Drawing strategies for generalized tic-tac-toe (p, q)
Diptarama Diptarama, Kazuyuki Narisawa, Ayumi Shinohara · AIP conference proceedings · 2016
GTTT(p, q) is an achievement game for polyominoes, which is an extension of Harary’s generalized tic-tac-toe. Two players alternately put p stones over a board with the exception that the first player Black puts q stones for the first move. The player who first achieves a given polyomino wins the game. Unlike the generalized tic-tac-toe, we define winner for polyomino that Black can achieve, loser that White can achieve, and draw that both players cannot achieve in each GTTT(p, q). In this paper we define three classes of polyominoes for GTTT(p, q) and show that any polyomino that satisfies some conditions for each classes is a draw.