MEMO 2016 ekipno problem 4
A class of high school students wrote a test. Every question was graded as either point for a correct answer or points otherwise. It is known that each question was answered correctly by at least one student and the students did not all achieve the same total score.
Prove that there was a question on the test with the following property: The students who answered the question correctly got a higher average test score than those who did not.