Complex Solutions for Simple Problems

Von Neumann is a famous Physics Professor. He was a scientist in the first generation of atomic energy. Once in a party, a beautiful lady asked him a difficult question. The following was the question.

Two cyclists are at a distance of 30 Kms from each other. Both are cycling towards other with a speed of 15 kms per hour. After one hour both reach the middle point. When they have started, a fly also started along with the first cyclist at 20 kms per hour, and touched the other cyclist, and returned to the first cyclist and after touching him again went to the second cyclist. It was doing repeatedly till both reach the middle point. How much distance did the fly travel?

This kind of problems are difficult to solve. Since, the distance needs to be traveled by the fly is reducing gradually. This has to be done by using infinite series, and that would take lot of time to solve.

Von Neumann told the answer in half a minute.

There is a trick in this problem. If we think the problem in a different direction, it would be easy to solve. The fly is travelling at a speed of 20 kms per hour. It traveled for one hour (since it took one hour for cyclists to reach the middle point). So, the total distance traveled by the fly is 20 kms.

Then the lady congratulated him and told him that, she thought he would take lot of time in solving the problem by using infinite series, but, he found the trick easily.

Then Von Neumann said, "I solved by using Infinite series only. Is there any simpler method?"

Courtesy: Mohana Makarandam by Mohan Kanda

(By the way, I am also solving problems in the similar way)