## Sunday, May 20, 2007

### Interesting Maths Problem

I just encountered an interesting maths problem which I would like to share.

There are three classes in a school, each with the same number of students. The fraction of girls in class A is the same as the fraction of boys in class C. Also, class B has one-fifth of all the boys in the school.

What is the fraction of girls in the school ?

For your info, this question is a Sec One question. Frankly, I'm quite surprised at this fact. In anycase, I didn't use algebra to solve this problem - that felt unfair. Anyway intuition should prove helpful in tackling this question.

## Saturday, May 05, 2007

### The Problem of the Bones

I've just stumbled upon an extremely interesting problem, to which I've only been able to derive a partial solution after some intuitive thinking. The problem itself is called "The Problem of the Bones". Here's the problem statement :

Imagine that a creature from outer space walks you before a pit. In the pit are 10,000 leg bones. The creature tells you, "I have cracked each bone at random into two pieces by throwing them against a rock. What's the average ratio of the length of the long piece to the length of the short piece?

This problem is pretty difficult to solve. I've only been able to obtain a solution for the case where there are infinity leg bones in the pit.

I'm now attempting a simulation to obtain the answer. If you are able to solve this problem, please leave the solution in the comments.