Abstract
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.
The second author was supported by Prin 2010/11 – Varietà reali e complesse: geometria, topologia e analisi armonica – Italy and also by INdAM. GNSAGA-Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni.
References
[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, 1982.10.1007/978-1-4684-7779-5Search 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).10.1007/JHEP08(2011)143Search 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 2011.10.1007/978-3-642-23719-5_58Search 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 848392.10.1155/2013/848392Search 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, 2008.10.56021/9780801890123Search 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).10.1140/epjb/e2008-00301-0Search 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).10.4169/college.math.j.45.4.267Search 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).10.4169/college.math.j.45.4.242Search 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).10.1137/120867366Search 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, 2013.10.1007/978-3-319-02937-5_5Search in Google Scholar
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