Crack the number lock puzzle 068 in two steps from 5 clues each with a 3 digit code and statement on digit and position correctness on the hint code.
3 Digit Number Lock Puzzle Including Hint Code 068
Following are the five clues:
Clue 1: Code 0 6 8: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 2: Code 9 6 7: One digit is correct and in the right place.
Clue 3: Code 0 4 1: Two digits are correct but both are in the wrong places.
Clue 4: Code 9 6 5: One digit is correct and in the right place.
Clue 5: Code 3 6 1: One digit is correct and in the right place.
Find the code to open the number lock in two analytical steps.
Time to solve 10 minutes.
Hints: Go through all the clues carefully. Search for promising patterns of common digits in the clues. For quick and confident solution, such patterns in multiple clues to be used for breakthroughs.
Solution to Crack the Number Lock Puzzle 068 in Two Steps
Position and correctness description conflict spotted in two clues.
Step 1. Find the incorrect digit by position and correctness conflict
In Clues 3 and 5, digit 1 is in same position and stated as correct but in one clue it is wrongly placed and in the other in right place.
Clue 3: Code 0 4 1: Two digits are correct but both are in the wrong places.
Clue 5: Code 3 6 1: One digit is correct and in the right place.
- In both, 1 is rightmost. To be the correct digit as stated in the clues, its position description must also be same. But, in Clue 3, both correct digits are wrongly placed, while in Clue 5, the single correct digit is in right place → the position and correctness description for 1 are conflicting → 1 is incorrect → it follows from Clue 3, digits 0 and 4 are correct, but wrongly placed → 0 in middle or rightmost, 4 leftmost or rightmost.
Step 2. False assumption logic identifies third correct digit and confirms all digit positions
6 appears in common in Clues 1 and 4. If it is in correct, four digits are to be correct—candidate for applying false assumption logic.
Clue 1: Code 0 6 8: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 4: Code 9 6 5: One digit is correct and in the right place.
- False assumption: If 6 is wrong, digits (0,4,8 and 5 or 9) are to be correct → four correct digits in 3 digit lock code is impossible → contradiction proves 6 must be correct → 0 correct and wrongly placed (from Step 1, position of 0 can only be middle or rightmost) → 6 is the second correct digit in its correct middle place.
- With middle place taken up by 6, digit 0 has to be rightmost.
- The third digit 4 occupies the vacant leftmost position.
- Secret code [ 4 6 0 ].
Solution in two steps. Clue 2 remains unused in solution, but will be used in verification.
Verify the secret code solution against all the clues. It is a good practice to double-check, and it takes just a little time more.
Clue 1: Code 0 6 8: Two digits are correct — 1 in the right place and 1 in the wrong place. (correct code 460)
- Correct 6 in right place, second correct 0 in wrong place. Secret code verified.
Clue 2: Code 9 6 7: One digit is correct and in the right place. (correct code 460)
- Correct 6 in right place. Secret code verified.
Clue 3: Code 0 4 1: Two digits are correct but both are in the wrong places. (correct code 460)
- Both correct digits 0 and 4 are wrongly placed. Secret code verified.
Clue 4: Code 9 6 5: One digit is correct and in the right place. (correct code 460)
- Correct 6 is in its correct position. Secret code verified.
Clue 5: Code 3 6 1: One digit is correct and in the right place. (correct code 460)
- Correct 6 in right position. Secret code verified.
Secret code [4 6 0] satisfies all the clues.
Lessons Learned
1. Combined Clue Pair Analysis on Positional Correctness + Digit correctness Conflict:
- Analyze Clues 3 and 5, both include digit 1, but it cannot be correct because if it were so, it would have been wrongly placed in Clue 3 and correctly placed in the other— the contradiction identifies digit 1 as incorrect.
2. Follow up implications:
- Digit 3 incorrect identifies digits 0 and 4 both correct in Clue 3 — a double breakthrough.
3. Importance of extracting all implications in an analytical step:
- Even after identifying an incorrect digit and two correct digits by analyzing Clues 3 + 5, the probable positions of digit 0 are identified as middle or rightmost, and that proved to be the key information behind confirming positions of all three correct digits in the next step.
4. False assumption logic: False Assumption + Contradiction = Proof of correctness.
- In Clues 1 and 4, Assuming "6 is wrong" led to four correct digits (0, 4, 8 and 5 or 9) — impossible in a 3 digit code. This contradiction proves 6 must be correct — a powerful logical tool. This also confirms position of 6 in middle, position of 0 at rightmost and 4 at leftmost.
5. Chain Reasoning, Not Guessing.
- Each deduction feeds into the next:
- Step 1. Use Positive Clues 3+5 to prove 1 is incorrect → fixes 0, 4 as correct → valid position of 0 middle or rightmost.
- Step 2. Use Clue 1+4 to confirm 6 correct and its position in middle → with middle position eliminated, valid position of 0 left out as rightmost → position of 4 at leftmost.
- Solution [ 4 6 0 ] in only two steps.
- All logic in structured progression.
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