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29 students write numbers on boards

Source: 2022 Turkey JBMO TST P5

March 15, 2022
combinatorics

Problem Statement

Each of the nn students writes one of the numbers 1,21,2 or 33 on each of the 2929 boards. If any two students wrote different numbers on at least one of the boards and any three students wrote the same number on at least one of the boards, what is the maximum possible value of nn?
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