Pascal's Triangle Game

Date: 03/23/2001 at 14:10:07
From: Stephen Arsenault
Subject: Pascal's triangle

Dear Dr. Math,

I am in the Math Fair at my school. My topic is Pascal's triangle. 
Someone does this topic every year, but this year I wanted to do 
something different. I want to make a game. How could I make a 
game using Pascals triangle?

Date: 03/24/2001 at 05:22:51
From: Doctor Floor
Subject: Re: Pascal's triangle

Hi, Stephen,

Thanks for writing.

There is a way to represent Pascal's triangle that is suitable to play 
games with: Galton's board (Francis Galton, UK, 1822-1911).

It consists of a triangle of pins, and a number of boxes:

                *
              *   *
            *   *   *
          *   *   *   *
        *   *   *   *   *
    |___|___|___|___|___|___|


On the top pin you gently drop a marble or a small ball, which 
descends, passing by a pin in each row and eventually ending in one of 
the boxes. If the board is made in the correct way, at each pin the 
marble is as likely to go to the left as to go to the right.

If you drop a lot of marbles, the numbers of marbles in the boxes will 
be distributed proportional to the corresponding row of Pascal's 
triangle.

Now you can imagine a game where you are given points according to in 
which box the marble ends. Have fun!

If you need more help, just write back.

Best regards,
- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/