Skip to content
Accessible Unlicensed Requires Authentication Published by De Gruyter June 5, 2017

The first law of cubology for the Rubik’s Revenge

Stefano Bonzio, Andrea Loi and Luisa Peruzzi
From the journal Mathematica Slovaca


We state and prove the first law of cubology of the Rubik’s Revenge and provide necessary and sufficient conditions for a randomly assembled Rubik’s Revenge to be solvable.

(Communicated by Anatolij Dvurečenskij)


[1] Adams, J.: How to Solve Rubik’s Revenge, The Dial Press, New York, 1982.Search in Google Scholar

[2] Bandelow, C. L.: Inside Rubik’s Cube and Beyond. Birkhäuser, 1982.Search in Google Scholar

[3] Bonzio, S.—Loi, A.—Peruzzi, L.: On the nxnxn Rubik’s Cube, submitted.Search in Google Scholar

[4] Chen, J.: Group theory and the Rubik’s Cube, Notes.Search in Google Scholar

[5] Czech, B.—Larjo, K.—Rozali, M.: Black holes as Rubik’s Cubes, Journal of High Energy Physics 8, (2011).Search in Google Scholar

[6] Demaine, E. D.—Demaine, M. L.—Eisenstat, S.—Lubiw, A.—Winslow, A.: Algorithms for Solving Rubik’s Cubes. In: Proceedings ESA 2011.Search in Google Scholar

[7] Diaconu, A.—Loukhaoukha, K.: An improved secure image encryption algorithm based on Rubik’s Cube principle and digital chaotic cipher, Math. Probl. Eng. 2013 (2013), Art. ID 848392.Search in Google Scholar

[8] Frey, A.—Singmaster, D.: Handbook of Cubik Math, Enslow Publishers, 1982.Search in Google Scholar

[9] Joyner, D.: Adventures in Group Theory, The Johns Hopkins University Press, 2008.Search in Google Scholar

[10] Kosniowski, C.: Conquer that Cube. Cambridge University Press, 1981.Search in Google Scholar

[11] Kunkle, D.—Cooperman, G.: Twenty-six Moves Suffice for Rubik’s Cube. In: Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, 2007.Search in Google Scholar

[12] Larsen, M. E.: Rubik’s Revenge: The group theoretical solution, Amer. Math. Monthly 92, (1985).Search in Google Scholar

[13] Lee, C.-L.—Huang, M.-C.: The Rubik’s Cube problem revisited: a statistical thermodynamic approach, Eur. Phys. J. B 64(2) (2008).Search in Google Scholar

[14] Michael, B. C. S.—Jones, A.—Weaverdyck, M. E.: On God’s number(s) for Rubik’s slide, College Math. J. 45(4) (2014).Search in Google Scholar

[15] Miller, J.: Move-count Means with Cancellation and Word Selection Problems in Rubik’s Cube Solution Approaches, PhD Thesis, Kent State University, 2012.Search in Google Scholar

[16] Rokicki, T.: Towards God’s number for Rubik’s cube in the quarter-turn metric, College Math. J. 45(4) (2014).Search in Google Scholar

[17] Rokicki, T.—Kociemba, H.—Davidson, M.—Dethridge, J.: The diameter of the Rubik’s Cube group is twenty, SIAM J. Discrete Math. 27(2) (2013).Search in Google Scholar

[18] Volte, E.—Patarin, J.—Nachef, V.: Zero Knowledge with Rubik’s Cubes and Non-abelian Groups. Cryptology and Network Security, 12th International Conference, 2013.Search in Google Scholar

Received: 2015-4-28
Accepted: 2015-5-29
Published Online: 2017-6-5
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences