New Winning and Losing Positions for 7×7 Hex

In this paper we apply a decomposition method to obtain a new winning strategy for 7x7 Hex. We also show that some positions on the 7x7 Hex board, called trivial positions, are never occupied by Black among all of the strategies in the new solution. In other words, Black can still win the game by using the strategies described in this paper even if White already has pieces placed on those positions at the start of the game. Considering the symmetry properties of a Hex board for both players, we also derive 14 losing positions for Black’s first move on a 7x7 Hex board.