# Hint to Puzzle #59: 25 Horses, Find the Fastest 3

59. You have 25 horses, you want to pick the fastest 3 horses out of those 25. In each race, only 5 horses can run at the same time. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?
The first stage is probably obvious, we races 5 groups of 5. Let's label them by the following scheme, that is all those that are in the first heat will be labelled A followed by a number representing where they came in their heat. So B3 came third in the second race, for example.
 Race A B C D E Position 1st A1 B1 C1 D1 E1 2nd A2 B2 C2 D2 E2 3rd A3 B3 C3 D3 E3 4th A4 B4 C4 D4 E4 5th A5 B5 C5 D5 E5

Think how we've eliminated the every horse that finished below 3rd in it's own race what else we can eliminate, what else can we race?

It's significant to realise that in a knockout tournament the runner-up isn't necessarily the second best, the second best could have met the best in an earlier round and been eliminated.

Where next?

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