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Problem of the Week 964

A Bullet-Riddled Stop Sign Riddle

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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.

Source: The American Mathematical Monthly (#10936 by A Lukacs and A Szilard)