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The Mathematics of the Game SET

The Cover Image for the Game SET

SET is an extremely addictive, fast-paced card game found in toy stores nationwide. Although children often beat adults, the game has a rich mathematical structure linking it to the combinatorics of fi nite affine and projective spaces and the theory of error-correcting codes. Last year an unexpected connection to Fourier analysis was used to settle a basic question directly related to the game of SET, and many related questions remain open.

So begins a recent paper on the elegant mathematics of the card game SET. For those of us who enjoy card games that require logic and quick thinking, rather than simply luch, and the mathematical beauty and surprising interconnectedness of different mathematical fields, this paper is interesting. Warning: you need a certain level of algebraic understanding to follow the paper (having had an algebraic structures course beyond “linear algebra” in college will help). The paper starts out by giving the background of the development of the game, and how it is played. Then the authors turn to problems of algebraic interest regarding the game and show how to answer some of these questions.

Personally, I love the game. I was introduced while visiting my graduate alma mater (Virginia Tech) by a former student here at Messiah College who was in graduate school at Tech. She introduced my wife and I to the game, and I fell in love. For those familiar with the game SET, or would like to try it out, it is available online here.


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