Board game

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.

Your question's a little unclear. Are there 25 counters at the start of the game? 12 or 13 black counters?

Sorry there are 13 black and 12 white counters. The top row is black, white, black, white, black. Each row then alternates.Kindest regards

Ah okay. I can't really visualize several moves in (hence my inability to play blind chess). You could try small cases, e.g. 2x2 or 3x3 board and see if it generalizes?