Here is yet another (unoriginal) game of mine played on a square grid.

(It takes some explaining, but is actually pretty simple. It seems,

perhaps, like it would be fun to play.)

You start with an n-by-n grid drawn on paper. (I suggest n be at least

6,

but not huge {at least for beginners}.)

The game is for 2 players.

Definition: If a square of the grid has a line-segment drawn from it

or to it, the square is "taken". Otherwise it is "untaken".

The first move is from the upper-left square of the grid.

The players take turns alternately drawing segments (vertical or

horizontal, from the center of a square to the center of an adjacent

square).

Players draw each segment from any taken square to any adjacent

(up/down/left/right) untaken square.

(On the first move, however, the segment starts in the upper-left

square.)

Each player must draw their segment from the last taken square (taken

in

the previous move by the player's opponent) IF possible.

(ie. if possible: if there is an untaken square adjacent to the last

taken square)

When a square is taken, and this square has no adjacent untaken

squares,

the player who took the square must put an X in this square.

(The X's correspond to the dead-end's of a maze whose passageways are

the lines

of the completed game.)

(By the way, the upper-left square does *not* have an X in it.)

After an X is drawn, the next player may draw his/her segment from any

taken square on the grid to any adjacent untaken square.

After each square is taken, which is a total of {n^2 -1} segments

being

drawn, the game is over.

(With a large grid especially, perhaps someone should keep track of

how

many moves are made so as to ensure all squares are eventually taken.)

Player 1 (first player to move) wins if there is an ODD number of X's.

Player 2 wins if there are an EVEN number of X's.

--

When the game is complete, if you or your computer (if game played on

computer) were to take a grid and erase the unit-walls (unit-wall =

wall along one square) which correspond with those crossed in the game

by segments, and then erase a

unit wall in the upper-left and a unit-wall in the lower-right, you

would have a maze.

Thanks,

Leroy Quet

## Thursday, September 18, 2008

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