The qualification round was easier than I expected. It's probably just meant to filter out the curious. I was able to do both problems in about 30 minutes, and qualified to the next phase.
Tupper's Self-Referential Formula
... seems to be making the rounds on the internet. Two different people sent me the link. It's cute, but there's nothing magical about it, really - perhaps if some people look at it as a simple Perl script they'll realize that it's just a way to rasterize the big number, and the bitmap could be anything.