> He [Morgenstern] also told of von Neumann's prodigious mind. That > JvN was asked how thick a coin need be so that the probability of > its landing on its edge is 1/3. This, he answered (using reasonable > assumptions) in seconds.
Another problem posed to John von Neumann:
Two trains, 200 kilometres apart, are moving toward each other. Each one is moving at a constant speed of 50 kilometres per hour. A fly starting on the front of one of them flies back and forth between the trains at a rate of 75 kilometres per hour. It does this until the trains collide (with unfortunate results for the fly). What is the total distance the fly has flown?
He immediately replied, "150 miles."
"Interesting," said the poser, "but nearly everyone tries to sum the infinite series."
"What do you mean?" asked Von Neumann. "That's how I did it!"