Can you crack the code and solve the number lock puzzle using minimum number of clues? Given: five clues with hints on code and correctness information.
Solve the Number Lock Puzzle with Minimum Clues
Find the 3 digit code from the five clues to open the number lock:
Clue 1: Code 7 2 5 : One digit right and but wrongly placed.
Clue 2: Code 3 1 7 : Two digits are right both in wrong place.
Clue 3: Code 7 9 3 : One digit correct and in place.
Clue 4: Code 8 4 9 : Nothing is correct.
Clue 5: Code 8 9 1 : One digit correct but in wrong place.
Time for the minimum clue solution: 15 minutes.
Hint: Look for common patterns in which a digit appears in multiple clues, use the patterns, and carry on from there.
Minimum Clue Solution to the 5 Clue 3 Digit Number Lock Puzzle with 725 in Clues
First step must be to identify a key incorrect or a correct digit as,
- Identifying a position is meaningless before identifying the correct digit,
- An incorrect digit may easily uncover correct digits from a suitable clue later.
Step 1. Identify a correct or the key incorrect digit
From Clues 1 and 3, digit 7 is wrong because of position and correctness conflict.
Clue 1: Code 7 2 5 : One digit right and but wrongly placed.
Clue 3: Code 7 9 3 : One digit correct and in place.
- Digit 7 cannot be correct in both and in wrong position in one and in correct place in the other as it appears in the same position in both.
- Digit 7 is the key incorrect digit.
Step 2. Find first two correct digits and then determine their places
Identify Clue 2 with link reference of incorrect digit 7 to get two correct digits. Use Clue 3 together to fix places of the two correct digits.
Clue 2: Code 3 1 7 : Two digits are right both in wrong place.
Clue 3: Code 7 9 3 : One digit correct and in place.
- With 7 incorrect in Clue 2, both 1 and 3 are correct in Clue 2.
- In Clue 3, correct digit 3 gets its rightmost place fixed.
- As the rightmost position is taken up by 3, and middle position for the second correct digit 1 is wrong by Clue 2, the digit 1 gets its leftmost position fixed.
- The secret code is of the form [ 1 ? 3 ].
Step 3. Positional Constraint on Middle Position Provides the Breakthrough
Use positional constraint on middle position in Clue 1.
Clue 1: Code 7 2 5 : One digit right and but wrongly placed.
- With only the middle position available and digit 2 in the position wrongly placed, digit 5 is the single correct digit in the clue (as digit 7 is also wrong).
- The only vacant middle position in the code must have 5 in it. The "Wrong" placement description of 5 in the clue supports this placement.
- Lock opening code is [ 1 5 3 ].
Solution in three steps using three clues — that is the minimum number of clues to solve the puzzle. This should also be the minimum step solution.
Your task: Try to find a solution with lesser number of steps and/or using lesser number of clues. Is it possible?
Use the remaining two clues unused (following the inventive principle of free resource use) to verify the lock opening code.
Clue 4: Code 8 4 9 : Nothing is correct.
- None of the three incorrect digits are in the code 153, which is verified indirectly.
Clue 5: Code 8 9 1 : One digit correct but in wrong place.
- The only correct digit 1 is indeed in the wrong place in the hint code 891. Code 153 verified.
What are the lessons from the solution
In this unusual solution, you have used a host of effective digit patterns and inventive techniques.
- Position and correctness conflict: More often than not, the conflict in position descriptions of a digit appearing in the same position in two clues identifies it as the key incorrect digit. In this solution, digit 7 identified as the key incorrect digit by analyzing Clues 1 and 3 together.
- Further use of the key incorrect digit by link reference produces correct digits: Appearance of the incorrect digit in the promising Clue 2 identified digits 1 and 3 as correct. Immediate use of Clue 3 fixed the position of digit 3.
- Positional conflict: Additional conflict in positions of digits in Clue 3 and Clue 2 together finalized the position of digit 1 as well.
- Positional constraint: With the stage set for applying the positional constraint of only the middle position available, Clue 1 provided the final breakthrough digit 5.
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 fuss or random steps.
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