Can you Crack the 3 digit number lock puzzle 360 with 4 clues? Each clue hints at code and digit and placements in its hint code. Solve in minimum steps.
Number Lock Puzzle 360 With 4 Clues
Clue 1: Code 3 6 0: One digit is correct but in a wrong place.
Clue 2: Code 2 0 1: Two digits are correct — one in the right place, one in the wrong place.
Clue 3: Code 6 0 2: Two digits are correct and in the right places.
Clue 4: Code 9 8 2: Two digits are correct and in the right places.
Find the code to open the number lock in minimum steps.
Time: 10 minutes.
Hint: Look for common digits in multiple clues and use the patterns in best possible way.
Solution to Number Lock Puzzle 360 With 4 Clues in Minimum Steps
A quick scan reveals:
- Digit 2 appears in Positive Clues 3 and 4 in the same position — a highly promising breakthrough pattern.
- The positive clues enable quick breakthrough to identify a correct or incorrect digit.
Positive clues have hints on both digit and placement correctness of the hint code "right".
Step 1. Identify first correct digit using multiple positive clues and false assumption logic
Analyze first the two high-promise positive Clues 3 and 4 together.
Clue 3: Code 6 0 2: Two digits are correct and in the right places.
Clue 4: Code 9 8 2: Two digits are correct and in the right places.
- Both claim two correct digits in correct positions. Since 2 is in 3rd position in both, it must be correct. Otherwise, no way the two pairs of non-overlapping digits (0, 6, 8 and 9 - total 4) can be fitted into three places of secret code. This is false assumption logic.
- 2 correct in rightmost place → Partial code [ ? ? 2 ].
- Additional information: When 2 is correct in the two clues, either (9 and 0) or (6 and 8) correct, as only these two pairs cover the remaining two positions in the secret code - digit pair correctness analysis.
- Example: If 2 were a wrong digit in Clues 3 and 4, four correct digits are to be fitted into three secret code places - an impossibility that proved the original assumption of 2 wrong to be false. 2 must be a correct digit in the secret code.
- Example: Out of two pairs (0,9) and (6,8), one pair must be correct to fulfill the secret code position and the pair of clues requirements.
- If 0 or 9 right, the other must be right, and both 6 and 8 must be false.
- If 6 or 8 right, the other must be right, and both 0 and 9 false.
- This ensures identification of one new correct and two incorrect digits the moment one of the four digits is identified as CORRECT - a powerful pattern based technique.
Step 2. Identify rest two correct digits from a clue that includes the known correct digit - link reference technique, positional conflict
Correct digit 2 reappears in Clue 2. Examine the clue with genuine interest.
Clue 2: Code 2 0 1: Two digits are correct — one in the right place, one in the wrong place.
- With correct digit 2 in wrong place in the Clue (its correct position in the secret code rightmost), either 0 or 1 must be the second correct digit in its place.
- As 1 suffers positional conflict with 2 in rightmost position of the secret code, 0 must be correct in the middle along with 9 in the leftmost (as concluded in first step, both 0 and 9 have to be correct or both false - 9 if correct, it appears in its leftmost place in Clue 4).
- Second correct digit either 0 or 1 must be in its correct place. But, 1 gets eliminated by positional conflict with 2 in rightmost place.
Solution: Lock opening code: [ 9 0 2 ].
Two compound-step solution — achieved using contradiction, positional logic, and chain reasoning.
Verify Against the Unused Clue.
Now verify the derived code 902 against the clue not used in the two-step solution.
Clue 1: Code 3 6 0: One digit is correct but in a wrong place.
- 0 is the only digit common with the secret code and is indeed in a wrong position in the hint code. Secret code 902 verified.
Final solution: Secret lock opening code 902.
Solution Outline (Concise Version)
Step 1: Analyze most promising positive Clues 3 and 4 having digit 2 common in the same position.
- Clue 3 (6 0 2) + Clue 4 (9 8 2), two digits right in right positions in both — Assume 2 is wrong → leads to 4 correct digits (6,0,9,8) → contradiction → 2 must be correct in its position → either (0,9) or (6,8) correct.
Step 2: Analyze Clue 2 with correct digit 2 in its hint code - link reference.
- Clue 2 - Code 2 0 1, two digits correct, 1 in right place, 1 in wrong place — digit 2 correct in wrong place, 1 wrong by position conflict → 0 right in middle position → 9 right from step 1 and in leftmost position → solution code 902.
Lessons Learned
- Common Digits Are Logical Anchors:
- Digit 2 appears in three clues. Its recurrence, especially in the same position, makes it a prime candidate for combined clue analysis. Always group clues by common digits.
- In Clues 3 and 4, assuming "2 is wrong" led to four correct digits (6,0,9,8) — impossible in a 3-digit code. This contradiction proves 2 must be correct — a powerful logical tool.
- In Clue 2, 1 cannot be correct because it would need to be in 3rd place — but 2 already occupies it. Positional logic is often the key to breaking ties.
- Correctness of one of two pairs of digits is a necessary condition for correctly filling up two vacant positions of the secret code and in the pair of clues.
- Example: Out of two pairs (0,9) and (6,8), one pair must be correct to fulfill the position conditions in the secret code and the pair of clues.
- If 0 or 9 right, the other must be right and 6, 8 must be false.
- If 6 or 8 right, the other must be right and 0, 9 false.
- This ensures identification of one new correct and two incorrect digits the moment one of the four digits is identified as CORRECT.
- Each deduction feeds into the next:
- Step 1. Use Positive Clues 3+4 to prove 2 is correct → fix its position → identify one of the two pairs (0,9) or (6,8) correct.
- Step 2. Use Clue 2 to confirm 0 and eliminate 1 → 0 correct confirms its position and 9 correct and its position → finds the secret code.
- All logic in structured progression.
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