Author

Ashley Cotten

Date Approved

2009

Degree Type

Open Access Senior Honors Thesis

Department

Mathematics

Abstract

Cyclic fads often boomerang our childhood toys, sending them back to us with renewed popularity during our adulthood. Recently, Rubik's Cube has made a startling comeback and is once again a staple in most toy stores. Invented by Erno Rubik in his hometown of Budapest, Hungary, the original \Magic Cube" was released in 1974. Upon its world debut in 1980, the toy named after this Hungarian architect became an instant classic. Over 350 billion Rubik's Cubes have been sold worlwide [sic] over the past 30 years, making it easily the top-selling puzzle toy in documented history.

This seemingly innocuous puzzle has frazzled countless children, and perhaps even more adults. The mathematical complexity of the Cube attracted group theorists and other mathematicians upon its release over three decades ago, and the many layers of its structure continue to intrigue the mathematics community. Most of us place emphasis on unscralmbing [sic] the Cube, solving the puzzle. Rather than focusing on the construction of algorithms or solutions to the Cube, we chose to take a group theoretic approach to analyzing this infamous toy. Here, treating Rubik's Cube as a group, we will examine subgroups of the Cube, particularly those constructed via semidirect products. These constructions aid us in describing the possible color arrangements of the Cube.

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