{"id":15831,"date":"2021-09-16T10:03:11","date_gmt":"2021-09-16T07:03:11","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=15831"},"modified":"2021-10-12T16:32:20","modified_gmt":"2021-10-12T13:32:20","slug":"problem-of-the-month-september-2021","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-september-2021\/","title":{"rendered":"Problem of the Month \u2013 September 2021"},"content":{"rendered":"<p>There are 777 points located on a circle \u03c9 each coloured into one of the colours 1, 2, . . . , k.<br \/>\nFor each of these points and for each colour 1 \u2264 r \u2264 k there exists an arc of \u03c9 containing<br \/>\nthis point such that at least half of the points located on this arc are r coloured. Find the<br \/>\nmaximal possible value of k.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>M\u00fcmtaz Ula\u015f Keskin Antalya<\/li>\n<li>Jepbar Asgarov Hitrowka, Turkmenistan<\/li>\n<li>Myrat Chashemov<\/li>\n<li>Roger Bengtsson Lund, Sweden<\/li>\n<li>Burak Bu\u011fra \u00d6nder\u00a0\u0130stanbul Erkek Lisesi<\/li>\n<li>Bar\u0131\u015f Koyuncu\u00a0\u00d6zel Enka Lisesi, \u0130stanbul<\/li>\n<li>Muhammed \u0130kbal Ulvi\u00a0Bo\u011fazi\u00e7i University<\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2109a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2109a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are 777 points located on a circle \u03c9 each coloured into one of the colours 1, 2, . . . , k. For each of these points and for each colour 1 \u2264 r \u2264 k there exists an arc of \u03c9 containing this point such that at least [\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-september-2021\/\" 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-15831","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/15831","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=15831"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/15831\/revisions"}],"predecessor-version":[{"id":15991,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/15831\/revisions\/15991"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=15831"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}