Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 9, 13 November 2023
Open
Access | Article
Group theory behind Rubik’s Cube
* Author to whom correspondence should be addressed.
Abstract
The Rubik’s Cube is a widely recognized puzzle. The mathematics behind the Rubik’s Cube is group theory. Group theory studies algebraic structures in mathematics such as groups, rings, and fields. The operation of the Rubik’s Cube is rotation, which can be considered an operation of a group. The combination of two rotations of the Rubik’s Cube can be considered the association of two operations of a group. The rotations and the combination operation of two rotations form a group called the Rubik’s Cube group, and this paper presents the order of this group which is also the quantity of possible valid configurations of the Rubik’s Cube. The valid configurations are the configurations that can be reached by a series of rotations from the starting configuration. This paper presents a method to illustrate the configurations of the Rubik’s Cube, the requirements for making the configurations valid, and calculate the quantity of possible valid configurations.
Keywords
Group theory, Rubik’s Cube, Sign Homomorphism
References
1. Frey Jr, Alexander H, and David Singmaster 2010 Handbook of Cubik Math. The Lutterworth Press.
2. Tim, Reynolds 2023 World Cube Association Official Results. World Cube Organization.
3. Travis, Michale 2007 The mathematics of the rubik’s cube. University of Chicago.
4. Joyner, David 2014 The man who found God's number. The College Mathematics Journal, 258-266.
5. Chen, Janet 2007 Group theory and the Rubik’s cube. Harvard University.
6. Jacobson, Nathan 2012 Basic algebra I. Courier Corporation.
7. Provenza, Hannah 2009 GROUP THEORY AND THE RUBIK’S CUBE. University of Chicago.
8. Dummit, David Steven, and Richard M 2004 Abstract algebra. Hoboken: Wiley.
9. Isaksen, Carl Joakim 2012 Rubik's cube and Group Theory. MS thesis.
10. Joyner, David 2008 Adventures in group theory: Rubik's Cube, Merlin's machine, and other mathematical toys. JHU Press.
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Authors who publish this series agree to the following terms:
1. Authors retain copyright and grant the series right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this series.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the series's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this series.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See Open Access Instruction).
- Volume Title
- Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
- ISBN (Print)
- 978-1-83558-129-2
- ISBN (Online)
- 978-1-83558-130-8
- Published Date
- 13 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/9/20240732
- Copyright
- 13 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited