Lock key is 042
Explanation:
- Step 1: Through each clue, eliminate numbers to find the lock.
738 - all digits are wrong
⇒ the numbers are not 7, 3 or 8
380 - one digit is right but in the wrong place
⇒ since 3 and 8 are wrong digits, 0 is the right digit but place is wrong
682 - one digit is right and in its place
⇒ since 8 is a wrong number, the right digit could be 6 or 2
614 - one digit is right but in the wrong place
⇒ since 6 was in the same position in the previous clue, it can be concluded that 6 is also wrong.
206 - two digits are right but are in the wrong place
⇒ from the above clues 0 and 2 are the right digits.
∴ 0, 2 and 4 are the right digits.
- Step 2: Find the positions of the digits.
0 can't be in 2nd or 3rd position based on the clues.
2 should be in the 3rd position.
⇒ Order is 042