I've really enjoyed watching people noodle on the probability puzzle I posted earlier. One of the things I like about it is that even for mathematically literate people, the answer that they find intuitively is usually wrong. Mine was. I've seen a lot of really smart people get this one wrong, though they usually get to the right answer eventually.
If you want to noodle on it yourself, but are finding it too hard, here's a non-spoiler hint. It's not really a 52-card problem-- it's a 5-card problem. Think about it with a deck that contains five cards-- four aces and the two of clubs-- and it starts to look easier to solve.