Last night, a friend of mine was about to get off her msn, before doing so, with some unknown but surely evil intentions, sent me a problem to solve, ¡°it is fun! Try it.¡± She said Gnight.

Poor me, for the next two hours, I did something I haven’t done ever since I left college exactly ten years ago. I scrawled mathematic equations all over¡ The equations says one thing, but my mind won¡¯t corporate. How could it be? It doesn¡¯t make any sense! I was convinced the pathetic math knowledge that I still managed not to forget was not sufficient to solve it.

Desperate and decided to stop worrying myself sick regarding the fate of this evil bee and went to bed. Before doing so, I, with some evil intention of my own, forwarded on the problem to my sister. My sister solved it with one page of formulas. Dissertation style. 🙂

So here is the problem. Enjoy!

Two trains A and B are separated by a distance of L, they started approaching each other at the speed of a and b respectively. Mean while, a bee, traveling at the speed of c, is leaving with Train A at the same time and same location. c>a, and c>b. Once c reaches train B, it immediately turns back and goes toward A, so on and so forth. Question is what is the number of round trip the bee has to travel before the two trains collide?

Here’s another one:

There are 100 seats on an airplane. 100 people have tickets, each specifying a unique seat. An old lady boards the plane first, and without consideration for her ticket, sits in a random seat. Each subsequent person to board the plane attempts to sit in his prescribed seat, and if it is taken, sits in a random seat. What is the probability that the last person gets his correct seat?