Date of Award
Honors Program Director
In John P. Bonomo’s and Carolyn K. Cuff's paper How Do You Stack Up? a mathematical problem was posed. This question was regarding a common children’s toy known as a stacking ring tower. The problem the authors addressed came as a result of a common occurrence: the event that not all of the rings are placed on the tower in the “proper” order. When the rings are placed on the tower in a variation of that “proper” order, some of them will inevitably stick over the top of the tower. The problem the authors decided to tackle was to find the average number of rings that stick over the top of the tower when examining all possible placements of the rings. The authors found a solution and proved their solution to be true within their paper.
At the beginning of this project, it was my goal to solve the same problem independently of Bonomo and Cuff, and then to compare my results with theirs. I ended up taking a very different approach, but in the end, my work ended up corresponding with theirs. In my paper, I will explain my thought process and my methods for solving this problem. I will guide the reader through my strategies and explain how they did (or did not) work out for me. We will begin with some basic definitions and explanation of the problem in greater detail, and then commence with my research.
Johnson, Jillian J., "Playing with Permutations: Examining Mathematics in Children’s Toys" (2014). Honors Senior Theses/Projects. 10.