Barrus, Michael, D

Advisor Department





problem solving; Rubik’s Cube; puzzles; critical thinking

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.


Stumbling upon a difficult problem to solve is inevitable. A difficult problem is defined as a problem in which the solution is not easily discovered for a typical person. These problems can range from real-life situations, such as quitting an addiction or finding a cure for cancer, to recreational puzzles such as a game of chess or a Rubik’s Cube. Due to their complexity, and in some cases lack of information on the subject, it is easy to get frustrated and not try when one encounters such a problem. For this reason, it is imperative to have a skill set that one can utilize in these situations. By having a process to follow, it will be easier to avoid the trap of frustration and continue working towards a solution. Many scholars have researched this topic, including mathematicians George Polya and Wayne Wickelgren. Their work reflects several problem solving skills that are invaluable to mathematical problems.

Using Polya’s and Wickelgren’s research as a foundation, I have done an analysis of various techniques one might use to approach a difficult problem. These techniques are, by nature, based in mathematical reasoning, but made more concrete through their application to solving a 2x2x2 Rubik’s Cube. Some of these techniques include starting small, drawing figures, and measuring progress. Many of these techniques can be explained simplistically, but others require in-depth analysis using techniques such as theoretical probability and deduction. It is important to note that the aim of this project is not to find a new solution set to the 2x2x2 Rubik’s Cube, but to find a set of skills one may need to utilize in order to determine a solution. The results of this project include a suggested list of problem solving skills that are able to be applied to a variety of problems.

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Mathematics Commons