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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: No Subject | Comment 5 of 11 |
(In reply to No Subject by Chris, PhD)

In the sixth paragraph, we have 5 people who are friends with A and enemies with B. Then, you let C and D be two people in this group that are enemies. You say, "If C is enemies with another member in the group of 5 besides D, a quartet of enemies is formed." How? If C and D are both enemies with E, then B, C, D, and E are 4 mutual enemies. However, if just C is enemies with E, then what are the 4 mutual enemies?

Edited on August 7, 2012, 9:26 am
  Posted by Math Man on 2012-08-07 09:25:32

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