Puzzle | (Round table coin game)

Suppose two player, player A and player B have the infinite number of coins. Now they are sitting near a perfectly round table and going to play a game. The game is, in each turn, a player will put one coin anywhere on the table (not on the top of coin already placed on the table, but on the surface of the table). And the player who places the last coin on the table will win the game. Given player A will always move first suggest a strategy such that player A will always win, no matter how player B will play.

Solution:
On the first move place the coin on the center of the table. Then player B will place his coin anywhere on the table. Now, you put your coin on the line of diameter passing through the coin placed by player B, at the same distance away from the boundary of the circle (i.e mimic his placement on the opposite side of the table). Refer figure for better understanding. If player A has space to place a coin, so will player B. Player B will run out of place before player A.

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