Challenge question! It’s either very easy or somewhat difficult depending on how clever you are at approaching it. No fair answering if you’ve already seen the problem before, though if no one’s managed it in a few hours I’d say it’s fair game to post the solution if you already know it.
Two trains are 100 miles apart on the same track, headed on a collision course towards each other. Both are traveling 50 miles per hour. A very speedy bird takes off from the first train and flies at 75 miles per hour toward the second train. The bird then immediately turns around and flies back to the first train. Then he flies back to the second train, and repeats the process over and over as the distance between the trains diminishes. How far will he have flown before the trains collide?
Famously John von Neumann was given this problem by a colleague, and he solved it instantly. His colleague remarked on how clever John had been to see the trick and not have to work out the sum of the infinite series. “There’s a trick?”, John asked. Von Neumann, however, was one of those higher-order geniuses – brilliant even in comparison to many of the other 20th century mathematical geniuses. Don’t feel so bad if the problem is more difficult for you.
For the record, I was posed this question on my first or second day of class as a physics undergrad. I didn’t see the shortcut.