Two trains start 200 miles apart. They travel towards each other,
one at 40 miles an hour, the other at 60. At the same time a fly
starts from one train and flies at 75 miles an hour (unlikely though
that may be) towards the other train. At the instant it reaches it
the fly turns around and flies back again. It continues to zigzag
between the trains until it is crushed in the inevitable collision.
So the story goes that a student had been given this problem, had
solved it the hard way (infinite series), found the easy solution
(that you've just given) and was trying it out on lots of people.
He met von Neumann at a party and posed it to him, whereupon he
(von Neumann) thought for a moment, and then gave the right answer.
The student was disappointed, and said "You'd be surprised just how
many people try to sum the infinite series." Von Neumann looked
puzzled and said: "Is there another way?"
How far did the fly fly?
This is one of the Big List of Topics pages, which is my random
ramblings that I may turn into a book of "shared stories".
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