Higher Education Institutions are required to solve the problem of scheduling teaching activities each semester throughout its existence. Institutions may develop a workable solution over a significant series of attempts but are required to re-solve the problem whenever there are new courses or new course group selections as determined by student preferences. Within an institution, the existing process is time consuming, tedious and error prone resulting in unacceptable levels of timetable clashing for a student and frequent clashing of course activities. We examine the teaching scheduling problem, various scheduling algorithms, and use these as the basis for purporting a solution that ensures no room clashes, a best fit use of facilities and minimal or zero time clashes, and inter-department and intra-department clashes. Our solution provides for the usage of prior or current year registration, priority teaching times, course concurrency and the generation of a usable clash matrix. We propose Ricoché, a scheduling system that uses graph coloring with heuristics as the basis for a solution towards optimality. Ricoché provides for ease of adaptability as curricula, teacher preferences and students' course needs change.