{"id":18979,"date":"2023-03-21T08:05:49","date_gmt":"2023-03-21T05:05:49","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=18979"},"modified":"2023-04-11T09:09:45","modified_gmt":"2023-04-11T06:09:45","slug":"problem-of-the-month-march-2023","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-march-2023\/","title":{"rendered":"Problem of the Month \u2013 March 2023"},"content":{"rendered":"<p>Any two pupils in the school are either friends or not, the friendship is mutual. For each<br \/>\ninteger 1 \u2264 <span style=\"font-size: 18;\">\u2113<\/span> \u2264 111 there is a school pupil having exactly\u00a0<span style=\"font-size: 18;\">\u2113<\/span> friends in the school. Given that<br \/>\nthere is no triple of school pupils such that any two of them are friends, find the minimal<br \/>\npossible number of pupils in this school.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Choi Min Kyu\u00a0South Korea<\/li>\n<li>Mustafa Kerem Y\u00fcksel Bilkent University<\/li>\n<li>Vedat deveci \u0130stanbul<\/li>\n<li>H\u00fcseyin Ege Olcay\u00a0Bilkent University<\/li>\n<li>Alper Balc\u0131 Ohio State University,\u00a0 USA<\/li>\n<li>Henrik Aberg Gothenburg, Sweden<\/li>\n<li>Jakob Aberg Lund, Sweden<\/li>\n<li>K\u00fcr\u015fad Mestav New Jersey, USA<\/li>\n<li>Abdulkadir Tanr\u0131verdi Eski\u015fehir<\/li>\n<li>Magnus Jakobsson,\u00a0Lund, Sweden<\/li>\n<li>Roger Bengtsson, Lund,\u00a0 Sweden<\/li>\n<li>Mustafa Burak Topal \u0130stanbul<\/li>\n<li>Cenk Ba\u011fr\u0131yan\u0131k NFA, New York, USA<\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2303a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2303a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Any two pupils in the school are either friends or not, the friendship is mutual. For each integer 1 \u2264 \u2113 \u2264 111 there is a school pupil having exactly\u00a0\u2113 friends in the school. Given that there is no triple of school pupils such that any two of them are [\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-march-2023\/\" 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-18979","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/18979","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=18979"}],"version-history":[{"count":9,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/18979\/revisions"}],"predecessor-version":[{"id":19185,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/18979\/revisions\/19185"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=18979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}