Given 4 clues each with a hint code and digit and position correctness information. Crack the combination lock code to open the 3 digit number lock.
Crack the Code for Combination Lock Puzzle with 348 in 4 Clues: The Puzzle
Find the 3 digit code from the four clues to crack the number lock puzzle in minimum steps:
Clue 1: Code 3 4 8 : One digit right and in right position.
Clue 2: Code 8 5 4 : Nothing is correct.
Clue 3: Code 8 9 3 : Two digits right but wrongly placed.
Clue 4: Code 5 9 1 : Two digits right but wrongly placed.
Time for minimum step solution: 5 minutes.
Hint: Find and use the key patterns of a digit appearing in multiple clues.
Minimum Step Solution to the 3 Digit Combination Lock Puzzle with 348 in 4 Clues
The most desirable first step in this puzzle is to use the three digit wrong information in Clue 2 to identify as many correct digits as possible at the earliest.
Step 1: Identify maximum number of correct digits at one go
Clue 2 identifies 8, 5 and 4 and incorrect. Look for clues with the incorrect digits - link reference technique.
Clue 2: Code 8 5 4 : Nothing is correct.
Clue 3: Code 8 9 3 : Two digits right but wrongly placed.
Clue 4: Code 5 9 1 : Two digits right but wrongly placed.
- With digit 8 wrong in Clue 3, digits 9 and 3 are correct.
- With digit 5 wrong in Clue 4, digits 9 and 1 are correct.
- Three correct digits are 1, 3 and 9.
- 9 can either be in the leftmost or the rightmost position. This key additional information will help to crack the code in just one more step.
Step 2: Fix the positions of the correct digits
The positive Clue 1 (with both correctness and position descriptions stated right) includes the correct digit 3.
Clue 1: Code 3 4 8 : One digit right and in right position.
- The position of correct digit 3 is the leftmost.
- Lock opening code: [ 3 ? ? ].
- In Step 1, position of 9 was curtailed to the leftmost or the rightmost. 3 occupying the leftmost, 9 must be in the rightmost.
- The third correct digit 1 takes up the middle position violating no clue condition.
- Lock opening code [ 3 1 9 ].
The two step solution should be the minimum step solution.
Lessons from the solution
- Objective for the first step and strategic insight: Must use the clue with three wrong digits to find the correct digits as quickly as possible.
- Link reference technique helps to identify the clues with already identified wrong clues common. Analysis of these clues together revealed all three correct digits in the first compound step itself.
- Extraction of maximum information in an analysis is vitally important in achieving quick and elegant success.
- Even after identifying the three correct digits information retrieval was continued for valuable insight into the positional constraints on digit 9 (only leftmost and rightmost valid for 9).
- Link reference technique again identified positive Clue 1 with the correct digit common. This fixed the position of digit 3 as leftmost and digit 9 as rightmost, digit 1 rightfully fell into the vacant middle position in just one more step.
Overall, it has been an exercise of choosing the most suitable combination of clues individually or together for the series of breakthroughs following a strategic approach.
Coupled with the ability to identify a useful pattern and use the pattern for a breakthrough, the strategic analytic approach could deliver the minimum clue, minimum step solution with no complications or random steps.
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