In one version of Zeno's paradox, Achilles can run ten times as fast as the tortoise, but the tortoise has a 100-yard head start. Achilles cannot catch the tortoise, says Zeno, because when Achilles runs another 10 yards, the tortoise will have moved 1 yard ahead, and so on. Convince Zeno that Achilles will catch the tortoise and tell him exactly how many yards Achilles will have to run to do it?