FHSST-Maths: A raw newbie...

[Gustav Bertram]

Hi,

It seems that you guys have managed to maliciously trap another volunteer.

My name is Gustav Bertram.

I'm a programmer who hopes to turn himself into a computer scientist. I'm
deeply interested in the mathematics used in computer science, algorithms
and in heuristic methods of problem solving. I like to mathematically
analyse puzzles, so hopefully the examples in this book can be made more
interesting.

I'm no maths genius. In fact, the way maths was taught to me in highschool
didn't agree with me. As a result, I don't remember much, but I'm always
willing to learn.

It is my dream to have an MIT degree before I turn 30.

Here's an example puzzle:

You have three balls. One of these balls is slightly heavier than the
others, but not enough for you to detect. You are given an old fashioned
balance scale, and are told you may use it only once. Are you able to
determine which ball is heavier? And if so, how?

The answer is that the scale can indicate three states:

1. The left ball is heavier
2. The right ball is heavier
3. Both are equally heavy 

You weigh any two balls and take the heavier one, or if both are equal, the
third ball is the heavier one.

What happens if you have nine balls and you may use the scale only twice?

The answer is that you can divide the balls into three groups, and weigh
them once, and then weigh that group.

To get to this answer, you can tell them to think about the similar problem
(that of the three balls), and you can tell them to think about the states
of the scale.

Once that is done, get them to recognise the exponential relationship of the
number of states to the number of times the scale can be used. Then ask them
what the maximum number of balls you can weigh with X number of tries is.

Then ask them what would happen if the scale had more than three states. Get
them to construct a formula.

To bring logarithms into it, ask them to predict the minimum number of times
they need to use the scales for Y number of balls. 

Regards,
Gustav