Konane is a board game which can be played with black and white stones on the squares of a rectangular board of any size. This game, also known as Hawaiian checkers, was popular among ancient Hawaiians, who often played it on 18x18 boards. Initially, the board is filled with stones in a checkerboard pattern, white and black each occupying alternate diagonals. Initially two stones, one of each color, are removed from an adjacent pair of locations in the center or as near to the center of the board as possible. Then play begins. Each player, at his turn, must jump an adjacent opposing stone either horizontally or vertically, in either direction. The jumped piece is removed from the board. A multiple-jump on the same turn is permitted if in a straight line, but prohibited if it would turn a 90 degree corner. The number of stones on the board decreases until eventually the game ends when someone has no legal move, and that player then loses.
"Playing Konane mathematically: A combinatorial game-theoretic analysis" by Michael D. Ernst. UMAP Journal, 16:2, Spring 1995, 95-121