{"id":10283,"date":"2019-02-08T09:43:30","date_gmt":"2019-02-08T06:43:30","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=10283"},"modified":"2019-03-13T09:15:28","modified_gmt":"2019-03-13T06:15:28","slug":"problem-of-the-month-february-2019","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-february-2019\/","title":{"rendered":"Problem of the Month \u2013 February 2019"},"content":{"rendered":"<p>There are <em>k<\/em> heaps of beads containing 2019 beads in total. In each move we choose a heap: either remove it or divide it into two not necessarily equal parts. Find the maximal possible value of <em>k<\/em> such that for any initial distribution of beads after finite number of moves one can get <em>k<\/em> heaps with pairwise distinct number of beads.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Susanne Tegler\u00a0Lund, Sweden<\/li>\n<li>Steffen Webber Ismaning, Germany<\/li>\n<li>Vedat Deveci\u00a0\u0130stanbul<\/li>\n<li>Magnus Jakobsson Lund, Sweden<\/li>\n<li>Dovran\u00a0 Nurgeldiyev Magtumguly Turkmen State University, Turkmenistan<\/li>\n<li>Serdar Hojayev\u00a0Dashoguz, Turkmenistan<\/li>\n<li>Berkay Unlu Dokuz Eyl\u00fcl University, \u0130zmir<\/li>\n<li>Hasan Z\u00fcbeyr Demir\u00a0\u00d6zel Ankara \u00c7a\u011flayan Fen Lisesi<\/li>\n<li>Asude Ebrar K\u0131z\u0131lo\u011flu\u00a0\u00d6zel Kad\u0131k\u00f6y E\u011fitmen\u00a0 Fen ve Anadolu Lisesi, \u0130stanbul<\/li>\n<li>\u0130rem Nur \u00c7evikcan\u00a0Buca Fen Lisesi, \u0130zmir<\/li>\n<li>Henrik Aberg\u00a0Gothenburg, Sweden<\/li>\n<\/ul>\n<ul>\n<li><strong>Solution:\u00a0<\/strong><a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1902a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1902a.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>There are k heaps of beads containing 2019 beads in total. In each move we choose a heap: either remove it or divide it into two not necessarily equal parts. Find the maximal possible value of k such that for any initial distribution of beads after finite number of moves [\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-february-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-10283","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10283","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=10283"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10283\/revisions"}],"predecessor-version":[{"id":10599,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/10283\/revisions\/10599"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=10283"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}