Chris and Michael play a game on a $5 \times 5$ board, initially containing some black and white counters as shown below: Chris begins by removing any black counter, and sliding a white counter from an adjacent square onto the empty square. From that point on, the players take turns. Michael slides a black counter onto an adjacent empty square, and Chris does the same with white counters (no more counters are removed). If a player has no legal move, then he loses. (a) Show that, even if Chris and Michael play cooperatively, the game will come to an end. (b) Which player has a winning strategy?