# IMO 2011 (Problem 2)

Let $\mathcal{S}$ be a finite set of at least two points in the plane. Assume that no three points of $\mathcal{S}$ are collinear. A windmill is a process that starts with a line $l$ going through a single point $P \in\mathcal{S}$. The line rotates clockwise about the pivot $P$ until the first time that the line meets some other point belonging to $\mathcal{S}$. This point, $Q$, takes over as the new pivot, and the line now rotates clockwise about $Q$, until it next meets a point of $\mathcal{S}$. This process continues indefinitely.
Show that we can choose a point $P$ in $\mathcal{S}$ and a line going through $P$ such that the resulting windmill uses each point of S as a pivot infinitely many times.