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?
fastest horse and jockey 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?

Where next?
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