Project 10.1

Write a paper on the famous Tower of Hanoi problem.

When my daughter was 2 years old, she had a toy that consisted of colored rings of different sizes:



Suppose you wish to move the "tower" from stand A to stand C, and to make this interesting we agree to the following rules:
1. move only one ring at a time;
2. at no time may a larger ring be placed on a smaller ring.

For three rings it will take 7 moves (try it).
For four rings it will take 15 moves.

The ancient Brahman priests were to move a pile of 64 such rings,and the story is that when they complete this task the world will end. How many moves would be required, and if it takes one second per move, how lond would this take?

References
Frederick Schuh, The Masterbook of Mathematical Recreations (New York: Dover Publications, 1968).
Michael Schwager, "Another Look at the Tower of Hanoi," The Mathematics Teacher, Sepetember 1977, pp. 528-533.

Project 10.2

Draw a Venn Diagram with five sets.

For two sets, there are 4 regions.
For three sets, there are 8 regions.
For four sets, there are 16 regions.
For five sets, there must be 32 regions.

Symbolically name each of these 32 regions.

Project 10.3

Write a report discussing the creation of colors using additive color mixing and subtractive color mixing.

Project 10.4

How can all the constructions of Euclidean be done by paper folding?
What assumptions are made when paper is folded to construct geometric figures from Euclidean geometry?
What is orgami?
What is a hexaflexagon?
What is a hexahexaflexagon?

Project 10.5

This problem illustrates a numerical solution for the Instant Insanity puzzle. Let's associate numbers with the sides of the cubes of the Instant Insanity problem. Let White = 1;   Blue = 2;   Green = 3;   Red = 5




Now, the product across the top must be 30, and the product across the bottom must also be 30 (why?). It follows that a solution must have a product of 900 for the faces on the top and bottom. Consider the four cubes: