{"id":25903,"date":"2025-11-12T20:09:45","date_gmt":"2025-11-12T17:09:45","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=25903"},"modified":"2025-12-14T23:00:18","modified_gmt":"2025-12-14T20:00:18","slug":"problem-of-the-month-november-2025","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-november-2025\/","title":{"rendered":"Problem of the Month \u2013 November 2025"},"content":{"rendered":"<p>Let <em>P<sub>1<\/sub>,\u00a0. . . , P<sub>1024<\/sub><\/em> be distinct points marked on a circle, and let <em>a<sub>1<\/sub>, a<sub>2<\/sub>, . . . , a<sub>1024<\/sub><\/em> be distinct real numbers written on these points, respectively. For each point <em>Q<\/em> on this circle different than <em>P<sub>1<\/sub>,\u00a0. . . , P<sub>1024<\/sub><\/em>, we say that <em>P<sub>i<\/sub><\/em>\u00a0is <em>Q-good<\/em> if ai is the greatest number on at least one of the two arcs <em>P<sub>i<\/sub>Q<\/em> on this circle. Let the score of <em>Q<\/em> be the number of <em>Q\u2212good<\/em> points on the circle. Determine the greatest integer <em>k<\/em> such that regardless of the values of <em>a<sub>1<\/sub>, a<sub>2<\/sub>, . . . , a<sub>1024<\/sub><\/em>, there exists a point <em>Q<\/em> with score at least <em>k<\/em>.<\/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>Mehmet Sarak Bilkent University<\/li>\n<li>Yunus Orazow 40th Specialized School, Ashkabat, Turkmenistan<\/li>\n<li>Emir Kara\u00a0Gazi Anadolu Lisesi, Ankara<\/li>\n<li>Mustafa Kaynak\u00a0Gaziantep<\/li>\n<li>Erenalp Yuca\u00a0Bilkent University<\/li>\n<li>Abdulkadir Tanr\u0131verdi Eski\u015fehir<\/li>\n<li>Magnus Jakobsson\u00a0Lund, Sweden<\/li>\n<li>Roger Bengtsson\u00a0Lund, Sweden<\/li>\n<li>Alper Balc\u0131\u00a0Ohio State University, USA<\/li>\n<li>\u00d6zg\u00fcr Soysal\u00a0Bilkent University<\/li>\n<li>Ananda Raidu\u00a0Rajahmundry, India<\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"https:\/\/math.bilkent.edu.tr\/Problem\/2511a.pdf\">https:\/\/math.bilkent.edu.tr\/Problem\/2511a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let P1,\u00a0. . . , P1024 be distinct points marked on a circle, and let a1, a2, . . . , a1024 be distinct real numbers written on these points, respectively. For each point Q on this circle different than P1,\u00a0. . . , P1024, we say that Pi\u00a0is Q-good [\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-november-2025\/\" 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-25903","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25903","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=25903"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25903\/revisions"}],"predecessor-version":[{"id":25906,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25903\/revisions\/25906"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=25903"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}