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Omni-MATH / Professor Ma has formulated n different but equivalent statements A_1, A_2,…

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problem

Professor Ma has formulated n different but equivalent statements A_{1}, A_{2}, \ldots, A_{n}. Every semester, he advises a student to prove an implication A_{i} \Rightarrow A_{j}, i \neq j. This is the dissertation topic of this student. Every semester, he has only one student, and we assume that this student finishes her/his dissertation within the semester. No dissertation should be a direct logical consequence of previously given ones. For example, if A_{i} \Rightarrow A_{j} and A_{j} \Rightarrow A_{k} have already been used as dissertation topics, Professor Ma cannot use A_{i} \Rightarrow A_{k} as a new dissertation topic, as the implication follows from the previous dissertations. What is the maximal number of students that Professor Ma can advise?

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Source and history

task_id
87c5d384-5fc2-5b0e-bf72-eafa85c87f08
task_key
test--87c5d384-5fc2-5b0e-bf72-eafa85c87f08
task_revision_id
1
config / split
/ test

Official source

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