A given triangle is divided into n triangles in such a way that any line segment which is a side of a tiling triangle is either a side of another tiling triangle or a side of the given triangle. Let s be the total number of sides and v be the total number of vertices of the tiling triangles (counted without multiplicity).
(a) Show that if n is odd then such divisions are possible, but each of them has the same number v of vertices and the same number s of sides. Express v and s as functions of n.
(b) Show that, for n even, no such tiling is possible combinatorial geometryTilingtilingsTrianglecombinatorics