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#### Abstract/Description

Logic puzzles and games are popular amongst many people for the purpose of entertainment. They also provide intriguing questions for mathematical research. One popular game that has inspired interesting research is Rubik’s Cube. Researchers at MIT have investigated the Rubik’s Cube to find the maximum number of moves, from any starting position, needed to win the game [6]. Another logic puzzle that has recently become very popular is Sudoku. Sudoku is a Japanese number game where a 9x9 grid is set up with a few numbers scattered on the grid. Mathematicians have been investigating Sudoku, exploring questions such as the number of possible Sudoku grids there are [7].

Sadisticube is a newer logic puzzle, created by a mathematician. A Sadisticube set is made up of eight separate blocks that form a 2x2x2 cube when placed together. The individual blocks can be rotated and swapped with each other to any position in the cube. The goal of the game is the same as in Rubik’s Cube where each face of the cube needs to be one color. However, because there are trillions of ways to arrange the blocks and we do not know what our solution will look like, Sadisticube is far more difficult than Rubik’s Cube to solve by hand. Fortunately, we can use mathematics to find solutions. Graphs can be used to model the cube so that a solution can be determined for any particular set of blocks. The methods used to create the matrices were adapted from a paper by Jean- Marie Magnier [5]. We will describe how to generate the matrices and their corresponding graphs and will then focus on the graphs in the second half of the paper. After describing how to generate graphs, we will discuss the analysis done on several graphs and the results we found while searching for characteristics common to all graphs.

#### Note on the Author

Danica Baker graduated in May 2014 with a Bachelor of Science in Mathematics and minors in Accounting and Finance and Music. She was mentored by Dr. Shannon Lockard (Mathematics). This project was funded by a 2013 Adrian Tinsley Summer Research Grant and was presented at 2013 BSU Summer Research Symposium as well as the 2014 National Conference on Undergraduate Research (NCUR) in Lexington, KY.

#### Rights Statement

Articles published in The Undergraduate Review are the property of the individual contributors and may not be reprinted, reformatted, repurposed or duplicated, without the contributor’s consent.

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