Round Table Coin Game

Here is an old puzzle that I have used in my classes for years. Puzzle. Two people take turns placing quarters on a round table so that the quarters fit on the table and no two quarters overlap. The person who can’t move loses. Who has a winning strategy? It is easy to see that the first player always wins by using the symmetry of the table. On the first move, the first player puts the first coin directly in the center of the table. For each subsequent move, the first player places a coin in the spot that is centrally symmetric to where the coin was placed on the previous move. This year, something unusual happened. It seems I have a couple of true mathematicians among my STEP students. They added the following detail. The first player wins, except when the table is smaller than the quarter. Share: