{"id":1347,"date":"2019-11-22T08:56:25","date_gmt":"2019-11-22T13:56:25","guid":{"rendered":"http:\/\/josmfs.net\/?p=1347"},"modified":"2024-04-10T13:30:06","modified_gmt":"2024-04-10T17:30:06","slug":"movie-projector-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/11\/22\/movie-projector-problem\/","title":{"rendered":"Movie Projector Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1345\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/11\/Movie-Projector-Prob-Fig.jpg\" alt=\"\" width=\"200\" height=\"207\" \/>Here is another Brain Bogglers problem from 1987.<\/p>\n<p>\u201cExactly four minutes after starting to run\u2014when the take-up reel was rotating one and a half times as fast as the projecting reel\u2014the film broke. (The hub diameter of the smaller take-up reel is 8 cm and the hub diameter of the projecting reel is 12 cm.) How many minutes of film remain to be shown?\u201d<\/p>\n<p>This feels like another problem where there is insufficient information to solve it, and that makes it fun and challenging. In fact, I was stumped for a while until I noticed something that was the key to completing the solution.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Movie-Projector-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/11\/Movie-Projector-Problem-191010.pdf\">Movie Projector Problem<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another Brain Bogglers problem from 1987. \u201cExactly four minutes after starting to run\u2014when the take-up reel was rotating one and a half times as fast as the projecting reel\u2014the film broke. (The hub diameter of the smaller take-up reel is 8 cm and the hub diameter of the projecting reel is 12 cm.) [&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":[133,163,32],"class_list":["post-1347","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-algebra","tag-brain-bogglers","tag-calculus"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1347","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=1347"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1347\/revisions"}],"predecessor-version":[{"id":3792,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1347\/revisions\/3792"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}