{"id":4648,"date":"2025-11-08T12:18:27","date_gmt":"2025-11-08T17:18:27","guid":{"rendered":"https:\/\/josmfs.net\/?p=4648"},"modified":"2025-11-08T12:18:27","modified_gmt":"2025-11-08T17:18:27","slug":"functional-equation-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2025\/11\/08\/functional-equation-puzzle\/","title":{"rendered":"Functional Equation Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4645\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/11\/Functional-Equation-Puzzle-Fig2.jpg\" alt=\"\" width=\"248\" height=\"156\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/11\/Functional-Equation-Puzzle-Fig2.jpg 500w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/11\/Functional-Equation-Puzzle-Fig2-300x189.jpg 300w\" sizes=\"auto, (max-width: 248px) 100vw, 248px\" \/>This is a math Olympiad <a href=\"https:\/\/medium.com\/puzzle-sphere\/only-geniuses-can-solve-this-harvard-entrance-exam-level-functional-equation-054fe8476a41\">problem<\/a> from Puzzle Sphere where Muhammad Zain Sarwar claims it is at Harvard entrance exam level.<\/p>\n<p>\u201cGiven the functional relationship\u00a0 <em>f<\/em>(<em>x + y<\/em>) = <em>f<\/em>(<em>x<\/em>) + <em>f<\/em>(<em>y<\/em>) + <em>xy <\/em>with the known value\u00a0 <em>f<\/em>(4) = 10, determine the value of <em>f<\/em>(2023).\u201d<\/p>\n<p>Just try some examples and detect the pattern that defines the function.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/11\/Functional-Equation-Puzzle-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2025\/11\/Functional-Equation-Puzzle-251011.pdf\">Functional Equation Puzzle<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a math Olympiad problem from Puzzle Sphere where Muhammad Zain Sarwar claims it is at Harvard entrance exam level. \u201cGiven the functional relationship\u00a0 f(x + y) = f(x) + f(y) + xy with the known value\u00a0 f(4) = 10, determine the value of f(2023).\u201d Just try some examples and detect the pattern that [&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":[133,288,277],"class_list":["post-4648","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-algebra","tag-functional-equation","tag-puzzle-sphere"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4648","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=4648"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4648\/revisions"}],"predecessor-version":[{"id":4649,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4648\/revisions\/4649"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}