2004 OIM Problems/Problem 6
Problem
For a set of points in the plane, a point in the plane is said to be a "cut point" of if there are four different points and in such that the lines and are different and intersect at . Given a finite set of points in the plane, a sequence of sets is constructed as follows: for any , is the union of with the set of all cut points of . Show that if the union of all the sets of the sequence is a finite set, then for any we have .
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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