My personal favorite, was when, after I had apparently survived a 4-hour interviewing + whiteboarding stint, and thought I'd be able to head out onto the street (as it was already quite late in the day)....

...a math PhD told me "hey, I got one more ya..." and proceeded to give me a mis-articulated mathematical search problem which -- going by his own statement of the problem, ended up having as its "solution" -- an empty class.