The Fly and Trains Problem
The problem is this: Two trains are on the same line, 100 miles apart, heading towards each other, each traveling at 50 MPH. A fly that can travel at 60 MPH leaves one engine flying towards the other. Upon reaching the other engine, it instantaneously turns around, and heads back to the first engine. This is repeated until the two trains crash and the fly is crushed in the collision.
Question: How far does the fly travel before the crash?
The interesting story: According to several persons who were present, this problem was presented to the famous mathematician John von Neumann at a cocktail party. After thinking about it for a few seconds, he answered “60 miles”. The disappointed questioner said “Oh, you discovered the shortcut. I thot you were going to try to sum an infinite series.” Von Neumann then asked “What shortcut?”, because he had, in his head, summed the infinite series. (Hint: The shortcut is that the trains take exactly an hour to cover the 100 miles between them, during which time the fly has covered 60 miles at 60 MPH. Figuring out how to do it as an infinite series is left as an exercise for the student.)
July 31, 2013