Use the common digits to crack number lock puzzle 692 in two steps
Can you crack number lock puzzle 692 in two steps? The puzzle gives 5 clues with a hint code and digit and position correctness of the hint code.
3 Digit Number Lock Puzzle Including Hint Code 692
Following are the five clues:
Clue 1: Code 4 0 7: No digit is correct.
Clue 2: Code 6 9 2: Two digits are correct and in the right places.
Clue 3: Code 9 1 2: Two digits are correct - 1 in right place and 1 in wrong place.
Clue 4: Code 2 6 5: Two digits are correct but both wrongly placed.
Clue 5: Code 2 8 9: Two digits are correct but both wrongly placed.
Find the code to open the number lock in minimum number of steps.
Time to solve 10 minutes.
Hints: Analyze the clues to spot and use breakthrough patterns in common digits among multiple clues.
Solution to 3 Digit Number Lock Puzzle 692 in Two Steps
None of the three wrong digits appear in any of the other clues. Clues 2 to 4 are to be analyzed for solution.
Step 1. False assumption logic to identify a correct digit in place
Clue 2: Code 6 9 2: Two digits are correct and in the right places.
Clue 3: Code 9 1 2: Two digits are correct - 1 in right place and 1 in wrong place.
Clue 5: Code 2 8 9: Two digits are correct but both wrongly placed.
- Clues 2+3+5: Assume 2, common to all three clues, wrong => four digits (1,6,8,9) correct => impossibility => 2 right in rightmost => partial code [ ? ? 2 ].
- Same way assume 9 wrong => four digits (2,6,1,8) correct => impossibility => 9 right in middle place from Clue 2 => partial code [ ? 9 2 ].
- Additional information: 1, 6 and 8 are incorrect.
Step 2. Incorrect digit elimination produces the third correct digit
Only Clue 4 can give us the third correct digit 5.
Clue 4: Code 2 6 5: Two digits are correct but both wrongly placed.
- With 6 wrong and 2 right, 5 is the second right digit in the clue and the third right digit in the secret code. Secret code [ 5 9 2 ].
Answer: Lock opening code is [ 5 9 2 ].
Unused Clue 1 doesn't have any of its three digits common to any of the other four clues, and so, it indirectly verifies the lock opening secret code.
End note
Effective techniques based on common digits in clue codes:
- False assumption logic works best on a digit appearing in most of the clues. Selecting a suitable pair of clues identifies the focal digit as wrong or right on assuming it as false. Occasionally, the false assumption may be right. The technique always produces results. In this puzzle, analyzing three clues together based on false assumption logic produced two correct digits.
- Importance of additional information could be realized in second step when elimination of incorrect digit 6, noted as additional information in first step, easily produced the third correct digit 5.
- Using multiple clues together can only harness the power of common digit patterns. Technically, if all clues are analyzed together in a logic chain, solution should be quickest. An example is here.
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