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 Inventive Number Lock Puzzle 567 in Minimum Steps Using Minimum Number of Clues: The Puzzle
Find the 3 digit code from the five clues to open the number lock using minimum number of clues:
Clue 1: Code 567 : One digit correct and well placed.
Clue 2: Code 435 : Nothing is correct.
Clue 3: Code 067 : Two digits right and well placed.
Clue 4: Code 102 : One digit right and in right position.
Clue 5: Code 721 : One digit correct but in wrong place.
Time: 15 minutes.
Hints: Find and use the key patterns of a digit in multiple clues. Must think out-of-the-box.
Minimum Clue Solution to the 3 Digit Inventive Number Lock Puzzle 567 with 5 Clues
First step is to find a correct or an incorrect digit.
Step 1: Identify a correct or an incorrect digit
Strategy: Ignore Clue 2 with all three digits wrong, as with only one digit 5 common with other clues, its potential for breakthrough isn't significant.
With two digits in same position common in clues 1 and 3, it is identified as the key pattern that should give you the first breakthrough. Logical reasoning, based on position and correctness descriptions must be your forte.
Clue 1: Code 567 : One digit correct and well placed.
Clue 3: Code 067 : Two digits right and well placed.
- Both the digits 6 and 7 cannot be correct as restricted by Clue 1, but both cannot also be wrong by Clue 3.
- Conclude: One of 6 or 7 is correct, 6 occupying the middle position if correct and 7 the rightmost if correct.
- It follows from Clue 3, the third digit 0 must be correct and is well placed.
- The code is of the form: [ 0 ? ? ].
Step 2: Identify rest of the correct digits and crack the code by inventive thinking based on persistent logical reasoning
Look for a clue having the correct digit 0 in its hint code (link reference technique). Clue 4 is the one for you.
Clue 4: Code 102 : One digit right and in right position.
- Correct digit 0 appears again, but in the middle position while the clue says: the single correct digit is well placed.
- Your immediate reaction might be, "The puzzle must be wrong!" (It was my first reaction as well!)
- But when I thought over the dilemma, the second thought was, "Any other possibilities?" This is when the breakthrough inventive possibility shows its tricky face - "Yes, there is no restriction in the puzzle about a digit being used twice!"
- This classifies the number lock puzzle as an inventive puzzle.
- Conclude: 0 appears twice in its correct positions: the leftmost and the middle.
- Blocking the middle position (positional block) by 0 identifies digit 6 as wrong and digit 7 as the third correct digit in the rightmost position.
- Lock opening code is: [ 0 0 7 ].
A two step solution using only three clues, the steps though involved multiple clues and relatively more complex logical reasoning. This is a minimum clue, minimum step inventive solution.
Verify your solution against the unused Clues 2 and 5.
Clue 2: Code 435 : Nothing is correct.
- None of the three wrong digits are in your lock opening code 007. Verified.
Clue 5: Code 721 : One digit correct but in wrong place.
- The single correct digit 7 in your code 007 appears in the hint code in the wrong place indeed. Verified.
Lessons from the solution
- Strategy of ignoring the all-incorrect digits clue if the three incorrect digits appear rarely in other clues. This saves a valuable step and use of an extra clue.
- Logical reasoning based on common digit occurrence: Clues 1 and 3 showed significant promise in two digits 6 and 7 common in the same places and their correctness descriptions differing slightly. That identified the first correct digit 0 in leftmost place and also restricted probable positions of the second correct digit one of 6 or 7.
- Link reference technique: Clue 4 chosen next, as the correct digit 0 appeared in its hint code again, but in a different place. That must have confused you first.
- Persistent reasoning often leads to inventive thinking: 0 being correct in both Clues 3 and 4 and also in correct places,
- Either the puzzle is wrong,
- Or, a digit may appear multiple times in the lock opening code.
- With no constraint on a digit to be used more than once, the lock opening code must be 007, the puzzle correct and a rare inventive puzzle.
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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