{"id":2783,"date":"2022-07-09T08:15:09","date_gmt":"2022-07-09T12:15:09","guid":{"rendered":"https:\/\/josmfs.net\/?p=2783"},"modified":"2024-10-19T09:54:49","modified_gmt":"2024-10-19T13:54:49","slug":"pinocchios-hats","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/07\/09\/pinocchios-hats\/","title":{"rendered":"Pinocchio\u2019s Hats"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2790\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/07\/Pinocchios-Hats-Fig2b.jpg\" alt=\"\" width=\"184\" height=\"369\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/07\/Pinocchios-Hats-Fig2b.jpg 252w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/07\/Pinocchios-Hats-Fig2b-150x300.jpg 150w\" sizes=\"auto, (max-width: 184px) 100vw, 184px\" \/>This <a href=\"https:\/\/mindyourdecisions.com\/blog\/2022\/06\/22\/brazilian-olympiad-pinocchios-green-hats-viral-question\">problem<\/a> in logic from Presh Talwalkar recalled an article I wrote a while ago but did not publish.\u00a0 So I thought I would post it as part of the solution.<\/p>\n<p>\u201cAssume that both of the following sentences are true:<\/p>\n<ol>\n<li>Pinocchio always lies;<\/li>\n<li>Pinocchio says, \u201cAll my hats are green.\u201d<\/li>\n<\/ol>\n<p>We can conclude from these two sentences that:<\/p>\n<ul>\n<li>(A) Pinocchio has at least one hat.<\/li>\n<li>(B) Pinocchio has only one green hat.<\/li>\n<li>(C) Pinocchio has no hats.<\/li>\n<li>(D) Pinocchio has at least one green hat.<\/li>\n<li>(E) Pinocchio has no green hats.\u201d<\/li>\n<\/ul>\n<p>Actually, the question is which, none or more, of statements (A) \u2013 (E) follow from the two sentences?<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Pinocchios-Hats-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/07\/Pinocchios-Hats-220627.pdf\">Pinocchio\u2019s Hats<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This problem in logic from Presh Talwalkar recalled an article I wrote a while ago but did not publish.\u00a0 So I thought I would post it as part of the solution. \u201cAssume that both of the following sentences are true: Pinocchio always lies; Pinocchio says, \u201cAll my hats are green.\u201d We can conclude from these [&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":[174,17,256,247],"class_list":["post-2783","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-logic","tag-presh-talwalkar","tag-truth-tables","tag-vacuous-truth"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2783","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=2783"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2783\/revisions"}],"predecessor-version":[{"id":3611,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2783\/revisions\/3611"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2783"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2783"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2783"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}