{"id":13610,"date":"2020-06-12T04:16:46","date_gmt":"2020-06-12T01:16:46","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=13610"},"modified":"2020-07-23T23:30:22","modified_gmt":"2020-07-23T20:30:22","slug":"problem-of-the-month-june-2020","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-june-2020\/","title":{"rendered":"Problem of the Month \u2013 June 2020"},"content":{"rendered":"<p>99 dwarves have in total 166 hats. Each of these hats belongs to only one of the dwarves\u00a0and is painted into one of 99 colors. Several festivals with participation of all 99 dwarves\u00a0are organized. In each festival each dwarf wears one of its hats. No dwarves wear the same\u00a0coloured hats in any given festival. For any pair of festivals there is at least one dwarf\u00a0which wears differently coloured hats in these festivals. Find the maximal possible number<br \/>\nof organized festivals.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu, Kawasaki, Japan<\/li>\n<li>Roger Bengtsson, Lund, Sweden<\/li>\n<li>Magnus Jakobsson, Lund, Sweden<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<ul>\n<li><strong>Solution:\u00a0<\/strong><a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2006a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2006a.pdf<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>99 dwarves have in total 166 hats. Each of these hats belongs to only one of the dwarves\u00a0and is painted into one of 99 colors. Several festivals with participation of all 99 dwarves\u00a0are organized. In each festival each dwarf wears one of its hats. No dwarves wear the same\u00a0coloured hats [\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-2020\/\" 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-13610","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/13610","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=13610"}],"version-history":[{"count":3,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/13610\/revisions"}],"predecessor-version":[{"id":13712,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/13610\/revisions\/13712"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=13610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}