From : John Von Neumann and the Mathematician’s Trap

The story goes that someone once posed to Von Neumann the following problem:

Two trains are 20 miles apart on the same track heading towards each other at 10

miles per hour, on a collision course. At the same time, a bee takes off from

the nose of one train at 20 miles per hour, towards the other train. As soon as

the bee reaches the other train, it bangs huwey and heads off at 20 miles per

hour back towards the first train. It continues to do this until the trains

collide, killing the bee.

The question is, how far does the bee fly (d) before the collision?

When posed with the above problem (or some variation of it), JVN took all of

five to ten seconds to come up with the correct solution. This floored the

questioner who said “I’m impressed that you didn’t fall for the Mathematician’s

Trap.” After getting a perplexed look from our genius, he asked “How did you

solve the problem?”

*“By infinite series, of course!”*