Further Explorations with the Towers of Hanoi
Jon Stadler · Mathematical Association of America eBooks · 2009
This project is a supplement to the usual introduction to the Towers of Hanoi problems that appear in most discrete mathematics texts. Many concepts from discrete mathematics are discussed, including Hamiltonian paths, representation of integers in other bases, graph theory, and number theory. Notes for the instructor Puzzles are a great way to pass time. However, they can also be an excellent source for mathematical applications. There are few puzzles more famous than the Towers of Hanoi. The point of this project is not to teach the students how to solve the puzzle, nor is it designed to teach a formula for the minimum number of moves required to solve the puzzle. In fact, it is highly probable that you have already discussed these things with your class. Instead, the purpose of this project is to tie together many of the topics that you have taught in your discrete mathematics course. If you have not already done so, introduce the students to the Towers of Hanoi in your textbook. If your textbook does not discuss the puzzle, write to the author and demand that it be included in the next edition of the book and then find a reference on how to solve the puzzle on the Internet. Students will be ready when they know how to solve the puzzle and a formula for the minimum number of moves required to solve a puzzle with n disks.