You receive 15 applications for a place in a mathematics competition and plan to interview all 15 candidates in a random order. Since your time is limited you have decided to use the following strategy for the interview: Reject the first \(k-1\) candidates and then accept the first of the following candidates who is better than all those previously interviewed. If no such candidate appears then select the last candidate. Once a candidate is accepted no further interviews take place.

What is the optimal number \(k\) for which you have the highest probability of selecting the best candidate?

Mathsbombe Competition 2018 is organised by the The Department of Mathematics at The University of Manchester.
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