Does anyone here know the game "set"?
Today it occured to me that you can represent each card in the game with a 4 dimensional vector space over the field GF(3).
If you do so, you can represent each set as a matrix with rows/columns (depending on your representation) of a constant sum - 0 (mod 3). I.E - in each set, the sum of the vectors is 0.
Also, the coordinates of the 3 vectors must be collinear.
Just thought I'd share this nice insight with you. If anyone has some more mathematical insights about the game, feel free to write them down.
The geometric representation of SET has been studied earlier. See http://homepage.tudelft.nl/64a8q/set-machazine.pdf, for example.