We present new results on how to play Reverse Hex, also known as Rex, or Misère Hex, on boards. We give new proofs–and strengthened versions–of Lagarias and Sleator’s theorem (for boards, each player can prolong the game until the board is full, so the first/second player can always win if is even/odd) and Evans’s theorem (for even , the acute corner is a winning opening move for the first player). Also, for even , we find another first-player winning opening (adjacent to the acute corner, on the first player’s side), and for odd , and for each first-player opening, we find second-player winning replies. Finally, in response to comments by Martin Gardner, for each , we give a simple winning strategy for the board.
Highlights
► We extend a classic result of Lagarias and Sleator, and also one of Evans. ► For -by- boards, we give new strengthened proofs that each player can prolong the game until the board is full. ► For -by- boards with at least 2, we find a new first-player winning opening. ► In response to a comment of Martin Gardner, we give simple winning strategies on small boards.