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Mutually friendly (Posted on 2002-07-01) Difficulty: 2 of 5
Prove that any group of six people contains either 3 mutual friends or 3 mutual strangers.

(For the purpose of this problem any pair of people must be either friends or strangers.)

  Submitted by levik    
Rating: 3.0000 (5 votes)
Solution: (Hide)
Imagine the six people. Of them, some person X either has at least three friends among the other 5, or at least three strangers.

If X has at least three friends, (call them A, B and C), then either the three of them are all mutual strangers (and satisfy the condition), or at least two of them are friends, and then the these two plus X are the three people that satisfy the condition.

The above paragraph applies likewise to the case where A, B and C are strangers to X.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionMutual friendsMath Man2011-04-25 20:08:22
SolutionSolutionK Sengupta2008-09-05 06:36:10
re: possible solution?calla tah-n2003-05-22 20:59:50
possible solution?calla tah-n2003-05-22 20:53:54
"Myou-tyou-el"Tim Axoy2003-03-21 12:32:03
Ramsey TheoryJosh Myer2002-11-15 05:11:33
re(3): IQ Testlevik2002-07-02 11:56:51
re(2): IQ TestTomM2002-07-02 08:01:25
re: IQ Testlevik2002-07-02 02:11:03
SolutionNo SubjectDulanjana2002-07-02 00:23:15
SolutionNo SubjectTomM2002-07-01 15:08:34
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