TacTix
History
TacTix was invented by Piet Hein, a Danish poet who was also well known for dabbling in mathematics and science. 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
TacTix is played on an N-row, N-column grid. Most commonly, N=4.
The Pieces
There are N² pieces that cover all spaces of the grid at the start of the game, as shown in the following image:
Rules
To move: On their turn, a player may remove as many pieces as they want as long as the pieces (1) either lie on the same row or lie on the same column and (2) are contiguous.
To win: In non-misere gameplay, a player wins if they remove the last piece(s) from the board, i.e., leave their opponent with no pieces left to remove.
An example sequence of removals is shown in the following animation:
Strategies
- 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.
Variants
- Board Size: TacTix can be played with any value of N.
- Misere: What is normally considered the misere variant is actually the standard for this game. The objective of the misere variant is to force your opponent to remove the last piece(s) from the board.
Alternate Names
Bulo (in Denmark)
2-Dimensional Nim.
References
"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.
GamesCrafters
Dan Garcia (Backend, Solving, Tcl/Tk interface that GamesmanUni GUI is based on)
Cameron Cheung (GamesmanUni GUI)