Whoa, I forgot this question was in my inbox. My bad.
Well, every patient you see is a puzzle. The puzzles range from 10 piece kiddie puzzles to 1000 piece 3D jigsaws. Some don’t require much thought, while others can be very challenging.

Many patients will have something about their case that makes you go “hmm”. It may be something like “what drug did they overdose with,” “why is their sodium 124,” “what’s causing that weird feeling I get when I talk to the family,” “they’re allergic to every antibiotic I want to give them” or “is this appendicitis or something ovarian”.
In the hospital, I’d say that maybe 1 in 40 patients is a real head scratcher. In an outpatient setting, it’s less. But almost all patients have some element of mystery. Also, every patient is different, so patient X with electrolyte imbalances may be handled very differently than patient Y with the same thing. That’s where your intellectual challenge comes in to play.

Regardless of your specialty, you’ll get challenging cases. You don’t have to be double boarded in nephrology and infectious disease (which is totally random, btw) like House to get good cases.