Puzzle: The horse race problem
A friend of mine from Australia sent me this problem yesterday. It turns out to be a very interesting puzzle. See if you can get it. Feel free to send in your answers or attempts in the Comments section and I will try to respond.
In a horse race, 25 horses show up to win the gold, silver and bronze medals. Unfortunately for the organizers, there are only 5 tracks available – which means you can race only 5 horses at a time. The owners/jockeys agree that their horses will have to run multiple times to decide the first, second and third ranks. You can assume that a horse can run any number of times and always retains the same speed anytime it runs.
Here is the question: What is the minimum number of races you have to have to decide the gold, silver and bronze medalist?