Still not getting anyone trying this. In one of the comments I showed how a proof for k=3 goes. Hint for general case: pick a sequence of 2k-2 people using a “majority” criterion and show that within the sequence is a k-clique or a k-anticlique.https://twitter.com/joe_shipman/status/1270123256637505536 …
Stupid question probably but I can’t figure it out. If k = 3 I need to show that at a party of 8 or more, either 3 people all know each other or 3 people don’t know each other at all? Why can’t 8 people not know each other?
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The question says one of two conditions must be true (3 people are all mutual friends, or 3 people are all mutual strangers). In your example, if 8 people are all mutual strangers, then certainly any 3 of them are as well. So the second condition is true.
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Another way to state the problem: in a group of 8 people, it can’t be the case that every combination of 3 of them has at least one pair of friends and one pair of strangers.
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