{"id":22209,"date":"2024-06-06T19:35:31","date_gmt":"2024-06-06T16:35:31","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=22209"},"modified":"2024-07-17T22:17:14","modified_gmt":"2024-07-17T19:17:14","slug":"problem-of-the-month-june-2024","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-june-2024\/","title":{"rendered":"Problem of the Month \u2013 June 2024"},"content":{"rendered":"<p>There are 353 red balls, 535 white balls and 888 empty boxes numbered 1, 2\u2026.888 on the table. Alice distributed these 888 balls to 888 boxes so that each box contains one ball. Bob is going to find out ball colors in all 888 boxes. In order to do this Bob writes <em>N<\/em> pairs (<em>i, j<\/em>) 1 <em>i<\/em> &lt; <em>j<\/em> 888 to the board. After that for each pair (<em>i, j<\/em>) on the board Alice informs Bob, whether balls in the boxes <em>i<\/em> and <em>j<\/em> are same-coloured. Find the minimal value of <em>N<\/em> for which Bob can guarantee to determine the ball colors in all 888 boxes.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Mehmet \u00c7a\u011fatay \u00dcnl\u00fc\u00a0Istanbul Atat\u00fcrk Fen Lisesi<\/li>\n<li>Roge \u0130samil Toy\u00a0TOBB University<\/li>\n<li>Roger Bengtsson\u00a0Lund, Sweden<\/li>\n<li>Magnus Jakobsson Lund, Sweden<\/li>\n<li>Mustafa Dortluo\u011flu\u00a0Robert College, \u0130stanbul<\/li>\n<li>Tu\u011fra \u00d6zbey Eratl\u0131\u00a0Kocaeli Enka Okullar\u0131<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>Solution:\u00a0<a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2406a.pdf\">2406a.pdf (bilkent.edu.tr)<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are 353 red balls, 535 white balls and 888 empty boxes numbered 1, 2\u2026.888 on the table. Alice distributed these 888 balls to 888 boxes so that each box contains one ball. Bob is going to find out ball colors in all 888 boxes. In order to do this [\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-2024\/\" 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-22209","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/22209","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=22209"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/22209\/revisions"}],"predecessor-version":[{"id":22388,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/22209\/revisions\/22388"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=22209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}