a win for m ≥ 30 (Lustenberger, 1967) and a draw for m ≤ 8. It is unknown if (m,4,4) is a win or a draw for 9 ≤ m ≤ 29. Computer search by Wei-Yuan Hsu and Chu-Ling Ko has shown that both (7,7,5) and (8,8,5) are draws, which means that (m,n,5) is a draw for m ≤ 8 and n ≤ 8. Computer search by L. Victor Allis has shown that (15,15,5) is a win, even with one of the restrictive rules of Gomoku. (9,6,6) and (7,7,6) are both draws via pairings. Multidimensional variant It is possible to consider variants played on a multidimensional board instead of a bidimensional board. For the case of k-in-a-row where the board is an n-dimensional hypercube with all edges with length k, Hales and Jewett proved that the game is a draw if k is odd and k ≥ 3n − 1 or if k is even and k ≥ 2n+1 − 2. They conjecture that the game is a draw also when the number of cells is at least twice the number of lines, which happens if and only if 2 kn ≥ (k + 2)n. See also Connect Four Connect6 Gomoku Harary's generalized tictactoe Kaplansky's game Nd game Pente References Abstract strategy games In-a-row games Partially solved games