{"id":4301,"date":"2025-03-01T08:35:42","date_gmt":"2025-03-01T13:35:42","guid":{"rendered":"https:\/\/josmfs.net\/?p=4301"},"modified":"2025-05-20T13:39:48","modified_gmt":"2025-05-20T17:39:48","slug":"circular-ant-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2025\/03\/01\/circular-ant-problem\/","title":{"rendered":"Circular Ant Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4298\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/03\/Circular-Ant-Problem-Fig2.jpg\" alt=\"\" width=\"201\" height=\"201\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/03\/Circular-Ant-Problem-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/03\/Circular-Ant-Problem-Fig2-300x300.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/03\/Circular-Ant-Problem-Fig2-150x150.jpg 150w\" sizes=\"auto, (max-width: 201px) 100vw, 201px\" \/>This is a wicked variation of the ant problem on a <a href=\"https:\/\/josmfs.net\/wordpress\/2018\/12\/28\/ant-problem\/\">stick<\/a> by Peter Winkler.<\/p>\n<p>\u201cTwenty-four ants are randomly placed on a circular track of length 1 meter; each ant faces randomly clockwise or counterclockwise.\u00a0 At a signal, the ants begin marching at 1\u00a0cm\/sec; when two ants collide they both reverse directions.\u00a0 What is the probability that after 100 seconds, every ant finds itself exactly where it began?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/03\/Circular-Ant-Problem-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/03\/Circular-Ant-Problem-250223.pdf\">Circular Ant Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a wicked variation of the ant problem on a stick by Peter Winkler. \u201cTwenty-four ants are randomly placed on a circular track of length 1 meter; each ant faces randomly clockwise or counterclockwise.\u00a0 At a signal, the ants begin marching at 1\u00a0cm\/sec; when two ants collide they both reverse directions.\u00a0 What is the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[282,138],"class_list":["post-4301","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-peter-winkler","tag-probability"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4301","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=4301"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4301\/revisions"}],"predecessor-version":[{"id":4302,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4301\/revisions\/4302"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}