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Find the fastest 3 horses

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You have 25 horses. When they race, each horse runs at a different, constant pace. A horse will always run at the same pace no matter how many times it races.

argaiv1352

You want to figure out which are your 3 fastest horses. You are allowed to race at most 5 horses against each other at a time. You don't have a stopwatch so all you can learn from each race is which order the horses finish in.

What is the least number of races you can conduct to figure out which 3 horses are fastest?

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