In this incredibly geeky Numberphile video, Dr. Hannah Fry discusses various issues inherent in typical Secret Santa implementations. If you're not familiar with Secret Santa, it's a custom in which people within a group (say, an office) anonymously buy gifts for other members of the group. Fry says:

"I think there are two fundamental things that you need for a perfect Secret Santa. One, total anonymity. And two, everyone should have an equal probability of being selected by anybody else. ... The normal way you do this—everybody writing their name down and picking it from a hat—fails on both counts."

Where it gets interesting is her suggestion for how to make it work better. Tune in and geek out:

(Incidentally, the comments on this YouTube video are amusing. Lots of people discuss their own computer-based approaches for the same problem, while others take issue with Dr. Fry's characterization of a Klein bottle as a poor choice for a gift.)