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Students getting the top mark in n subjects

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November 7, 2010
combinatorics unsolvedcombinatorics

Problem Statement

Students have taken a test paper in each of n≥3n \ge 3 subjects. It is known that in any subject exactly three students got the best score, and for any two subjects exactly one student got the best scores in both subjects. Find the smallest nn for which the above conditions imply that exactly one student got the best score in each of the nn subjects.
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