A Recursive Approach to a Multi-State Cylindrical Lights Out Game

Abstract

Lights Out is a game featuring a grid of light-up buttons that begins with some lights on and some off. The goal is to turn off all lights but pressing a button changes its state and the states of the cardinal neighboring buttons. In this paper, we explore a Lights Out game in which the board is placed on a cylinder and the lights have k states with a specific starting configuration. We try to turn off all lights using a light chasing strategy in which we methodically turn off the lights row by row. We model this process using recursive equations. A connection to the Fibonacci sequence then allows us to determine the number of rows of buttons the board should have in order for us to turn off all lights using our light chasing strategy.