Fifteen: Difference between revisions
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Created page with "==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..." |
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{{Hint| Try to reinterpret the game as taking place on a 3x3 grid.}} | {{Hint| Try to reinterpret the game as taking place on a 3x3 grid.}} | ||
{{Answer| No. At most he can guarantee a draw.}} | {{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 | {{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.}} | ||
==See also== | ==See also== | ||
[[Category:Game theory]] | [[Category:Game theory]] | ||
Revision as of 18:12, 6 November 2010
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
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.