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Two friends, Sam and Lloyd, play the following game | ==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== | ==Help== | ||
{{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 | {{Answer| No. At best Sam (going first) 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.}} | {{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.}} | ||
[[Category:Game theory]] | [[Category:Game theory]] | ||
Current revision as of 12:10, 18 November 2010
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
Hint
Try to reinterpret the game as taking place on a 3x3 grid.
Answer
No. At best Sam (going first) 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.