Paradox Day, which happens on a random day during the year such that it is unexpected which day it is, except of course it couldn't happen December 31st because we'd know by December 30th that it'd have to happen the next day, so it couldn't happen December 30th by the same logic, and so on until January 1st, so logically the holiday couldn't happen, except it ends up happening anyway on say March 4th and is a total surprise.

Cake will both be provided and not provided.