IT-CESENATICO 2006 Problem 6

Alberto and Barbara play the following game. Initially, there are some piles of coins on a table. Each player in turn, starting with Albert, performs one of the two following ways:

1. take a coin from an arbitrary pile;
2. select a pile and divide it into two non-empty piles. The winner is the player who removes the last coin on the table. Determine which player has a winning strategy with respect to the initial state.