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 by Amanda)

I was thinking along the same line as Amanda. Here is what I came up with:

First of all, the question asks whether the ant will reach the end, the answer to this is yes. Most of the people are trying to prove whether the ant will ever "pass" the end, the answer is no.

To further explain this, let us assume two things:

1. That on his front leg, the ant has two fingers, one is longer than the other, though the difference is inifitesimal.

2. At the end of the rubber band, there is a small indent, which the ant puts his foot (with fingers) on.

Now at the end of the first 1000th second, the ant touches the indent with his larger finger (meaning reaches the end point), but at that exact instance, and before his second finger touches the indent, the band expands by another meter, meaning that the ant could not pass end.

Do I make any sense?

Posted by Javed Iqbal on 2003-02-17 04:54:24