Tsering draws a polygon with 12 sides and then joins every pair of vertices that are not next to each other. How many diagonals does he draw?

Explanation

1. 01

   From each vertex you can draw a diagonal to every vertex except itself and its two neighbours: $12 - 3 = 9$.

2. 02

   12 vertices × 9 counts every diagonal twice, so diagonals = $\frac{12 \times 9}{2} = 54$.