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 Mutually friendly (Posted on 2002-07-01)
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.

 Subject Author Date Mutual friends Math Man 2011-04-25 20:08:22 Solution K Sengupta 2008-09-05 06:36:10 re: possible solution? calla tah-n 2003-05-22 20:59:50 possible solution? calla tah-n 2003-05-22 20:53:54 "Myou-tyou-el" Tim Axoy 2003-03-21 12:32:03 Ramsey Theory Josh Myer 2002-11-15 05:11:33 re(3): IQ Test levik 2002-07-02 11:56:51 re(2): IQ Test TomM 2002-07-02 08:01:25 re: IQ Test levik 2002-07-02 02:11:03 No Subject Dulanjana 2002-07-02 00:23:15 No Subject TomM 2002-07-01 15:08:34

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