Can you crack the code and solve the number lock puzzle with minimum clues? Given, five clues with hints on possible code and correctness information.
Solve the Number Lock Puzzle with Minimum Clues
Find the 3 digit code from the five clues to unlock the number lock:
Clue 1: Code 7 2 5 : One digit right and but wrongly placed.
Clue 2: Code 3 1 7 : Two digits are right both in wrong place.
Clue 3: Code 7 9 3 : One digit correct and in place.
Clue 4: Code 8 4 9 : Nothing is correct.
Clue 5: Code 8 9 1 : One digit correct but in wrong place.
Solution to the 5 clue 3 digit number lock puzzle with 725 in clues: Use least number of clues
Step 1: Identify the first pair of incorrect digits
From Clue 1 and 3, digit 7 is wrong due to correctness and positional conflict.
Clue 1: Code 7 2 5 : One digit right and but wrongly placed.
Clue 3: Code 7 9 3 : One digit correct and in place.
- Digit 7 cannot be correct in both and in wrong position in one and in correct place in the other as it appears in the same position in both.
- Digit 7 in incorrect.
In the same way, from Clue 3 and Clue 5, digit 9 is incorrect.
Clue 3: Code 7 9 3 : One digit correct and in place.
Clue 5: Code 8 9 1 : One digit correct but in wrong place.
- Digit 9 cannot be correct in both and in wrong position in one and in place in the other, as it appears in the same position in both.
- Digit 9 is incorrect.
Step 2: Identify the first correct digit and its place
From Clue 3, digit 3 is correct and in 3rd place.
Clue 3: Code 7 9 3 : One digit correct and in place.
- As both 7 and 9 are incorrect, digit 3 is the single correct digit and is in 3rd position in the correct code.
Step 3: Identify the second correct digit and its place
From Clue 2, the second correct digit is 1.
Clue 2: Code 3 1 7 : Two digits are right both in wrong place.
- Digit 7 is incorrect and digit 3 correct. Digit 1 must be the second correct digit.
- As 3rd place is taken up by digit 3 and 2nd place wrong for digit 1, its correct position is 1st.
Step 4: Identify the third correct digit and crack the code
From Clue 1, digit 5 is the third correct digit.
Clue 1: Code 7 2 5 : One digit right and but wrongly placed.
- With digit 7 wrong, either of digits 2 or 5 is right.
- Both 1st and 3rd positions are taken up and 2nd position is wrong for digit 2. It has no place to go and must be incorrect.
- Digit 5 is the third correct digit and in 2nd position.
Code to open the number lock is 1 5 3.
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 expert logical reasoning with no loophole.
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