Posted by: Prof. Kate | December 4, 2008

## The game of SET

Today in class we took a ten minute break to play a game called SET.  This website for SET is here:

http://www.setgame.com/

where you can learn to play.  There’s a deck of 81 cards, each of which has four characteristics: number, shape, colour and textrure.  For example, the card

has shape SQUIGGLE, colour RED, number THREE and texture SOLID.

There are three options for each characteristic, hence 3^4 possibilities — that’s the 81 cards.

The game is simply to find SETs which are collections of three cards such that with respect to each characteristic, the cards are either all the same or all different. For example, this is a set:

and these are not:

For the game SET of 81 cards (4 attributes), the largest subset of cards which does not contain a SET is 20.  For 1 attribute it is 2, for 2 attributes it is 4, for 3 attributes it is 9 and for 4 attributes it is 20, for 5 attributes it is 45.

For k attributes, for k > 5, it is unsolved!

http://www.setgame.com/ – the manufacturer of SET

http://www.math.yorku.ca/~zabrocki/set/ – where you’ll find a computer game that lets you play higher attribute versions of Set, and some background on the math

http://en.wikipedia.org/wiki/Set_(game) – Wikipedia’s take on things

http://www.math.rutgers.edu/~maclagan/papers/set.pdf – much more mathematical exploration of SET

Enjoy!

Prof. Kate.

## Responses

1. I had heard of the game SET several times from some of my math inclined friends but today was the first time I actually got to “play” (well, more like huddle in the front of the classroom).

Now it’s on my Christmas wish list.