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!

Here are some links to learn more:

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.

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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.

By:

sclee09on December 4, 2008at 5:26 pm