This one is rather a number theory than "real" combinatorical problem. I found it in The Principia Discordia by Malaclypse the Younger.

By the way: When googling for "Malaclypse", I accidentally discovered this page: www.poee.org. But please don't cheat (since POEE have published the entire book on their page).


Situation:
An even number of delegates sits (in any random distribution) around a table. At every seat, there is a reservation card with the name of one delegate on it.

To prove:
It is always possible to rotate the table so that there are at least two delegates who sit opposite to (or in front of, that is equivalent) their respective reservation cards.