Group-Theoretical Aspects of a Family of Puzzles
Anna Marie Madras · BearWorks (Missouri State University) · 2011
We investigated questions inspired by the puzzle Top Spin by Binary Arts using concepts from abstract algebra. We attempted to determine whether every configuration can be obtained by some set of moves or if not, which permutations can be realized. In other words, we asked whether a given set of generators generates the entire symmetric group or a proper subgroup of the symmetric group. We represented the puzzle using Cayley graphs; the diameter of these graphs gives the fewest moves needed to solve the particular puzzle.