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.
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.