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Homework Help: Question on proofs for a CS related class

  1. Apr 5, 2010 #1
    1. The problem statement, all variables and given/known data
    As a background to this...I have no experience with proofs at all. I did not take a formal geometry class in high school (took a shortened summer course that gave a VERY brief overview of proofs) and have not gotten to discrete math in university, so I really do not know how to approach/write proofs.

    At the top of my homework, it says: "For each problem solution, attempt to adhere to mathematical rigor. Proofs and arguments should be detailed and complete." I've never heard of mathematical rigor and after looking it up I still don't really know how to "conform" to it. Seems like it's some kind of standard for proofs.

    Here is one of the questions for my HW:
    "Six people enter a room. Either there are three people who know each other or there are three people who are strangers to each other.

    Prove the above statement. Where does a variant of the pigeonhole principle come in?"

    I don't quite know where to start - I looked up the pidgeonhole principle and didn't really understand how it applies to this problem. Maybe someone can point me in the right direction as to how to write a proof for this problem?

    This HW is due Thursday at 11:59 PM EST, help before then is very appreciated.


    2. Relevant equations
    None that I know of.


    3. The attempt at a solution

    ???
     
  2. jcsd
  3. Apr 6, 2010 #2

    LCKurtz

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    Hint: Think of the 6 people sitting around a table. Focus on one of them, call him A. Since he sees 5 people, there must be three he either knows or doesn't know. (There coudn't be just two of each). Examine that situation a little further.
     
  4. Apr 6, 2010 #3
    I'm still not quite understanding - isn't it possible that he doesn't know all 5 of them and is simply in the same room with random people? Do you mean "AT LEAST 3 he either knows or 3 he doesn't know?"
     
  5. Apr 7, 2010 #4

    LCKurtz

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    Yes that's what I mean. So you can pick 3 to go with A. Analyze them; try drawing solid or dashed lines for know, don't know and see what happens.
     
  6. Apr 7, 2010 #5
    Here's a hint:

    If you know someone, then they know you.
     
  7. Apr 7, 2010 #6
    i'll go with NOUSE post
     
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