{"id":25053,"date":"2025-07-08T13:11:56","date_gmt":"2025-07-08T10:11:56","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=25053"},"modified":"2025-07-08T13:14:43","modified_gmt":"2025-07-08T10:14:43","slug":"problem-of-the-month-june-2025","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-june-2025\/","title":{"rendered":"Problem of the Month \u2013 June 2025"},"content":{"rendered":"<p>Let <em>n<\/em> \u2265 4 is an integer. Suppose that some unit squares of <em>n<\/em> \u00d7 <em>n<\/em> grid are marked. We say that two distinct marked unit squares are line related if they are on the same line and there is no any other marked unit square on the same line located between them. We say that two distinct marked unit squares are column related if they are on the same column and there is no any other marked unit square on the same column located between them. We say that two marked unit squares are related if they are line or column related. Find the maximal possible number of marked unit squares on the <em>n<\/em> \u00d7 <em>n<\/em> grid if any marked unit square is related with an odd number of marked unit squares.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Murat Be\u015fli\u00a0Politecnico di Torino, Italy<\/li>\n<li>Magnus Jakobsson Lund, Sweden<\/li>\n<li>Roger Bengtsson\u00a0Lund, Sweden<\/li>\n<li>Arda Karahan\u00a0Trabzon Fen Lisesi<\/li>\n<li>Burak \u0130\u015finer Eker\u00a0Bilkent University<\/li>\n<li>Tamer T\u00fcrko\u011flu<\/li>\n<li>M\u00fcmtaz Ula\u015f Keskin<\/li>\n<li>Ramazan Kara\u015fahin\u00a0Ankara<\/li>\n<li>Choi Min Kyu\u00a0South Korea<\/li>\n<\/ul>\n<p><strong>Solution\u00a0<a href=\"https:\/\/math.bilkent.edu.tr\/Problem\/2506a.pdf\">2506a.pdf (bilkent.edu.tr)<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let n \u2265 4 is an integer. Suppose that some unit squares of n \u00d7 n grid are marked. We say that two distinct marked unit squares are line related if they are on the same line and there is no any other marked unit square on the same line [\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-june-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-25053","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25053","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=25053"}],"version-history":[{"count":2,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25053\/revisions"}],"predecessor-version":[{"id":25060,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25053\/revisions\/25060"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=25053"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}