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Diagonals of a 2002-gon

Source: Tournament of Towns, Fall 2002, Junior O Level, P1

May 15, 2014
geometry proposedgeometry

Problem Statement

In a convex 2002-gon2002\text{-gon} several diagonals are drawn so that they do not intersect inside the polygon. As a result the polygon splits into 20002000 triangles. Isit possible that exactly 10001000 triangles have diagonals for all their three sides?
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