The Worm and the Rubber Band


I got this problem from Rustan Leino, who got it from Jay Misra.

I solved it and wrote up my solution.


A rubber band (well, a rubber string, really) is 10 meters long. There's a worm that starts at one end and crawls toward the other end, at a speed of 1 meter per hour. After each hour that passes, the rubber string is stretched so as to become 1 meter longer than it just was. Will the worm ever reach the other end of the string?

Solution     Reveal