{"id":189,"date":"2016-08-27T16:29:16","date_gmt":"2016-08-27T20:59:16","guid":{"rendered":"http:\/\/www.blogs.euni.org\/?p=189"},"modified":"2016-08-27T16:29:16","modified_gmt":"2016-08-27T20:59:16","slug":"the-cube-towers","status":"publish","type":"post","link":"https:\/\/www.blogs.euni.org\/?p=189","title":{"rendered":"The Cube Towers"},"content":{"rendered":"<p>An eccentric billionaire decided to build two tall pointed towers consisting of a series of stacked cubes. They would serve decorative purposes being placed in parallel at a large futuristic gate in his theme park. The material to be used would be a high-strength, transparent nanomaterial. The billionaire stated that rainwater and some kind of energy would be collected for undisclosed purposes.<\/p>\n<p>The first cube was to have a side length of 1 cm, the subsequent cube sides 1 cm greater than the previous, up to the last cube with a side length of 100 cm.<\/p>\n<p>The architect scratched his head thinking how to add up the volumes. Can you help him greatly simplify the calculations?<\/p>\n<p><em>What would be the height of the towers, and their combined volume?<\/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-189\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=189&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-189\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=189&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-189\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=189&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=189&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>An eccentric billionaire decided to build two tall pointed towers consisting of a series of stacked cubes. They would serve decorative purposes being placed in parallel at a large futuristic gate in his theme park. The material to be used would be a high-strength, transparent nanomaterial. The billionaire stated that rainwater and some kind 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-189\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=189&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-189\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=189&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-189\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=189&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=189&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":[40,47],"tags":[52],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7zDaf-33","jetpack-related-posts":[{"id":232,"url":"https:\/\/www.blogs.euni.org\/?p=232","url_meta":{"origin":189,"position":0},"title":"The Riddle of the Dragon","date":"October 18, 2016","format":false,"excerpt":"Sir Lancelot was riding far from Camelot in pursuit of the Holy Grail when he came upon an abyss over which a bridge was stretched. As he arrived, he saw another knight being confronted by a large, flame-snorting dragon named Dragon of the Abyss who roared: \u201cMortal, answer my riddle\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":189,"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":78,"url":"https:\/\/www.blogs.euni.org\/?p=78","url_meta":{"origin":189,"position":2},"title":"The Three Hats","date":"May 24, 2016","format":false,"excerpt":"A billionaire enters a reality show saloon with five bellboy hats, three red and two white. \"I need three volunteers to play a game for a million dollars,\" he said. \"Any takers?\" Three men put down their beer mugs immediately and volunteered: Jack, Tobias and Charlie. \"Very well. Set up\u2026","rel":"","context":"In &quot;Combinations&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":393,"url":"https:\/\/www.blogs.euni.org\/?p=393","url_meta":{"origin":189,"position":3},"title":"The Triple Pyramid","date":"May 28, 2017","format":false,"excerpt":"A man named Chadwick wanted to build a square pyramid with three levels to house his wife and kids. Chadwick wanted the ground floor to be 2000 square feet larger in area than the first floor, which would have 2000 square feet more than the second floor, where he figured\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":128,"url":"https:\/\/www.blogs.euni.org\/?p=128","url_meta":{"origin":189,"position":4},"title":"The Twelve Shields","date":"July 8, 2016","format":false,"excerpt":"Twelve captured soldiers were presented to Tamerlane, the Turco-Mongol conqueror, in his palace. \u201cI feel generous today as it is the birthday of my favorite concubine, Lalila, and we have killed enough people this week and built sufficient skull pyramids. You all fought bravely against your capture.\u201d \u201cEach of you\u2026","rel":"","context":"In &quot;Probability&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":417,"url":"https:\/\/www.blogs.euni.org\/?p=417","url_meta":{"origin":189,"position":5},"title":"Captain John\u2019s Boat","date":"June 30, 2017","format":false,"excerpt":"Captain John has a boat with a crew consisting of his family: his wife Jeannie, sons Jack and Marvin, daughters Mary and Molly, and Troi the parrot. Captain John is very proud of his boat, especially its length in feet, and travels the world with his family to share the\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\/189"}],"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=189"}],"version-history":[{"count":2,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/189\/revisions"}],"predecessor-version":[{"id":191,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/189\/revisions\/191"}],"wp:attachment":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}