IMO 1989 LL MON67

A family of sets A1, A2, . . . , An has the following properties:

imolonglistmathematicsolympiad

IMO 1989 LL MON67

Origin: MON

Problem

A family of sets A1, A2, . . . , An has the following properties: (i) Each Ai contains 30 elements. (ii) Ai \capAj contains exactly one element for all i, j, 1 \leqi < j \leq30. Find the largest possible n if the intersection of all these sets is empty.