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There is a story (perhaps apocryphal, but cute anyway) about Richard Feynman and this problem.

Somebody once asked RF an analogous problem, and he thought for a few seconds and promptly answered: 1000 miles.  The asker said, "Ah, I see you know the trick" to which RF replied something to the effect of "What trick? It's a simple summation problem.  I did it in my head..."

Jonathan Segal
Thursday, December 13, 2001

I believe I've seen this story attributed to either Norbert Wiener or John Von Neumann.  Definitely not Feynman, in any case.  Does anybody know a reference?

Michael Eisenberg
Thursday, December 13, 2001

The question posed was something like:

Two cars head toward each other from cities 100 miles apart.  One car is going 20mph and the other 30mph.  A bumblebee, sitting on the front bumper of one of the cars takes off toward the other car as soon as the cars begin moving, flying at 40mph.  When it reaches the other car, it immediately turns around heads back, only to meet and turn around again, etc, until it meets its untimely death when the cars collide.  How far, in total, did the bee travel?

Jon von Neumann reportedly answered similarly to what's stated above.

The "trick" is to realize the cars approach each other at 50mph and therefore collide in two hours.  The bee, flying at 40mph for two hours, travels 80 miles.

Chad Hulbert
Thursday, December 13, 2001

It's certainly the type of thing Feynman would have been capable of.  I remember the story of him in the Los Alamos Lab, suddenly leaping up in the cafeteria and stating that if anyone could state a math problem within (details are fuzzy here) ten seconds, he could come up with an answer within fifteen seconds that was within five percent of the real answer.  (He made good on that statement for quite a while, but was finally stumped by an ingenious question.)

On another occasion he gave a poor Japanese abacus salesman fits by doing computations with pencil and paper faster than the salesman could on his abacus.

Paul Brinkley
Friday, December 14, 2001

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