Matrix multiplication is widely used in a variety of tasks, such as Computer Graphics, MRI scans, and neural networks. In 2005, Cohn and Umans proposed a new method for developing matrix multiplication algorithms, which showed the potential to surpass the previous fastest algorithms by Coppersmith and Winograd. They showed that the existence of large strong uniquely solvable puzzles (matrices with only one solution, similar to sudokus) imply faster algorithms for matrix multiplication. Since checking whether or not a puzzle is a strong uniquely solvable puzzle is not instantaneous, my focus was on efficiently searching for large puzzles in order to minimize the search time while still exhausting all possibilities. I will begin by discussing the framework put forward by Cohn and Umans, and will then discuss my work with Professor Anderson in designing and implementing algorithms used to search for strong uniquely solvable puzzles. I will talk about each algorithm we implemented, and will discuss the benefits and drawbacks of each one.