Figure this one out Twist (it's a word problem, er... sort of)

I came across the following and some other ineresting things at Famous Problems in the history of Mathematics:

Paradox 1: The Motionless Runner
A runner wants to run a certain
distance - let us say 100 meters - in a finite time. But to reach the 100-meter
mark, the runner must first reach the 50-meter mark, and to reach that, the
runner must first run 25 meters. But to do that, he or she must first run 12.5
meters.
Since space is infinitely divisible, we can repeat these
'requirements' forever. Thus the runner has to reach an infinite number of
'midpoints' in a finite time. This is impossible, so the runner can never reach
his goal. In general, anyone who wants to move from one point to another must
meet these requirements, and so motion is impossible, and what we perceive as
motion is merely an illusion.

Don't think about it too hard or you'll get a nose bleed.