Question 40
A school will form $n$ clubs, where $n\ge3$, each with 3 members, such that every pair of clubs has exactly one student in common.
a) Give an example of 7 clubs satisfying these conditions.
b) Prove that if a student belongs to 4 clubs, that student must belong to every club.
c) Find the smallest $n$ for which every collection of clubs satisfying the conditions must have one student common to all clubs.
a) Give an example of 7 clubs satisfying these conditions.
b) Prove that if a student belongs to 4 clubs, that student must belong to every club.
c) Find the smallest $n$ for which every collection of clubs satisfying the conditions must have one student common to all clubs.