Multivariate Calculus

Multivariable Calculus

Dr. Allen Hibbard, instructor

29 October 2010

Port-and-Sweep Solitaire Reaction

In my perusing of the September 2010 issue of Math Horizons, I ran across the article, “Port-and-Sweep Solitaire” by Jacob Siehler on page and decided I would try to gain a better understanding than what I gleamed from my initial glance. The basis of Port-and-Sweep Solitaire (PaSS) stems from Ordinary Peg Solitaire (OPS) and allows for two unique moves rather than the one simple move of OPS. Although I did not understand some of the mathematics to which the author referred, such as the mod 3 arithmetic, I still felt as though I was able to comprehend the ideas about which he was writing. The game he introduced intrigues me, and I feel as though I would really enjoy spending some time attempting to solve one of his squares, however, I will probably hold off on trying to solve the square in figure 8. I did find it interesting that imaginary numbers came into play in his solving of a system that only involved simple addition and subtraction. One question that goes unanswered in the article is the one of how to reduce the total possible solvable squares to the number of ones in the “Goldilocks region”, but perhaps this concept is so elementary that Siehler thought it superfluous to discuss.

When it comes to my thoughts on the article, I would begin by saying that I enjoyed reading it. It was well written and relevant to mathematicians in general and therefore appropriate for the magazine. On a more intellectual level, I do wish that more explanation would have been given, but I do realize the limitations of a magazine article. Lastly, I would recommend this reading to other people who have a mathematically inclined disposition and an aptitude in mathematics sufficient to understand the material.