{"id":3150,"date":"2023-04-22T15:44:04","date_gmt":"2023-04-22T19:44:04","guid":{"rendered":"https:\/\/josmfs.net\/?p=3150"},"modified":"2025-01-29T10:52:14","modified_gmt":"2025-01-29T15:52:14","slug":"the-tired-messenger-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/04\/22\/the-tired-messenger-problem\/","title":{"rendered":"The Tired Messenger Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3148\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/04\/Tired-Messenger-Fig2.jpg\" alt=\"\" width=\"156\" height=\"217\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/04\/Tired-Messenger-Fig2.jpg 397w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/04\/Tired-Messenger-Fig2-216x300.jpg 216w\" sizes=\"auto, (max-width: 156px) 100vw, 156px\" \/>Here is another challenging problem from the Polish Mathematical Olympiads.\u00a0 Its generality will cause more thought than for a simpler, specific problem.<\/p>\n<p>\u201cA cyclist sets off from point <em>O<\/em> and rides with constant velocity <em>v<\/em> along a rectilinear highway.\u00a0 A messenger, who is at a distance <em>a<\/em> from point <em>O<\/em> and at a distance <em>b<\/em> from the highway, wants to deliver a letter to the cyclist.\u00a0 What is the minimum velocity with which the messenger should run in order to attain his objective?\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/04\/Tired-Messenger-Problem-210814.pdf\">Tired Messenger Problem<\/a><\/p>\n<p><strong>(Update 1\/29\/2025)\u00a0 Dan Steinitz Solution<\/strong><\/p>\n<p>Dan Steinitz from Israel has sent an elegant solution that only involves vectors and geometry without calculus.\u00a0 I have edited slightly his email and added excerpts from his whiteboard solution, though without the Hebrew annotations, which unfortunately I cannot read.\u00a0 But that is the glory of the universal language of mathematics: it can be read and understood in any language.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/01\/Dan-Steinitz-Solution-250129.pdf\">Dan Steinitz Solution<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another challenging problem from the Polish Mathematical Olympiads.\u00a0 Its generality will cause more thought than for a simpler, specific problem. \u201cA cyclist sets off from point O and rides with constant velocity v along a rectilinear highway.\u00a0 A messenger, who is at a distance a from point O and at a distance b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[32,222,41],"class_list":["post-3150","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-calculus","tag-polish-math-olympiads","tag-trigonometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3150","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=3150"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3150\/revisions"}],"predecessor-version":[{"id":4250,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3150\/revisions\/4250"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}