Question 81
A three-digit natural number $n$ is initially written on the board. Two players, $A$ and $B$, take turns, with $A$ going first. The player whose turn it is reduces the number on the board by one of its proper divisors (i.e., a divisor other than $1$ and the number itself). For example, if at some point the number on the board is $6$, it can be reduced by $2$, and then the number on the board will be $4$. Whoever cannot make a move loses, and the other wins. It is known that player $A$ has a winning strategy no matter how player $B$ plays. What are all the possible $n$?
(Ivaylo Kortezov)
(Ivaylo Kortezov)