Can you crack number lock puzzle 602 with 5 clues? Each of the clues shows a 3 digit hint code stating how many are correct in correct or wrong position.
3 Digit Number Lock Code Puzzle With 602 in a Hint
Following are the five clues as hints:
Clue 1: Code 6 0 2: One digit is correct and in the right place.
Clue 2: Code 2 4 1: One digit is correct and in the right place.
Clue 3: Code 7 1 6: Two digits are correct but both are in the wrong places.
Clue 4: Code 5 7 3: One digit is correct but in the wrong place.
Clue 5: Code 9 8 4: One digit is correct but in the wrong place.
Find the number lock code from the clues.
Time to solve: 10 minutes.
Solution: Crack the challenging number lock puzzle 602
Step 1. Common digit with positional discrepancy in two positive clues gives first incorrect digit
Clues analyzed in combination:
Clue 1: Code 6 0 2: One digit is correct and in the right place.
Clue 2: Code 2 4 1: One digit is correct and in the right place.
Digit patterns that determined the choice of clues:
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Both clues are positive with digit and positions (one or two) stated correct.
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2 common in both clues.
Logic analysis
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Clues 1+2: 2 wrong by positional discrepancy: correct in both, stated to be in correct positions, but in different position in hint codes.
Hang on to Clue 2 with the incorrect digit, so that you can use false assumption logic on a common digit.
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Clue 2: With 2 wrong, assume 1 wrong that will make 4 right and in middle, and from Clue 1, digit 0 wrong by positional conflict leading to 6 right and in leftmost.
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Secret code on the assumption of 1 wrong is [ 6 4 ? ].
Step 2. Continue with the assumption of 1 wrong till you meet a contradiction
Reason for clue choice:
Next clue choice determined by two digits 1 and 6 in Clue 3, when we know true identity of both the digits—that is an important advantage.
Clue 3: Code 7 1 6: Two digits are correct but both are in the wrong places.
Logic analysis:
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With 1 wrong (assumed) and 6 right (implied by the assumption), digit 7 is right. It falls in line without any contradiction and takes up the vacant rightmost position.
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The secret code is [ 6 4 7 ] based on assumption of 1 wrong.
Step 3. To be sure, verify the code against the other two clues
Verification of secret code against unused clues to test the truth or falsity of the assumption of 1 wrong:
Clue 4: Code 5 7 3: One digit is correct but in the wrong place: Digit 7 in secret code 647 is indeed in wrong place in the clue. Assumption and secret code 647 verified.
Clue 5: Code 9 8 4: One digit is correct but in the wrong place: Digit 4 in secret code 647 also tallies with its wrong position in the clue code. Assumption and secret code verified.
Final solution: Secret code [ 6 4 7 ] as this code satisfies all the clues.
Key Strategies You Learned:
1. The Positional Discrepancy (Rare): When the same digit is stated as "correct and well-placed" in two clues but in different positions, it creates an irreconcilable conflict. This proves the digit is incorrect.
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Ex: Digit 2 in Clues 1 (position rightmost) and 2 (position leftmost) must be wrong.
2. The "False Assumption" Shortcut: Following a primary conflict, a clue is left with a known wrong digit. Strategically assuming, "a second digit in that clue is wrong" can quickly unlock the solution if it leads to a code that satisfies all other clues.
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Ex: With 2 wrong in Clue 2, assuming 1 was also wrong forced 4 to be correct and well-placed in middle position.
3. The Positional Conflict (Common): Once a digit's correct position in secret code is locked in, it creates a positional claim. Any other digit claiming that same position in a subsequent clue must be incorrect.
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Ex: With 4 confirmed in middle position of secret code, the 0 in middle position in Clue 1 hint code was eliminated, confirming remaining 6 correct in leftmost position.
4. Verification is Key: The final step is to test the proposed code against all clues, especially those not used in the deduction, to ensure it explains every condition correctly.
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