MathDB

Eight students were asked to solve

8

problems (the same set of problems for each of the students).
(a) Each problem was solved by

5

students. Prove that one canfind two students so that each of the problems was solved by at least one of them.
(b) If each problem was solved by

4

students, then it is possible that no such pair of students exists. Prove this.
(S Tokarev)

(492) 5