TacTix
TacTix is a simple piece-taking game, a kind of "two-dimensional Nim." Two players alternate taking pieces from the board — any number of contiguous pieces in a row or column. Whoever takes the last piece loses. TacTix was invented by Piet Hein, and popularized by Martin Gardner in his February 1958 Mathematical Games column.
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TacTix (at least on the 4×4 board) may have limited appeal as a two-player game, but makes a great family of puzzles. The implementation here will serve you a random position. Should you play first or second? If you reason it out correctly, you'll be able to win. But the computer is unforgiving if you make a mistake.