{"id":6535,"date":"2017-07-24T19:22:06","date_gmt":"2017-07-24T16:22:06","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=6535"},"modified":"2017-09-14T11:58:09","modified_gmt":"2017-09-14T08:58:09","slug":"problem-of-the-month-july-august-2017","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-july-august-2017\/","title":{"rendered":"Problem of the Month \u2013 July, August 2017"},"content":{"rendered":"<p>There are 2017 nonempty bags each containing finite number of colored balls. Find the smallest value of <em>k<\/em> for which no matter how the contents of bags are arranged the bags can be distributed into <em>k<\/em> boxes so that for each box at least one of the following two conditions is held:<br \/>\n\u2022 all bags of a box contain a ball of the same color<br \/>\n\u2022\u2022 each bag of a box contains a ball colored differently from all balls of all other bags of this box.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu, Kawasaki, Japan<\/li>\n<li>Serdar Hojayev Dashoguz, Turkmenistan<\/li>\n<li>Hasan Zubeyr Demir, \u00d6zel \u00c7aglayan Fen Lisesi, Ankara<\/li>\n<li>Tomas Jurik, Kosice, Slovakia<\/li>\n<li>Leo Chin Ho, National University of Singapore, Singapore,<\/li>\n<li>Mehmet Ali Y\u0131ld\u0131r\u0131m, Florya Final Anadolu Lisesi, \u0130stanbul<\/li>\n<li>Roger Bengtsson Lund, Sweden<\/li>\n<\/ul>\n<ul>\n<li><strong>Solution:\u00a0<\/strong><a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1707a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/1707a.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>There are 2017 nonempty bags each containing finite number of colored balls. Find the smallest value of k for which no matter how the contents of bags are arranged the bags can be distributed into k boxes so that for each box at least one of the following two conditions [\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-july-august-2017\/\" 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-6535","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/6535","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=6535"}],"version-history":[{"count":2,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/6535\/revisions"}],"predecessor-version":[{"id":6668,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/6535\/revisions\/6668"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=6535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}