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Claude-3-Opus ·
This is a logic puzzle where you need to deduce a 4-digit code based on clues
Clue 1 (9 2 8 5): one number is correct but wrongly placed.
Clue 2 (1 9 3 7): Two numbers are correct but wrongly placed.
Clue 3 (5 2 0 1): One number is right and well placed.
Clue 4 (6 5 0 7): nothing is correct.
Clue 5 (8 5 2 4): Two numbers are correct but wrongly placed.
Can you crack the code?
Sure, let's solve this step by step:
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From Clue 4, we know that the code doesn't contain 6, 5, 0, or 7.
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From Clue 3, we know that either 5, 2, 0, or 1 is in the correct position. But since 0 is not in the code (from Clue 4), it must be either 5, 2, or 1.
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From Clue 1, one of 9, 2, 8, or 5 is in the code but in the wrong position. We know it's not 5 because if 5 was in the code, it would be in the correct position (from Clue 3).
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From Clue 2, two of 1, 9, 3, or 7 are in the code but in the wrong positions. We know 7 is not in the code (from Clue 4), so it must be two of 1, 9, or 3.
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From Clue 5, two of 8, 5, 2, or 4 are in the code but in the wrong positions. We know it's not 5 (from step 3), so it must be two of 8, 2, or 4.
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Combining the information, we have:
- 1, 2, or 5 in the correct position (from step 2)
- One of 2, 8, or 9 in the wrong position (from step 3)
- Two of 1, 3, or 9 in the wrong positions (from step 4)
- Two of 2, 4, or 8 in the wrong positions (from step 5)
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The only way to satisfy all these conditions is:
- 1 in the correct position
- 2, 3, and 4 in the wrong positions
Therefore, the code must be 2341, 2431, 3241, 3421, 4231, or 4321.
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