Recurrence relations with minimization and maximization, called minmax recurrence relations are commonly encountered in the analysis of algorithms. In this paper we present the solution of one such challenging recurrence relation. We characterize the optimal partition sizes as well as derive the order of complexity of the overall recurrence relation. It is proved that ad hoc equal partitioning is never the optimal choice. We also provide a survey of three other interesting minmax recurrence relations found in the literature.