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dissecting a convex n-gon is into m triangles

Source: Spanish Mathematical Olympiad 1994 P6

July 31, 2018
combinatoricsconvex polygon

Problem Statement

A convex nn-gon is dissected into mm triangles such that each side of each triangle is either a side of another triangle or a side of the polygon. Prove that m+nm+n is even. Find the number of sides of the triangles inside the square and the number of vertices inside the square in terms of mm and nn.
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