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students taking exams

Source: MEMO 2016 T4

August 25, 2016
combinatoricscombinatorics proposed

Problem Statement

An exam was taken by some students. Each problem was worth 11 point for the correct answer, and 00 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.