Northcott's game is a two-player game on a rectangular board with one black and one white checker in each row in which the players control opposite colors, alternately move one of their checkers any distance along its row without jumping the opposing checker, and the first player unable to move loses.
Although color ownership makes Northcott's game a partisan game in form, its outcome structure reduces to the impartial game of nim.
Associate to each row a nim-heap whose size is the number of empty squares between its two checkers. A move toward the opposing checker decreases the nim-heap, while a move away increases it. The latter kind of move is reversible and does not change the winning criterion. Consequently a position is losing exactly when the nim-value of the row gaps is zero.
