Maybe you remember playing the game, Mancala, as a kid. Did you ever wonder how to move certain stones to specified bins in as few moves as possible? With the help of Aquinas professor, Dr. Joseph Spencer, Noah Armstrong ‘14 is spending his summer researching exactly that.

Dr. Spencer, a professor of mathematics at Aquinas, contacted Armstrong wondering if he would be interested in participating in a summer research project. Armstrong is a math major with chemistry and physics minors. “I had Noah in some classes and was impressed by how well he did in them,” said Spencer. “So I asked if he was interested in doing a summer research problem.”

They decided to focus their research on the game, Mancala, which Armstrong specifies is actually the Americanized version of a group of Mancala games from around the world. Spencer decided which problem they were going to tackle based on his knowledge that both he and Armstrong shared a mutual love for board and card games. “Dr. Spencer has done a great job facilitating the project and picking an interesting topic,” said Armstrong.

The research problem may go over the heads of the not so mathematically inclined but Armstrong was able to provide a brief explanation of the project. Spencer and Armstrong will be looking specifically at the sowing action of the stones, which Armstrong defines as the action “when all the stones from a single pit are removed from one pit and dropped one-by-one into the successive pits until all of the stones are gone.”

Armstrong and Spencer’s research will then deal with certain stones they call “kings” and the attempts by those “kings” to reach a specified bin that Armstrong and Spencer refer to as “home.” “Different variations of the number of stones beginning in each pit, the total number of pits on the board, and even the number of kings will come in to play,” said Armstrong.

Both Armstrong and Spencer enjoy working on this research as a team and appreciate each other’s contributions to the research and discussions. “I am really enjoying working with Noah and thinking about the mathematics we are doing,” said Spencer. “I have been very happy with Noah’s approach to the summer research project. He has been very responsible in getting things done. We are making good progress toward answering our initial problem and have found a few other questions that are worth working on too.”

It is a good thing that the two have developed a good relationship because they meet almost daily for up to two hours in order to make sure Armstrong’s math is correct and also explore and discuss new topics together. “Usually Noah is sent off with some work to do on our research. Our discussions are mostly very collaborative; I don’t have all the answers so there is a back and forth about solving the problems we come upon,” said Spencer.

The research duo is planning to work on the project until the end of July 2013. In the fall, they will present their research at the Mohler Thompson Research Presentation. They are hoping to write a paper on the topic as well.

>Read more about undergraduate student research at AQ