Question 8
Call a natural number *acceptable* if it has at most 9 distinct prime divisors. There is given a pile of $100! = 1 \cdot 2 \cdot \dots \cdot 100$ stones. A legal move is to remove $k$ stones from the pile where $k$ is an *acceptable number*. Players $A$ and $B$ take turns in making legal moves; $A$ goes first. The one who removes the last stone wins. Decide which player has a winning strategy.