A variation of the game of nim is played with three stacks. Two stacks are blue and one is red. Play consists of removing some positive number of counters from one stack, like normal. But the red stack cannot be touched until one of the blue stacks has been depleted.

Find a winning strategy for this nim variant. (The winner is the person to take the last counter.)

Assume a non trivial problem- all quantities bigger than one:

,if b1=b2 and b1 NEQ r- losing situation-let your opponent start
you can lead him thru series of equal blue stacks into one of the 2losing positions:1,1,r  or  0,b=r,r

if b1 NEQ b2 ==>> make them equal by your first move.

Posted by Ady TZIDON on 2009-12-05 03:34:28