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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.

See The Solution Submitted by Math Man    
Rating: 5.0000 (1 votes)

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re(4): No Subject | Comment 8 of 11 |
(In reply to re(3): No Subject by Chris, PhD)

I've been on that same drawing board for quite a length of time now, as you can see with the proof I came up with for a total of 20.  Because of what was pointed out about "Ramsey's Theorem", I can somewhat buy into the idea that it can indeed be shown to be true among a group of 18 -- but I'm at a complete loss as to why this is the case...
  Posted by Caleb on 2012-08-07 12:33:13

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