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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)

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Some Thoughts The enemy of my enemy is my friend? | Comment 1 of 4
If it is true that the enemy of my enemy is my friend, then it is not possible to have 3 mutual enemies.  So, I guess it is not true, at least not if there is a group of 17 or more people. 
  Posted by Steve Herman on 2011-07-01 14:43:25
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