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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(2): No Subject | Comment 6 of 11 |
(In reply to re: No Subject by Math Man)

Agreed, I got hung up on that bit as well.  It's important to remember that the requirements for a quartet are significantly stricter than that for a trio.  With a trio, only three relationships of matching status are needed (confined to three people, of course).  But for a quartet, we have a total of *six* relationships that must match among the four people: 1 to 2, 1 to 3, 1 to 4, 2 to 3, 2 to 4, and 3 to 4.

  Posted by Caleb on 2012-08-07 10:58:20

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