Every Saturday the Wall Street Journal includes a couple of challenging (for most people) math problems supplied by the National Museum of Mathematics. On May 6-7, 2017, the problems were about horse racing in conjunction with the Kentucky Derby and Triple Crown. The problems make some unrealistic assumptions, but are nonetheless challenging.
I have posted the answers as a comment (so you won’t inadvertently glance at them).
Problem 1:
“Some team members are watching a different race to get in the mood for the Derby, and because of late scratches there are only four horses running. The odds on the horses are listed at 5-1, 4-1, 3-1, and 2-1. One team member exclaims, ‘If only we were at the track, we could guarantee that we would make money on this race.’
What is the total amount of money you could bet on this race (possibly different amounts on different horses) so that you would end up with a net gain of exactly $3 no matter how the race turns out? (Assume that there is a single valid winning horse and ignore payoffs except for the winner.)”
Problem 2:
“A stable has 16 horses and wants to select the three fastest. There’s only room on the practice track to race four horses at a time, and the track has no timer, so the only information from each race is the order in which the horses finish. (Assume for simplicity that each horse runs the track in exactly the same amount of time in each race, and that no two horses run the course in exactly the same amount of time.)
What is the smallest number of races the stable can run on the practice track to determine the three fastest horses?”
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Problems were published in the Wall Street Journal, May 6-7, 2017, on page C13.
Problem 1 answer is $57
Problem 2 answer is at least six races.
Here is a link explaining the solutions.
http://momath.org/home/varsity-math/varsity-math-week-87/