# Board game

• Aug 10th 2012, 02:47 PM
farlap
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.
• Aug 10th 2012, 02:58 PM
richard1234
Re: Board game
Your question's a little unclear. Are there 25 counters at the start of the game? 12 or 13 black counters?
• Aug 10th 2012, 03:06 PM
farlap
Re: Board game
Sorry there are 13 black and 12 white counters. The top row is black, white, black, white, black. Each row then alternates.Kindest regards
• Aug 10th 2012, 03:09 PM
richard1234
Re: Board game
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?