MEMO 2016 T4
An exam was taken by some students. Each problem was worth point for the correct answer, and points for an incorrect one.
For each question, at least one student answered it correctly. Also, there are two students with different scores on the exam.
Prove that there exists a question for which the following holds: The average score of the students who answered the question correctly is greater than the average score of the students who didn't.
Dataset text AI-MO AoPS. Quoted with source.
Solutions
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