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Find Top 3 Fastest Horses

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Your question is Find Top 3 Fastest Horses. Take a moment with it on the right.

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Problem

You have 25 horses, and you need to find the top three fastest ones. You can organize races, but only 5 horses at most can participate in each race, and your stopwatch can only take the fastest time for each race (the rest of the finishing times are discarded). How many races will it take to retrieve the top 3 fastest horses out of the 25 total with these constraints?