{"id":735,"date":"2018-10-17T20:12:07","date_gmt":"2018-10-18T00:12:07","guid":{"rendered":"http:\/\/www.blogs.euni.org\/?p=735"},"modified":"2018-10-17T20:12:07","modified_gmt":"2018-10-18T00:12:07","slug":"the-emperors-triangular-array","status":"publish","type":"post","link":"https:\/\/www.blogs.euni.org\/?p=735","title":{"rendered":"The Emperor\u2019s Triangular Array"},"content":{"rendered":"<p>To emulate and surpass the famous emperor Qin\u2019s necropolis achievement, emperor Wu Shu, who preferred to be known as \u201cHe Who Cannot Be Counted,\u201d decided that after the end of his life he wanted to be buried at the head of an army of 10,440 terracotta soldiers standing at attention in a triangular array of rows.<\/p>\n<p>\u201cChow Sao, I want to know the cumulative Grand Sum of the number of ways of arranging soldiers in each respective row,\u201d said emperor Wu Shu to his Feng Shui advisor.<\/p>\n<p>\u201cThis Grand Sum must be perfectly divisible by 12, the number of heavenly animals in the Shengxiao zodiac,\u201d added emperor Wu Shu.<\/p>\n<p>\u201cYes, my glorious emperor,\u201d moaned Chow Sao, \u201cyour wish is my command,\u201d starting to genuflect reversing himself out of the emperor\u2019s lush palace quarters.<\/p>\n<p>\u201cIf the Grand Sum is not perfectly divisible by 12, I want you to tell me exactly which rows of soldiers must be removed to obtain a zero remainder,\u201d commanded emperor Wu Shu.<\/p>\n<p>\u201cAs you wish, my illustrious emperor,\u201d said Chow Sao, shuffling more rapidly to increase his reverse velocity as he saw empress Soo Lao enter the palace room.<\/p>\n<p>\u201cThis grand sum must be perfectly divisible by 12. Empress Soo Lao has informed me that I shall suffer great misfortune in the heaven life unless this is so,\u201d emphasized emperor Wu Shu, waving his scepter.<\/p>\n<p>\u201cThis is so, Chow Sao,\u201d said empress Soo Lao sternly, \u201cany mistakes, and I will have sorceress Ba Fa turn you into stone and place you as the first soldier in the first row.\u201d<\/p>\n<p>\u201cThe Gods forbid,\u201d said Chow Sao accelerating his backward velocity at a phenomenal rate and absconding from the emperor\u2019s quarters in a great hurry to begin his calculating task.<\/p>\n<p><em>Would you say that this Grand Sum was divisible by 12, and if not, would any rows of soldiers have to be removed from the triangular array of soldiers envisioned<\/em>?<\/p>\n<p>&nbsp;<\/p>\n<p>Intriguing Puzzles Book 1, containing 50 fascinating puzzles selected from <a href=\"http:\/\/www.blogs.euni.org\">Ken&#8217;s Blog<\/a>, is now available in the e-book formats mobi and epub.<\/p>\n<p>Click <a href=\"https:\/\/tinyurl.com\/yazmevk8\">here<\/a> for more details.<\/p>\n<p>&nbsp;<\/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-735\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=735&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-735\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=735&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span 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class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>To emulate and surpass the famous emperor Qin\u2019s necropolis achievement, emperor Wu Shu, who preferred to be known as \u201cHe Who Cannot Be Counted,\u201d decided that after the end of his life he wanted to be buried at the head of an army of 10,440 terracotta soldiers standing at attention in a triangular array of [&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-735\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=735&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 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the Chinese emperor Wang Shu summoned his spymaster Lang Dang to his private suite in the palace. He was worried, as he had received information from the palace cook Chu Shi that his enemy, the warlord Dui Yuan, had planted ten\u2026","rel":"","context":"In &quot;Probability&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":349,"url":"https:\/\/www.blogs.euni.org\/?p=349","url_meta":{"origin":735,"position":1},"title":"The Square Armies","date":"March 13, 2017","format":false,"excerpt":"Emperor Manos was standing outside his tent on a hill overlooking his vast army camped in tents in the square formation normally used in battle. General Pathos and a Royal Guard were with the Emperor, as was his sorcerer Morgan. A raven briskly landed on a large branch of an\u2026","rel":"","context":"In &quot;Number Theory&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":314,"url":"https:\/\/www.blogs.euni.org\/?p=314","url_meta":{"origin":735,"position":2},"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":[]},{"id":679,"url":"https:\/\/www.blogs.euni.org\/?p=679","url_meta":{"origin":735,"position":3},"title":"The Chinese Round Table","date":"August 31, 2018","format":false,"excerpt":"One fine evening, Jack and Jill were dining at the Fu Manchu Magic Noodle House, their favorite Chinese restaurant. They sat at a round table served by their regular waitress, Wang Shu. A number of dishes containing delicious tidbits for plucking off with their chopsticks were situated in front of\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":624,"url":"https:\/\/www.blogs.euni.org\/?p=624","url_meta":{"origin":735,"position":4},"title":"The Sequential Number","date":"May 11, 2018","format":false,"excerpt":"\u201cLennie, have you done your math homework?\u201d asked daddy, while driving home from school. \u201cYes, daddy I did it during math class,\u201d said Lennie with a bored expression. \u201cThat was fast,\u201d said daddy in surprise, \u201cwas it so easy?\u201d \u201cYes, daddy, too simplistic. Can you give me something interesting to\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":433,"url":"https:\/\/www.blogs.euni.org\/?p=433","url_meta":{"origin":735,"position":5},"title":"The Army Sizes","date":"July 30, 2017","format":false,"excerpt":"The generals Chi Wong and Chow Loo were having a discussion one day on the top of a hill overlooking the plains of their respective army camps. \u201cMy army is bigger than yours,\u201d said general Chi Wong to general Chow Loo. \u201cI\u2019ll wager my best concubine on it.\u201d \u201cWager likewise\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\/735"}],"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=735"}],"version-history":[{"count":1,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/735\/revisions"}],"predecessor-version":[{"id":736,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/735\/revisions\/736"}],"wp:attachment":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}