Zeno's Paradox

Unfortunately, you took too many guesses to realize the tetrahedron is the logical choice for a primitive solid. Euclid doesn't believe you are really from the future and says to, "Now leave me alone. I've got a puzzle to solve."

Before leaving, you look over his shoulder and see a diagram of a running man where in each time-increment, the runner moves half way to the finish line. You recognize this as Zeno's paradox. It shows that motion is impossible according to the following proof:

1. Suppose a runner always moves half the distance to the finish line during each step.
2. Now allow an infinite number of steps.
3. Since the runner can never reach the finish line even with an infinite number of steps, the runner will never reach the finish line.
4. Therefore, motion is an illusion.

You wonder if you could resolve the paradox and explain it to Euclid, maybe he would be so grateful that he'll help you fix your time machine. It's worth a shot. Now you just have to figure out what's wrong with the proof.

Good luck.