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Exploring the “Rubik's Magic” Universe

Maurizio Paolini
Published Online: 2017-06-09 | DOI: https://doi.org/10.1515/rmm-2017-0013


By using two different invariants for the Rubik’s Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configurations of the puzzle. Finding the set of actually constructible shapes remains however a challenging task, that we tackle by first reducing the target shapes to specific configurations: the octominoid 3D shapes, with all tiles parallel to one coordinate plane; and the planar “face-up” shapes, with all tiles (considered of infinitesimal width) lying in a common plane and without superposed consecutive tiles. There are still plenty of interesting configurations that do not belong to either of these two collections. The set of constructible configurations (those that can be obtained by manipulation of the undecorated puzzle from the starting situation) is a subset of the set of configurations with vanishing invariants. We were able to actually construct all octominoid shapes with vanishing invariants and most of the planar “face-up” configurations. Particularly important is the topological invariant, of which we recently found mention in [7] by Tom Verhoeff.

Keywords: Rubik's Magic puzzle; octominoid 3D shapes; topological invariants


  • [1] Rubik's Magic - Wikipedia, https://en.wikipedia.org/wiki/Rubik's_Magic, retrieved Jan 15, 2014.Google Scholar

  • [2] Köller, J.. Rubik's Magic, http://www.mathematische-basteleien.de/magics.htm , retrieved Jan 15, 2014.Google Scholar

  • [3] Nourse, J.G. Simple Solutions to Rubik's Magic, New York, 1986.Google Scholar

  • [4] Paolini, M. Rubik's Magic, http://rubiksmagic.dmf.unicatt.it/, retrieved Jan 15, 2014.Google Scholar

  • [5] Paolini, M. rubiksmagic project, Subversion repository, 2015, https://svn.dmf.unicatt.it/svn/projects/rubiksmagic/trunk.Google Scholar

  • [6] Scherphuis, J. Rubik's Magic Main Page, http://www.jaapsch.net/puzzles/magic.htm, retrieved Jan 15, 2014.Google Scholar

  • [7] Verhoeff, T. \Magic and Is Nho Magic", Cubism For Fun, 15, 24–31, 1987.Google Scholar

About the article

Published Online: 2017-06-09

Published in Print: 2017-05-24

Citation Information: Recreational Mathematics Magazine, Volume 4, Issue 7, Pages 29–64, ISSN (Online) 2182-1976, DOI: https://doi.org/10.1515/rmm-2017-0013.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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