If you are like me, you have played the game SET and have probably been perplexed at how quickly some people can play the game! Even as the game is quite easy to explain, it takes some time to build various strategies and pattern recognition to play the game effectively. If you have never heard of SET, don’t fret because we will soon review its layout. For my final masters project at Texas A&M University, we had the autonomy to research any higher-level mathematical topic and I felt SET would be a great venue to tap into some deeper mathematics. Little did I know how truly complex and elegant SET really is with connections to combinatorial geometry, finite affine geometry, and vector spaces over finite fields, some of these problems still open in research-level mathematics. All of these topics (and more) are included in a great resource I highly recommend for some summer reading. Check out The Joy of Set by McMahon, et al. to dig deeper into what is presented below.
I rediscovered this nice paper by Kenneth P. Bogart in my Interesting Esoterica collection, and decided to read through it. It turned out that, while the solution presented is very neat, there’s quite a bit of hard work to do to along the way. I’m not particularly experienced with combinatorics, so the little facts that the paper skips over took me quite a while to verify.
Once I was happy with the proof, I decided to record a video explaining how it works. Here it is:
I probably made mistakes. If you spot one, please write a polite correction in the comments.
Sam’s dad is in a mathematical conundrum – so she’s asked Katie, one of our editors, if maths can save the day.
Dear The Aperiodical,
My dad is going away on a golfing holiday with seven of his friends and, since I know a little bit about mathematics, he’s asked me to help him work out the best way to arrange the teams for the week. I’ve tried to work out a solution, but can’t seem to find one that fits.
They’ll be playing 5 games during the week, on 5 different days, and they’d like to split the group of 8 people into two teams of four each day. The problem is, they’d each like to play with each of their friends roughly the same amount – so each golfer should be on the same team as each other golfer at least twice, but no more than three times.
The Institute of Mathematics and its Applications has launched a new journal, Information and Inference: a Journal of the IMA. This aims to
publish high quality mathematically-oriented articles, furthering the understanding of the theory, methods of analysis, and algorithms for information and data.
Articles should be written in a way accessible to researchers in the associated topics in pure and applied mathematics, statistics, computer sciences, and electrical engineering. Articles are published in, but not limited to: information theory, statistical inference, network analysis, numerical analysis, learning theory, applied and computational harmonic analysis, probability, combinatorics, signal processing, and high-dimensional geometry.
The first take-home lesson of this note is that you too can be unique. You’ll have to keep shuffling to get there, but it is an attainable goal.
Several years ago it dawned on me that the number of possible ways to order or permute the cards in a standard deck of size $52$ was inconceivably large. Of course it was — and still is — $52!$. That’s easy enough to scribble down (or even surpass spectacularly) without understanding just how far we are from familiar territory.