Question 187
Suppose there is a class with some students, and out of all the pairs formed from any four students, an even number are friend pairs. Show that it is possible for the students to enroll in clubs such that the following conditions are satisfied:
(i) Any two members of the same club are friends.
(ii) For any pair of students who are friends, there is exactly one club that has them both as members.
(iii) Each student is a member of one or two clubs.
(i) Any two members of the same club are friends.
(ii) For any pair of students who are friends, there is exactly one club that has them both as members.
(iii) Each student is a member of one or two clubs.