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330 logic/friends.p




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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

330 logic/friends.p


Any group of 6 or more contains either 3 mutual friends or 3 mutual strangers.
Prove it.

logic/friends.s

Take a person X. Of the five other people, there must either be at least three
acquaintances of X or at least three strangers of X. Assume wlog that X has
three strangers A,B,C. Unless A,B,C is the required triad of acquaintances,
they must include a pair of strangers, wlog A,B. Then X,A,B is the required
triad of strangers, QED.

 

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