MathDB

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.

Problem Statement