Fifteen

Puzzle

Two friends, Sam and Lloyd, play the following game with nine ping-pong balls, numbered 1 to 9. Each boy, on their turn, takes a ball (without replacement). The winner of the game is the first one to obtain 3 balls that sum to 15. Does either player have a winning strategy in this game?

Help

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Hint

Try to reinterpret the game as taking place on a 3x3 grid.

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Answer

No. At best Sam (going first) can guarantee a draw.

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Solution

This game is actually "equivalent" to Tic Tac Toe on a 3x3 magic square (i.e. each row, column and diagonal sums to 15). Since there is no winning strategy for Tic Tac Toe neither is there for this game.