Find the minimum step solution to the 3 digit number lock puzzle with 4 clues, each with a hint code and hints on correct digits and their placements.
The 3 Digit Number Lock Puzzle 012 with 4 Clues
Find the 3 digit code from the four clues to open the number lock using minimum number of clues and steps:
Clue 1: Code 0 1 2 : One digit correct and well placed.
Clue 2: Code 2 3 0 : One digit correct but wrongly placed.
Clue 3: Code 1 8 0 : One digit correct and well placed.
Clue 4: Code 3 1 4 : One digit correct but wrongly placed.
Time for minimum clue, minimum step solution: 15 minutes.
Hint: Identify key patterns in the clues for breakthroughs.
Minimum Step Solution to the 3 Digit Number Lock Puzzle 012 with 4 Clues
First step should be to find the incorrect digit as,
- Most times, finding first an incorrect digit is the only feasible step.
- Finding the correct digit in the first step, though rare, should always be the most favorable outcome.
- Finally, finding first an incorrect digit easily uncovers correct digits later.
Step 1: Identify the first incorrect digit and as a result a correct digit
No single clue helps you to find a correct or an incorrect digit. More than one clue to be analyzed.
Key digit pattern: Clues 1 and 3 together promise significant breakthroughs as,
- Both are positive clues (with digit and position correctness both right).
- Include two common digits at different places.
Clue 1: Code 0 1 2 : One digit correct and well placed.
Clue 3: Code 1 8 0 : One digit correct and well placed.
- Both the common digits 0 and 1 appear in different places in the clues.
- Both 0 and 1 are incorrect.
- From Clue 1, digit 2 is correct in its place.
- From Clue 3, digit 8 is correct in its place.
- Lock opening code is of the form: [ ? 8 2 ].
Step 2: Identify the third correct digit and crack the code
You need a new digit, the more candidates, the better it is. As none of the two correct digits appear in Clue 4, with digit 1 already known as incorrect, either digit 3 or digit 4 must be the third correct digit.
You have ignored Clue 2 altogether, striving to crack the code using only three clues - the minimum clue solution.
Clue 4: Code 3 1 4 : One digit correct but wrongly placed.
- The partially formed lock opening code has only the leftmost position free, and digit 3 is in this position with placement wrong.
- Result: digit 3 is locked out of the code having no place for it in the code. It must be wrong.
- With 1 already incorrect, digit 4 must be the third correct digit in the code.
Solution: Code to open the lock is [ 4 8 2 ].
Two step Solution using the minimum of three clues.
Verify the solution against the unused Clue 2.
Clue 2: Code 2 3 0 : One digit correct but wrongly placed.
- Digit 2 is the only correct code digit in the hint code and is indeed in the wrong place. Code verified.
Lessons from the solution
- Key pattern identification plays the most critical role for quick success:
- Identification of the key pattern in the high promise pair of clues 1 and 3 resulted in identification of two correct digits with their correct places.
- The key pattern of two common digits in the pair of positive clues with different positions identified both as incorrect. As a result, two correct digits 8 and 2 in correct places were fixed.
- This is a type of position and digit correctness conflict (which occur in a pair of positive clues).
- Positional lockout of digit 3 in Clue 4 provided the third correct digit and correct code.
- Digit 3 appeared in the leftmost position, the only free position in the partially formed code. As the clue stated the position of its single correct digit wrong, digit 3 had no position to go and proved to be incorrect and digit 4 the third correct one.
- Use of this advanced pattern enabled reaching the solution without using Clue 2 - a minimum step, minimum clue solution.
Positive clue: A clue with both the digit and position description "right" is a positive clue. This type of clue is more promising in producing breakthroughs.
- In this puzzle, both Clues 1 and 3 are the positive clues and produced the crucial breakthroughs as promised.
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 random steps.
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