A rubber band is 1 meter long. An ant starts at one end, crawling at 1 millimeter per second. At the end of each second, the rubber band is instantaneously stretched by an additional meter. (So, at the end of the nth second, the rubber band becomes n+1 meters long.)

Does the ant ever reach the far end of the band? If so, when?

(In reply to some math by James D Brown)

You seem to be making the assumption that all the stretching occurs in the portion of the rubber band ahead of the ant. You don't need any math to prove that he'll never reach the end under those conditions Since every second he subtracts 1 mm from the distance he still needs to go but adds 1000 mm, it is obvious that his journey is ever-increasing.

It is when the rubber band stretches evenly, allowing him to claim more distance than he actually walked, that the puzzle becomes interesting.

Posted by TomM on 2002-10-03 19:26:38