Three-Color Territory Game for Two

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The board is covered with "polysquare" areas, each painted in light blue, light red, or light yellow.


The player Blue plays against the player Red. The players alternate, claiming one polysquare tile per round.

Claiming a polysquare of your own color adds to your points; claiming one of the other player's polysquares reduces your points.

How is claiming done? The player whose turn it is clicks the unclaimed polysquare tile at a board position that is adjacent to a position already claimed by the player (this "adjacent" requirement does not apply to the first move of a player).

For Blue, the value of a light blue polysquare is the square of its land area (or equal to it), hence a pentasquare is worth 25 points (or 5 points, depending on the choice the players agree upon).

For Blue, the value of a light red polysquare is the (negative of the) square of its land area (or equal to it); hence a pentasquare is worth minus 25 points (or minus 5 points).

For Red, the value of a claimed polysquare is opposite to what it would be for Blue.

Yellow tiles have no value.

Click a polysquare to claim it; it is marked in blue (or red) dots. From your second move onward, you can only click next to an already-claimed position.

Your task is to create a sphere of ownership (territory) whose value (shown below the playing board) is larger than your opponent's territory value.


Contributed by: Karl Scherer (January 2016)
Open content licensed under CC BY-NC-SA



To eliminate any advantage for the first player, the players always play two games in a row, such that each of them starts once, using the same board position.

Another option is that after the first move of Blue, the Red player declares "I take over" and swaps places with Blue. That stops Blue from starting with an extremely dominating move.

Since a player can easily get into a position with no next move, a special exceptional move is allowed: the player may drop the next token anywhere on the board.


The game is over when all polysquares on the board (and hence all positions on the board) have been claimed. The player with the most points wins.


Click "challenge" to select the board size (10×10, 15×15, 20×20, and 25×25).

Click "reset" to go back to the beginning.

Click "new" to randomize the setup.

Click "take back" to go back one step (undo the last move).

Click "tile value linear/square" to give each blue area either the value equal to the tile's size or to the square of the tile's size. The value of the yellow areas is always zero.

Below the controls, some numbers are shown on the left: - "area size" (of last clicked area) - "value" (of last clicked area) - total area of blue polysquares remaining - total area of yellow polysquares remaining - total area of red polysquares remaining


There is also a Demonstration, "Three-Color Territory Puzzle", available (solitaire game) from the same author.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.