My friend Mickey asked me to play the following game with him.
The number $1$ is written on the whiteboard. Me and Mickey take turns to do the following, starting with me.
If the number written on the board is $n$, then replace it by $n+d\le2019$ where $d|n$. The player who can not replace the number written on the whiteboard losses.
But I always lose. Actually, does Mickey has a winning strategy?
Any help is appreciated!