I think they care more about a working prototype with a few users. Also, they care a lot about the team. Are you a solo founder?
For an official answer try to send an email to info@ycombinator.com
If you're smart and you have a good idea, I don't see why not.
I only have high school (I haven't needed to pitch an idea yet :)) Don't let that bug you -- if the idea is good, they'll listen.
I think being smart is one of the requirements. Education doesn't necessarily mean you're smarter, but it correlates. Attitude matters a lot though - if you feel like your education level is an obstacle, that could be a negative.
That said, YC loves investing in underdogs, which is why a lot of founders there are young and unusual.