6

Part of 1994 Spain Mathematical Olympiad

Problems(1)

dissecting a convex n-gon is into m triangles

Source: Spanish Mathematical Olympiad 1994 P6

n

-gon is dissected into

m

triangles such that each side of each triangle is either a side of another triangle or a side of the polygon. Prove that

m+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

m

n

combinatoricsconvex polygon