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Least number of conspiring students

Source:

November 9, 2010
combinatorics proposedcombinatoricsItaly TSTTSTTeam Selection Testdouble counting

Problem Statement

A stage course is attended by n≥4n \ge 4 students. The day before the final exam, each group of three students conspire against another student to throw him/her out of the exam. Prove that there is a student against whom there are at least (n−1)(n−2)3\sqrt[3]{(n-1)(n- 2)} conspirators.
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