{"id":4197,"date":"2024-12-14T09:47:52","date_gmt":"2024-12-14T14:47:52","guid":{"rendered":"https:\/\/josmfs.net\/?p=4197"},"modified":"2024-12-14T09:47:52","modified_gmt":"2024-12-14T14:47:52","slug":"sphere-and-plane-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/12\/14\/sphere-and-plane-puzzle\/","title":{"rendered":"Sphere and Plane Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4196\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/12\/Sphere-and-Plane2-Fig2.jpg\" alt=\"\" width=\"251\" height=\"149\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/12\/Sphere-and-Plane2-Fig2.jpg 500w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/12\/Sphere-and-Plane2-Fig2-300x178.jpg 300w\" sizes=\"auto, (max-width: 251px) 100vw, 251px\" \/>This is another <a href=\"https:\/\/medium.com\/bellas-weekly-math-games\/whats-the-difference-between-max-and-min-6857f13001b5\">puzzle<\/a> from BL\u2019s Weekly Math Games.<\/p>\n<p style=\"text-align: center;\"><em>\u201ca + b + c <\/em>= 2, and<\/p>\n<p style=\"text-align: center;\"><em>a<\/em><sup>2<\/sup> + <em>b<\/em><sup>2<\/sup> + <em>c<\/em><sup>2<\/sup> = 12<\/p>\n<p>where <em>a, b,<\/em> and <em>c<\/em> are real numbers.\u00a0 What is the difference between the maximum and minimum possible values of <em>c<\/em>?\u201d<\/p>\n<p>The original problem statement mentioned a fourth real number <em>d<\/em>, but I considered it a typo, since it was not involved in the problem.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/12\/Sphere-and-Plane-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/12\/Sphere-and-Plane-Puzzle-241211.pdf\">Sphere and Plane Puzzle<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is another puzzle from BL\u2019s Weekly Math Games. \u201ca + b + c = 2, and a2 + b2 + c2 = 12 where a, b, and c are real numbers.\u00a0 What is the difference between the maximum and minimum possible values of c?\u201d The original problem statement mentioned a fourth real number d, [&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":[40,274,32],"class_list":["post-4197","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-analytic-geometry","tag-bl-puzzles","tag-calculus"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4197","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=4197"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4197\/revisions"}],"predecessor-version":[{"id":4198,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4197\/revisions\/4198"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}