Problem of the Week 821

Playing with Matches

A matchstick graph is a set of unit-length sticks in the plane, with the proviso that two sticks may meet only at their endpoints. The points that are matchstick-ends are called the vertices of the graph. For example, an equilateral triangle with unit side-length is a matchstick graph with 3 vertices in which each vertex is connected to two others. Find a matchstick graph in which each vertex is connected to exactly three other vertices. Try to minimize the number of vertices.

© Copyright 1996 Stan Wagon. Reproduced with permission.

The Math Forum

2 October 1998