Can you take up the challenge and crack the 3 digit number lock code to open the number lock with least number of clues? Good logic analysis is the key.
Challenge to Crack the Number Lock Code Using Least Number of Clues: 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.
Solution to 3 digit number lock puzzle 460 with 5 clues: Use least number of clues
Step 1: Identify the first incorrect digit
From Clue 1 and 5, digit 6 is wrong due to correctness and positional conflict. So, one of 0 and 4 is correct.
Clue 1: Code 4 6 0 : One digit right and in right position.
Clue 5: Code 5 6 8 : One digit correct but in wrong place.
- Digit 6 is wrong due to positional conflict between two clues. It cannot be right and occupy same position in both clue codes.
- Either of digits 0 or 4 is correct.
Step 2: Identify the first correct digit
From Clue 3, digit 8 is right.
Clue 3: Code 0 8 4 : Two digits right but wrongly placed.
- As one of 0 and 4 is correct, the other correct digit must be 8.
Step 3: Identify the position of the correct digit
From Clue 3 and 5, digit 8 takes the first place.
Clue 3: Code 0 8 4 : Two digits right but wrongly placed.
Clue 5: Code 5 6 8 : One digit correct but in wrong place.
- In the two clues together, positions second and third are wrong for digit 8, so its position in the correct code must be the first.
Step 4: Identify the second incorrect and the second correct digits
From Clue 1 and 2, digit 0 is correct.
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 is wrong due to correctness and positional conflict in the two clues. It cannot occupy the same position in both clues and be a correct one because of opposite position description.
- From Clue 1, digit 0 must be the second correct digit occupying third position.
- Code of form 8 ? 0.
Step 5: Identify the third correct digit and crack the code
From Clue 2, digit 2 is the third correct digit.
Clue 2: Code 4 9 2 : One digit correct but in wrong place.
- One of 2 or 9 must be correct and the correct digit is in wrong position. For digit 9 no place is available in the correct code because positions 1 and 3 are already taken up.
- Digit 2 must be the third correct digit taking up second position.
Code to open the number lock is 8 2 0.
Verify the code against the 5 clues.
Note: Only 4 clues are used. Clue 4 remains unused. This is the hallmark of efficient solution using least number of clues by watertight logical reasoning.
Puzzles you may enjoy
Easy to hard brain teasers with systematic solutions
Challenging brain teasers with solutions: Long list.
This will always be the most up-to-date full list with the brain teasers classified into categories that can be browsed separately.