MathDB

Eight students solved

8

problems.
a) It turned out that each problem was solved by

5

students. Prove that there are two students such that each problem is solved by at least one of them.
b) If it turned out that each problem was solved by

4

students, it can happen that there is no pair of students such that each problem is solved by at least one of them. (Give an example.)
Proposed by S. Tokarev

Problem Statement