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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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Hints/Tips Hint | Comment 4 of 11 |
(In reply to "Solution"....but only for a total of 20 people by Caleb)

Let A be one of the 18 people. Then, A either has at least 9 friends or at least 9 strangers. Suppose A has at least 9 friends. Let B be one of the 9 people. Out of the 8 other people, find out how many friends and strangers B must have.

  Posted by Math Man on 2012-08-07 09:14:37
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