Coins in piles
Source: ITAMO 2006 q6
May 8, 2006
combinatorics proposedcombinatorics
Problem Statement
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.