{"id":736,"date":"2019-03-12T12:44:27","date_gmt":"2019-03-12T16:44:27","guid":{"rendered":"http:\/\/josmfs.net\/?p=736"},"modified":"2024-04-14T12:13:51","modified_gmt":"2024-04-14T16:13:51","slug":"missing-pages-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/03\/12\/missing-pages-puzzle\/","title":{"rendered":"Missing Pages Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-731\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/03\/Missing-Pages-Fig.jpg\" alt=\"\" width=\"200\" height=\"143\" \/>Setting aside my chagrin that the following problem was given to pre-university students, I initially found the problem to be among the daunting ones that offer little information for a solution. It also was a bit \u201cinelegant\u201d to my way of thinking, since it involved considering some separate cases. Still, the end result turned out to be unique and satisfying (Talwalkar\u2019s Note 2 was essential for a unique solution, since the problem as stated was ambiguous).<\/p>\n<p>\u201cKshitij from India sent me this problem from the 1994 India Regional Mathematics Olympiad.<br \/>\u2018<strong>A leaf is torn from a paperback novel. The sum of the numbers on the remaining pages is 15000. What are the page numbers on the torn leaf?<\/strong>\u2019<br \/><strong>Note 1<\/strong>: a \u2018leaf\u2019 means a single sheet of paper.<br \/><strong>Note 2<\/strong>: the quoted problem is actual wording from the competition. But let me add an important detail: the book is numbered in the usual sequential way starting with the first page as page 1.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Missing-Pages-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/03\/Missing-Pages-Puzzle-180426.pdf\">Missing Pages Puzzle<\/a> for a solution.<\/p>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Setting aside my chagrin that the following problem was given to pre-university students, I initially found the problem to be among the daunting ones that offer little information for a solution. It also was a bit \u201cinelegant\u201d to my way of thinking, since it involved considering some separate cases. Still, the end result turned out [&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":[17],"class_list":["post-736","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-presh-talwalkar"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/736","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=736"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/736\/revisions"}],"predecessor-version":[{"id":3878,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/736\/revisions\/3878"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}