Web-based Practice
Towers of Hanoi by NLVM
Subject
Math, Science & Technology
Virtual Manipulative
Click here for this interactive resource.
Description
This is an electronic implementation of a classic puzzle that has all kinds of legends associated. It may be interesting for individuals or as a class project to find some of the resources on the web that apply. Classically, temple monks were to move a set of 64 disks from one peg onto another, after which, depending on the legend, something a great significance was to happen.
As indicated in the instructions, only one disk can be moved at a time, and disks can only be placed on an empty peg or onto a larger disk. By experimenting with two or three disks, students should be able to decide that the minimum number of moves required to move a set of n disks from one peg onto another is 1 less than 2 raised to the power of n, so that two disks can be transferred in 4-1 moves, and three disks can be transferred in 8-1 moves. Actually shifting four disks in 15 moves or five disks in 31 moves requires some planning. As students gain some proficiency, they can take on more challenging tasks.
As an extension for older students, it is delightful to revisit the temple monk legend. If it were possible to move one peg per second without error, how long would it take to move a set of 64 disks from one peg to another? (More than 584 trillion years). The class might discuss how many pegs might be moved in some more reasonable length of time.
Content Provider
The National Library of Virtual Manipulatives is a three-year NSF supported project to develop a library of uniquely interactive, web-based virtual manipulatives or concept tutorials, mostly in the form of Java applets, for mathematics instruction (K-8 emphasis). The project includes dissemination and extensive internal and external evaluation. For more information, please visit http://nlvm.usu.edu/en/nav/vlibrary.html.
Credits
Principal Investigators
Larry Cannon
Jim Dorward
Bob Heal
Leo Edwards
Java Applet Programming
Ethy Cannon
Joel Duffin
David Stowell
Zeke Susman
Richard Wellman
Jennifer Youngberg
Web Site Programming
Joel Duffin
