Date of Graduation

Fall 2011

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

Lights Out puzzle, linear algebra, Fibonacci polynomials, σ+ game, all ones problem

Subject Categories

Mathematics

Abstract

Lights Out is a puzzle sold by Tiger Electronics. It consists of a 5 x 5 array of buttons that are also lights that toggle between on and off. Pressing a button will switch the light state of that button as well as its horizontally and vertically adjacent neighbors. The object of the game is to switch all lights off. We analyze this game for an abstract m x n board. Using linear algebra, we explore the solvability of this game under different conditions. We establish a recursive relationship using Fibonacci polynomials for null space vectors and use this to determine the dimension of the null space without direct computation. Starting with all lights on, we develop rules for small values of n for the minimal actions in which to solve the puzzle. We then look briefly at variations to the game and the effect these variations may have on the analysis.

Copyright

© Rima J. Freeman

Campus Only

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