Communicating Mathematics III (MATH3131) 2011-12

The mathematics of Rubik's Cube

Jens Funke


In this project, we explore the group theory and graph theory underlying Rubik's Cube and related puzzles!

The possibles moves of Rubik's Cube form a group. It is a subgroup of the group of rotations in space. In this project, we will study this group and use this to describe solutions to this puzzle!


  • David Joyner has written a book on the mathematics of Rubik's Cube. Here are the lectures notes on which the book is based.
  • Here are the notes of an elementary introductory talk on the mathematics of Rubik's cube.
  • This paper gives the solution to Rubik's Revenge, the 4 x 4 x4 version of the Cube.

In the course of the project we will then also consult other resources and other puzzles.


  • Algebra II
  • Representation Theory III might be helpful but is not essential.

email: J Funke