Fifteen - Revision history

Oscarlevin at 19:10, 18 November 2010

2010-11-18T19:10:33Z

← Older revision		Revision as of 13:10, 18 November 2010
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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~~?		==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 ~~most he~~ can guarantee a draw.}}		{{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]]

Vampire Library at 00:37, 8 November 2010

2010-11-08T00:37:16Z

← Older revision		Revision as of 18:37, 7 November 2010
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	~~==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?		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?

Vampire Library at 01:22, 7 November 2010

2010-11-07T01:22:05Z

← Older revision		Revision as of 19:22, 6 November 2010
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	{{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 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.}}

	~~==See also==~~

	[[Category:Game theory]]		[[Category:Game theory]]

Vampire Library: /* Help */

2010-11-07T01:12:27Z

Help

← Older revision		Revision as of 19:12, 6 November 2010
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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 in 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.}}

	==See also==		==See also==

	[[Category:Game theory]]		[[Category:Game theory]]

Vampire Library: 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..."

2010-11-07T01:02:27Z

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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==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 in Tic Tac Toe neither is there for this game.}}

==See also==

[[Category:Game theory]]