Mentors: Prof. Lior Fishman and Sarah McCall (UNT Graduate)

Title: Rubik's Square: The solvability of the 2x2 case

Abstract: 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 how the cube operates, the Rubik's Group was formed to represent all possible moves one could perform on the cube. Interesting characteristics arose from the study of this group, such as God's number, the maximum number of moves required to solve the cube from any solvable starting position. In this talk we define a planar analogue to the Rubik's cube, aptly dubbed the Rubik's Square. We then show that any starting position of the square is solvable and end the talk on open questions that we plan to study.