Once again it’s time for the International Math Olympiad. As we talked about last year, that’s an international competition for some of the best (high school aged) math problem solvers in the world. It’s like the Putnam, but even more extreme!

As last year, Terence Tao is hosting a mini polymath group. That’s a online group discussion to solve one of the IMO problems. It started yesterday at 2pm Oklahoma time and already has 130+ comments! If you’re interested in joining in, go here. This year’s question is geometric:

**Problem 2.** Let

be a finite set of at least two points in the plane. Assume that no three points of

are collinear. A

*windmill* is a process that starts with a line

going through a single point

. The line rotates clockwise about the pivot

until the first time that the line meets some other point

belonging to

. This point

takes over as the new pivot, and the line now rotates clockwise about

, until it next meets a point of

. This process continues indefinitely.

Show that we can choose a point

in

and a line

going through

such that the resulting windmill uses each point of

as a pivot infinitely many times.

For the full list of IMO questions, go

here.

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