{"id":2454,"date":"2021-11-06T09:34:27","date_gmt":"2021-11-06T13:34:27","guid":{"rendered":"https:\/\/josmfs.net\/?p=2454"},"modified":"2021-11-06T09:34:27","modified_gmt":"2021-11-06T13:34:27","slug":"existence-proofs-ii","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/11\/06\/existence-proofs-ii\/","title":{"rendered":"Existence Proofs II"},"content":{"rendered":"<p><em><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2452\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Existence-Proofs-II-Fig2.jpg\" alt=\"\" width=\"200\" height=\"200\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Existence-Proofs-II-Fig2.jpg 404w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Existence-Proofs-II-Fig2-300x300.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Existence-Proofs-II-Fig2-150x150.jpg 150w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Futility Closet<\/em> has another <a href=\"https:\/\/www.futilitycloset.com\/2021\/10\/26\/exercise-3\/\">example<\/a> of an existence proof like their previous <a href=\"https:\/\/www.futilitycloset.com\/2021\/06\/15\/state-house\/\">one<\/a> taken from Peter Winkler\u2019s 2021 <em>Mathematical Puzzles<\/em> (see my post \u201c<a href=\"https:\/\/josmfs.net\/2021\/09\/11\/existence-proofs\/\">Existence Proofs<\/a>\u201d):<\/p>\n<p>\u201cFour bugs live on the four vertices of a regular tetrahedron. One day each bug decides to go for a little walk on the tetrahedron\u2019s surface. After the walk, two of the bugs have returned to their homes, but the other two find that they have switched vertices. Prove that there was some moment when all four bugs lay on the same plane.\u201d<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/11\/Existence-Proofs-II-211027.pdf\">Existence Proofs II<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Futility Closet has another example of an existence proof like their previous one taken from Peter Winkler\u2019s 2021 Mathematical Puzzles (see my post \u201cExistence Proofs\u201d): \u201cFour bugs live on the four vertices of a regular tetrahedron. One day each bug decides to go for a little walk on the tetrahedron\u2019s surface. After the walk, two [&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":[16],"class_list":["post-2454","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-futility-closet"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2454","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=2454"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2454\/revisions"}],"predecessor-version":[{"id":2456,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2454\/revisions\/2456"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2454"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2454"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}