Can you solve number lock puzzle 392 in three short and quick steps? Each clue shows hint code and digit-position correctness.
3 Digit Number Lock Puzzle With 392 in Hint Codes
Clue 1: Code 3 9 2: One digit is correct and in the right place.
Clue 2: Code 1 8 6: One digit is correct and in the right place.
Clue 3: Code 6 4 7: Two digits are correct but both are in the wrong places.
Clue 4: Code 8 1 7: One digit is correct but in the wrong place.
Clue 5: Code 5 3 0: All digits wrong.
Time to solve: 8 minutes.
Solution to Number Lock Puzzle 392 in Quick Logic Analysis
Step 1. First Breakthrough: False Assumption on Common Digit 6
Clues Used: 2, 3, and 4.
- Clue 2: Code 1 8 6: One digit is correct and in the right place.
- Clue 3: Code 6 4 7: Two digits are correct but both are in the wrong places.
- Clue 4: Code 8 1 7: One digit is correct but in the wrong place.
Digit patterns behind the choice: Clues 2 and 3 have 6 common and Clues 3 and 4 have 7 common. This pattern of common digits in multiple clues helps breakthroughs.
Logic analysis:
- Assume 6 is wrong => From Clue 3, both 4 and 7 must be correct => From Clue 4, 8 and 1 must be wrong => Clue 2 now has no correct digits => Contradiction!
- Conclusion: Therefore, 6 must be correct and in rightmost position from Clue 2.
- Partial Code: [ ? ? 6 ].
Step 2. Second Breakthrough: Positional Conflict and Digit Elimination
Clues Used: 1 and 5.
- Clue 1: Code 3 9 2: One digit is correct and in the right place.
- Clue 5: Code 5 3 0: All digits wrong.
Reason for the choice:
- The "all digits wrong" Clue 5 shares its wrong digit 3 with Clue 1 promising further breakthrough.
Logic analysis:
- Clue 5 eliminates 3, 5, 0 => Clue 1 has one correct, well-placed digit => 2 cannot be correct (position conflict with 6 in rightmost) => 9 must be correct and in middle position.
- Updated partial Code: [ ? 9 6 ]
Step 3. Third Breakthrough: Correct Digit by Elimination
Clues Used: 2 and 4.
- Clue 2: Code 1 8 6: One digit is correct and in the right place.
- Clue 4: Code 8 1 7: One digit is correct but in the wrong place.
Digit pattern behind the choice:
- Both 1 and 8 are common between the two clues. This creates a powerful pattern for breakthrough.
Logic analysis:
- From Clue 2, 1 and 8 are wrong (6 right) => Clue 4: 8 and 1 are wrong, so 7 must be correct and in wrong position => 7 goes in leftmost, the only open position.
Final Secret Code: [ 7 9 6 ].
Verification:
Let's verify the secret code 796 against all five clues.
- Clue 1: 3 9 2. The digit 9 is correct and in the right place => Correct.
- Clue 2: 1 8 6. The digit 6 is correct and in the right place => Correct.
- Clue 3: 6 4 7. Two digits are correct (6 and 7) but both are in the wrong places (6 is not leftmost, 7 is not rightmost) => Correct.
- Clue 4: 8 1 7. One digit is correct (7) but in the wrong place (it's leftmost, not rightmost) => Correct.
- Clue 5: 5 3 0. All digits are wrong => Correct.
All clues are satisfied.
Key Strategies You Learned:
- False Assumption Leading to Contradiction: Assuming a common digit (6) is wrong led to a violation of another clue (Clue 2 having no correct digits), proving the digit assumed wrong must be correct and in rightmost position.
- Digit Elimination via a "All Wrong" Clue: A clue stating all digits are wrong (Clue 5) is extremely powerful for instantly eliminating multiple candidates from other clues. It helped eliminate incorrect 3 in Clue 1. With further elimination of 2 by positional conflict with 6 in rightmost left 9 as the correct digit in the middle. The key is: multiple strategies work together in getting a breakthrough.
- Positional Conflict: Once a digit's position is confirmed (6 in rightmost), any other digit claiming that same position in another clue (2 in Clue 1) must be incorrect, helping to identify the truly correct digit 9.
- Correct Digit by Elimination: When two digits in a clue are proven to be incorrect, the remaining digit must be the correct one (finding 7 in Clue 4 after eliminating 8 and 1).
To enjoy solving many more such number lock puzzles, click here.
Puzzles you may enjoy
Easy to hard brain teasers with systematic solutions:
Challenging brain teasers with solutions: Long list.