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| Mutually friendly 3 (Posted on 2012-08-05) |
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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.
Confirmed: 18 is the minimum
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 | Comment 3 of 11 | 
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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.
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