A family of multicolor lights out games

Abstract

Traditional two-color lights out games and their solutions have been studied extensively. This paper focuses on the existence, or lack there of, of solutions in more general lights out games, which take on a prime number of color states. The result in this paper generalizes the existence of solutions in the family of lights out games on a [Formula: see text] grid with [Formula: see text]-colors where [Formula: see text] and [Formula: see text].