ABSTRACT
One of the mysteries of Hex is that there exists a winning strategy for the first player, even though — except for smaller boards — a particular winning strategy is not known. The proof that the first player wins Hex assumes that the second player can steal the first player’s strategy. The common room in Fine Hall was where graduate students in the Princeton Mathematics Department gathered to relax and play games, such as Go and Kriegspiel. On the filled Hex board, draw a line segment along each cell edge that separates stones of different colour. That three cells coloured black, white, red must meet in the case follows — without needing the continuous path argument — from a property known as Sperner’s Simplex Lemma. In fact, the statement that a full Hex board has either a black path joining the black sides or a white path joining the white sides is equivalent to the two-dimensional case of this lemma.
