1. bookVolume 4 (2017): Issue 7 (May 2017)
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
access type Open Access

Exploring the “Rubik's Magic” Universe

Published Online: 09 Jun 2017
Volume & Issue: Volume 4 (2017) - Issue 7 (May 2017)
Page range: 29 - 64
Journal Details
License
Format
Journal
eISSN
2182-1976
First Published
16 Apr 2016
Publication timeframe
2 times per year
Languages
English
Abstract

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

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

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

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

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

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