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?
The first player to make his move has a strategy that will assure him victory.
As his first move, he should set his coin at the very center of the table. For each subsequent move, he should place his coin exactly opposite of where his opponent set the coin last, picking a spot diametrically opposite to his opponent's. This way, the pattern of coins on the table will always be symmetrical with respect to the center, and therefore any spot the second player chooses will have a corresponding empty spot of the same size on the other side of the table.
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