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Consider a person A. Either A knows at least 3 people, or A does not know 3 or more people. Without loss of generality (WLOG), let's assume that A knows at least 3 people. Let three of these people be B, C and D. Now, if B, C and D do not know each other, we are done. However, if even one pair does not know each other (WLOG we can assume this to be B and C), then we A, B and C know each other. Hence in a group of 6 people, we must have either 3 mutual acquaitences, or three mutual strangers.
Who's next?
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