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Which player (if any) has a strategy that will guarantee a win?

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

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

asked Sep 30, 2015 by Swanky

1 Answer

The table is circular. we can you use the symmetry of the table to derive the answer. There is always a symmetrical opposite possible for each placement of the coin.

Player 1 has a strategy to win. His first move is to put a quarter in the exact center of the table.
Player 2 then places a quarter anywhere on the table (but not in the center, of course). Now convince yourself that Player 1 always has a legal move: by playing a quarter diametrically opposite from the quarter Player 2 just put down (i.e., Player 1’s first quarter is the midpoint of the line between Player 2’s last quarter and Player 1’s last quarter). We continue until we fill up the table, but since Player 1 always has a legal move, it is only Player 2 that will be faced with no legal move. Then Player 1 wins.

answered Sep 30, 2015 by Gaurav
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