by Danny Roth
Published August 19 2018 (link)
We’ve all heard of Heligoland but George and Martha are on holiday in Polygoland. This is an island and when it was first inhabited, the authorities created as many national parks as possible subject to the restriction that each such park will be a regular polygon with the angle between each side being an integral number of degrees, and all the parks have different numbers of sides. Walking along the border between two such parks, Martha commented that the angle (A) of one of them was an exact multiple of the number of sides (S) in the other. George mentioned that the multiple was equal to the number of parks on the island.
What are A and S?