IMO Shortlist 2002 problem C5
Dodao/la:
arhiva2. travnja 2012. Let
![r\geq2](/media/m/6/5/b/65b79626e2e9c065c9a7a51e89d82938.png)
be a fixed positive integer, and let
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
be an infinite family of sets, each of size
![r](/media/m/3/d/f/3df7cc5bbfb7b3948b16db0d40571068.png)
, no two of which are disjoint. Prove that there exists a set of size
![r-1](/media/m/9/f/3/9f303f12885d9aa5336d6b5178cf5bba.png)
that meets each set in
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
.
%V0
Let $r\geq2$ be a fixed positive integer, and let $F$ be an infinite family of sets, each of size $r$, no two of which are disjoint. Prove that there exists a set of size $r-1$ that meets each set in $F$.
Izvor: Međunarodna matematička olimpijada, shortlist 2002