Board game

[farlap]

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.

[richard1234]

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

[farlap]

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

[richard1234]

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?