Mathematics Colloquium Talk Series - Fibonacci Plays Lights Out

Abstract: This talk will discuss a current research project that uses recursion, number theory, and linear algebra to explore the classic 1990s game, Lights Out. The original Lights Out game consists of a grid of lights, some of which are on and some of which are off. The goal of the game is to turn off all lights, but pressing a light changes the state of that light and changes the states of its neighboring lights. In this talk, we discuss a variation of the Lights Out game in which the lights have multiple states instead of just on and off. We can think of the states as different levels of brightness. For example, if the lights have three states we can think of them as off, dim, and bright. The game begins with all lights set to their brightest state, and we attempt to turn off the lights by employing a “light chasing” strategy in which we systematically turn off lights one row at a time. Mathematically, we represent this strategy as a recursion, which allows us to apply known results about the Fibonacci sequence to determine when this strategy works to turn off all lights.