Last month, I was introduced to the card game SET. The game raises several interesting questions eg what's the probability that n randomly drawn cards contain k sets, is it possible to end with 12 (or 15) cards which contain no sets... I would like to present the solution to a question like this to undergrads, and through it introduce them to an area of mathematics. For example, as mentioned previously, there is the issue of maximal caps, which Davis and MacLagan's paper relates to projective space and error-correcting codes. Can you give me any similar ideas? Perhaps relating to a variation of SET listed here?
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While I personally don't remember the mathematics, I can give you two leads which, if you follow it up, should give you some ideas.