### Project 12.1

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:

- move only one ring at a time;
- 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 long 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,* September 1977, pp. 528-533.