Color Switching Games

In this paper the authors study one- and two-dimensional color switching problems by applying methods ranging from linear algebra to parity arguments, invariants, and generating functions. The variety of techniques offers different advantages for addressing the existence and uniqueness of minimal solutions, their characterizations, and lower bounds on their lengths. Useful examples for reducing problems to easier ones and for choosing tools based on simplicity or generality are presented. A novel application of generating functions provides a unifying treatment of all aspects of the problems considered.