Rukhin, AndreyIn this thesis, we examine the Tower of Hanoi puzzle with p posts (p >= 3) and n disks (n in N). We examine the puzzle in the context of a cluster space: a hierarchical partitioning of the space of all possible disk configurations. This thesis includes two theorems that address the topic of minimal paths connecting disk configurations.en-USThesisMathematicsTower of HanoiCombinatoricsCluster SpacesClusters