Difference between revisions of "2011 IMO Shortlist Problems/C3"
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Latest revision as of 06:44, 28 October 2013
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.
