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Group theory behind Rubik’s Cube
- 1 University of Nottingham Ningbo China
* 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
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Cite this article
Qiu,S. (2023). Group theory behind Rubik’s Cube. Theoretical and Natural Science,9,151-156.
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Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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