{"id":8387,"date":"2018-04-11T11:49:34","date_gmt":"2018-04-11T08:49:34","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=8387"},"modified":"2018-05-15T18:50:56","modified_gmt":"2018-05-15T15:50:56","slug":"problem-of-the-month-april-2018","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-april-2018\/","title":{"rendered":"Problem of the Month \u2013 April 2018"},"content":{"rendered":"<p>We say that a group of 18 students is a team if any two students in this group are friends.\u00a0It is known that in the school any student belongs to at least one team but if any two\u00a0students end their friendships at least one student does not belong to any team. We say\u00a0that a team is special if at least one student of the team has no friend outside of this\u00a0team. Show that any two friends belong to some special team.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Hasan Zubeyr Demir \u00d6zel \u00c7aglayan Fen Lisesi, Ankara<\/li>\n<li>Tomas Jurik Kosice, Slovakia<\/li>\n<li>Serdar Hojayew Dashoguz, Turkmenistan<\/li>\n<li>Nizameddin Ordulu, \u0130stanbul<\/li>\n<li>Eren Can K\u0131z\u0131lda\u011f, Massachusets Institute of Technology, USA<\/li>\n<li>Lamis Al Sheikh IMB, Dijon, France<\/li>\n<li>Mokdad Mokdad, University of Burgundy, France<\/li>\n<li>Mehmet Ali Y\u0131ld\u0131r\u0131m, \u00d6zel Florya Final Anadolu Lisesi, \u0130stanbul<\/li>\n<li>Nurullah Giray Kuru, \u0130stanbul Lisesi, \u0130stanbul<\/li>\n<li>\u00d6z\u011fen \u015eafak Karaku\u015f, \u00d6zel Antalya Final Fen Lisesi, Antalya<\/li>\n<li>\u00d6mer Topalo\u011flu, \u00d6zel \u0130zmir Fen Lisesi, \u0130zmir<\/li>\n<li>Halil Alperen G\u00f6zeten, \u00d6zel Final Anadolu Lisesi, Denizli<\/li>\n<li>Hakan Karaku\u015f, Yusuf Ziya \u00d6ner Fen Lisesi, Antalya<\/li>\n<li>Ender Do\u011fan I\u015f\u0131k, \u00d6zel Final Anadolu Lisesi, Ankara<\/li>\n<li><strong>Solution:\u00a0\u00a0<a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1804a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1804a.pdf<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>We say that a group of 18 students is a team if any two students in this group are friends.\u00a0It is known that in the school any student belongs to at least one team but if any two\u00a0students end their friendships at least one student does not belong to any [\u2026] <\/p>\n<div class=\"clear\"><\/div>\n<p><a class=\"more_link clearfix\" href=\"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-april-2018\/\" rel=\"nofollow\">Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-8387","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/8387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/comments?post=8387"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/8387\/revisions"}],"predecessor-version":[{"id":8781,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/8387\/revisions\/8781"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=8387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}