Nd game

A n^d game (or n^k game) is a generalization of the game Tic-tac-toe to higher dimensions. It is a game played on a n^dhypercube 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 n^d 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.

There are a total of ((n + 2)^d - n^d)/2 winning lines in a n^d game.

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