two idiots
Me and H. are the complete opposite when it comes to our approach in problem-solving.
I am the conservative. What toolkit of knowledge could I use at the moment to answer a problem? To do so, I strive to religiously read the textbook and notes (whether I retain the information is a different matter). Everything is rigid (euphemism for close-minded). Meanwhile H. is the adventurer. Sometimes I'd wonder if he's read the notes at all. But what I've noticed, in the broadest simplification, he gets things either completely right or completely wrong.
Putting our brains together on a difficult problem, what you'll get is:
"Great. We're now stuck"
"Hmm..." H. might say.
I'd employ all the possible resources and methods I have: deriving from basic principles, imitating the Socratic method, look up the notes, idk (little progress gets made). Then H will come up with something completely outrageous and I, since it completely goes beyond my head, would have to ask him to explain them bit by bit.
To do so, he'll usually draw a sketch. What usually ends up happening is, as we both watch the sketch unfold, H. would realize that the idea was IN FACT outrageous. Acknowledging the absurdity, we'd fall completely silent.
"Soo.... Do you wanna just look at the answer key?"
"Yeah. Sure"