Hannah Gordon won the championship for the game Set in 2006 the one time it was held. She returned to Columbus, Ohio, this week with her parents Liz McMahon and Gary Gordon, for the Mathematical Association of America MathFest 2016. She challenged conference attendees to the game. In the unlikely event she were to be defeated, attendees would get a free copy of their book The Joy of Set.
The card game of Set was invented by a population geneticist by the name of Marsha Jean Falco in 1974. She was studying the condition of epilepsy in German Shepherds and began representing genetic data on the dogs by drawing symbols on cards and then searching for patterns in the data. After realizing the potential as a challenging puzzle, with some encouragement from friends and family she developed and marketed the card game
Officially released in 1991, Set has gained a widespread, loyal following. Set’s eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify “sets” of three cards for which each characteristic is the same—or different—on all the cards. See rules for details.
The rules of Set are summarized by: If you can sort a group of three cards into “Two of ____ and one of _____,” then it is not a set. These three cards form a set because they have different shapes, different colors, different numbers of symbols and the same shading.
The book The Joy of Set was a family endeavor: Liz McMahon and Gary Gordon are both professors of mathematics at Lafayette College in Easton, Pennsylvania, and serve as faculty co-advisors of the Lafayette Hillel. They wrote the book with their daughters Hannah and Rebecca Gordon. Hannah is the current world champion of Sets. She studies nutrition and health policy at New York University’s Global Institute of Public Health. Rebecca teaches middle school mathematics at Newark Academy in Livingston, New Jersey.
Since MathFest is a mathematics conference, Hannah and Liz gave a talk about the mathematics of the game Set with some of the highlights from their book, The Joy of Set.
The “fundamental theorem of Sets” states that any pair of cards can be completed by a unique third card to form a Set. For example, these two cards share a common shape (oval), shading (empty) and color (red), but have different numbers (3 and 2), so they are completed by the card with that same shape, shading and color, but the remaining number (1).
They proved that the last three cards left at the end of a game of Set automatically form a Set. They also showed how you could figure out what card was missing if you “accidentally” forgot to deal out one out. In fact, Hannah and her family enjoy leaving a card out on purpose as an extra challenge. Anyone who can make a Set including this “ghost” card gets special bragging rights.
If there are six cards left, there may very well not be any Sets. However, if you divide the remaining cards into pairs and find the cards which complete the three pairs, then these three cards will form a Set.
Set is, arguably, the most popular of all commercially sold mathematical games. This is the only book that gives a solid mathematical treatment of this game. Using a range of ideas, from counting to geometry, the authors answer most of the questions you would ever want to know about Set. Humorous and conversational, this book is a pleasure to read.