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Problem of the Week 1143

Another Racy Problem

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You are arranging races for 25 horses on a track that can accommodate five horses at a time. Each horse always runs the distance in the same time, and the horses have distinct speeds.

You have no stopwatch, but can make deductions from the finishing order in the races. It is not possible to deduce the top two horses in six races.

Devise an algorithm that will race the horses in six races and select two horses so that, over 84% of the time, those two horses are the fastest two, in order.

Note that the algorithm need not work with certainty: when it finds the top two, it is not expected to provide proof that they are the top two. The algorithm is simply required to find the top two in order at least 84% of the time.

© Copyright 2011 Stan Wagon. Reproduced with permission.

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28 September 2011