Find the minimum step solution to the 3 digit number lock puzzle 142 with 4 clues, each with a hint code and hints on correct digits and their placements.
The 3 Digit Number Lock Puzzle 142 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 1 4 2 : One digit correct and well placed.
Clue 2: Code 3 0 9 : Two digits right and well placed.
Clue 3: Code 4 5 6 : Nothing is correct.
Clue 4: Code 1 3 9 : 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 142 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 two correct digits
No single clue helps you to find a correct or an incorrect digit. More than one clue to be analyzed.
Key digit pattern: Clues 2 and 4 together promise one incorrect digit and two correct digits in right positions.
Clue 2: Code 3 0 9 : Two digits right and well placed.
Clue 4: Code 1 3 9 : One digit correct but wrongly placed.
- 9 appears in both clues in rightmost positions. If it is one of the two correct digits in the clue, its position is also correct. But, Clue 4 says the correct digit wrongly placed. This is position and correctness conflict caused by a common digit appearing in same position in two clues with different positional descriptions.
- Digit 9 is incorrect.
- By Clue 2, both 3 and 0 are correct and in right positions in the lock opening code.
- Lock opening code is of the form: [ 3 0 ? ].
Step 2: Identify the third correct digit and crack the code
Identify the second breakthrough pattern of positional conflict in Clues 1 and 4 in addition to another position and correctness conflict.
You have ignored Clue 3 altogether, striving to crack the code using only three clues - the minimum clue solution.
Clue 1: Code 1 4 2 : One digit correct and well placed.
Clue 4: Code 1 3 9 : One digit correct but wrongly placed.
- Common digit 1 in the leftmost position in both suffers from position and correctness conflict and so, is wrong.
- Digit 4 in Clue 1 occupying already filled middle position in the partially formed correct code [ 3 0 ? ] must also be wrong. This is positional conflict.
- The third correct digit is 2 by incorrect digit elimination of 1 and 4 in Clue 1.
Solution: Code to open the lock is [ 3 0 2 ].
Two step Solution using the minimum of three clues.
Verify the solution against the unused Clue 3.
Clue 3: Code 4 5 6 : Nothing is correct.
- None of the three incorrect digits appear in your lock opening code, which thus stands verified.
Lessons from the solution
Key pattern identification and use played the critical role for quick success.
Breakthroughs in Step 1
- Identification of the key pattern in the high promise pair of clues 2 and 4 resulted in identification of two correct digits with their correct places.
- First, the key pattern of position and correctness conflict suffered by common digit 9 appearing in same position in the clues but with different positional correctness descriptions identified digit 9 as incorrect.
- Additional gains in identification of two correct digits 3 and 0 both in their correct places.
Breakthroughs in Step 2
- Position and correctness conflict on common digit 1 in Clues 1 and 4 provided the second breakthrough in identifying digit 1 as incorrect.
- Positional conflict was the second type of pattern that identified digit 4 as wrong in analyzing the same pair of clues as it occupied in Clue 1 an already filled position in the partially formed code.
- Digit elimination of 1 and 4 fixed 2 as the third correct digit.
Coupled with the ability to identify a useful pattern and use the pattern for a breakthrough, the strategic analysis of multiple clues could deliver the minimum clue, minimum step solution with no random steps.
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