This game is for two players, and it involves (as do many of my games)

an n-by-n grid drawn on paper.

First, each player makes a list of n positive integers (where n is

the number of squares along a side of the grid), each integer in the

list being <= n-1. (The order of the integers is significant.) Each

player makes his/her list without knowlege of the other player's list.

Players then write their numbers, in order, along the edges of the

grid.

Player 1 writes her/his integers above the top row of the grid,

exactly

one integer above each square. Player 2 writes his/her integers to the

left of the left-most column of the grid, exactly one integer to the

left of each square.

One of the players plays offense, the other defense. After the round

is

complete, the players switch who is offense and who is defense, using

the same numbers in the same order, but using a new unmarked grid.

To start, player 1 places a "1" in any of the grid's squares.

Players take turns placing integers in the grid. Player 1 places

1,3,5,7,..the odd positive integers, in order, in the grid. Player 2

places 2,4,6,8,... the even positive integers, in order, in the grid.

A player, on move k of the game, places the integer k in any EMPTY

grid

square. He/she places the k directly to the right, to the left, above,

or below the square with (k-1) in it. ((k-1) is in the last number put

in the grid by the other player.)

Let the integer written above the column the integer (k-1) is written

in

be c. Let the integer written to the left of the row (k-1) is written

in

be r.

The player placing the integer k in a square must place that integer

EITHER c or r squares (in any of the 4 main directions) from the

square

the (k-1) is written in.

(The side of the grid that an integer is written next to does not have

anything to do with what direction the k-square is from the (k-1)-

square.)

The players act as if the top and bottom of the grid are connected,

and

act as if the left and right sides of the grid are connected.

(Toroidal

topology.)

So if a move, say, is off the grid to the right, the players acts as

if

the row forms a circle, and continues counting from the left side,

counting to the right.

A move to the left off the grid continues from the right side on the

same

row, continuing to the left. A move upward off the grid continues from

the

bottom of the same column, continuing upward. And a move downward off

the

grid continues from the top of the same column, continuing downward.

And remember. All moves must end up on empty squares.

If a player can move, she/he must.

The round is over when the players can't move anymore.

The offensive player gets a point for every square that has a number

in it.

(Ie the offensive player gets a score equal to the largest number in

any

square of the grid.)

The players switch who is defense and who is offense, as I said above,

with

the same numbers along the edges of the grid, but with a new unmarked

grid.

Highest score wins.

Thanks,

Leroy Quet

## Sunday, September 21, 2008

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