Problem

Source: 2016 Saudi Arabia IMO TST , level 4+, II p3

Tags: combinatorics, set, Subsets



Given two positive integers $r > s$, and let $F$ be an infinite family of sets, each of size $r$, no two of which share fewer than $s$ elements. Prove that there exists a set of size $r -1$ that shares at least $s$ elements with each set in $F$.