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.