Presented are solutions to variations of a combinatorics problem from a recent International Mathematics Olympiad. In particular, the matrix algebra solution illustrates an interaction among the undergraduate areas of geometry, combinatorics, linear algebra, and group theory. (JJK)

This paper first defines the bridge club scheduling problem that was presented to the author and then explores the meaning of an optimal solution. Next, an analytical solution is sought based on the classification of the problem as a resolvable partially balanced incomplete block design. Finally, four increasingly sophisticated techniques of…