0 8 0 0 8 8 8 0 0 0 0 8 8 8 8 8 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 8 8 8 0 8 0 0 0 0 0 0 0 0 0 8 0 8 0 8 0 0 0 0 0 0 0 0 0 8 8 8 0 8 0 0 8 8 8 0 0 0 0 0 0 8 8 8 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x14): ``` 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 1 1 1 1 1 0 0 2 0 2 0 0 0 0 1 0 0 0 1 0 0 2 2 2 0 0 0 0 1 1 1 1 1 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 0 3 3 3 0 3 0 0 0 0 0 0 0 0 0 3 0 3 0 3 0 0 0 0 0 0 0 0 0 3 3 3 0 3 0 0 1 1 1 0 0 0 0 0 0 3 3 3 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 14x11): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 0 8 0 8 0 8 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 0 8 0 8 0 0 0 8 8 8 0 0 8 0 8 0 0 0 8 0 8 0 0 8 8 8 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 8 0 8 0 0 0 8 8 8 8 0 8 8 8 8 8 0 8 0 0 8 0 8 0 0 0 8 0 8 0 0 8 0 8 8 8 8 8 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x11): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 0 2 0 0 0 1 1 1 0 0 2 0 2 0 0 0 1 0 1 0 0 2 2 2 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 3 0 3 0 0 0 1 1 1 1 0 3 3 3 3 3 0 1 0 0 1 0 3 0 0 0 3 0 1 0 0 1 0 3 3 3 3 3 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 15x14): ``` 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 8 0 8 8 8 8 8 8 8 8 0 0 0 0 8 8 8 0 8 0 0 8 0 8 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 8 8 8 8 0 0 8 0 0 8 0 0 0 0 8 0 0 8 0 0 8 8 8 8 0 0 0 0 8 0 0 8 0 0 8 0 0 8 0 0 0 8 8 8 8 8 0 0 8 8 8 8 0 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 8 8 8 0 0 0 8 0 0 8 0 0 0 0 8 0 8 0 0 0 8 8 8 8 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x14): ``` 0 0 4 4 4 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 4 4 4 4 4 4 0 0 0 0 4 4 4 0 4 0 0 4 0 4 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 2 2 2 2 0 0 3 0 0 3 0 0 0 0 2 0 0 2 0 0 3 3 3 3 0 0 0 0 2 0 0 2 0 0 3 0 0 3 0 0 0 2 2 2 2 2 0 0 3 3 3 3 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 1 1 1 0 0 0 2 0 0 2 0 0 0 0 1 0 1 0 0 0 2 2 2 2 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 4 - Input (shape: 9x11): ``` 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 8 0 0 8 0 0 8 8 8 0 0 8 8 8 8 0 0 8 0 8 0 0 0 0 0 0 0 0 8 8 8 0 8 8 8 0 0 0 0 0 0 0 0 8 0 8 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 8 0 8 0 0 0 0 0 0 0 0 8 8 8 0 0 ``` - Output (shape: 9x11): ``` 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 3 3 3 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 3 3 3 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 15x17): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 8 8 8 0 0 0 8 0 0 8 0 0 8 8 8 0 0 8 0 8 0 0 0 8 8 8 8 8 8 8 0 8 0 0 8 8 8 0 0 0 0 0 8 0 8 0 8 0 8 0 0 8 0 8 0 0 0 0 0 8 8 8 8 8 8 8 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 8 0 0 8 8 8 8 8 8 8 0 0 8 8 8 8 8 8 0 0 8 0 0 8 0 0 8 0 0 0 0 0 0 0 0 0 0 8 0 0 8 0 0 8 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 0 0 0 0 0 0 0 2 2 2 0 0 0 4 0 0 4 0 0 4 4 4 0 0 2 0 2 0 0 0 4 4 4 4 4 4 4 0 4 0 0 2 2 2 0 0 0 0 0 4 0 4 0 4 0 4 0 0 2 0 2 0 0 0 0 0 4 4 4 4 4 4 4 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 3 3 3 3 3 3 3 0 0 1 1 1 1 1 1 0 0 3 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 22x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 22x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 ``` ### Training Pair 2 - Input (shape: 7x23): ``` 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 7x23): ``` 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 0 0 0 0 0 1 0 0 3 0 0 1 0 0 3 0 0 1 0 0 3 0 0 ``` ### Training Pair 3 - Input (shape: 24x8): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 24x8): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 ``` ### Training Pair 4 - Input (shape: 10x25): ``` 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x25): ``` 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 0 0 0 0 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 2 0 8 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 11x27): ``` 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 0 0 0 4 0 0 0 0 3 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 18x19): ``` 2 0 2 2 2 2 0 0 0 0 2 0 2 2 2 2 0 0 2 2 2 2 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 2 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 0 2 0 2 2 0 0 0 0 0 2 2 2 2 2 2 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 2 0 2 0 0 0 2 0 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 0 0 0 0 3 3 3 3 3 0 3 3 0 2 2 0 0 2 2 0 0 0 3 3 3 0 0 0 3 3 0 0 2 2 0 0 2 0 0 0 0 3 3 3 0 3 0 3 0 0 2 2 2 0 0 2 2 0 0 0 3 3 0 0 0 3 3 3 3 2 0 0 2 2 2 0 0 0 0 3 0 0 0 3 0 3 0 3 2 0 2 0 0 0 2 0 0 0 0 3 3 0 3 3 3 0 3 0 2 2 0 2 2 0 0 0 0 0 3 3 0 0 3 0 3 0 ``` - Output (shape: 7x9): ``` 0 3 3 3 3 3 0 3 3 3 3 3 0 0 0 3 3 0 3 3 3 0 3 0 3 0 0 3 3 0 0 0 3 3 3 3 3 0 0 0 3 0 3 0 3 0 3 3 0 3 3 3 0 3 0 3 3 0 0 3 0 3 0 ``` ### Training Pair 2 - Input (shape: 21x21): ``` 8 8 8 8 8 0 8 8 8 8 0 0 0 0 8 8 8 8 0 8 8 8 0 0 8 0 8 0 8 8 8 0 0 0 0 8 8 8 0 0 0 8 8 8 8 0 0 0 8 8 8 8 0 0 0 0 8 8 0 8 8 8 8 8 8 0 8 8 8 8 0 8 8 0 0 0 0 8 8 0 0 0 8 8 8 8 8 8 0 8 8 0 8 8 0 0 0 0 8 8 8 0 8 8 8 0 0 0 8 8 0 8 0 0 8 0 0 0 0 8 0 0 0 8 0 0 8 8 8 8 0 0 8 0 8 0 0 0 0 0 8 8 8 0 8 8 8 8 0 0 8 0 0 8 8 0 8 0 0 0 0 8 0 8 8 8 8 8 8 8 8 8 8 8 0 8 0 0 0 0 0 0 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 2 2 2 2 0 0 0 0 8 8 0 8 8 0 8 2 0 2 2 2 0 0 2 2 2 0 0 0 0 8 8 8 8 0 8 0 0 2 2 2 2 2 2 0 2 0 0 0 0 0 8 8 8 0 0 0 8 2 2 2 2 0 2 2 2 2 2 0 0 0 0 8 8 0 8 8 8 0 2 2 2 2 2 2 0 2 0 0 0 0 0 0 8 8 8 8 8 0 0 2 2 2 2 2 0 2 0 2 2 0 0 0 0 8 0 8 0 8 8 8 2 2 0 2 2 0 0 0 0 0 0 0 0 0 8 8 0 8 0 0 8 0 2 2 0 0 2 2 0 0 2 0 0 0 0 8 0 0 0 8 8 0 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 8 8 0 0 8 8 2 0 2 2 0 2 2 2 2 2 0 0 0 0 8 8 8 0 8 8 8 ``` - Output (shape: 10x10): ``` 0 2 2 2 0 0 2 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 2 2 2 2 2 0 2 0 2 2 2 2 0 2 2 2 2 2 2 2 2 2 2 2 0 2 0 0 2 2 2 2 2 0 2 0 2 2 2 2 0 2 2 0 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 2 2 2 2 ``` ### Training Pair 3 - Input (shape: 19x17): ``` 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 4 0 0 1 0 0 1 1 1 1 1 1 4 4 4 4 0 4 0 0 1 0 1 1 1 1 1 1 0 4 0 4 0 0 4 0 0 0 1 0 0 1 1 1 1 1 0 4 4 4 4 0 0 0 1 1 0 0 1 0 1 0 1 4 4 4 0 4 4 0 0 1 1 1 1 1 1 1 1 0 0 4 4 4 4 0 0 0 0 1 0 0 0 0 1 1 1 0 4 4 4 0 4 0 0 0 1 0 1 0 1 1 1 0 0 4 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 4 4 0 4 0 4 0 0 1 1 1 0 0 1 1 1 0 ``` - Output (shape: 9x6): ``` 4 0 0 4 0 4 4 4 4 4 0 4 4 0 4 0 0 4 0 4 4 4 4 0 4 4 4 0 4 4 0 4 4 4 4 0 0 4 4 4 0 4 0 4 0 0 0 0 4 4 0 4 0 4 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 15x17): ``` 1 1 1 1 0 1 0 0 3 0 3 3 3 3 3 3 0 1 0 1 0 1 1 0 0 0 3 0 3 3 3 0 0 0 1 1 0 1 1 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 1 1 1 0 0 3 3 0 3 3 0 3 0 0 1 1 1 1 1 1 0 0 0 3 0 3 3 3 0 3 3 1 1 1 1 1 1 0 0 3 3 0 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 3 0 0 3 3 3 0 3 0 3 0 3 0 3 3 0 0 3 0 0 0 3 0 3 3 3 0 0 0 3 3 3 3 3 0 0 0 3 0 0 0 3 0 0 0 3 3 0 3 0 3 0 0 0 0 3 3 3 3 3 3 0 3 0 3 3 0 0 0 0 0 0 0 3 3 3 0 3 3 0 ```
``` 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 15x15): ``` 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 15x15): ``` 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 15x13): ``` 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 3 3 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 0 0 2 2 0 1 0 0 0 0 0 0 0 0 2 2 2 0 1 0 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5 0 1 0 0 0 0 0 0 0 0 5 5 5 0 1 0 0 8 0 8 0 0 0 0 5 0 0 1 0 0 0 8 0 0 0 0 0 0 0 0 1 0 0 8 0 0 0 0 0 ``` - Output (shape: 6x6): ``` 0 2 2 3 0 0 2 2 2 0 3 3 0 2 0 0 3 0 0 0 5 8 0 8 5 5 5 0 8 0 0 5 0 8 0 0 ``` ### Training Pair 2 - Input (shape: 12x13): ``` 0 0 1 1 0 0 0 2 0 0 0 3 3 0 0 0 1 0 0 0 2 0 0 3 3 0 0 0 0 1 1 0 0 2 0 0 0 3 0 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 4 0 0 0 0 2 0 0 0 0 0 0 4 0 4 0 0 0 2 0 5 5 0 0 0 0 4 0 0 0 0 2 0 0 5 0 0 0 0 0 0 0 0 0 2 0 0 0 5 0 0 0 0 0 0 0 0 2 0 0 0 0 0 ``` - Output (shape: 6x6): ``` 1 1 0 0 3 3 0 1 0 3 3 0 0 1 1 0 3 0 0 4 0 5 5 0 4 0 4 0 5 0 0 4 0 0 0 5 ``` ### Training Pair 3 - Input (shape: 16x12): ``` 0 0 0 0 0 0 3 0 0 1 1 0 0 0 2 2 0 0 3 0 1 0 0 0 0 2 0 2 0 0 3 0 0 1 0 0 0 0 2 0 0 0 3 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 5 0 0 0 0 0 0 0 3 0 0 5 0 5 0 0 0 0 0 0 3 0 0 5 5 5 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 3 0 0 0 0 0 4 4 4 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 ``` - Output (shape: 6x6): ``` 0 2 2 0 1 1 2 0 2 1 0 0 0 2 0 0 1 0 4 0 0 0 5 0 4 4 4 5 0 5 0 4 0 5 5 5 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 14x13): ``` 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 3 3 3 0 0 0 2 2 0 0 1 0 0 0 3 3 0 0 0 2 0 0 0 1 0 0 3 0 0 0 0 2 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 4 0 0 0 0 6 6 0 0 1 0 0 4 0 4 0 0 6 0 6 0 0 1 0 0 0 4 0 0 0 6 6 0 0 0 1 0 0 0 0 0 0 ```
``` 0 2 2 3 3 3 0 2 0 0 3 3 2 0 2 3 0 0 0 6 6 0 4 0 6 0 6 4 0 4 6 6 0 0 4 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 10x10): ``` 1 3 0 0 0 0 0 0 0 0 2 8 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 3 3 3 3 1 8 0 0 0 0 3 3 2 0 8 8 0 0 0 0 0 0 2 0 8 8 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 1 3 0 0 0 0 0 0 0 0 2 8 0 0 0 0 3 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 0 0 3 3 3 0 0 0 0 0 1 1 1 1 3 2 0 0 0 0 1 1 8 0 2 2 0 0 0 0 0 0 8 0 2 2 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 10x10): ``` 4 2 0 0 0 0 0 0 0 0 3 7 0 0 0 0 4 0 0 0 0 0 0 0 0 3 4 4 0 0 0 0 0 0 0 3 2 4 0 0 0 0 0 7 7 3 2 4 0 0 0 0 0 7 3 3 2 0 0 0 0 0 0 7 0 0 2 2 0 0 0 0 0 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 4 2 0 0 0 0 0 0 0 0 3 7 0 0 0 0 2 0 0 0 0 0 0 0 0 7 2 2 0 0 0 0 0 0 0 7 4 2 0 0 0 0 0 3 3 7 4 2 0 0 0 0 0 3 7 7 4 0 0 0 0 0 0 3 0 0 4 4 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 10x10): ``` 9 4 0 0 0 0 0 0 0 0 7 6 0 0 0 9 9 0 0 0 0 0 0 0 0 7 9 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 7 4 0 0 0 0 0 0 0 6 6 7 0 0 0 0 0 0 0 7 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 9 4 0 0 0 0 0 0 0 0 7 6 0 0 0 4 4 0 0 0 0 0 0 0 0 6 4 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 6 9 0 0 0 0 0 0 0 7 7 6 0 0 0 0 0 0 0 6 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 10x10): ``` 8 9 0 0 0 0 0 0 0 0 2 4 0 0 0 9 9 0 0 0 0 0 0 8 8 8 9 0 0 0 0 0 0 2 8 8 9 0 0 0 0 0 0 2 4 2 0 0 0 0 0 0 0 2 2 4 0 0 0 0 0 0 0 2 4 4 0 0 0 0 0 0 0 9 4 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 8 9 0 0 0 0 0 0 0 0 2 4 0 0 0 8 8 0 0 0 0 0 0 9 9 9 8 0 0 0 0 0 0 4 9 9 8 0 0 0 0 0 0 4 2 4 0 0 0 0 0 0 0 4 4 2 0 0 0 0 0 0 0 4 2 2 0 0 0 0 0 0 0 8 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 3x4): ``` 5 5 9 9 9 5 5 5 5 7 5 7 ``` - Output (shape: 6x8): ``` 7 5 7 5 5 7 5 7 5 5 5 9 9 5 5 5 9 9 5 5 5 5 9 9 9 9 5 5 5 5 9 9 5 5 5 9 9 5 5 5 7 5 7 5 5 7 5 7 ``` ### Training Pair 2 - Input (shape: 3x4): ``` 6 2 4 2 2 2 6 6 6 4 2 4 ``` - Output (shape: 6x8): ``` 4 2 4 6 6 4 2 4 6 6 2 2 2 2 6 6 2 4 2 6 6 2 4 2 2 4 2 6 6 2 4 2 6 6 2 2 2 2 6 6 4 2 4 6 6 4 2 4 ``` ### Training Pair 3 - Input (shape: 3x4): ``` 3 3 5 5 5 8 5 8 8 8 5 8 ``` - Output (shape: 6x8): ``` 8 5 8 8 8 8 5 8 8 5 8 5 5 8 5 8 5 5 3 3 3 3 5 5 5 5 3 3 3 3 5 5 8 5 8 5 5 8 5 8 8 5 8 8 8 8 5 8 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 3x4): ``` 8 5 7 8 7 7 8 8 5 5 8 5 ```
``` 5 8 5 5 5 5 8 5 8 8 7 7 7 7 8 8 8 7 5 8 8 5 7 8 8 7 5 8 8 5 7 8 8 8 7 7 7 7 8 8 5 8 5 5 5 5 8 5 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 13x4): ``` 0 0 0 2 2 0 0 0 0 2 2 2 0 0 0 2 2 0 2 0 0 2 2 0 7 7 7 7 6 0 6 6 6 0 0 6 0 6 6 6 6 0 0 0 6 0 0 6 0 0 6 0 ``` - Output (shape: 6x4): ``` 0 8 0 0 0 8 8 0 8 0 0 0 0 8 8 0 0 8 0 0 8 0 0 8 ``` ### Training Pair 2 - Input (shape: 13x4): ``` 2 2 0 2 2 0 2 2 2 2 0 0 0 2 0 2 0 2 2 0 2 0 0 2 7 7 7 7 6 0 6 6 0 6 0 0 0 0 0 0 0 0 0 6 6 6 0 0 6 0 6 0 ``` - Output (shape: 6x4): ``` 0 0 0 0 0 0 0 0 0 0 8 8 8 0 8 0 0 0 0 8 0 8 0 0 ``` ### Training Pair 3 - Input (shape: 13x4): ``` 2 2 0 0 0 2 2 0 2 2 0 0 2 0 0 0 0 0 0 2 2 2 0 0 7 7 7 7 6 6 6 6 6 0 6 6 6 6 0 0 0 0 0 0 6 6 0 0 0 0 6 0 ``` - Output (shape: 6x4): ``` 0 0 0 0 0 0 0 0 0 0 8 8 0 8 8 8 0 0 8 0 0 0 0 8 ``` ### Training Pair 4 - Input (shape: 13x4): ``` 0 2 2 0 2 0 0 0 0 2 0 2 2 2 2 2 0 0 2 0 0 0 2 2 7 7 7 7 0 6 6 0 0 0 0 0 6 6 6 6 6 6 0 6 0 6 6 6 0 0 6 0 ``` - Output (shape: 6x4): ``` 8 0 0 8 0 8 8 8 0 0 0 0 0 0 0 0 8 0 0 0 8 8 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 13x4): ``` 0 0 0 2 0 2 2 0 2 0 0 2 0 2 2 0 2 0 2 2 0 0 0 2 7 7 7 7 6 6 0 6 6 6 6 0 0 0 0 0 6 6 0 6 6 0 6 0 0 0 6 6 ```
``` 0 0 8 0 0 0 0 8 0 8 8 0 0 0 0 0 0 8 0 0 8 8 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 9x9): ``` 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 9x9): ``` 0 0 0 8 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 7 0 0 0 2 0 0 0 7 1 7 0 4 0 4 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 4 0 4 0 0 7 1 7 0 0 2 0 0 0 0 7 0 0 4 0 4 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 7 1 7 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 7 0 0 0 0 0 0 0 7 1 7 0 0 0 0 0 0 0 7 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 9x9): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 4 0 4 0 7 1 7 0 0 0 2 0 0 0 7 0 0 0 4 0 4 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 4 0 4 0 6 0 0 0 0 0 2 0 0 0 0 0 0 0 4 0 4 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 3x3): ``` 5 8 6 5 8 6 5 8 6 ``` - Output (shape: 3x3): ``` 1 9 2 1 9 2 1 9 2 ``` ### Training Pair 2 - Input (shape: 3x3): ``` 2 3 8 2 3 8 2 3 8 ``` - Output (shape: 3x3): ``` 6 4 9 6 4 9 6 4 9 ``` ### Training Pair 3 - Input (shape: 3x3): ``` 9 4 2 9 4 2 9 4 2 ``` - Output (shape: 3x3): ``` 8 3 6 8 3 6 8 3 6 ``` ### Training Pair 4 - Input (shape: 3x3): ``` 3 1 2 3 1 2 3 1 2 ``` - Output (shape: 3x3): ``` 4 5 6 4 5 6 4 5 6 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 3x3): ``` 8 1 3 8 1 3 8 1 3 ```
``` 9 5 4 9 5 4 9 5 4 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 10x20): ``` 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 0 0 0 0 0 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x20): ``` 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 1 0 0 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 0 0 1 0 0 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 20x20): ``` 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2 0 0 0 0 0 2 2 2 2 0 0 0 0 1 0 0 2 2 2 2 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 20x20): ``` 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 13x14): ``` 0 0 2 2 2 0 0 1 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 1 0 2 2 2 0 0 2 2 2 0 0 0 1 0 0 2 2 2 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 2 2 0 0 0 0 2 2 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 2 2 2 2 2 0 0 0 0 0 2 2 2 0 2 2 2 2 2 0 1 0 0 0 0 0 0 ``` - Output (shape: 13x14): ``` 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 2 0 0 1 1 1 1 1 1 0 0 0 0 2 2 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 2 2 2 0 0 0 0 1 1 1 1 1 1 0 2 2 2 0 0 0 0 1 1 1 1 1 1 0 2 2 2 0 0 0 0 0 0 0 1 0 0 0 2 2 2 0 2 2 2 2 2 0 1 0 0 0 2 2 2 0 2 2 2 2 2 0 1 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 23x25): ``` 0 0 0 0 0 1 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 2 2 2 0 0 2 2 2 0 2 2 2 2 2 0 2 2 2 2 0 0 1 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 0 1 0 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 2 2 2 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 2 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 2 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 14x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 4 0 0 0 0 0 0 0 0 0 0 1 3 3 3 3 2 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 14x18): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 8 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 8 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 4 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 14x18): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 4 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 8 8 8 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 16x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 8 0 0 0 8 0 0 0 0 0 0 0 0 0 1 8 8 8 2 8 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 16x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 1 8 8 8 2 8 0 0 0 0 0 0 0 0 8 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 24x19): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 5 5 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
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Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 5 5 5 5 5 5 5 5 5 5 0 0 5 0 0 0 0 0 0 0 0 0 5 0 0 5 0 0 0 0 0 0 0 0 0 5 0 0 5 0 0 0 0 0 0 0 0 0 3 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 5 5 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 5 5 5 5 5 5 5 5 5 2 0 0 0 5 0 0 5 0 0 0 0 0 0 0 0 0 4 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 0 0 0 0 0 0 0 5 5 0 0 0 0 2 5 5 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 4 - Input (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 5 5 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 5 5 5 5 5 5 5 4 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 13x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 5 4 0 0 0 0 0 0 0 0 0 5 0 0 5 0 0 0 0 0 0 0 0 0 5 0 0 5 0 0 0 2 5 5 5 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 7 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ``` ### Training Pair 2 - Input (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ``` ### Training Pair 3 - Input (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ``` ### Training Pair 4 - Input (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 15x15): ``` 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 15x15): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 8 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 22x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 0 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 8 8 8 0 0 0 8 8 8 0 0 0 8 8 8 0 0 0 8 8 8 0 0 0 8 8 8 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 22x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 0 0 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 4 4 4 0 0 0 0 0 0 2 2 2 4 4 4 0 0 0 0 0 0 2 2 2 4 4 4 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 0 0 0 3 3 3 3 3 3 0 0 0 4 4 4 0 0 0 1 1 1 0 0 0 4 4 4 0 0 0 1 1 1 0 0 0 4 4 4 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 24x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 3 4 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 0 0 8 8 8 8 8 8 0 0 0 0 0 8 8 0 0 8 8 0 0 0 0 0 0 0 8 8 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 24x13): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 2 0 3 4 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 3 3 3 3 0 0 0 0 0 0 0 1 1 3 3 3 3 0 0 0 0 0 4 4 0 0 4 4 0 0 0 0 0 0 0 4 4 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 16x26): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 3 0 2 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 8 8 8 8 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 3 0 2 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 4 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 5x3): ``` 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 ``` - Output (shape: 10x6): ``` 8 0 8 8 0 8 0 4 0 0 4 0 8 0 8 8 0 8 0 8 8 0 8 0 4 0 0 4 0 0 8 8 8 8 8 8 0 4 0 0 4 0 8 0 8 8 0 8 0 8 8 0 8 0 4 0 0 4 0 0 ``` ### Training Pair 2 - Input (shape: 3x4): ``` 0 0 6 0 0 0 0 0 0 6 0 0 ``` - Output (shape: 6x8): ``` 0 0 6 0 0 0 6 0 8 8 8 8 8 8 8 8 0 6 0 8 0 6 0 8 8 0 6 0 8 0 6 0 8 8 8 8 8 8 8 8 0 6 0 0 0 6 0 0 ``` ### Training Pair 3 - Input (shape: 4x4): ``` 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 8x8): ``` 8 0 8 0 8 0 8 0 0 2 0 0 0 2 0 0 8 0 8 0 8 0 8 0 0 0 0 0 0 0 0 0 8 0 8 0 8 0 8 0 0 2 0 0 0 2 0 0 8 0 8 0 8 0 8 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 4 - Input (shape: 2x4): ``` 0 0 0 0 0 5 0 0 ``` - Output (shape: 4x8): ``` 8 0 8 0 8 0 8 0 0 5 0 0 0 5 0 0 8 0 8 0 8 0 8 0 0 5 0 0 0 5 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 6x5): ``` 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 ```
``` 0 3 0 0 0 0 3 0 0 0 8 0 8 0 0 8 0 8 0 0 0 0 8 0 8 0 0 8 0 8 0 0 0 3 0 0 0 0 3 0 8 0 8 0 8 8 0 8 0 8 8 3 8 0 0 8 3 8 0 0 8 3 8 0 0 8 3 8 0 0 8 0 8 0 0 8 0 8 0 0 0 0 8 0 8 0 0 8 0 8 0 0 0 3 0 0 0 0 3 0 8 0 8 0 8 8 0 8 0 8 0 3 0 0 0 0 3 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 3 0 4 0 3 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 2 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 3 0 4 0 3 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 2 0 3 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 3 0 8 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 8 0 3 0 8 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 3 0 8 0 3 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 8 0 3 0 8 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 3 0 8 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 3 - Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 8 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 8 0 1 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 8 0 8 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 8 0 1 0 8 0 0 0 0 0 0 4 0 4 0 0 0 0 0 0 8 0 8 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 10x10): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 1 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 1 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 4 0 1 0 4 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 1 0 4 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 10x10): ``` 0 0 0 0 6 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 7 9 5 1 8 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 2 3 6 6 6 6 2 3 7 9 4 2 3 6 6 2 3 7 9 5 4 4 2 3 2 3 7 9 5 1 4 4 4 2 3 7 9 5 1 8 4 4 2 3 2 3 7 9 5 1 4 2 3 0 0 2 3 7 9 5 2 3 0 0 0 0 2 3 7 9 3 0 0 0 0 0 0 2 3 7 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 2 ``` ### Training Pair 2 - Input (shape: 10x10): ``` 0 0 0 0 7 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 9 0 0 0 0 4 0 0 0 0 9 0 0 0 0 6 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ``` - Output (shape: 10x10): ``` 8 7 7 7 7 7 7 7 8 4 4 8 7 7 7 7 7 8 4 9 0 4 8 7 7 7 8 4 9 9 0 0 4 8 7 8 4 9 9 9 0 0 0 4 8 4 9 9 9 9 0 0 0 8 4 8 9 9 9 9 0 0 8 4 6 4 8 9 9 9 0 8 4 6 3 6 4 8 9 9 8 4 6 3 2 3 6 4 8 9 4 6 3 2 1 2 3 6 4 8 ``` ### Training Pair 3 - Input (shape: 4x4): ``` 0 0 0 0 8 0 3 0 8 0 2 0 0 0 4 0 ``` - Output (shape: 4x4): ``` 2 3 0 3 8 2 3 2 8 3 2 3 3 2 4 2 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 8x8): ``` 0 0 0 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 7 0 0 4 0 0 0 0 7 0 0 8 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 3 0 0 0 0 0 ```
``` 9 9 9 9 9 2 4 7 2 9 9 9 2 4 7 7 4 2 9 2 4 7 7 7 0 4 2 4 7 7 7 7 0 2 4 2 7 7 7 7 2 4 8 4 2 7 7 7 4 8 6 8 4 2 7 7 8 6 3 6 8 4 2 7 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 11x11): ``` 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 8 8 8 8 8 8 8 8 8 8 8 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 1 1 1 1 8 1 1 1 1 1 1 8 8 8 8 8 8 8 8 8 8 8 1 1 1 1 8 1 1 1 1 1 1 ``` - Output (shape: 3x2): ``` 1 1 1 1 1 1 ``` ### Training Pair 2 - Input (shape: 15x15): ``` 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 3 7 3 3 3 3 3 3 3 3 7 3 3 7 3 ``` - Output (shape: 2x4): ``` 3 3 3 3 3 3 3 3 ``` ### Training Pair 3 - Input (shape: 27x27): ``` 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 1 3 1 3 ``` - Output (shape: 6x5): ``` 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 22x22): ``` 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 5 1 ```
``` 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 3 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 5 5 7 7 7 7 7 7 7 2 2 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ``` - Output (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 5 7 7 7 7 7 7 7 7 7 7 2 5 7 7 7 7 7 7 7 7 7 7 2 2 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ``` ### Training Pair 2 - Input (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 2 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ``` - Output (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 2 2 7 7 7 7 7 7 7 7 7 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 5 7 7 7 7 7 7 7 7 7 7 7 7 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ``` ### Training Pair 3 - Input (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 2 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 ``` - Output (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 7 7 7 7 7 7 7 7 7 7 7 7 7 5 7 7 7 7 7 7 7 7 7 7 7 7 5 5 7 7 7 7 7 7 7 7 7 7 7 2 2 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 13x13): ``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 2 7 7 7 7 7 7 5 5 7 7 7 2 2 7 7 7 7 7 7 5 5 7 7 7 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ```
``` 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 7 7 2 7 7 7 7 7 7 7 7 7 5 5 2 2 7 7 7 7 7 7 7 7 7 7 5 2 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 2 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 12x11): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 12x11): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 8 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ### Training Pair 2 - Input (shape: 10x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 10x12): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 12x14): ``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 8 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
Your task is to infer the rule from the "input" and "output" pairs in the "train" data. Then, apply that rule to the "test" input to generate the correct "output". "train": demonstration input/output pairs. It is a list of "pairs" (typically 3 pairs). "test": test input - your model should predict the output. A "pair" is a dictionary with two fields: "input": the input "grid" for the pair. "output": the output "grid" for the pair. A "grid" is a rectangular matrix (list of lists) of integers between 0 and 9 (inclusive). The smallest possible grid size is 1x1 and the largest is 30x30. ## Training Data - This consists of 5 pairs. - Each pair has an "input" and an "output". ### Training Pair 1 - Input (shape: 13x6): ``` 5 0 0 3 3 0 5 0 0 3 2 0 5 0 0 2 3 0 5 0 0 8 8 0 0 0 0 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 13x6): ``` 5 0 0 3 3 0 5 0 0 3 2 0 5 0 0 2 3 0 5 0 0 8 8 0 0 0 0 8 8 0 0 0 0 3 3 0 0 0 0 3 2 0 0 0 0 2 3 0 0 0 0 8 8 0 0 0 0 3 3 0 0 0 0 3 2 0 0 0 0 2 3 0 0 0 0 8 8 0 ``` ### Training Pair 2 - Input (shape: 8x7): ``` 5 0 8 8 0 0 0 5 0 0 7 0 0 0 5 0 0 4 4 0 0 0 0 3 3 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 8x7): ``` 5 0 8 8 0 0 0 5 0 0 7 0 0 0 5 0 0 4 4 0 0 0 0 3 3 0 0 0 0 0 1 1 0 0 0 0 0 8 8 0 0 0 0 0 0 7 0 0 0 0 0 0 4 4 0 0 ``` ### Training Pair 3 - Input (shape: 9x7): ``` 5 0 0 4 4 0 0 5 0 8 8 8 0 0 0 0 0 2 0 0 0 0 0 0 3 3 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 9x7): ``` 5 0 0 4 4 0 0 5 0 8 8 8 0 0 0 0 0 2 0 0 0 0 0 0 3 3 0 0 0 0 4 4 0 0 0 0 0 0 4 4 0 0 0 0 8 8 8 0 0 0 0 0 4 4 0 0 0 0 8 8 8 0 0 ``` ### Training Pair 4 - Input (shape: 7x6): ``` 5 0 6 8 0 0 0 0 8 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 7x6): ``` 5 0 6 8 0 0 0 0 8 3 0 0 0 0 6 8 0 0 0 0 6 8 0 0 0 0 6 8 0 0 0 0 6 8 0 0 0 0 6 8 0 0 ``` ### Training Pair 5 - Input (shape: 5x5): ``` 5 0 6 0 0 5 4 4 4 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 ``` - Output (shape: 5x5): ``` 5 0 6 0 0 5 4 4 4 0 0 0 6 0 0 0 0 6 0 0 0 4 4 4 0 ``` ## Test Data - Now, apply the rule you found to the test input below. - Test Input (shape: 10x7): ``` 5 0 4 4 4 0 0 5 0 0 8 0 0 0 5 0 0 6 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ```
``` 5 0 4 4 4 0 0 5 0 0 8 0 0 0 5 0 0 6 0 0 0 0 0 2 2 0 0 0 0 0 4 4 4 0 0 0 0 0 8 0 0 0 0 0 0 6 0 0 0 0 0 4 4 4 0 0 0 0 0 8 0 0 0 0 0 0 6 0 0 0 ```
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