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The first law of cubology for the Rubik’s Revenge

  • Stefano Bonzio EMAIL logo , Andrea Loi und Luisa Peruzzi
Veröffentlicht/Copyright: 5. Juni 2017
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 67 Heft 3

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.

MSC 2010: Primary 05E99; Secondary 20B99
Keywords: combinatorial puzzles; Rubik’s Revenge; group theory

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.

(Communicated by Anatolij Dvurečenskij)

References

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

[2] Bandelow, C. L.: Inside Rubik’s Cube and Beyond. Birkhäuser, 1982.10.1007/978-1-4684-7779-5Suche in Google Scholar

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

[4] Chen, J.: Group theory and the Rubik’s Cube, Notes.Suche 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)143Suche 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_58Suche 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 848392.10.1155/2013/848392Suche in Google Scholar

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

[9] Joyner, D.: Adventures in Group Theory, The Johns Hopkins University Press, 2008.10.56021/9780801890123Suche in Google Scholar

[10] Kosniowski, C.: Conquer that Cube. Cambridge University Press, 1981.Suche 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, 2007.10.1145/1277548.1277581Suche in Google Scholar

[12] Larsen, M. E.: Rubik’s Revenge: The group theoretical solution, Amer. Math. Monthly 92, (1985).10.2307/2322445Suche 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/e2008-00301-0Suche 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.45.4.267Suche 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.Suche 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.45.4.242Suche 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).10.1137/120867366Suche 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_5Suche 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

Artikel in diesem Heft

  2. Some results in local Hilbert algebras
  4. A note on residuated po-groupoids and lattices with antitone involutions
  6. The first law of cubology for the Rubik’s Revenge
  8. Conditional associativity in orthomodular lattices
  10. A monotonicity property for generalized Fibonacci sequences
  12. Systems of conditionally independent sets
  14. On the k-th order lfsr sequence with public key cryptosystems
  16. On parametric spaces of bicentric quadrilaterals
  18. Character sums with an explicit evaluation
  20. Some remarks on formal power series and formal Laurent series
  22. The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
  24. On prime and semiprime generalized hyperaction of hypermonoid
  26. On O’Malley ϱ-upper continuous functions
  28. Uniqueness theorems for finitely additive probabilities on quantum structures
  30. Some results on differential-difference analogues of Brück conjecture
  32. Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
  34. On support, separation and decomposition theorems for t-Wright-concave functions
  36. A characterization of holomorphic bivariate functions of bounded index
  38. Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
  40. The geometry of two-valued subsets of Lp-spaces
  42. Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
  44. A comparison of two tests in multivariate models
  46. Modelling prescription behaviour of general practitioners
  48. Characterization of congruence lattices of principal p-algebras
https://doi.org/10.1515/ms-2016-0290
Schlagwörter für diesen Artikel
combinatorial puzzles; Rubik’s Revenge; group theory

Artikel in diesem Heft

  2. Some results in local Hilbert algebras
  4. A note on residuated po-groupoids and lattices with antitone involutions
  6. The first law of cubology for the Rubik’s Revenge
  8. Conditional associativity in orthomodular lattices
  10. A monotonicity property for generalized Fibonacci sequences
  12. Systems of conditionally independent sets
  14. On the k-th order lfsr sequence with public key cryptosystems
  16. On parametric spaces of bicentric quadrilaterals
  18. Character sums with an explicit evaluation
  20. Some remarks on formal power series and formal Laurent series
  22. The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
  24. On prime and semiprime generalized hyperaction of hypermonoid
  26. On O’Malley ϱ-upper continuous functions
  28. Uniqueness theorems for finitely additive probabilities on quantum structures
  30. Some results on differential-difference analogues of Brück conjecture
  32. Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
  34. On support, separation and decomposition theorems for t-Wright-concave functions
  36. A characterization of holomorphic bivariate functions of bounded index
  38. Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
  40. The geometry of two-valued subsets of Lp-spaces
  42. Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
  44. A comparison of two tests in multivariate models
  46. Modelling prescription behaviour of general practitioners
  48. Characterization of congruence lattices of principal p-algebras
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