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Omni-MATH / Somewhere in the universe, n students are taking a 10-question math competition. Their collective performance is called laughable if, for some pair of questions, there exist 57 stu…

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problem

Somewhere in the universe, nn students are taking a 10-question math competition. Their collective performance is called laughable if, for some pair of questions, there exist 57 students such that either all of them answered both questions correctly or none of them answered both questions correctly. Compute the smallest nn such that the performance is necessarily laughable.
Plain-text mathematical notation (without MathML)
Somewhere in the universe, n students are taking a 10-question math competition. Their collective performance is called laughable if, for some pair of questions, there exist 57 students such that either all of them answered both questions correctly or none of them answered both questions correctly. Compute the smallest n such that the performance is necessarily laughable.
Original LaTeX notation
Somewhere in the universe, $n$ students are taking a 10-question math competition. Their collective performance is called laughable if, for some pair of questions, there exist 57 students such that either all of them answered both questions correctly or none of them answered both questions correctly. Compute the smallest $n$ such that the performance is necessarily laughable.

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Source and history

task_id
2917ecfe-30fc-58be-92e9-6cfd3210363b
task_key
test--2917ecfe-30fc-58be-92e9-6cfd3210363b
task_revision_id
1
config / split
/ test

Official source

initial import