Combinatorial Games and Puzzles

Combinatorial games and puzzles are ones in which perfect information is available, no chance element exists and where a counting argument often leads to a "win" or a solution. Winning, solutions and the analysis of possible outcomes can also be aided by ideas originating in linear algebra. Such examples of this include the Lights Out puzzle and the card game SET, both of which we will examine. In this course we will study the underlying mathematics of these games and puzzles. Basic notions in graph theory, combinatorics, combinatorial design theory, and combinatorial game theory will be introduced. There is a prerequisite of linear algebra.