{"id":14584,"date":"2021-01-11T11:33:55","date_gmt":"2021-01-11T08:33:55","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=14584"},"modified":"2021-02-08T14:45:27","modified_gmt":"2021-02-08T11:45:27","slug":"problem-of-the-month-january-2021","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-january-2021\/","title":{"rendered":"Problem of the Month \u2013 January 2021"},"content":{"rendered":"<p>There are 2021 distinguishable boxes on the table. Starting Alice, Alice and Bob take turn<br \/>\nwriting an unordered box pair to the table (each unordered box pair can be written at most<br \/>\nonce). They stop when there are 4038 written pairs on the table. After that Bob numerates<br \/>\nall box pairs by numbers 1, 2, . . . , 4038 and for each <em>k<\/em> = 1, 2, . . . , 4038 puts <em>k<\/em> balls into each<br \/>\nbox belonging to the pair numbered <em>k<\/em>. Can Bob guarantee that any two boxes will contain<br \/>\ndifferent number of balls?<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu, Kawasaki, Japan<\/li>\n<li>Alper Balc\u0131, Bilkent University<\/li>\n<li>Hasan Z\u00fcbeyr Demir, \u00d6zel Ankara \u00c7a\u011flayan Fen Lisesi, Ankara<\/li>\n<li>Muhammed \u0130kbal Ulvi,\u00a0Orta Do\u011fu Teknik \u00dcniversitesi, Ankara<\/li>\n<li>Roger Bengtsson, Lund, Sweden<\/li>\n<li>Magnus Jakobsson, Lund, Sweden<\/li>\n<li>Kadyr Annabayev,\u00a0Turkmen State Institute of Architecture and Construction, A\u015fkabat<\/li>\n<li>Jepbar Asgarov,\u00a0Hitrowka, Turkmenistan<\/li>\n<li>Halil \u00d6zkan,\u00a0Bo\u011fazi\u00e7i University<\/li>\n<li>\u00d6mer Topalo\u011flu, Bo\u011fazi\u00e7i University<\/li>\n<\/ul>\n<ul>\n<li><strong>Solution:\u00a0<a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2101a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2101a.pdf<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>There are 2021 distinguishable boxes on the table. Starting Alice, Alice and Bob take turn writing an unordered box pair to the table (each unordered box pair can be written at most once). They stop when there are 4038 written pairs on the table. After that Bob numerates all box [\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-january-2021\/\" 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-14584","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/14584","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=14584"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/14584\/revisions"}],"predecessor-version":[{"id":14713,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/14584\/revisions\/14713"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=14584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}