1. 042. Yes, 042 is the key of this lock. How? Please look into the below detailed explanation.

2. Begin with first number. Here one digit is right and well placed and the three digits we are having here is 682. If we take 6 as right digit then it will contradict with second statement where one digit is right but wrongly placed but in first and second statements both the 6 is at same place. So 6 is wrong and we will discard it. Now take 8 as a number but from the fourth statement 738 all the digits are wrong. So we will discard 8 too. Finally from this statement 2 is the correct digit at third place.

3. For the time being skip second statement before this first look into third statement having number 206. Here two digits are right but both are wrongly placed. We already discarded 6 and accepted 2 at third place. Hence other accepted number is 0 which is wrongly placed so the correct position of the 0 is first place. Now, Finally we have two numbers 0 at first place and 2 at third place.

4. Now look into the second statement having number 614. Here one digit is right but wrongly placed. In this number 6 has already been discarded. If we consider 1 as correct number then it will come either at first or third place because of wrongly placed condition but both these places are already filled. Hence we will discard 1 as well. So, our accepted digit is 4 but it is wrongly placed. So, the correct place of 4 is second place. Finally we have all the three digits as 0 at first place, 4 at second place and 2 at third place.

Our number will 042.

Note:- No need to look into last statement having number 380 as it is of no use, just given for confusion.

I hope you understood the problem with the solution. Still if you have any doubt please feel free to reach me through comments section. I will be more than happy to help you further.