IMO Shortlist 2001 problem C3
Kvaliteta:
Avg: 2,0Težina:
Avg: 7,0 Define a
-clique to be a set of
people such that every pair of them are acquainted with each other. At a certain party, every pair of 3-cliques has at least one person in common, and there are no 5-cliques. Prove that there are two or fewer people at the party whose departure leaves no 3-clique remaining.
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
Izvor: Međunarodna matematička olimpijada, shortlist 2001