{"id":880,"date":"2019-04-04T15:33:33","date_gmt":"2019-04-04T19:33:33","guid":{"rendered":"http:\/\/josmfs.net\/?p=880"},"modified":"2024-04-14T10:50:01","modified_gmt":"2024-04-14T14:50:01","slug":"putnam-octagon-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/04\/04\/putnam-octagon-problem\/","title":{"rendered":"Putnam Octagon Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-875\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/04\/Putnam-Octagon-Prob-fig.jpg\" alt=\"\" width=\"200\" height=\"203\" \/>Here is a problem from the famous (infamous?) Putnam exam, presented by Presh Talwalkar. Needless to say, I did not solve it in 30 minutes\u2014but at least I solved it (after making a blizzard of arithmetic and trigonometric errors).<\/p>\n<p>\u201cToday\u2019s problem is from the 1978 test, problem B1 (the easiest of the second set of problems). A convex octagon inscribed in a circle has four consecutive sides of length 3 and four consecutive sides of length 2. Find the area of the octagon.&#8221;<\/p>\n<p>My solution is horribly pedestrian and fraught with numerous chances for arithmetic mistakes to derail it, which happened in spades. As I suspected, there was an elegant, \u201ceasy\u201d solution (as demonstrated by Talwalkar)\u2014<em>once you thought of it!<\/em> Again, this is like a Coffin Problem.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Putnam-Octagon-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/04\/Putnam-Octagon-Problem-181112.pdf\">Putnam Octagon Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a problem from the famous (infamous?) Putnam exam, presented by Presh Talwalkar. Needless to say, I did not solve it in 30 minutes\u2014but at least I solved it (after making a blizzard of arithmetic and trigonometric errors). \u201cToday\u2019s problem is from the 1978 test, problem B1 (the easiest of the second set of [&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":[71,13,17,131],"class_list":["post-880","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-coffin-problem","tag-plane-geometry","tag-presh-talwalkar","tag-putnam-exam"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/880","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=880"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/880\/revisions"}],"predecessor-version":[{"id":3860,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/880\/revisions\/3860"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}