Solving the Rubik\u27s Cube using Group Theory

While he was working in his mother\u27s apartment in 1974, the professor of architecture from Budapest, Erno Rubik, had no idea he was inventing one of the most popular toys in history, the Rubik\u27s Cube. As an estimated 350 million Rubik\u27s cubes have been sold, and approximately one in every seven people have played with one (which is about 1 billion people) it is not surprising to see that the algorithm of solving the Rubik\u27s cube has been applied to the eld of mathematics. By using abstract algebra and more specially, group theory, the Rubik\u27s Cube, no matter what the starting configuration, can be solved. The notes on an intensive course written by Janet Chen guide this project by making the Rubik\u27s cube a group where all of the possible moves are the elements in the group. By looking at the different subgroups and the moves in said subgroups, we can find the algorithm in which we can reconfigure the Rubik\u27s cube back into its starting configuration. A Mathematical Approach To Solving Rubik\u27s Cube by Raymond Tran also helped provide some different methods in achieving the correct configuration the Rubik\u27s Cube. By utilizing these two texts we will prove that using these methods indeed gives us a viable solution to solve a Rubik\u27s cube