Here is my Reading Project on the maximum number of cards needed to guarantee a SET.

Dan

What immortal hand or eye / could frame thy fearful symmetry?

Posted by: **danb** | December 11, 2008
## The SET Game

Here is my Reading Project on the maximum number of cards needed to guarantee a SET.

Dan

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I’ve always found this problem fascinating, so I’m glad you picked this for your reading project. I enjoyed learning the proofs from your review. This problem falls into a class of problems that tend to go around mathematics departments and get everyone puzzled. These problems are easy to state, and there seem to be lots of approaches to the problem, but no one can come up with a general proof! Everyone talks about it over tea and no one ever solves it! It’s really amazing to me that this problem is open in general (unsolved)!

As for how to move to larger finite fields, I think most mathematicians would take more of an interest in the question of the largest subset of F_q^n which contains no lines than of how to generalise the SET game itself by considering same and different attributes. But I’m sure the creators of SET have thought hard about it. There’s now a sort of SET scrabble variant too.

When you state it as a question about subsets without lines in F_q^n, it makes you wonder about subsets without planes etc. I also wonder what combinatorial problems (counting problems) reduce to this question. It seems like it must come up other places too.

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Prof. Kateon January 15, 2009at 10:16 pm