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MathNet 2019-part-04 — 184 problems (EN–VI) Question 78

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 78

There are $n$ guests at a party. Any two guests are either friends or not friends. Every guest is friends with exactly four of the other guests. Whenever a guest is *not* friends with two other guests, those two other guests cannot be friends with each other either.
What are the possible values of $n$?