{"id":570,"date":"2018-02-21T21:59:12","date_gmt":"2018-02-22T01:59:12","guid":{"rendered":"http:\/\/www.blogs.euni.org\/?p=570"},"modified":"2018-02-21T21:59:12","modified_gmt":"2018-02-22T01:59:12","slug":"the-strange-number-pair","status":"publish","type":"post","link":"https:\/\/www.blogs.euni.org\/?p=570","title":{"rendered":"The Strange Number Pair"},"content":{"rendered":"<p>One evening, Jack found Jill sitting at a caf\u00e9 table with her attention riveted on a small, well-worn and water-logged ship\u2019s logbook in her hand.<\/p>\n<p>\u201cWhat\u2019s up, Jill,\u201d he said cheerfully. \u201cYou look puzzled.\u201d<\/p>\n<p>\u201cI really am, Jack. My great uncle drowned recently when his sailboat sank in the Aegean Sea near Skiathos, and I\u2019m trying to make sense of a message he wrote in his logbook before sinking regarding my inheritance. They found it floating with him in the sea,\u201d said Jill.<\/p>\n<p>She gestured for Jack to sit down, calling for the waitress to bring a coffee.<\/p>\n<p>\u201cSorry about your great uncle, Jill. What\u2019s the message?\u201d asked Jack, sitting down.<\/p>\n<p>\u201cIt says I have to go to the SchwitzerliBank in Zurich to obtain my inheritance, but I need to give them a special code number to receive it,\u201d said Jill in frustration, pulling on a black hair lock.<\/p>\n<p>\u201cAnd what\u2019s the number?\u201d asked Jack, preparing his coffee with a spoon.<\/p>\n<p>\u201cWell, that\u2019s the problem. It\u2019s in some kind of code,\u201d said Jill with a baffled look on her face.<\/p>\n<p>\u201cExplain, please,\u201d said Jack, taking a careful sip of his hot coffee.<\/p>\n<p>\u201cOn this page my great uncle says:<\/p>\n<p><em>\u2018Move the last to the first of the six, then find the four greater twin and use it,\u2019\u201d <\/em><\/p>\n<p>said Jill, \u201cwhich doesn\u2019t make any sense to me,\u201d she groaned, randomly flipping the pages of the logbook.<\/p>\n<p>\u201cHmm, that really is a mouthful,\u201d said Jack. \u201cSeems your great uncle didn\u2019t want to advertise the number.\u201d<\/p>\n<p>\u201cNo joke. Got any ideas?\u201d Jill looked up at Jack with big green eyes full of hope.<\/p>\n<p>After thinking a while on the strange statement, Jack suddenly got an idea.<\/p>\n<p>\u201cYou have to give a number to the SchwitzerliBank in Zurich to get your inheritance, right? Maybe this is a six-digit number,\u201d said Jack.<\/p>\n<p>\u201cCould be you are right, but what about \u2018\u2026move the last to the first of the six\u2019?\u201d<\/p>\n<p>\u201cHey, maybe the word \u2018twin\u2019 means another number derived from the first,\u201d said Jack enthusiastically.<\/p>\n<p>\u201cIn this case you get it by moving the last digit to the first position.\u201d<\/p>\n<p>\u201cYea, that really makes sense. But what about the \u2018four greater\u2019 part?\u201d<\/p>\n<p>\u201cSeems the second number is four times greater than the first, and since it says \u2018use the twin\u2019 I would guess this is the number to present to the bank,\u201d said Jack.<\/p>\n<p>\u201cGood thinking, Jack. But how do we work out what the twin number is?\u201d<\/p>\n<p>\u201cWell, I\u2019m taking a course in Number Theory and I\u2019m sure I can work it out. So, what will you give me in return,\u201d said Jack with a roguish grin.<\/p>\n<p>\u2018How about dinner at your favorite Hindu restaurant \u2013 followed by some dessert,\u201d said Jill demurely.<\/p>\n<p>\u201cDeal! Give me a pen and a piece of paper, Jill.\u201d<\/p>\n<p><em>What would you say the number Jill had to give to the SchwitzerliBank in Zurich<\/em> <em>was?<\/em><\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-icon sd-sharing\"><h3 class=\"sd-title\">Share this:<\/h3><div class=\"sd-content\"><ul><li class=\"share-twitter\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-twitter-570\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=twitter\" target=\"_blank\" title=\"Click to share on Twitter\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Twitter (Opens in new window)<\/span><\/a><\/li><li class=\"share-facebook\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-facebook-570\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Facebook (Opens in new window)<\/span><\/a><\/li><li class=\"share-linkedin\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-linkedin-570\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=linkedin\" target=\"_blank\" title=\"Click to share on LinkedIn\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on LinkedIn (Opens in new window)<\/span><\/a><\/li><li class=\"share-jetpack-whatsapp\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"\" class=\"share-jetpack-whatsapp sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=jetpack-whatsapp\" target=\"_blank\" title=\"Click to share on WhatsApp\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on WhatsApp (Opens in new window)<\/span><\/a><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>One evening, Jack found Jill sitting at a caf\u00e9 table with her attention riveted on a small, well-worn and water-logged ship\u2019s logbook in her hand. \u201cWhat\u2019s up, Jill,\u201d he said cheerfully. \u201cYou look puzzled.\u201d \u201cI really am, Jack. My great uncle drowned recently when his sailboat sank in the Aegean Sea near Skiathos, and I\u2019m [&hellip;]<\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-icon sd-sharing\"><h3 class=\"sd-title\">Share this:<\/h3><div class=\"sd-content\"><ul><li class=\"share-twitter\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-twitter-570\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=twitter\" target=\"_blank\" title=\"Click to share on Twitter\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Twitter (Opens in new window)<\/span><\/a><\/li><li class=\"share-facebook\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-facebook-570\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Facebook (Opens in new window)<\/span><\/a><\/li><li class=\"share-linkedin\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-linkedin-570\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=linkedin\" target=\"_blank\" title=\"Click to share on LinkedIn\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on LinkedIn (Opens in new window)<\/span><\/a><\/li><li class=\"share-jetpack-whatsapp\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"\" class=\"share-jetpack-whatsapp sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=570&amp;share=jetpack-whatsapp\" target=\"_blank\" title=\"Click to share on WhatsApp\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on WhatsApp (Opens in new window)<\/span><\/a><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false},"categories":[29,50],"tags":[170,171],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7zDaf-9c","jetpack-related-posts":[{"id":844,"url":"https:\/\/www.blogs.euni.org\/?p=844","url_meta":{"origin":570,"position":0},"title":"The Friendly Safe","date":"December 27, 2018","format":false,"excerpt":"\u201cAre you telling me that another uncle has passed away, Jill!!\u201d exclaimed Jack, taking another sip of a hot chocolate while sitting at a caf\u00e9 table at Chez Pierre\u2019s, \u201chow many uncles do you have??\u201d \u201cWell, Jack, I do have quite a number of them, ten on either side of\u2026","rel":"","context":"In &quot;Number Theory&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":931,"url":"https:\/\/www.blogs.euni.org\/?p=931","url_meta":{"origin":570,"position":1},"title":"The Coded Prize","date":"June 29, 2019","format":false,"excerpt":"As Jill swung through the door of the Blue Swan caf\u00e9 one busy Saturday afternoon, she saw Jack sitting at a window table staring intently at his mobile phone, nervously sipping a coffee. \u201cWhat\u2019s so fascinating on your phone, Jack? \u201d \u201cJill, I could win a ten thousand dollar prize\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":915,"url":"https:\/\/www.blogs.euni.org\/?p=915","url_meta":{"origin":570,"position":2},"title":"The Square Estate","date":"May 26, 2019","format":false,"excerpt":"As Jack entered the Blue Swan caf\u00e9 that, as usual, was filled with the most enticing coffee aromas wafting among the many occupied tables, he saw Jill sitting by a window fixedly peering at a manuscript. \u201cWhat are you studying so intently, Jill?\u201d asked Jack. \u201cLooks like your life depended\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":352,"url":"https:\/\/www.blogs.euni.org\/?p=352","url_meta":{"origin":570,"position":3},"title":"The Special Number","date":"March 23, 2017","format":false,"excerpt":"On a late June afternoon, Jill sat on the green grass by a small lake at the university with a concentrated look on her face.\u00a0Some ducks were quacking nearby. \u201cHi Jill, I see you are thinking about something, anything important?\u201d said Jack, who had quietly walked up to her on\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":402,"url":"https:\/\/www.blogs.euni.org\/?p=402","url_meta":{"origin":570,"position":4},"title":"The Special Coins","date":"June 16, 2017","format":false,"excerpt":"During a cold and crisp January afternoon with azure blue skies setting off peaked snow-capped mountains, Jack and Jill were enjoying a skiing holiday at a resort in the Bavarian Alps. They were busy checking out Dr. Feynstein\u2019s souvenir shop. \u201cJack, I want to buy you that cute lederhosen leather\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":314,"url":"https:\/\/www.blogs.euni.org\/?p=314","url_meta":{"origin":570,"position":5},"title":"Farmer Couples Out Shopping","date":"January 28, 2017","format":false,"excerpt":"In a late autumn afternoon, Jill was sitting under a tree on a campus hill looking despondent, \u00a0elbows on her knees and hands holding up her head. Sunlight was fading while yellowish and brown leaves floated erratically down from trees. Distracted, she did not notice that Jack was approaching from\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/570"}],"collection":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=570"}],"version-history":[{"count":7,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/570\/revisions"}],"predecessor-version":[{"id":577,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/570\/revisions\/577"}],"wp:attachment":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}