Given: 5 clues, each with a 3 digit code and information about digit correctness and positional accuracy. Crack the code using minimum number of clues.
The Number Lock Puzzle with 628: Clues
You are given the following five clues to deduce the correct 3 digit code:
Clue 1: Code 6 2 8: One digit is correct and in the right place.
Clue 2: Code 4 2 3: Two digits are correct — one in the right place, one in the wrong place.
Clue 3: Code 0 8 2: Two digits are correct but both are in the wrong places.
Clue 4: Code 8 0 4: One digit is correct but in the wrong place.
Clue 5: Code 5 3 9: One digit is correct but in the wrong place.
Your task is to determine the correct 3 digit code that opens the lock in minimum steps.
Time to solve: 15 minutes.
Hints: Identify first a correct digit using the clues with the breakthrough pattern of a single digit common. Carry on using same pattern to fix the position of the correct digit.
Step-by-Step Solution to the Number Lock Puzzle 628 in Minimum Steps
Default step: Overall scan of the clues to spot useful digit patterns and deciding the course of action
A quick scan of the clues reveals a recurring digit pattern — the digit 2 appears in Clue 1, Clue 2, and Clue 3. This is a rare and significant pattern. Following the golden rule of combined clue analysis with digits common, analyze the clues with common digits together to maximize breakthroughs.
Step 1: Use False Assumption Based Reasoning on Digit 2 to determine its correctness and its position
Analyze all three Clue 1, Clue 2 and Clue 3, together to achieve maximum breakthroughs in one step.
Clue 1: Code 6 2 8: One digit is correct and in the right place.
Clue 2: Code 4 2 3: Two digits are correct — one in the right place, one in the wrong place.
Clue 3: Code 0 8 2: Two digits are correct but both are in the wrong places.
False assumption reasoning:
This powerful technique is especially suitable for applying on digit 2 that appears in all three clues. In this technique, the common digit is assumed as wrong, and consequences of the assumption is analyzed. This path is confirmed to provide the desired breakthrough.
Assume temporarily that digit 2 is NOT correct (i.e., not in the final code).
Then:
- In Clue 2 (4 2 3): Since 2 is wrong, the two correct digits must be 4 and 3, with one in the right place and one in the wrong place.
- In Clue 3 (0 8 2): Since 2 is wrong, the two correct digits must be 0 and 8, both in the wrong places.
- That gives you four correct digits: 4, 3, 0, and 8 — but the lock code is only 3 digits long.
Contradiction!
It’s impossible to have four correct digits in a 3 digit code.
- Conclusion: Your assumption that 2 is incorrect must be false - it is a correct digit in the lock opening code.
- With 2 correct, by Clue 1 digit 2 is in the middle of the code.
- Partial code: [ ? 2 ? ] .
- Additional information: Digits 6 and 8 are both incorrect from Clue 2.
Continue analyzing the clues armed now with the breakthrough information.
We already know:
- In Clue 3 (0 8 2), 2 is correct, in the 3rd position, whereas we now know it is in the 2nd position — so it is correct but in the wrong place.
- 8 is also incorrect (from Clue 1).
- Therefore, the second correct digit in the clue must be 0, and its 1st position in the clue is wrong.
- Correct position of second correct digit must then be the only free position, the rightmost.
- Partial code: [ ? 2 0 ].
Now, we need to find the first digit.
Continue analyzing a suitable clue among the three most promising clues as you have now quite a significant insight into the correct code.
Identify Clue 2 that will produce the final correct digit.
Clue 2: Code 4 2 3: Two digits are correct — one in the right place, one in the wrong place
We already know:
- 2 is correct in the code and in the clue. It is also in the correct middle position.
- The correct digit wrongly placed must either be 4 or 3.
- Digit 4 in leftmost position is wrongly placed by the clue description. So it has to take either the middle or the rightmost position. But both these are already occupied by 2 and 4 in the code → 4 has no place in the lock opening code - it is locked out of the code, and so is wrong.
- The third right digit (second in the clue) must be 3 (in wrong position in the clue), and it can occupy leftmost position violating no condition.
Solution: Lock opening code [ 3 2 0 ] in just one step with a long chain of reasoning.
Now, verify the solution with unused Clues 4 and 5.
Clue 5: Code 5 3 9: One digit is correct but in the wrong place.
- Correct code digit 3 is in a wrong position in the clue. Solution code verified.
Clue 4: Code 8 0 4: One digit is correct but in the wrong place.
- Correct code digit 0 is in a wrong position in the clue. Solution code verified again.
Final Answer: The Lock Code is [ 3 2 0 ].
Solution Outline (Concise Version)
Step 1: Analyze most promising Clues 1, 2, and 3 having digit 2 common together
- Sub-step 1: Analyze Clue 2 (4 2 3) + Clue 3 — Assume 2 is wrong → leads to 4 correct digits (4,3,0,8) → contradiction → 2 must be correct.
- Sub-step 2: Clue 1 (6 2 8) → 2 is in correct place (middle), so partial code is ? 2 ?; 6 and 8 are wrong. Clue 3 ( 0 8 2) → 0 is correct but not in 1st place → must be in 3rd → partial code ? 2 0.
- Sub-step 3: Clue 2 (4 2 3) → 4 is locked out with no place to go (Clue 4 confirms 4 wrong via 0 being correct blocking the position for 0), so 3 is correct but in wrong place → must be in 1st → code [ 3 2 0 ].
Lessons Learned from the Solution
- Spot recurring digits: The digit 2 appears in three clues — a rare pattern. Analyzing these together leads to a series of breakthroughs.
- Use false assumption reasoning: Assuming 2 is wrong led to a contradiction (too many correct digits), proving it must be correct.
- Positional logic is key: Once 2 is confirmed in the middle, other digits are eliminated based on position identifying 0 as the second correct digit in the 3rd plc.
- Maximize information per clue: Clue 4 helped eliminate 4 because 0 was already known to be correct and in the wrong place.
- Chain reasoning across clues: Each deduction feeds into the next — no random guessing.
- Verify final code against unused clues: Ensures no oversight.
This solution uses logical deduction, contradiction, and positional analysis to solve the puzzle in minimum steps, avoiding trial and error. It exemplifies how pattern recognition and structured reasoning crack number lock puzzles efficiently.
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