{"id":101,"date":"2018-12-28T12:10:05","date_gmt":"2018-12-28T17:10:05","guid":{"rendered":"http:\/\/josmfs.net\/wordpress\/?p=101"},"modified":"2024-04-04T18:05:40","modified_gmt":"2024-04-04T22:05:40","slug":"power-of-2-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2018\/12\/28\/power-of-2-problem\/","title":{"rendered":"Power of 2 Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-609\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/01\/Power-of-2-Prob-Fig.jpg\" alt=\"\" width=\"200\" height=\"94\" \/>Virtually the very first \u201cmath\u201d problem I got interested in involved a 7th grade homework problem in 2005 that a colleague at work said her son had been given. I ended up commenting and helping on a number of further problems, which gave me some insight into the state of current public school teaching in mathematics. It was both encouraging and discouraging at the same time. I will join the math education commentary at a later date.<\/p>\n<p>The problem was not that bad: <em>What is the largest power of 2 that divides 800! without a remainder?<\/em> (where \u201c!\u201d means \u201cfactorial\u201d, for example, 5! = 5 x 4 x 3 x 2 x 1). I solved it in my usual pedestrian way. I showed it to a friend of mine (an algebraist!) and he of course had a nifty approach. He showed it to a colleague of his at NSF (a physicist) and he had the niftiest solution of all! (Most humbling.) See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2018\/12\/Power-of-2-Problem-181226.pdf\">Power of 2 Problem<\/a>.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Power-of-2-Answer.jpg\">Answer<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Virtually the very first \u201cmath\u201d problem I got interested in involved a 7th grade homework problem in 2005 that a colleague at work said her son had been given. I ended up commenting and helping on a number of further problems, which gave me some insight into the state of current public school teaching in [&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":[6,104],"class_list":["post-101","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-math-homework","tag-mathematical-induction"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/101","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=101"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/101\/revisions"}],"predecessor-version":[{"id":3493,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/101\/revisions\/3493"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}