Unlock the Locks

Logic Level 3

A thief has five keys, each of which unlocks one of five chests. The thief does not know which key unlocks which chest, and has to try until he finds a pair that works.

What is the minimum number of key-chest tries that he needs to unlock all the chests?


The answer is 15.

Kushal Bose by Kushal Bose , 28, India

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1 solution

Nikolas Кraj
May 18, 2019
  • First I claim that this problem has to define in the Worst case scenario of minimum tries. Because best case scenario is five ( with probability 1 5 ! \frac{1}{5!} )
  • The worst case is trying for the first key into the n n -th number of keys ( n = 5 n=5 in here ). After the first step, one chest is unlocked, four tries with another key.
  • For second key there should be in worst case scenario 4 tries since ( n = 4 n=4 locks in here ). . . . And it goes ( the nr of tries ) in this pattern : : 5 + 4 + 3 + 2 + 1 5+4+3+2+1 = 15 f i n fin
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