User:Vampire Library

I'm not certain of the origins of this puzzle.

Puzzle

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

We can translate the rules of the game to that of Tic Tac Toe on a 3x3 magic square (i.e. each row, column and diagonal sums to 15). Since there is no winning strategy in Tic Tac Toe neither is there for this game.