There are 25 mechanical horses and a single racetrack. Each horse completes the track in a pre-programmed time, and the horses all have different finishing times, unknown to you. You can race 5 horses at a time. After a race is over, you get a printout with the order the horses finished, but not the finishing times of the horses. What is the minimum number of races you need to identify the fastest 3 horses?

I was suggested this puzzle via email by Terry Stickels. This is also a popular interview question at tech companies like Google. See a list of all sources in my blog post for this video:
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