Daniel Wentzel: Rubik’s Cube - A Mathematical Model

Abstract.

The Rubik’s cube is a mechanical puzzle invented in 1974 by Ernö Rubik. Solving a scrambled cube can be a difficult task unless you know a solution method. Even if you know a solution method it can be hard to understand why it works and how the different manipulations will affect the cube. This thesis will constuct a mathematical model of the cube using basic group theoretic tools. The model will begin with the colored facets of the cube and proceed to the subcubes, or cubies, that are directly manipulated when playing with a cube. The restrictions of movement and orientation of these cubies will be explained leading to a theorem about what moves and positions are possible on the cube. Finally a theoretically simple method of solving a scrambled cube based on the model will be presented