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From the people behind the Alan Turing Cryptography Competition.
You are reading the website of the 2018 edition of the MathsBombe, which ended on Saturday 28th April at 11:59 pm
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Puzzle 3.

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?

Your answer:
No answers can currently be submitted as the competition is closed.
MathsBombe 2017 is organised by the The School of Mathematics at the University of Manchester.
Contact us via mathsbombe@manchester.ac.uk with any queries.