In article <Pine.OSF.4.02A.email@example.com>, Chris Hillman <firstname.lastname@example.org> writes:
> Another story concerns a skeptical mathematician, hoping to test von > Nuemann's legendary ability to think on his feet, who started to tell him > about a hard problem to which there was a very clever "shortcut" solution > which someone else had discovered.
I read the story as `a couple of students' with JvN overhearing the conversation; certainly the problem wasn't hard (in the version I read).
> The "obvious" approach to solving this > particular problem, however, involved summing a very difficult infinite > series which would require several minutes of hard computation and > ingenious manipulation by a good mathematician. Von Neumann interrupted > almost immediately to give the correct answer. The other man exclaimed > "Oh, you heard about the short proof!" Von Neumann replied: "What short > proof? I just summed the series!".
The problem being: Two trains are 60 miles apart and approaching each other at 30 miles per hour. There is a fly flying between the cowcatchers of each train, at 60 miles per hour, back and forth, turning around immediately. What is the total distance covered by the fly (relative to the ground, NOT taking the motion in opposite directions to cancel) until the trains hit?