{"id":27051,"date":"2026-03-09T18:08:51","date_gmt":"2026-03-09T15:08:51","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=27051"},"modified":"2026-05-09T19:09:11","modified_gmt":"2026-05-09T16:09:11","slug":"problem-of-the-month-march-2026","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-march-2026\/","title":{"rendered":"Problem of the Month \u2013 March 2026"},"content":{"rendered":"<p>On each vertex of a regular <em>n<\/em> \u2265 3 sided polygon there is a real number so that the sum of these <em>n<\/em> numbers is zero. For any two vertices of the polygon with numbers x and y consider the line passing through these vertices dividing the polygon into two parts. Let the sum of numbers written on one of these parts be <em>A<\/em> and the sum of numbers written on the other part be <em>B<\/em>. If<\/p>\n<p style=\"text-align: center;\">|x \u2212 y| \u2265 |A \u2212 B|<\/p>\n<p>we say that this pair of vertices is good. For each fixed <em>n<\/em> find the minimal possible number of good vertex pairs.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li class=\"solver-item\"><span class=\"solver-name\">Toshihiro Shimizu\u00a0<\/span><span class=\"solver-aff\">Kawasaki, Japan<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Abdulkadir Tanr\u0131verdi\u00a0<\/span><span class=\"solver-aff\">Eski\u015fehir<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Ahmet Y\u00fcksel\u00a0<\/span><span class=\"solver-aff\">Ayd\u0131n<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Murat Bur\u00e7\u00a0<\/span><span class=\"solver-aff\">Soma, Manisa<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Magnus Jakobsson\u00a0<\/span><span class=\"solver-aff\">Lund, Sweden<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Roger Bengtsson\u00a0<\/span><span class=\"solver-aff\">Lund, Sweden<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Tamer T\u00fcrko\u011flu\u00a0<\/span><span class=\"solver-aff\">Bilkent University alumnus<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Mustafa Kaynak\u00a0<\/span><span class=\"solver-aff\">Gaziantep<\/span><\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"https:\/\/math.bilkent.edu.tr\/Problem\/2603a.pdf\">https:\/\/math.bilkent.edu.tr\/Problem\/2603a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>On each vertex of a regular n \u2265 3 sided polygon there is a real number so that the sum of these n numbers is zero. For any two vertices of the polygon with numbers x and y consider the line passing through these vertices dividing the polygon into two [\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-2026\/\" 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-27051","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/27051","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=27051"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/27051\/revisions"}],"predecessor-version":[{"id":27708,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/27051\/revisions\/27708"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=27051"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}