[tierack]

In a slight twist, and one that may only work for small classes of highly motivated students, I took a set theory class where the professor would sneak an impossible question into the homework. He warned us during the very first class that he would do that occasionally.

So every few weeks, the four of us in the class would spend days trying to prove the continuum hypothesis or something, and going over the homework, he'd get to the question and ask casually if anyone solved it. We'd all say no and he'd tell us no one could, and show us proof. But we all learned a hell of a lot trying. Sometimes an avenue we tried ended up proving something interesting on the way, and it sharpened our thinking.

Of course, we also got into the habit trying to prove something was provable before we started (which turned out helpful when, at the end of the year, we collectively recreated [with help] much of the groundwork for Gödel's big theorems).