Applying Linear Algebra in Solving the Lights Out Puzzle through Programming in Sage

Abstract

The Lights Out puzzle presents an interesting problem in mathematics, encompassing elements of linear algebra, number theory and programming. This paper will analyze the mathematics associated with a version of the Lights Out puzzle game developed by Tiger Electronics (c.1995) that is most often presented to users. Our goal is to implement Sage using an algorithm in linear algebra to solve a linear system derived from this game. We attained results regarding the solvability and the structure of the solution space to the linear system. Furthermore, we used Sage to investigate other models of Lights Out puzzles in different settings, such as modifying the shape of the game’s array and adding more states of display other than ‘on’ or ‘off’.