We say that a group of 18 students is a team if any two students in this group are friends. It is known that in the school any student belongs to at least one team but if any two students end their friendships at least one student does not belong to any team. We say that a team is special if at least one student of the team has no friend outside of this team. Show that any two friends belong to some special team.
Correct Solutions by,
- Toshihiro Shimizu Kawasaki, Japan
- Hasan Zubeyr Demir Özel Çaglayan Fen Lisesi, Ankara
- Tomas Jurik Kosice, Slovakia
- Serdar Hojayew Dashoguz, Turkmenistan
- Nizameddin Ordulu, İstanbul
- Eren Can Kızıldağ, Massachusets Institute of Technology, USA
- Lamis Al Sheikh IMB, Dijon, France
- Mokdad Mokdad, University of Burgundy, France
- Mehmet Ali Yıldırım, Özel Florya Final Anadolu Lisesi, İstanbul
- Nurullah Giray Kuru, İstanbul Lisesi, İstanbul
- Özğen Şafak Karakuş, Özel Antalya Final Fen Lisesi, Antalya
- Ömer Topaloğlu, Özel İzmir Fen Lisesi, İzmir
- Halil Alperen Gözeten, Özel Final Anadolu Lisesi, Denizli
- Hakan Karakuş, Yusuf Ziya Öner Fen Lisesi, Antalya
- Ender Doğan Işık, Özel Final Anadolu Lisesi, Ankara
- Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/1804a.pdf