Here is a simple game. (Possibly very unoriginal.)

(Do not worry, there is no more math than in Tic-Tac-Toe, and the game

could possibly be understood and enjoyed by children too.)

You start with a grid which is the same number of squares high as

wide.

(I suggest a 5-by-5 grid for beginners.)

The game is for 2 players, each with a different colored pencil

(or one player uses a regular pencil, the other uses a pen).

Players take turns filling in the yet-unfilled squares, one square per

move, as follows:

Player-1 can fill in any yet-unfilled square along the grid's _bottom_

or

_top_ borders, or he/she can fill in any yet-unfilled square

immediately

_above_ or _below_ a square already filled in by her/his opponent,

player-2.

Player-2 can fill in any yet-unfilled square along the grid's _left_

or

_right_ borders, or she/he can fill in any yet-unfilled square

immediately _left of_ or _right of_ a square already filled in by

his/her

opponent, player-1.

The winner is the last player who fills in a square.

Notes (mostly unnecessary):

Players can use the same color pencil/pen too, but one player fills in

the squares with x's, the other fills in the squares with o's (or

with

whatever symbols the players choose).

The corner squares can be filled in by either player.

If there is an even number of squares, player-2 might try to match

player-1's moves (but rotated by 90-degrees), so as to fill in the

grid

completely and be the last to fill in a square. This strategy can be

easily countered, however, by player-1.

I said the winner is the last player who fills in a square, instead of

saying the winner is the last player who is ABLE to fill in a square,

because part of the game is not overlooking any possible moves a

player

can make.

(This is much more of an issue with larger grids.)

In any case, the player who (thinks he/she) cannot move concedes to

the

other player at game's end.

Have fun!

Questions:

1) What are some strategies? Anything certain to win?

2) What is the number of the most pairs of squares filled in by the

same player which can, in theory, be immediately next to each other in

an n-by-n grid?

(Zero is the least number of same-player squares that can possibly be

adjacent. {Squares filled in with checkerboard pattern.})

Thanks,

Leroy Quet

## Thursday, September 18, 2008

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