In this puzzle, two bicycles begin 20 miles apart, and each travels toward the other at 10 miles per hour until they collide; meanwhile, a fly travels continuously back and forth between the bicycles at 15 miles per hour until it is squashed in the collision.
The questioner asks how far the fly traveled in total; the "trick" for a quick answer is to realize that the fly's individual transits do not matter, only that it has been traveling at 15 miles per hour for one hour.
As Eugene Wigner tells it, Max Born posed the riddle to von Neumann. The other scientists to whom he had posed it had laboriously computed the distance, so when von Neumann was immediately ready with the correct answer of 15 miles, Born observed that he must have guessed the trick. "What trick?" von Neumann replied. "All I did was sum the geometric series.”