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Mutually friendly 2 (Posted on 2011-07-01) Difficulty: 3 of 5
In Mutually friendly, we proved that if any two people are either friends or strangers, then any group of six people either contains 3 mutual friends or 3 mutual strangers, or both. Now, they can also be enemies.

Suppose that any two people are either friends, enemies, or strangers. Prove that any group of 17 people either contains 3 mutual friends, 3 mutual enemies, or 3 mutual strangers.

See The Solution Submitted by Math Man    
Rating: 5.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionConfirmed: 17 is the minimumSteve Herman2011-07-02 22:18:46
SolutionProof (spoiler)Steve Herman2011-07-01 17:31:51
re: The enemy of my enemy is my friend?Math Man2011-07-01 17:21:26
Some ThoughtsThe enemy of my enemy is my friend?Steve Herman2011-07-01 14:43:25
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