Question 6
At the National Mathematical Olympiad the students were given 4 problems. Each solution was awarded with an integral number of points between 0 and 7. There were 42 participants and exactly half of them achieved at least 50\% of the points. To win the award one had to get at least 22 points and one sixth of the contestants achieved this. Together, the students who did not get the award had three times as many points as those who did. Prove that there were at least 6 contestants such that each of them got at least 25\% of the points but none of them got more than 50\%.