Can you take up the challenge to crack the 3 digit number lock puzzle with 5 clues using minimum number of clues and in minimum steps?
Challenge to Crack the Number Lock Code Using Least Number of Clues in Minimum Steps: The Puzzle
Find the 3 digit code from the five clues to unlock the number lock:
Clue 1: Code 4 6 0 : One digit right and in right position.
Clue 2: Code 4 9 2 : One digit correct but in wrong place.
Clue 3: Code 0 8 4 : Two digits right but wrongly placed.
Clue 4: Code 5 1 6 : Nothing is correct.
Clue 5: Code 5 6 8 : One digit correct but in wrong place.
Find the lock opening code. Try for the minimum step, minimum clue solution.
Time for the minimum clue, minimum step solution: 15 minutes.
Hint: Find and use the key patterns of a digit in multiple clues.
Minimum Clue, Minimum Step Solution to the 3 Digit Number Lock Puzzle 460 with 5 Clues
Sensible first step is to find a correct or an incorrect digit as, attempts to find the correct place before finding the correct digit is senseless.
Step 1: Identify a correct or an incorrect digit
The common pattern that identifies an incorrect digit is position and correctness conflict when one digit appears in two clues in the same position, but with conflict in their position descriptions.
Such a pair of clues is Clues 1 and 2.
Clue 1: Code 4 6 0 : One digit right and in right position.
Clue 2: Code 4 9 2 : One digit correct but in wrong place.
- Digit 4 appears in the leftmost position in both the clues, but with different position descriptions. Both cannot be true.
- Digit 4 is the first incorrect digit you identify.
Step 2: Identify the two correct digits and their probable positions
Take up a new clue that refers to the incorrect digit 4 along with clue 1 that already has the potential to identify a correct digit.
Clue 3: Code 0 8 4 : Two digits right but wrongly placed.
Clue 1: Code 4 6 0 : One digit right and in right position.
- As digit 4 is wrong in Clue 3, both 0 and 8 are correct.
- In Clue 1, 0 is the single correct digit occupying the correct rightmost position.
- With both the middle and the rightmost positions gone for 8, the second correct digit 8 in Clue 3 must appear in the leftmost position.
- Lock opening code is of the form 8 ? 0. Only the middle position is available.
Step 3: Identify the third correct digit to crack the code
Take up Clue 2 again as, none of the two correct digits are included in its hint code. This is the use of a negative form of link reference technique that excludes the correct digits in the clue code—an extension of reasoning to modify an existing technique most suitable at this moment.
The second reason for choosing Clue 2 is, as digit 4 is already known as wrong, either digit 9 or 2 must be the third correct digit.
Clue 2: Code 4 9 2 : One digit correct but in wrong place.
- Digit 9 occupying the only available middle position cannot be right as its position is described as wrong. This is what is known as position block or position constraint condition.
- With 4 also wrong, the only correct digit in the clue must be 2, and it will take up the middle position.
- The lock opening code is 8 2 0.
Solution in 3 steps and should be the minimum clue, minimum step solution.
Clues 4 and 5 are not used.
This is a measure of efficiency of the solution, but being free resources now, these can be used (following the inventive principle of free resource use) for verification of the lock opening code 820.
Clue 4: Code 5 1 6 : Nothing is correct.
- None of the three wrong digits are in the lock opening code, and the clue verifies it by not violating the code. This is a negative type of verification.
Clue 5: Code 5 6 8 : One digit correct but in wrong place.
- The only correct digit common with your code 820 is 8, and it indeed is in the wrong position. Code verified.
First task for you: Try the path of solution starting with apparently the most informative Clue 4 that gives you three incorrect digits at one go.
Second task for you: Try for a new three step solution.
Third task for you: Try for a two step solution. If you can discover such a one, you will prove me wrong in identifying our solution as the minimum step solution.
Takeaways
- Position and correctness conflict of a single digit common in two clues identified a digit as incorrect to give you the first breakthrough.
- Link reference technique that identified a pair of clues both including the incorrect digit 4. Analyzing the clues, two correct digits and their positions could be fixed in the second step.
- Negative form of link reference technique helped you to choose a clue that didn't include the correct digits and so it had the potential to identify the third correct digit.
- The leftmost and rightmost positions block created position constraint on the middle position. This helped to identify the third correct digit.
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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