2

Part of 1967 Kurschak Competition

Problems(1)

convex n-gon is divided into triangles by diagonal

Source: 1967 Hungary - Kürschák Competition p2

n

-gon is divided into triangles by diagonals which do not intersect except at vertices of the n-gon. Each vertex belongs to an odd number of triangles. Show that

n

must be a multiple of

3

combinatoricscombinatorial geometry