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Quarters on a Table

Consider a two-player game played on a circular table of unspecified diameter.

Each player has an infinite supply of coins, and take turns placing a coin on the table such that it is completely on the table and does not overlap with any other coins already played.

A player wins if he makes the last legal move.

Which player (if any) has a strategy that will guarantee a win? Assume that the diameter of the table is greater than the diameter of the coin.

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