Players take turns drawing an edge between points on a square grid of dots. Every time a player completes a square, that player marks the square and goes again. Whoever has marked the most squares at the end wins...

Ex: In the above game the players took turns moving, and player 2 was able to make a box. As a result, player 2 gets to move again.

Variation: 'Glue' opposite edges of the board together (see game boards). How does this affect the game?

Game Board 1:

Dots on part of a plane.

Game Board 2: Dots on an `annulus' (a cylinder).

The sides with arrows are glued so that if one moves through a vertical side then one returns at the same height on the opposite side.

Game Board 3: Dots on a `Möbius Strip'.

The vertical sides are glued with a flip so that if one goes through a glued side a certain distance from the bottom, then one comes out on the opposite side the same distance from the top! For instance, you could connect dot A to dot B by moving through the glued sides with a horizontal line segment. Whenever a surface has two sides glued this way, it is called nonorientable.

More Variations: Play some games where dots are placed on the glued sides. Play some games where each pair of opposite sides are glued together. How do these variations alter game play?