The number lock puzzle has 5 Clues on 3 digit codes as hints. From the Clues, find the correct 3 digit code to open the lock. Time to solve 10 mins.
Number lock puzzle: Can you crack the code to open the lock?
Following shows five Clues based on 3 digit codes for a number lock.
Clue 1: Code 291: One digit is right and is in its place.
Clue 2: Code 245: One digit is right and is in the wrong place.
Clue 3: Code 463: Two digits are right but both are in the wrong place.
Clue 4: Code 578: No digit is correct.
Clue 5: Code 569: One digit right but is in the wrong place.
From the five Clues, find the 3Â digit code that will open the number lock.
Time to solve: 10 minutes.
Solution to the 3 Digit Number lock puzzle: Can you crack the code?
Step A. Identify the correct or wrong digits
STRATEGY 1: Choose Clues with Position and Correctness Conflict:
Clue 1 and Clue 2 together provide position and correctness conflict.
Clue 1: Code 291: One digit is right and is in its place.
Clue 2: Code 245: One digit is right and is in the wrong place.
- Digit 2 is leftmost in 291 and 245, but in Clue 1, it is in correct position and in Clue 2 in wrong position. The contradiction between its position and correctness marks it incorrect.
Identify more incorrect digits from Clue 4.
Clue 4: Code 578: No digit is correct.
- Digits 5, 7 and 8 are incorrect.
STRATEGY 2: Link reference:
Identify a correct digit from Clue 2, which refers to the incorrect digits 2 and 5.
Clue 2: Code 245: One digit is right and is in the wrong place.
- As both 2 and 5 are wrong, digit 4 must be the right digit and its position is not the middle one.
Step B. Confirm the position of the correct digit by Link reference
STRATEGY 2: Link reference:
Clue 3 refers to the correct digit 4 and helps to confirm its correct place - link reference.
Clue 3: Code 463: Two digits are right but both are in the wrong place.
- Since 4 is not in the middle or leftmost position, it must be in the rightmost position.
- The lock opening code is in the form: ? ? 4, with first two digits from the left not yet known.
Step C. Identify the second correct digit by positional constraint
In Clue 1, digit 1 is in rightmost position, and the Clue provides a position and correctness conflict.
Clue 1: Code 291: One digit is right and is in its place.
As rightmost position in the lock opening code has already been occupied by digit 4, the digit 1 in the position conflicts with its correctness and position constraint.
- Digit 1 must be wrong.
- As digit 2 has already been identified as wrong, the correct digit in the hint code must be 9 which is in its correct middle position.
The lock opening code is in the form: ? 9 4.
Step D. Identify the third and last correct digit in the leftmost position
Clue 5 first identifies the key incorrect digit 6.
Clue 5: Code 569: One digit right but is in the wrong place.
- Only the digit 9 being correct and digit 5 already identified as wrong, digit 6 must also be wrong.
The Clue 3 referring to the key incorrect digit 6 provides the critical breakthrough by link reference.
Clue 3: Code 463: Two digits are right but both are in the wrong place.
- As digit 6 is wrong, digits 4 and 3 must be the two correct digit.
- The third correct digit in the lock opening code is then 3, and it is in leftmost position.
- The lock opening code is 3 9 4.
Summary
Strategies and techniques used:
- Position and correctness conflict: The digit 2 in Clues 1 and 2 is in the same place, but the descriptions clash. Digit 2 is identified as wrong.
- Mark maximum number of incorrect digits at one go: Clue 4 identifies all three digits 5, 7 and 8 as incorrect.
- Link reference of correct and incorrect digits:
- Clue 2 with hint code 245 invalidates digits 2 and 5 marking digit 4 as correct, and Clue 3 determines its position in the lock opening code as the last: ? ? 4.
- Positional constraint: Use a Clue with a digit requiring a position already occupied:
- In Clue 1 with hint 291, digit 1 requires unavailable rightmost position and is incorrect. With digit 2 wrong, correct digit 9 is in its correct position—lock opening code is in the form: ? 9 4.
- Identify a key incorrect digit to get the critical breakthrough:
- With digit 5 wrong and digit 9 right, digit 6 in Clue 5 with hint 569 is the key incorrect digit.
- Link reference of the key incorrect digit:
- In Clue 3 with hint 463, digit 4 correct and digit 6 wrong. Digit 3 the third correct digit in leftmost position in the lock opening code 3 9 4.
Use of strategic techniques and analysis of one or more Clues together in the right sequence ensured the most efficient solution.
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