Problem of the Week 1142

It's a Horse Race

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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. What is the smallest number of races needed to determine the three fastest horses, in order?

Source: Suggested by Stephen Morris (Newbury, England), who heard that it was a puzzle used in job interviews at Facebook.

© Copyright 2011 Stan Wagon. Reproduced with permission.