An informal geometric statement of the theorem is that for any positive integers "n" and "c" there is a number "H" such that if the cells of a "H"-dimensional "n"×"n"×"n"×...×"n" cube are colored with "c" colors, there must be one row, column, or certain diagonal (more details below) of length "n" all of whose cells are the same color. In other words, the higher-dimensional, multi-player, "n"-in-a-row generalization of a game of tic-tac-toe cannot end in a draw, no matter how large "n" is, no matter how many people "c" are playing, and no matter which player plays each turn, provided only that it is played on a board of sufficiently high dimension "H". By a standard strategy stealing argument, one can thus conclude that if two players alternate, then the first player has a winning strategy when "H" is sufficiently large, though no practical algorithm for obtaining this strategy is known.