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strangers to friends

Theorem on Friends and Strangers; Why in Any Party of Six People, Either at Least Three of Them Are Mutual Friends, or at Least Three of Them Are Mutual Strangers

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Let’s take a look at Alice first. To her, each one of the other five (Bob, Carol, Dave, Ellen, and Frank) is either a friend or a stranger. Suppose Bob, Dave, and Frank are friends to Alice, and…
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