An ant crawls along a rope that stretches faster than it can ever walk
An ant starts at one end of a taut rope 1 km long, crawling forward at a steady 1 cm per second. But the whole rope also stretches uniformly, at 1 km per second, carrying the ant forward along with everything ahead of it. The rope keeps stretching forever, always outpacing the ant by a huge margin. Does the ant ever reach the far end — and if so, roughly how long does it take?
Reveal the answer
Yes — remarkably, the ant does eventually reach the end, though it takes an absurd amount of time: on the order of 10^43421 years, unimaginably longer than the age of the universe. Even though the rope stretches by a kilometre every second, the ant's own progress gets stretched proportionally too, and that shrinking fraction still adds up without bound over time, the same reason the harmonic series 1 + 1/2 + 1/3 + ... never stops growing. The puzzle is a staple of recreational mathematics, popularised in various forms by writers including Martin Gardner.