Problem

Source: MEMO 2016 T4

Tags: combinatorics, combinatorics proposed



An exam was taken by some students. Each problem was worth 1 point for the correct answer, and 0 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.