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ISRO Mech 2016: Mathematics

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In the best case: will need N-1 tries.
In the worst case:
1st lock will need = N-1 tries [i.e. last no. of key not need to compare ]
2nd will need= N-2 tries
.
.
.
(N-1)th locks need = 

So, total tries  = N-1+N-2 +N-3 + ..... 1
                           =∑N−1n=1n∑n=1N−1n
                            = (N−1)N/2(N−1)N/2

so (20 *19)/2= 190

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