Use the common digits to crack number lock puzzle 105 in minimum steps
Can you crack number lock puzzle 105 in minimum 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 105
Following are the five clues:
Clue 1: Code 1 0 5: Two digits are correct but both are in the wrong places.
Clue 2: Code 5 2 8: Two digits are correct and in the right places.
Clue 3: Code 5 7 3: One digit is correct and in the right place.
Clue 4: Code 9 5 6: One digit correct and wrongly placed.
Clue 5: Code 2 1 0: One digit is correct and in the right place.
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 105 in Minimum Steps
Step 1. Correct digit by false assumption
Clue 2: Code 5 2 8: Two digits are correct and in the right places.
Clue 3: Code 5 7 3: One digit is correct and in the right place.
- Clues 2+3: Assume 5 wrong => (both 2,8 correct and one of 3,7 correct) => none of the four in Clue 4 => contradiction => 5 right in its place => partial code [ 5 ? ? ].
Step 2. Incorrect digit by positional conflict produces second correct digit
Clue 5: Code 2 1 0: One digit is correct and in the right place.
Clue 2: Code 5 2 8: Two digits are correct and in the right places.
- Clues 5+2: Clue 5: 2 incorrect by positional conflict => Clue 2: 8 correct in its place by incorrect digit elimination of 2 => partial code: [ 5 ? 8 ].
Step 3. Third correct digit by double positional conflicts
Clue 5: Code 2 1 0: One digit is correct and in the right place.
- Clue 5: 2, 0 eliminated as incorrect by positional conflict => 1 is the right digit in its place => secret code [ 5 1 8 ].
Answer: Lock opening code is [ 5 1 8 ].
Verify the secret code against the unused Clues 1 and 4.
Clue 1: Code 1 0 5: Two digits are correct but both are in the wrong places.
- 1, 5 common in both and both the digits are wrongly placed in the hint code. Secret code verified.
Clue 4: Code 9 5 6: One digit correct and wrongly placed.
- The only common digit 5 is indeed wrongly placed in the hint code. Secret code verified.
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.
- Positional conflict occurs when the position of a digit described as right in right position in a clue clashes with a digit already occupying the position in the partially formed secret code. It is a frequently used effective number lock solving technique, and it highlights the importance of forming the partial secret code at every stage.
- 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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