{"id":11280,"date":"2019-05-08T08:52:33","date_gmt":"2019-05-08T05:52:33","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=11280"},"modified":"2019-06-10T10:11:18","modified_gmt":"2019-06-10T07:11:18","slug":"problem-of-the-month-may-2019","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-may-2019\/","title":{"rendered":"Problem of the Month \u2013 May 2019"},"content":{"rendered":"<p>Let <em>S<\/em> = {1, 2, . . . , 2019} and A<sub>1<\/sub>, A<sub>2<\/sub>, . . . , A<sub>n<\/sub> be subsets of <em>S<\/em> such that the union of any<br \/>\nthree of them is equal to <em>S<\/em> and the union of any two of them is not equal to <em>S<\/em>.<br \/>\nFind 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>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Murat Chashmetov TSU Turkmenistan<\/li>\n<li>Bora Ege Duygun Bilkent University<\/li>\n<li>Magnus Jakobsson\u00a0Lund, Sweden<\/li>\n<li>Roger Bengtsson\u00a0Lund, Sweden<\/li>\n<li>Max Nilsson\u00a0Lund,\u00a0 Sweden<\/li>\n<li>Steffen Weber\u00a0Isman\u0131ng, Germany<\/li>\n<li>\u0130rem Nur \u00c7evikcan\u00a0Buca \u0130nci \u00d6zer T\u0131rnakl\u0131 Fen Lisesi<\/li>\n<li>Feray Lina Yence\u00a0Buca \u0130nci \u00d6zer T\u0131rnakl\u0131 Fen Lisesi<\/li>\n<li>Asude Ebrar K\u0131z\u0131lo\u011flu\u00a0Kad\u0131k\u00f6y \u00d6zel E\u011fitmen Fen ve Anadolu Lisesi<\/li>\n<li>Ay\u015fe Zehra \u015een\u00a0\u0130stanbul Lisesi<\/li>\n<li>Hasan Z\u00fcbeyr Demir\u00a0\u00d6zel Ankara \u00c7a\u011flayan Fen Lisesi<\/li>\n<li>Sude Filiz\u00a0\u0130zmir Bilfen Fen Lisesi<\/li>\n<li>Serdar Hojayev\u00a0Dashoguz, Turkmenistan<\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<\/strong><a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1905a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1905a.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let S = {1, 2, . . . , 2019} and A1, A2, . . . , An be subsets of S such that the union of any three of them is equal to S and the union of any two of them is not equal to S. Find the [\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-may-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-11280","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/11280","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=11280"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/11280\/revisions"}],"predecessor-version":[{"id":11543,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/11280\/revisions\/11543"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=11280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}