For those of you who haven't seen it before, I pose the question to you thusly:
A plane is standing on runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in opposite direction). Will the plane be able to take off?
Note to those who've seen this before: this is the question as originally stated, found on the physorg forums in July of 2005 (here). I have fixed the spelling errors and slightly reworded the final line. I do not believe that my changes have substantially changed the meaning of the question.