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MathNet 2022-part-03 — 197 problems (EN–VI) Question 142

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 142

A class has 30 students and they sit in three groups of 10 students each. At the beginning of each month, the teacher swaps the students' seats. What is the minimum number of months needed in order for every pair of students to sit in the same group for at least a month?
(Proposed by Otgonbayar Uuye)