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MMO 247 Moscow MO 1953 500 points in a convex 1000-gon, triangles

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August 9, 2019
combinatoricscombinatorial geometryTriangles

Problem Statement

Inside a convex 10001000-gon, 500500 points are selected so that no three of the 15001500 points — the ones selected and the vertices of the polygon — lie on the same straight line. This 10001000-gon is then divided into triangles so that all 15001500 points are vertices of the triangles, and so that these triangles have no other vertices. How many triangles will there be?
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