TacTix was invented by Piet Hein, a Danish poet who was also well known for dabbling in mathematics and science. The game is played in its misere form because the strategies listed above render the non-misere variant trivial. According to Martin Gardner, the board size most commonly played at the time he authored his article is 6x6, because it "is small enough to keep the game from being long and tiresome, yet complex enough to make for an exciting, unpredictable game." (Gardner 160)
The board is an NxN grid of squares.
The pieces are usually circles but they can be anything as long as you can pick it off the board. N^2 pieces are needed to play a game.
To move: The player removes as many pieces lying adjacently in a row or column as he or she wants. At least one piece must be removed.
To win: To force the opponent to remove the last piece from the board.
Set up the board so every square on the board is covered by a piece. The first player may then take as many pieces as they want off the board, provided that they are adjacent to each other and all lie in the same row or column. Players alternate doing this until the last piece is removed, in which case a winner is determined.
- First Player If N Is Odd (non-misere): Take the center piece. Now copy every move your opponent makes symmetrically. Eventually you will take the last piece and win.
- Second Player If N Is Even (non-misere): Copy your opponent's moves symmetrically. You will eventually take the last piece and win.
- Board Size: This game can be played with almost any value of N.
- Non-Misere: What is normally considered the misere variant is actually the standard for this game. Therefore the rule for non-misere is the player to remove the last piece from the board is the winner.
Bulo (in Denmark)
Sometimes Referred To As 2 Dimensional Nim.
"TacTix." MazeWorks. 11 Mar 2006. http://www.mazeworks.com/tactix/index.htm
Gardner, Martin. "Nim and TacTix." Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games. Chicago: University of Chicago Press, 1988. 151-162.