  The Rubik's cube was invented in 1974 by Erno Rubik, who had no idea of the
incredible popularity and mathematical fascinations his toy would bring.
Through the years of study on the mathematical properties of the cube, the
Rubik's Cube group was introduced to represent all possible moves one could
perform on the cube. In this paper, we define a planar analogue to the Rubik's
cube, which we dub the Rubik's Square, and prove that the Rubik's square is
complete in the sense that given any two configurations there is a sequence of
moves which changes one to the other. The Rubik's cube does not have this
property. We then abstract the concept of the Rubik's Square to a Rubik's Shape
and analyse the completeness in this more general setting.
