Exercise 68 Page 13

We need to count the number of rubber bands that can be placed at each vertex of a polygon. This is a practical way of asking about diagonals. One approach to this is to count the number of new rubber bands from each vertex.

Systematically, as we move around the hexagon, from A to F we get one less rubber band to connect to a vertex. This is because the rubber band from the previous vertex is already connected. Let's get our total. 5+4 + 3 + 2 + 1 = 15