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MathNet 2023-part-04 — 191 problems (EN–VI) Question 34

Math Olympiad Vault · MathNet 2023-part-04 — 191 problems (EN–VI)

Question 34

Consider a class of students. Within any group of six students, there are always two students who are not friends. Furthermore, if we select two of these non-friends, there will always be a student among the remaining four who is friends with both of the chosen students. What is the largest possible number of students in the class?
(Nyamdavaa Amar)