Samuel Hansen’s Strongly Connected Components podcast features interviews with all kinds of mathematical luminaries (that sounds familiar!) If you’ve been missing the Math Factor, be sure to check it out!

Here, we discuss, well, Chaim Goodman-Strauss—the tables are turned!

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25 horses have entered your race meeting.  You have to award ribbons to the three fastest, in order.

Only five horses can compete in one race.  

Assuming each horse always runs at the same pace, and that all 25 horses have different abilities, what is the fewest number of races you can use?

You can’t use stopwatches, you can only use the finishing order of each race.

UPDATE: Thanks for all the great comments.  At the time of writing we’ve had three correct answers; Mike and Blaise in the comments and Jim via email.

I have a follow up question: can you prove that this answer is minimal?  There is a neat spot, can you find it?

Apparantly this was an interview question for Facebook.  I found it in this list of impossible interview questions.  Math Factor afficionados will recognise some of these problems and not find them so impossible.  Have fun!
http://skymcelroy.tumblr.com/post/6244020081/impossible-interview-questions-from-facebook-goldman