I noticed something in a recent episode. There was a puzzle like the "15 puzzle"; they mentioned that mathematicians proved that it cannot be solved if the last two letters are exchanged. That is correct, and that was the case there. However, that doesn't apply if there are duplicated letters; in that case it is solvable. I do not know whether or not the author considered that. They did mention that you can get out if you are very clever; I do not know if it was intended to be solvable or not.