Question 115
Two players, $A$ and $B$, remove alternatively stones from a heap initially containing $n \ge 2$ stones. The first to move is $A$ who takes at least one stone and at most $n-1$ stones. Next, each player to move has to take at least one stone and at most as many stones as his opponent took in his previous move. The winner is the player who takes the last stone. Which player has a winning strategy?