This game is played by two players at a round table. They each take turns placing identical coins onto the table's surface. No two coins can overlap, and the entirety of the coin's surface must rest on the table. The loser of the game is the first person who is unable to put down a coin because there is no more room.
Which of the players has a winning strategy? What is it?
Mouse over for a hint:
There's no need to play the center first; you can actually start anywhere. Then, whenever the other player makes his move, play symmetrically, and if that can't be done, play the center.