MathDB

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

Problem Statement