Question 4
One hundred students take part in an oral examination. The panel consists of 25 examiners. Each student is questioned by one examiner. Every student likes at least 10 members of the panel.
(a) Prove that seven examiners can be selected so that every student likes at least one of them.
(b) Prove that the examination can be scheduled so that each student is questioned by exactly one examiner whom the student likes, and each examiner questions at most 10 students.
(a) Prove that seven examiners can be selected so that every student likes at least one of them.
(b) Prove that the examination can be scheduled so that each student is questioned by exactly one examiner whom the student likes, and each examiner questions at most 10 students.