Developing a Student Project in Abstract Algebra: The Lights Out Problem
Developing a Student Project in Abstract Algebra: The Lights Out Problem
John Wilson
Abstract of article: This article describes the development, solution, and results of a group project assigned during the second course of the abstract algebra sequence at Centre College. The Lights Out puzzle consists of 25 lights arranged in a square. When a light is touched, that light and each of the adjacent lights is toggled on or off. The students in this project were asked to develop a mathematical model for the puzzle and to determine how to turn off all of the lights starting with any given set of lights turned on. Several tips are given for faculty members who want to incorporate student projects into their courses.
About the author: John Wilson thoroughly enjoys explaining mathematics to people of any age. He has tutored or taught mathematics every year since he was in the seventh grade. After receiving his Bachelor of Science degree at the University of the South he earned his MS and Ph.D. at the University of North Carolina. He has taught at Centre College in Danville, Kentucky since 1985. He married his high school sweetheart and they have two children. He enjoys playing games and solving puzzles of all types but receives a special pleasure when they lead him to an interesting mathematical question.
Other links:
Tiger Electronics, original (or at least one-time) manufacturer of the puzzle
It can be purchased at http://www.virtuallyshopping.com/ (do a search for Lights Out)
a web site having a three-dimensional version
an on-line version
another on-line (java applet) version
web site dedicated to the problem