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:

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!

Here are some links to learn more: – the manufacturer of SET – where you’ll find a computer game that lets you play higher attribute versions of Set, and some background on the math – Wikipedia’s take on things – much more mathematical exploration of SET


Prof. Kate.


  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.

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