Brain Teasers

Expert brain teasers aren't just hard — they're counterintuitive. The correct answer feels wrong even after you've seen the proof. Monty Hall is the poster child: switching doors gives you 2/3 odds, not 1/2, and it takes most people a simulation (or a lot of arguing) to accept it.

The key at this level is to distrust your gut completely. Set up the problem formally — probability trees, explicit counting, whatever framework forces you to be precise. Intuition fails on these by design. The math doesn't.