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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.)

See The Solution Submitted by levik    
Rating: 3.0000 (5 votes)

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possible solution? | Comment 8 of 11 |
first split the group up into possible combinations:
6 and 0
5 and 1
4 and 2
3 and 3
considering these combinations, it is not possible to get a combination with both numbers less than 3, so no matter what there will be at least 3 mutual friends or 3 mutual strangers
  Posted by calla tah-n on 2003-05-22 20:53:54
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