Yes, I can confirm that all the levels in the game are possible!
If you want a hint, let me know what you've figured out so far.
Nevermind, I got it. It really was impossible according to the rules of the game as I understood them. After I realized this, then I concluded that I must be mistaken about the rules in some way.
Very nice! Deducing that can be very difficult. You have to challenge your assumptions one-by-one.