Alice: Take a look at that bullet-riddled stop sign. There are 16 bullet holes in it and they are arranged so that any triangle whose vertices are three of the vertices of the octagon contains a hole in its interior.

Bob: Very observant! But surely that could be achieved with fewer than 16 bullets.

Help our duo out by finding the smallest number of points in the interior of a regular octagon so that each triangle has one in its interior.