{"id":10867,"date":"2019-04-05T17:08:11","date_gmt":"2019-04-05T14:08:11","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=10867"},"modified":"2019-05-08T08:45:07","modified_gmt":"2019-05-08T05:45:07","slug":"problem-of-the-month-april-2019","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-april-2019\/","title":{"rendered":"Problem of the Month \u2013 April 2019"},"content":{"rendered":"<p>There are 2019 bags: each bag contains 2019 beads with total weight 2019 gr. In each bag<br \/>\nthe beads are numbered by 1, 2, . . . , 2019. A proper collection is a collection of differently<br \/>\nnumbered beads containing at most one bead from each bag and having total weight not<br \/>\nless than 2019 gr. Find the maximal possible value of <em>k<\/em>, if one can always choose at least<br \/>\n<em>k<\/em> different proper collections.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Max Nilsson Lund, Sweden<\/li>\n<li>Hakan Karaku\u015f\u00a0Antalya Yusuf Ziya \u00d6ner Fen Lisesi, Antalya<\/li>\n<li>Ender Do\u011fan I\u015f\u0131k\u00a0Final Okullar\u0131, Ankara<\/li>\n<li>\u00d6mer Topalo\u011flu\u00a0\u00d6zel \u0130zmir Fen Lisesi,\u00a0 \u0130zmir<\/li>\n<li>Hasan Z\u00fcbeyr Demir\u00a0\u00d6zel Ankara \u00c7a\u011flayan Fen Lisesi<\/li>\n<li>Halil Alperen G\u00f6zeten\u00a0Denizli \u00d6zel Denizli Koleji,\u00a0 Denizli<\/li>\n<li>Mustafa Emir \u00c7elebi\u00a0\u0130stanbul Erkek Lisesi,\u00a0 \u0130stanbul<\/li>\n<li>\u0130brahim Suat Evren\u00a0Denizli \u00d6zel Denizli Koleji, Denizli<\/li>\n<\/ul>\n<ul>\n<li><strong>Solution:\u00a0<\/strong><a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1904a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1904a.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>There are 2019 bags: each bag contains 2019 beads with total weight 2019 gr. In each bag the beads are numbered by 1, 2, . . . , 2019. A proper collection is a collection of differently numbered beads containing at most one bead from each bag and having total [\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-2019\/\" 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-10867","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10867","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=10867"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10867\/revisions"}],"predecessor-version":[{"id":11279,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10867\/revisions\/11279"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=10867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}