Solve 3 digit number lock puzzle 295 in two steps from 5 clues. Each clue contains a 3 digit hint code with code digit and position correctness description.
3 Digit Number Lock Puzzle With Hint Code 295
Following are the five clues:
Clue 1: Code 1 7 7: No digit is correct.
Clue 2: Code 2 9 5: One digit is correct and in the right place.
Clue 3: Code 4 8 6: One digit is correct but in the wrong place.
Clue 4: Code 3 6 0: One digit is correct but in the wrong place.
Clue 5: Code 2 4 9: Two digits are correct and in the right places.
Find the 3 digit code to open the number lock in a quick two-step logic analysis.
Time to solve: 10 minutes.
Challenge met: Solved 3 Digit Number Lock Puzzle 295 in Two Steps
Clue 1 hint code has all incorrect digits, none of which appear in other clues. The clue is of no help and the other clues only will give you the secret code.
Step 1. False assumption logic, positional conflict and incorrect digit elimination produce two correct digits
For combined analysis, choose Clues 2 and 5 because both are positive clues with position and digit correctness right — patterns promising assured breakthrough.
Clue 2: Code 2 9 5: One digit is correct and in the right place.
Clue 5: Code 2 4 9: Two digits are correct and in the right places.
- False assumption on Clues 2+5: Assume common digit 2 wrong ➡ In Clue 5, digits 4 and 9 correct ➡ Violates Clue 2+5 because of positional conflict in the middle between digits 4 and 9 ➡ contradiction proves digit 2 right in leftmost (from Clue 5).
- Additional Conclusions: 9 wrong in Clue 2 and so, in Clue 5, 4 is right in the middle.
- So we have partial code: [ 2 4 ? ].
Step 2. Third correct digit by positional lockout
The problem of choosing one among three probable correct digits 3, 6 and 8 should be resolved by analyzing Clues 3 and 4 as the two contain all three digits with 6 common in addition.
Clue 3: Code 4 8 6: One digit is correct but in the wrong place.
Clue 4: Code 3 6 0: One digit is correct but in the wrong place.
- Clues 3+4: With 4 right in Clue 3, both 6 and 8 wrong ➡ with 6 wrong in Clue 4 and 0 incorrect as it is locked out of feasible positions in the secret code (both middle and leftmost reserved in partial code), 3 must be the third correct digit in rightmost position.
- Solution: Lock opening code: [2 4 3].
Verification
Check all clues against correct code 243:
- Clue 1 (1 7 7): No digit is correct: None of 1 and 7 in correct code 243 and so are incorrect — matches.
- Clue 2 (2 9 5): One digit is correct and in the right place: Digit 2 is present and in correct leftmost position — matches.
- Clue 3 (9 3 5): One digit is correct but in the wrong place: Digits 3 correct and in the wrong middle place — matches.
- Clue 4 (3 6 0): One digit is correct but in the wrong place: 3 present and in wrong place in the clue — matches.
- Clue 5 (2 4 9): Two digits are correct and in the right places: 2 and 4 present and both are in right places — matches.
Answer: 243.
Lessons learned
1. Detection of key patterns identifies two clues to analyze in combination for breakthrough. The key patterns are based on a digit common in multiple clues:
- Pattern 1: Both are positive Clues 2 and 5 with positive digit and position correctness.
- Pattern 2: Digit 2 common to both clues.
- The patterns identify the clues most promising for combined analysis, and
- Ideal for applying false assumption logic on digit 2 to get the first breakthrough.
2. False assumption logic — Use of key patterns: Assume the common digit wrong. In case of a contradiction, the false assumption is proved wrong, and the wrong digit right. Otherwise, no contradiction (in rare cases) implies (does not ascertain) validity of the assumption in the clues analyzed. Verification from remaining clues would then create the breakthrough.
- Digit 2 assumed wrong led to a positional conflict in the middle position between digits 4 and 9 in Clues 2 and 5 proving assumption wrong and digit 2 right in left position (from Clue 5).
3. Additional conclusions are important:
- In the same step, analysis is carried on to conclude: 9 wrong in Clue 2 and so, in Clue 5, 4 is right in the middle.
- This led to formation of partial code [ 2 3 ? ].
4. Importance of forming the partial code:
- Partial code [ 2 3 ? ] revealed: Two places occupied in the lock opening code with only the rightmost still vacant for the third correct digit.
5. Choice of the Clues to analyze for next breakthrough: Digit and position correctness patterns in Clues 3 and 4 showed assured promise of finding the third correct digit.
- Clues 3+4: The third correct digit must be among 3, 6, 0 or 8.
6. Digit lockout: By position description of a digit in a clue, the digit suffered from digit lockout with no place in the correct code. This confirmed the digit incorrect.
- In Clues 3+4, Clue 3 confirmed two incorrect digits 6 and 8 ➡ 6 wrong in Clue 4 caused 0 locked out of feasible positions in the correct code ➡ Remaining digit 3 confirmed correct.
- With 0 incorrect, second candidate 7 automatically confirmed correct in rightmost position.
7. All in successive pattern based right clue choices, using the patterns for position and digit correctness analysis and successive breakthroughs in steps.
Solution reached in two confident steps.
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