Glue each pair of opposite sides together, as shown to the right. Now there are more ways to get three in a row!

(Try other gluings, too!) O wins in this torus

tic-tac-toe game.

Do you recall the Flatlanders' line of sight in the torus? We can use this to make torus tic-tac-toe easier to play. Put your real move in the middle board below. Then copy that move to the other boards. Whenever three X's or O's line up on any combination of boards, you win!

To make a line-of-sight board for surfaces with other gluings:

1) Make a board on a square and glue opposite sides together. (See

picture 1.) Copy the board through the paper.

2) Cut out the square and make 8 more copies.

3) Put copies around the board so that only the sides with the same

number of arrows touch, and on these sides, the arrows face the

same direction. (Flip the copy if needed) (See picture 2.)

4) Repeat step 3 until there are 9 boards connected in the shape of

a square, like the board to the right.

5) When playing, put your real move on the center board and copy

this move to all the squares numbered the same as the one you

moved in.

(1) (2)

Two copies joined to the original board, as in step 3. Note that in picture 2, the upper right copy had to be flipped.