1999 JBMO Problems/Problem 3
Let be a square with the side length 20 and let be the set of points formed with the vertices of and another 1999 points lying inside . Prove that there exists a triangle with vertices in and with area at most equal with .
Triangulate into triangles with vertices being the vertices of and the members of . There are triangles thusly formed, so by the pigeonhole principle, at least one of the holes has to have area at most , and we are done.
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