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Mutually friendly 3 (Posted on 2012-08-05) Difficulty: 4 of 5
Prove that if any two people are either friends or strangers, then any group of 18 people contains either 4 mutual friends or 4 mutual strangers.

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Some Thoughts Confirmed: 18 is the minimum | Comment 3 of 11 |
I just looked this up.  This is a problem addressed by "Ramsey's theorem" (look it up in Wikipedia).  The Ramsey number R(4,4) does in fact equal 18.
  Posted by Steve Herman on 2012-08-07 09:03:44
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