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Two friends, Sam and Lloyd, play the following game: each boy, on their turn, removes a number from 1,...,9 without replacement. The winner of the game is the one who first obtains 3 numbers that sum to 15. Does Sam have a winning strategy assuming he goes first? | Two friends, Sam and Lloyd, play the following game: each boy, on their turn, removes a number from 1,...,9 without replacement. The winner of the game is the one who first obtains 3 numbers that sum to 15. Does Sam have a winning strategy assuming he goes first? | ||
Revision as of 17:37, 7 November 2010
Two friends, Sam and Lloyd, play the following game: each boy, on their turn, removes a number from 1,...,9 without replacement. The winner of the game is the one who first obtains 3 numbers that sum to 15. Does Sam have a winning strategy assuming he goes first?
Help
Hint
Try to reinterpret the game as taking place on a 3x3 grid.
Answer
No. At most he can guarantee a draw.
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.