Monday, December 13, 2010

One x Twice

For 2 players.
Start with an n-by-n grid drawn on paper.

A move consists of both players each secretly picking an integer between 1 and n.
Both numbers are then revealed. An x is then drawn in the grid-square that has the column number of player 1's number, and has the row number of player 2's number.
So, in other words, player 1 picks the horizontal position of the number, and player 2 picks the vertical position.

If the x lands in an empty square, then the game continues.

But, however, the first time an x lands in a square that already has an x, then the game is over. Player 1 wins if this final x was written on an oddly numbered move. Player 2 wins if this x was written on an evenly numbered move.
So, in other words, if there are an odd number of x's at game's end -- and an even number of squares with x's -- then player 1 wins. If there are an even number of x's -- and an odd number of squares with x's -- then player 2 wins.

What kind of strategies will help you win at this game (if you cannot read the other player's mind)?

Leroy Quet

No comments: