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Meeting the average

Apparently there was once a Red Bull sponsored mountain biking race with one stipulation: “The winner will be the rider with the time closest to the average of all the participants—hence their unwillingness either to speed up or slow down.” (Source) What’s the best approach to this race, and is there a good way to trick yourself into a win?

I’m not great at this sort of probability math. I’m not even sure if that’s what it’s called. But suppose for simplicity’s sake that it was a footrace between three people. All three cross the finish line, making the person with the middle speed automatically win. The first and the final racers are the outliers just by definition. In order to win, I would have to trick one into crossing the finish line first. Maybe by making him think that the third racer was ahead of him, and he was second. It would be doable, anyway.

Once we add two more people, though, it gets nasty. Assuming we all have similar speeds, I would need to be in the middle again. But if one person in the front or the far back is separated from the rest, the prize goes to someone between the center person and the speeder/slacker. However, everyone knows this, and will therefore keep in a group, hovering just ahead of the slowest person. To win, I need to control the fastest person, letting him sprint ahead so that I can pick the right spot. I feel like there should be a better way.

Add five more people. Or a hundred. It gets tougher and tougher, and I really wouldn’t know how to win. It would still be fun to do, though. I should try to arrange a footrace for my friends…


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