Modeling the Game of Brain Cube
Professor Kathy Radloff Wijesinghe and two mathematics majors collaborated to model the puzzle game Brain Cube. Brain Cube is a puzzle game in which the goal is to move a game piece across a planar board, the size and shape of which varies from level to level, to a specified ending spot. The team considered the following three questions: for which types of boards does a solution (i.e. a possible way to move to the end spot) exist? Regarding those setups for which a solution exists, can we find a most efficient solution? Still regarding those setups for which a solution exists, is there a unique most efficient solution? They have answered these questions for all rectangular boards, and have answers for select boards to a few other questions.
Kristal Jameson '14
Why did you want to do a collaborative research project?
Kathy proposed her research idea to me. I love puzzles and problem-solving, so I was very excited to be invited to work on the project with her. I had never considered doing research before, but when I was invited I enthusiastically said “Yes!” without thinking about it much, because it sounded like so much fun to spend my summer analyzing a puzzle game with Leslie and one of my favorite professors.
How did you choose your research topic?
Our mentor is an avid fan of puzzle games. After seeing her daughter playing Brain Cube on her phone, she began to wonder about mathematical properties of the game and whether mathematical concepts could be employed in order to find solutions and analyze the game.
What was one of the highlights of your summer?
The highlight was simply the privilege of spending the summer being paid to do work that was fun, and did not even feel like work. Obviously it was great because I was paid to do mathematical things all summer. Additionally, Kathy is one of my favorite professors, and Leslie is one of my closest friends, so this experience has just been a blast.
What was it like being a research collaborator with a faculty member?
The math department is small, so in a way we’re already like a big family. Because of that, it definitely wasn't intimidating or anything like you might think. It was only different because instead of stopping by to chat whenever I’m in the math department, I went to her office at planned times to talk about our project.
How has this research helped you in school and/or other areas of your life and future?
I have gained experience with Mathematica (software that is used for mathematics), which is always a good thing. Additionally, being able to see different concepts from my courses come together to apply to a game was quite fun. It illuminated for me the versatility of the applications of mathematics, which has encouraged me to consider many different possibilities for my future.
Would you recommend Summer Scholars and/or collaborative research to other students?
I would recommend this opportunity on a practical level because many students need employment outside of school, and this is an opportunity which pays quite well for a campus job while you complete work that is relevant to your studies and enjoyable. The experience could certainly look good on applications for future employment or graduate school, and it undoubtedly gives students an edge over those who haven’t completed such work. Being able to have a job related to your studies before graduation is a priceless experience.
How has this experience added to your success at St. Kate’s and beyond?
It feels good to have been able to accomplish this kind of work as an undergraduate. I don’t really have time to participate in extracurricular activities because I need to work, so this is one of the many opportunities I have had at St. Kate’s to be employed in a position that entails meaningful work.
- Present at NCUR '13