How to do anecdotes in mathematics?

Once, at a party, Von Neumann was bravely posed a puzzle by his hostess:

Two trains were traveling on the same track at a speed of 3 miles per hour, with a distance of 1 mile. At this time, a fly perched in front of a burning train flew towards another train at a speed of 6 miles per hour. When it flew to another train, it

flew back quickly.

Most people, especially those who know a little math, first calculate the distance of each round trip, and then add up these results

. This involves the summation of infinite series, which is not difficult, but it is troublesome and time-consuming. In fact, there is a

skill here. First, calculate how long it takes for two trains to collide, and it is easy to calculate that it is one minute. One mile a minute is too easy.

Almost as soon as the hostess explained the problem, von Neumann replied, "One mile."

"I'm surprised that you worked it out so quickly," she said. "Most mathematicians didn't see the skill

in it, but used infinite series to calculate it, which took them a long time." I also use infinite series, "von Neumann replied.