There are 4 keys and 4 locks. What is the maximum total number of unlocking attempts you need to try so as to be guaranteed to have matched all 4 keys to their locks?
A. 4
B. 6
C. 10
D. 16
Do you need a hint? Read on...
The question is asking what is the 'maximum' number of attempts you need before you have matched all keys with their locks.
Two things; firstly, try and act out the scenario where you are as unlucky as possible in randomly matching keys to locks. But secondly, notice that if you've tried all the keys but one on a lock and they've all failed, you don't have to try the last key because you know it must be the one.
Happy unlocking!
ANSWER
Think about the unluckiest you can be in trying keys and locks. Pick up the first lock. The worst case scenario is that the first 3 keys you try all fail on the lock. If you unsuccessfully try 3 keys on the first lock, you will know that the fourth key is a match. So you don't need to try that fourth key, you only need a maximum of 3 attempts. Once you've matched that key to its lock, you have 3 locks and 3 keys left. So, the second lock needs a maximum of 2 tries, and the third only needs one. Once you've matched the first 3 locks to their keys, the remaining key obviously goes in the last lock. So there are, at most 3 + 2 + 1 = 6 tries needed to match all 4 locks to their key.
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