I have completed this assignment (although it still needs to be rated). I got a distinct feeling that i is not possible to avoid _all_ poles. Especially around the circular areas, you need to have a spot where you cannot avoid a pole.
I have been able to polish away quite a few poles or move them to areas where they are less obvious, such as near a rim or a crease. While doing this assignment I did manage to retopo several poles away that I thought was unavoidable.
For learning purposes, I can definitely recommend trying to retopo them away. I learned a lot about edge flow by doing that. I hope you do too
