Applying the Group Theory to Rubik’s Cube

Abstract

Gradually formed in the process of the study about the formula solution of the root of polynomial equations, group theory integrates some theoretical achievements in geometry and number theory, plays a fundamentally important role in abstract algebra, and is closely related to the intellectual toy named Rubik’s cube. Many theorems and positions of it are vividly reflected and verified, and can be applied to the study a kind of problems about the Rubik’s cube. These examples include the symmetry of Rubik’s cube, the combination and permutation of the colors on Rubik’s cube, and the God’s number. Besides, various properties and proportions about Rubik’s cube could also be analyzed and proved when the perspective of group theory is applied. This work demonstrates that group theory is a versatile method to solve many theoretical problems in nature and practical problems in life.