IMO 1969 LL MON42

Let Ak (1 \leqk \leqh) be n-element sets such that each two

imolonglistmathematicsolympiad

IMO 1969 LL MON42

Origin: MON

Problem

Let Ak (1 \leqk \leqh) be n-element sets such that each two of them have a nonempty intersection. Let A be the union of all the sets Ak, and let B be a subset of A such that for each k (1 \leqk \leqh) the intersection of Ak and B consists of exactly two different elements ak and bk. Find all subsets X of the set A with r elements satisfying the condition that for at least one index k, both elements ak and bk belong to X.