Rubik's Revenge: The Group Theoretical Solution

The first law of cubology for the Rubik’s Revenge

“…Z is the subgroup permuting centers only, leaving corners and edges fixed; E permutes edges only. 5 The proofs of these results can be found in [8]. However they are included in the present paper for sake of completeness.…”

“…We first introduce some already known results [8] on the structure of G which are of fundamental importance for proving Theorem 3.1.…”

“…Now we consider the subgroup E of moves involving edges only. Edges are 24 each of which can assume two different orientation, however no single edge can be flipped [8]. The direct consequence of this fact is that E S 24 .…”

“…For example we provide necessary and sufficient conditions for a randomly assembled Rubik's Revenge to be solvable. Our proof is based on the algebraic tools on the Rubik's Revenge developed in [8]. To authors' best knowledge reference [8] is the only place where a group theoretical approach to the Revenge is given (the reader is referred e.g.…”

“…Our proof is based on the algebraic tools on the Rubik's Revenge developed in [8]. To authors' best knowledge reference [8] is the only place where a group theoretical approach to the Revenge is given (the reader is referred e.g. to [1] and to several places in the web for the description of the instructions needed to solve the Rubik's Revenge).…”