Can you solve 3 digit number lock puzzle 738 in three short steps taking minimum time? Each of the 5 clues shows hint code and digit-position correctness.
3 Digit Number Lock Puzzle With New Hint Codes
Clue 1: Code 7 3 8: Two digits are correct and in the right places.
Clue 2: Code 7 0 6: One digit is correct and in the right place.
Clue 3: Code 1 9 9: No digit is correct.
Clue 4: Code 2 4 8: Two digits are correct and in the right places.
Clue 5: Code 7 5 8: Two digits are correct and in the right places.
Time to solve: 8 minutes.
Solution to 3 Digit Number Lock Puzzle 738 in a Quick Logic Analysis
Step 1. First Breakthrough by False Assumption on Common Digit 7
Clues 1, 2, and 5 chosen for combined analysis/
Reasons of choice: The breakthrough patterns promise breakthrough.
Breakthrough patterns:
- Digit 7 common in same position in three clues.
- The three clues describe its 1 or 2 hint code digits correct. All are positive clues.
Clues chosen:
- Clue 1: Code 7 3 8: Two digits are correct and in the right places.
- Clue 2: Code 7 0 6: One digit is correct and in the right place.
- Clue 5: Code 7 5 8: Two digits are correct and in the right places.
Logic analysis:
- False assumption: Assume 7 is wrong => From Clues 1 and 5, both 3 and 8 must be correct, from clue 2 0 or 6 correct and from Clue 5, both 5 and 8 correct => A total of four digits [3, 5, 8 and (0 or 6)] correct => Impossible for a 3 digit lock => Assumption of 7 wrong must be false.
- Conclusion: Therefore, 7 must be correct and in leftmost position from any of the three clues.
- Partial Code: [ 7 ? ? ].
Step 2. Second Breakthrough by False Assumption Positional Conflict and Digit Elimination
Clues Used: 1 and 5.
- Clue 1: Code 7 3 8: Two digits are correct and in the right places.
- Clue 5: Code 7 5 8: Two digits are correct and in the right places.
Logic analysis:
- Assume 8 wrong => both 3 and 5 claim the same middle position => Conflict => False assumption wrong.
- 8 second correct digit in rightmost position confirmed by both clues.
- Updated Partial Code: [ 7 ? 8 ].
Step 3. Third Breakthrough by Positional Conflict Digit Elimination
Clue 4 used:
- Clue 4: Code 2 4 8: Two digits are correct and in the right places.
Logic analysis:
- 2 in leftmost cannot be correct and occupy the position already reserved by correct digit 7 in secret code => 2 wrong by positional conflict => 4 is the third correct digit by incorrect digit elimination.
- Third correct digit 4 is in the middle.
- Solution: Secret code [ 7 4 8 ].
Verification:
Let's verify the secret code 748 against all five clues.
- Clue 1: 7 3 8. Two digits are correct (7 and 8) and both are in the right places => Correct.
- Clue 2: 7 0 6. One digit is correct (7) and in the right place => Correct.
- Clue 3: 1 9 9. No digit is correct => Correct.
- Clue 4: 2 4 8. Two digits are correct (4 and 8) and both are in the right places => Correct.
- Clue 5: 7 5 8. Two digits are correct (7 and 8) and both are in the right places => Correct.
All clues are satisfied.
Key Strategies You Learned:
- False Assumption Leading to Contradiction: Assuming a common digit (7) is wrong in Clues 1, 2 and 5 led to an impossible situation of for correct digit in a three digit lock, proving the digit assumed wrong must be correct and in leftmost position.
- Positional Claim Conflict: With 7 correct in leftmost position in Clues 1 and 5 meant assuming common digit 8 wrong led to a conflict of two dif=gits 3 and 5 claimed same middle position, proving assumption wrong and digit 8 correct in rightmost position.
- Positional Conflict: Once a digit's position is confirmed (7 in leftmost), any other digit claiming that same position in another clue (2 in Clue 4) must be incorrect, helping to identify the truly correct digits.
- Common Digit Analysis: Tracking digits that appear in multiple clues (like 7 and 8) provides powerful constraints for solving the puzzle.
- Correct Digit by Elimination: When some digits are proven to be incorrect through elimination, the remaining digits must be correct (finding 4 in Clue 4 after eliminating other possibilities).
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