Sprouts

1. Put some dots on a board.

2. Now take turns joining a dot to a dot with a path. No two paths can cross. Note that no dot can have more than three path connections to it. A dot can be joined to itself, but this counts as two path connections to that dot.

3. After a new path is drawn, put a new dot on that path.

4.When one player can no longer make a move, the other player wins.

Here is an example of game play.

(Dots were colored in when they were no longer useable.)

Variation: Draw a polygon with an even number of sides, like the one pictured below. Glue some pairs of opposite sides together (see earlier games). Then play on these new surfaces.

More Variations:

1) Play where each move must cross a glued side.

2) Play with `walls' on the board. A wall is a line which cannot be

Torus Tic-Tac Toe

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.

The Geometry Center Home Page

Author: Daniel Verinder; revised and edited by Michael Huberty
Comments to: webmaster@geom.umn.edu
Created: Jul 22 1995 --- Last modified: Jul 22 1996
Copyright © 1995-1996 The Geometry Center. All rights reserved.