A mathematical overview of the game of SET prepared by David Patrick.

1. The Mathematics of SET
David Patrick
Art of Problem Solving
November 2015
Overview of SET
The game of SET1 consists of cards with:
• One, two, or three identical figures;
• Each figure is a diamond, an oval, or a “squiggle”;
• Each figure is colored red, green, or purple; and
• Each figure is plain (unshaded), striped, or solid.
For example, the following is the card “two striped red squiggles”:
A SET is three cards such that, for each of the four properties listed above (number, shape, color,
and shading), the three cards are either all the same or all di↵erent. For example, the following
three cards make a SET:
The numbers are all di↵erent, the shadings are all di↵erent, the colors are all the same, and the
shapes are all di↵erent.
To play the game competitively: 12 cards are dealt face-up, and all the players compete to be
the first to find a SET amongst the 12 cards. When a SET is found, that player claims it, and 3 more
cards are dealt to bring the total back up to 12. If no one can find a SET, then 3 more cards can
be added. Play continues until the deck is exhausted, and the player with the most claimed SETs
wins.
1
SETR
is a registered trademark of Cannei, LLC. The game is available at www.setgame.com or from Amazon.
www.aops.com