http://www.spoj.com/problems/BOMBER/ I was trying to solve this game theory problem. basically at every step we split a block in 4 sub blocks. It is something like kayle's game, and hence its logic can be used. So we need to compute grundy number for every block of size X*Y. I am not able to think of an efficient method for this problem.

There was another problem. Variant of Nim. In this pile sizes should be in increasing order. In one move a person can either remove an entire pile, or reduce its size maintaining the property that pile sizes are strictly increasing in length. Can we simple consider new set of piles where each pile size is the difference between consequtive pile sizes.

Thanks in advance. Any help is greatly appreciated.