Lafayette and the Game of SET

Abstract: The card game SET is played with a special deck of cards, each of which has symbols on it.  There are 1, 2, or 3 symbols, green, purple, or red symbols, empty, striped, or solid symbols, and the symbols are diamonds, ovals or squiggles.  A SET is three cards whose symbols, for *each* of number, color, shading, or shape, are all the same or all different.  See below for examples of SETs. There is a tremendous amount of mathematics in the design of this game, most notably, geometry. The deck of cards is an excellent model for one particular finite geometry, the affine geometry of order 3 (3 cards in a set) and dimension 4 (there are four attributes).  Understanding the geometry helps us better appreciate the game, and playing the game leads to geometric insights and questions. We will also see connections of the game to other areas of math, including combinatorics, probability, and even linear algebra.  For practice, try the Daily Puzzle at https://www.setgame.com/set/puzzle and ask yourself: how many “different" puzzles are possible?  During the talk, we will highlight some Lafayette students who have contributed to our understanding of the game.