{"id":3042,"date":"2023-01-21T09:35:00","date_gmt":"2023-01-21T14:35:00","guid":{"rendered":"https:\/\/josmfs.net\/?p=3042"},"modified":"2024-10-19T09:53:17","modified_gmt":"2024-10-19T13:53:17","slug":"fermats-last-theorem-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/01\/21\/fermats-last-theorem-puzzle\/","title":{"rendered":"\u201cFermat\u2019s Last Theorem\u201d Puzzle"},"content":{"rendered":"

\"\"<\/p>\n

Here is a mind-numbing logic puzzle from Futility Closet<\/em>.<\/p>\n

\u201cA puzzle by H.A. Thurston, from the April 1947 issue of Eureka<\/em>, the journal of recreational mathematics published at Cambridge University:<\/p>\n

Five people make the following statements:\u2014<\/p>\n

\"\"<\/p>\n

Which of these statements are true and which false?\u00a0 It will be found on trial that there is only one possibility.\u00a0 Thus, prove or disprove Fermat\u2019s last theorem.\u201d<\/p>\n

Normally I would forgo something this complicated, but I thought I would give it a try.\u00a0 I was surprised that I was able to solve it, though it took some tedious work.\u00a0 (Hint: truth tables.\u00a0 See the \u201cPointing Fingers<\/a>\u201d post regarding truth tables.)<\/p>\n

One important note.\u00a0 The author is a bit cavalier about the use of \u201cEither \u2026, or \u2026\u201d.\u00a0 In common parlance this means \u201ceither P is true or Q is true, but not both<\/em>\u201d (exclusive \u201cor\u201d: XOR), whereas in logic \u201cor\u201d means \u201ceither P is true or Q is true, or possibly both<\/em>\u201d (inclusive \u201cor\u201d: OR).\u00a0 I assumed all \u201cEither \u2026, or \u2026\u201d and \u201cor\u201d expressions were the logical inclusive \u201cor\u201d, which turned out to be the case.<\/p>\n

See the Fermat\u2019s Last Theorem Puzzle<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Here is a mind-numbing logic puzzle from Futility Closet. \u201cA puzzle by H.A. Thurston, from the April 1947 issue of Eureka, the journal of recreational mathematics published at Cambridge University: Five people make the following statements:\u2014 Which of these statements are true and which false?\u00a0 It will be found on trial that there is only […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[234,16,174,256],"class_list":["post-3042","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-eureka-magazine","tag-futility-closet","tag-logic","tag-truth-tables"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3042","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=3042"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3042\/revisions"}],"predecessor-version":[{"id":3055,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3042\/revisions\/3055"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}