{"id":27709,"date":"2026-05-09T19:10:06","date_gmt":"2026-05-09T16:10:06","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=27709"},"modified":"2026-05-17T22:40:10","modified_gmt":"2026-05-17T19:40:10","slug":"problem-of-the-month-april-2026","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-april-2026\/","title":{"rendered":"Problem of the Month \u2013 April 2026"},"content":{"rendered":"<p>Alice and Bob play a game on a grid consisting of 2026 rowsande 9 columns. At the beginning of the game Alice inserts a number to each unit square such that all numbers of each row are different. After that they take turns to make move starting with Bob. Bob in each move chooses a number not chosen before and colour all unit squares containing this number to red. Alice in each move chooses a number not chosen before and colour all unit squares containing this number to blue. Suppose that Alice can guarantee that after colouring all unit squares there are at least <em>N<\/em> rows containing only blue unit squares. Determine the maximal possible value of <em>N<\/em>.<\/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<\/span><span class=\"solver-aff\">Kawasaki, Japan<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Hannes Nilsson<\/span><span class=\"solver-aff\">Copenhagen, Denmark<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">G\u00fcne\u015f Parlakg\u00fcl<\/span><span class=\"solver-aff\">University of California, Berkeley, USA<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Mustafa Kaynak<\/span><span class=\"solver-aff\">Gaziantep<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">\u00d6zg\u00fcr Soysal<\/span><span class=\"solver-aff\">Stanford University, USA<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Magnus Jakobsson<\/span><span class=\"solver-aff\">Lund, Sweden<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Roger Bengtsson<\/span><span class=\"solver-aff\">Lund, Sweden<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Murat Bur\u00e7<\/span><span class=\"solver-aff\">Soma, Manisa<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Mehmet Sarak<\/span><span class=\"solver-aff\">Bilkent University<\/span><\/li>\n<li class=\"solver-item\"><span class=\"solver-name\">Muhammed Cengiz<\/span><span class=\"solver-aff\">Bilkent University<\/span><\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"https:\/\/math.bilkent.edu.tr\/Problem\/2604a.pdf\">https:\/\/math.bilkent.edu.tr\/Problem\/2604a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alice and Bob play a game on a grid consisting of 2026 rowsande 9 columns. At the beginning of the game Alice inserts a number to each unit square such that all numbers of each row are different. After that they take turns to make move starting with Bob. Bob [\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-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-27709","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/27709","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=27709"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/27709\/revisions"}],"predecessor-version":[{"id":27778,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/27709\/revisions\/27778"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=27709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}