|
|
| (3 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| 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| 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]]
| |