Solving Puzzles related to

Permutation Groups

Abstract

Physical puzzles that can be solved with methods for permutation groups are considered and classified according to a number of abstract properties. The approach for solution is based on word stabilizer chains (the transversal elements are factored in words in a given list of generators). New methods are presented to construct word stabilizer chains that take advantage of the special structures present in physical puzzles. In many cases the methods are successful in avoiding the exponential growth of word length that plagues stabilizer chain methods to construct transversal elements. E.g. for Rubik's Cube we get solving moves of average length 60. Finally, a classification scheme for puzzles is presented which helps with finding the permutation group related to the puzzle.