## Connected Pentagon

#### Problem

How many triangles are in a fully connected pentagon?

#### Solution

By rotational symmetry, all triangles below exist in exactly five other positions.

Making a total of 7 5 = 35 triangles in the diagram.

What about a fully connected hexagon?

Can you generalise for n-gons?

Problem ID: 177 (Oct 2004) Difficulty: 1 Star