Two people play a board game on a 5 x 5 board, initially containing some black and white counters. These counters are spaced white black white black etc. One player begins by moving any black counter, and sliding a white counter from an adjacent square onto the empty square. From that point on, the players take turns. The other player slides a black counter onto an adjacent empty square, and the other player does the same with white counters (no more counters are removed). If a player has no legal move, then he loses.
Show that if both play co-operatively, the game will come to an end.
Show which player has a winning strategy.