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VN TST 1996 Question 5

VMO · VN TST 1996

Question 5

A number of students are to be invited to a meeting. Each is unacquainted with at least $56$ other invited students, and every pair who are unacquainted have at least one invited student acquainted with both. Can the number invited be $65$?

The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale.