There are 2009 boxes numbered from 1 to 2009, some of which contain stones. Two players, A and B, play alternately, starting with A. A move consists in selecting a non-empty box i, taking one or more stones from that box and putting them in box i \plus{} 1. If i \equal{} 2009, the selected stones are eliminated. The player who removes the last stone wins
a) If there are 2009 stones in the box 2 and the others are empty, find a winning strategy for either player.
b) If there is exactly one stone in each box, find a winning strategy for either player. combinatorics proposedcombinatorics