A nd game (or nk game) is a generalization of the game Tic-tac-toe to higher dimensions. It is a game played on a nd hypercube with 2 players. If one player creates a line of length n of their symbol (X or O) they win the game. However, if all nd spaces are filled then the game is a draw. Tic-tac-toe is the game where n equals 3 and d equals 2 (3,2). Qubic is the (4,3) game. The (n>0,0) or (1,1) games are trivially won by the first player as there is only one space (n0=1 and 11=1). The game with d=1, n>1 cannot be won because an opponents piece will block the one-dimensional line.
- "Mathllaneous" (PDF). Retrieved December 16, 2016.
- Beck, József (2008-03-20). Combinatorial Games: Tic-Tac-Toe Theory. Cambridge University Press. ISBN 9780521461009.
- Tichy, Robert F.; Schlickewei, Hans Peter; Schmidt, Klaus D. (2008-07-10). Diophantine Approximation: Festschrift for Wolfgang Schmidt. Springer. ISBN 9783211742808.
- Golomb, Solomon; Hales, Alfred. "Hypercube Tic-Tac-Toe" (PDF). Retrieved December 16, 2016.
- Shih, Davis. "A Scientific Study: k-dimensional Tic-Tac-Toe" (PDF). Retrieved December 16, 2016.
- Epstein, Richard A. (2012-12-28). The Theory of Gambling and Statistical Logic. Academic Press. ISBN 9780123978707.
|This game-related article is a stub. You can help Wikipedia by expanding it.|