1.

There are `n`locks and `n`matching keys. If all the locks and keys are to be perfectly matched, find the maximumnumber of trails required to open a lock.

Answer» The maximum number of trials needed for the first key is n. For the second key, it will be n-1.
Now, for the rth key, the maximum number of trials needed is n-r+1. Thus, the required answer is
`n+(n-1)+..+1=(n(n+1))/(2)`


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