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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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Nice game, I was introduced to it by a Hungarian friend a few years ago. –  Raskolnikov Dec 26 '10 at 16:21
    
ps. if you're an undergraduate, do you prefer talks that solve a problem (or outline a solution), as supposed to talks that introduce a subject from the beginning? –  Amy Pang Dec 26 '10 at 16:29
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Your "PS" comment is an entirely different question - maybe you want to ask it? –  Hans Parshall Dec 26 '10 at 16:52
    
@Amy: I certainly agree with Hans, this should be posted a Community Wiki sort of question. As for the answer on that question (though I'm a grad student now, I finished my B.Sc. in math only last year) I remember that I liked the mixture of the two, i.e. presenting me the basics of a subject through an outline of a problem (not necessarily the solution though.) –  Asaf Karagila Dec 26 '10 at 18:58
    
@Asaf: only moderators can make questions Community Wiki on SE2 websites. So please do not fault Amy or other users for that. –  Willie Wong Dec 27 '10 at 13:12
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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.

  • Try contacting Jordan Ellenberg. Several years ago he gave a talk to the Princeton University Undergraduate Math Club on precisely what you described in your question. He will definitely be able to give you some pointers.
  • Also, try asking Aaron Potechin. he is an expert Set player and I remember seeing a pre-print of his on the Maximal Cap issue a few years ago, when he was still an undergrad.
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BTW, Jordan's talk introduced, if I remember correctly, vector spaces over finite fields, and from there led to a nice discussion of arithmetic geometry. The ideas are very accessible, but has enough non-intuitive "Whoa" moments that made the talk very engaging. –  Willie Wong Dec 27 '10 at 13:20
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