{"id":11911,"date":"2024-06-03T00:50:13","date_gmt":"2024-06-03T03:50:13","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=11911"},"modified":"2024-06-13T15:17:54","modified_gmt":"2024-06-13T18:17:54","slug":"striped-magic-squares-of-order-18","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=11911","title":{"rendered":"Striped Magic Squares of Order 18"},"content":{"rendered":"\n<p class=\"has-text-align-justify\">This work brings striped magic squares of order 18.  Before we proceed further below examples of 8 stripes used in whole the work. <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(122,220,180) 0%,rgb(140,215,27) 66%,rgb(0,208,130) 100%)\">Striped Magic Rectangles<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p>Below are examples of magic rectangles used in this work. These are orders 2&#215;4 to 2&#215;18 used in this work.  Since all these are of equal width, we call them <strong>stripes<\/strong>. <\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1126\" height=\"1200\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/MR-2x-4-18.png\" alt=\"\" class=\"wp-image-11912\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/MR-2x-4-18.png 1126w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/MR-2x-4-18-282x300.png 282w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/MR-2x-4-18-961x1024.png 961w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/MR-2x-4-18-768x818.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/MR-2x-4-18-535x570.png 535w\" sizes=\"(max-width: 1126px) 100vw, 1126px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\">Whole the work on <strong>stripled magic squares of order 18<\/strong> are always among above 8 types of magic rectangles, where the width is always same. The change is only in lenght. According to order of the stripes the entries are different but the sums are always same.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\">Below are few examples of <strong>striped magic squares of order 18<\/strong>. Due to high quantity of magic squares these are divided in 9 parts.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>For online work click the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of 18, <strong>Zenodo<\/strong>, June 13, 2024, pp. 1-34, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.11629567\">https:\/\/doi.org\/10.5281\/zenodo.11629567<\/a><\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 16%,rgb(199,81,192) 50%,rgb(255,255,255) 80%,rgb(65,88,208) 100%)\">Striped Magic Squares of Order 18<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 1: Embedded with Striped Magic Squares of Order 14<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">This part is with striped magic squares of order 18. In this part, we have embedded striped magic squares of order <a href=\"https:\/\/numbers-magic.com\/?p=10587\">14 studied before<\/a>  (<a href=\"https:\/\/numbers-magic.com\/?p=10587\">Striped Magic Squares of Orders 4, 6, 8, 10, 12 and 14<\/a>) . It already contains striped magic squares of order 10 and 6. Below are few examples. The complete work is given in pdf attached with this part.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"539\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1-1024x539.png\" alt=\"\" class=\"wp-image-11926\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1-1024x539.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1-300x158.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1-768x405.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1-535x282.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1.png 1327w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"541\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4-1024x541.png\" alt=\"\" class=\"wp-image-11927\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4.png 1330w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"541\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-29-1024x541.png\" alt=\"\" class=\"wp-image-11928\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-29-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-29-300x158.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-29-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-29-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-29.png 1329w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"539\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-65-1024x539.png\" alt=\"\" class=\"wp-image-11929\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-65-1024x539.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-65-300x158.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-65-768x404.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-65-535x282.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-65.png 1328w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"545\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-154-1024x545.png\" alt=\"\" class=\"wp-image-11930\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-154-1024x545.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-154-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-154-768x409.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-154-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-154.png 1332w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 1<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-1-1-289.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-1-1-289.\"><\/object><a id=\"wp-block-file--media-d487f21c-fd17-48e7-a14f-1574d3e279c8\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-1-1-289.pdf\">Stripes-18&#215;18-1-1-289<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-1-1-289.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-d487f21c-fd17-48e7-a14f-1574d3e279c8\">Download<\/a><\/div>\n\n\n\n<p><strong>There are total 289 striped magic squares in this part.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 2: Embedded with Symmetric Magic Rectangles<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p>This part also contains embedded striped magic squares of order 6 and 10. The external part is different from the previous part. It contained symmetrical magic rectangles. See two examples below:<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"544\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-293-1024x544.png\" alt=\"\" class=\"wp-image-11938\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-293-1024x544.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-293-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-293-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-293-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-293.png 1325w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"545\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-309-1024x545.png\" alt=\"\" class=\"wp-image-11936\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-309-1024x545.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-309-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-309-768x409.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-309-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-309.png 1328w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p>More examples are in Pdf file given below.<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 2<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-2-290-361-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-2-290-361-1.\"><\/object><a id=\"wp-block-file--media-555359cf-fd33-45ff-803b-6a0e695cc783\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-2-290-361-1.pdf\">Stripes-18&#215;18-2-290-361-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-2-290-361-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-555359cf-fd33-45ff-803b-6a0e695cc783\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>There are total 72 striped magic squares in this part.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 3: Cornered with Striped Magic Squares of Order 14<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">In the first part we have seen that the magic squares of order 14 are embedded in the magic squares of order 18. This section includes striped magic squares of order 18, with magic squares of order 14 positioned at the corners. See below few examples. The complete work of this section is given as pdf file at the end of this work.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"542\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-596-1024x542.png\" alt=\"\" class=\"wp-image-11950\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-596-1024x542.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-596-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-596-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-596-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-596.png 1327w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-justify\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"541\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-608-1024x541.png\" alt=\"\" class=\"wp-image-11951\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-608-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-608-300x158.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-608-768x405.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-608-535x282.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-608.png 1322w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 3<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-3-362-622-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-3-362-622-1.\"><\/object><a id=\"wp-block-file--media-eb26825b-3746-42d8-ad0a-fe17ec98bd41\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-3-362-622-1.pdf\">Stripes-18&#215;18-3-362-622-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-3-362-622-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-eb26825b-3746-42d8-ad0a-fe17ec98bd41\">Download<\/a><\/div>\n\n\n\n<p class=\"has-text-align-justify\"><strong>There are total 261 striped squares in this part out of them 100 are magic squares and 161 are semi- magic squares. Later on these semi-magic squares shall be converted in magic squares after some simplifications.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 4: Cornered with Striped Magic Squares of Order 12. <br>Using Algebraic Formula (a+b)^2=a^2+b^2+2ab<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">This part is very much simiar to part 3. The difference is that here we have <strong>striped magic squares of order 12<\/strong> instead of order 14. The magic square of order 12 are already given in another work (<a href=\"https:\/\/numbers-magic.com\/?p=10587\">Striped Magic Squares of Orders 4, 6, 8, 10, 12 and 14<\/a>).  The <strong>striped magic squares of order 12<\/strong> are cornered in such a way that we apply the formula <em><strong>(a+b)^2=a^2+b^2+2ab<\/strong><\/em>. Here, the <em><strong>a=12<\/strong><\/em> and <strong><em>b=6<\/em><\/strong>. The expressions <em><strong>ab<\/strong><\/em> or <strong><em>ba<\/em><\/strong> are considered in different ways.  See below few examples. The whole work is given as pdf file in the end of this section.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"536\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-626-1024x536.png\" alt=\"\" class=\"wp-image-11958\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-626-1024x536.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-626-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-626-768x402.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-626-535x280.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-626.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"538\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-908-1024x538.png\" alt=\"\" class=\"wp-image-11959\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-908-1024x538.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-908-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-908-768x403.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-908-535x281.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-908.png 1341w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"533\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-954-1024x533.png\" alt=\"\" class=\"wp-image-11960\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-954-1024x533.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-954-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-954-768x400.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-954-535x278.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-954.png 1339w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>There are total 539 striped squares in this part. Out of them 259 are magic squares and 280 are semi- magic squares. Later on these semi-magic squares shall be converted in magic squares after some simplifications.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 4<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-4-623-1161.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-4-623-1161.\"><\/object><a id=\"wp-block-file--media-2dc518d3-e48a-4cb6-a11c-f33f19b63bd3\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-4-623-1161.pdf\">Stripes-18&#215;18-4-623-1161<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-4-623-1161.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-2dc518d3-e48a-4cb6-a11c-f33f19b63bd3\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 5: Cornered with Striped Magic Squares of Order 12<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">This section is very much similar to section 4. The difference is that here we havn&#8217;t divided the magic squares and\/or magic rectangles in terms of the algebraic expressions <em><strong>(a+b)^2=a^2+b^2+2ab<\/strong><\/em>. The lower part we have just considered as magic rectangles of order <strong><em>6&#215;18<\/em><\/strong>. This we have taken different forms. The upper is with stripled magic squares of order 12 and magic rectangles of order <strong><em>6&#215;12<\/em><\/strong> or better <strong><em>12&#215;6<\/em><\/strong> (vertical order). See below few examples. The whole work is given as pdf file in the end of this section.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1163-1024x535.png\" alt=\"\" class=\"wp-image-11963\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1163-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1163-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1163-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1163-535x280.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1163.png 1343w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1564-1024x535.png\" alt=\"\" class=\"wp-image-11965\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1564-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1564-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1564-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1564-535x280.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1564.png 1345w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"536\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1693-1024x536.png\" alt=\"\" class=\"wp-image-11966\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1693-1024x536.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1693-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1693-768x402.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1693-535x280.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1693.png 1340w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 5<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-5-1161-1959-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-5-1161-1959-1.\"><\/object><a id=\"wp-block-file--media-820f756f-7559-4e6c-b10e-b11df1c99e16\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-5-1161-1959-1.pdf\">Stripes-18&#215;18-5-1161-1959-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-5-1161-1959-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-820f756f-7559-4e6c-b10e-b11df1c99e16\">Download<\/a><\/div>\n\n\n\n<p class=\"has-text-align-justify\"><strong>There are total 798 striped squares in this part. Out of them 406 are magic squares and 392 are semi- magic squares. Later on these semi-magic squares shall be converted in magic squares after some simplifications.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 6: Cornered with Striped Magic Squares of Order 10. <br>Using Algebraic Formula (a+b)^2=a^2+b^2+2ab<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">This part is very much simiar to parts 3 and 4. The difference is that here we have <strong>striped magic squares of order 10<\/strong> instead of orders 14 and 12. The magic squares of order 10 are already given in another work (<a href=\"https:\/\/numbers-magic.com\/?p=10587\">Striped Magic Squares of Orders 4, 6, 8, 10, 12 and 14<\/a>).  The <strong>striped magic squares of order 10<\/strong> are cornered in such a way that we apply the formula <em><strong>(a+b)^2=a^2+b^2+2ab<\/strong><\/em>. Here, the <em><strong>a=10<\/strong><\/em> and <strong><em>b=8<\/em><\/strong>. The expressions <em><strong>ab<\/strong><\/em> or <em><strong>ba<\/strong><\/em> are considered in different ways.  See below few examples. The whole work is given as pdf file in the end of this section.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"538\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1961-1024x538.png\" alt=\"\" class=\"wp-image-11967\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1961-1024x538.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1961-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1961-768x403.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1961-535x281.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-1961.png 1341w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"538\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-2831-1-1024x538.png\" alt=\"\" class=\"wp-image-11975\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-2831-1-1024x538.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-2831-1-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-2831-1-768x403.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-2831-1-535x281.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-2831-1.png 1345w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3286-1024x535.png\" alt=\"\" class=\"wp-image-11969\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3286-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3286-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3286-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3286-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3286.png 1342w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 6<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-6-1960-3559.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-6-1960-3559.\"><\/object><a id=\"wp-block-file--media-ed852072-4012-46d5-93d1-d264108216bf\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-6-1960-3559.pdf\">Stripes-18&#215;18-6-1960-3559<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-6-1960-3559.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-ed852072-4012-46d5-93d1-d264108216bf\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>There are total 1600 striped squares in this part. Out of them 1440 are magic squares and 160 are semi- magic squares. Later on these semi-magic squares shall be converted in magic squares after some simplifications.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 7: Embedded with Striped Magic Squares of Order 14<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">This section is very much similar to section 5. The difference is that here we havn&#8217;t divided the magic squares and\/or magic rectangles in terms of the algebraic expressions <em><strong>(a+b)^2=a^2+b^2+2ab<\/strong><\/em>. The lower part we have just considered as magic rectangles of order 8<strong><em>x18<\/em><\/strong>. This we have taken different forms. The upper is with stripled magic squares of order 10 and magic rectangles of order <strong><em>8&#215;10<\/em><\/strong> or better <strong><em>10&#215;8<\/em><\/strong> (vertical order). See below few examples. The whole work is given as pdf file in the end of this section.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"538\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3561-1024x538.png\" alt=\"\" class=\"wp-image-11978\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3561-1024x538.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3561-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3561-768x403.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3561-535x281.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3561.png 1343w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"534\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3583-1024x534.png\" alt=\"\" class=\"wp-image-11979\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3583-1024x534.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3583-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3583-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3583-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3583.png 1343w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3630-1024x535.png\" alt=\"\" class=\"wp-image-11980\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3630-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3630-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3630-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3630-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-3630.png 1348w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-justify\"><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 7<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-7-3560-4039.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-7-3560-4039.\"><\/object><a id=\"wp-block-file--media-b0420333-9c5f-407a-a049-e422e9950f75\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-7-3560-4039.pdf\">Stripes-18&#215;18-7-3560-4039<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-7-3560-4039.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-b0420333-9c5f-407a-a049-e422e9950f75\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>There are total 480 striped squares in this part. All of them are semi-magic squares. Later all of on these semi-magic squares shall be converted in magic squares after some simplifications.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 8: Some Extra Magic Squares of Order 18<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">This part is not following any specific rule. These are just constructed based on some general idea. Any how all of them looks beautiful. See below few examples.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"533\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4041-1024x533.png\" alt=\"\" class=\"wp-image-11983\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4041-1024x533.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4041-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4041-768x399.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4041-535x278.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4041.png 1342w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"534\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4050-1024x534.png\" alt=\"\" class=\"wp-image-11984\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4050-1024x534.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4050-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4050-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4050-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4050.png 1344w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4095-1024x535.png\" alt=\"\" class=\"wp-image-11985\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4095-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4095-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4095-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4095-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4095.png 1340w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 8<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-8-4040-4097.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-8-4040-4097.\"><\/object><a id=\"wp-block-file--media-1793eee4-ead1-4542-a102-b130ca13c9fa\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-8-4040-4097.pdf\">Stripes-18&#215;18-8-4040-4097<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-8-4040-4097.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-1793eee4-ead1-4542-a102-b130ca13c9fa\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>There are total 58 striped squares in this part. All of them 39 are magic squares and 19 are semi-magic squares. Later all of on these semi-magic squares shall be converted in magic squares after some simplifications.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">Part 9: Cornered with Striped Magic Squares of Order 16<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\">This part is very much similar to part 3. He we have take striped magic squares of order 16 at the corner and then adjusted them in square of order 18. See below some examples:<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4132-1024x535.png\" alt=\"\" class=\"wp-image-11989\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4132-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4132-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4132-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4132-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4132.png 1350w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"533\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4216-1024x533.png\" alt=\"\" class=\"wp-image-11990\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4216-1024x533.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4216-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4216-768x400.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4216-535x278.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4216.png 1349w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"536\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4276-1024x536.png\" alt=\"\" class=\"wp-image-11991\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4276-1024x536.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4276-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4276-768x402.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4276-535x280.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4276.png 1343w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Part 9<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-9-4098-4363.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-9-4098-4363.\"><\/object><a id=\"wp-block-file--media-eea70bbd-4b73-4280-b43b-d616937837b0\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-9-4098-4363.pdf\">Stripes-18&#215;18-9-4098-4363<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-9-4098-4363.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-eea70bbd-4b73-4280-b43b-d616937837b0\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\"><strong>In this section, there are a total of 266 striped squares. Among these, 57 are magic squares and 209 are semi-magic squares. These semi-magic squares will be transformed into magic squares following certain simplification<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-pale-ocean-gradient-background has-background\">Pdf file of Complete Work<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-all-1-4363-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Stripes-18x18-all-1-4363-1.\"><\/object><a id=\"wp-block-file--media-125ff9dd-f51e-4225-8901-9b945d37b77c\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-all-1-4363-1.pdf\">Stripes-18&#215;18-all-1-4363-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/Stripes-18x18-all-1-4363-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-125ff9dd-f51e-4225-8901-9b945d37b77c\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 51%,rgb(255,105,0) 100%)\">References<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of Even Orders 6, 8, 10, 12 and 14,&nbsp;<strong>Zenodo<\/strong>, November 10, 2023, pp. 1-34,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.10107355\">https:\/\/doi.org\/10.5281\/zenodo.10107355<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=10587\">Even Orders Striped Magic Squares of Orders 4, 6, 8, 10, 12 and 14.<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;Striped Magic Squares of 16,&nbsp;<strong>Zenodo<\/strong>, May 16, 2024, pp. 1-22,&nbsp; <a href=\"https:\/\/doi.org\/10.5281\/zenodo.11205510\">https:\/\/doi.org\/10.5281\/zenodo.11205510<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=10587\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=11781\">Striped Magic Squares of Order 16.<\/a>\u00a0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of 18, <strong>Zenodo<\/strong>, June 13, 2024, pp. 1-34, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.11629567\">https:\/\/doi.org\/10.5281\/zenodo.11629567<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=11911\">Striped Magic Squares of Order 18.<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>This work brings striped magic squares of order 18. Before we proceed further below examples of 8 stripes used in whole the work. Striped Magic Rectangles Below are examples of magic rectangles used in this work. These are orders 2&#215;4 to 2&#215;18 used in this work. Since all these are of equal width, we call [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11927,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-11911","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-magic-squares"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/06\/18x18-4.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/11911","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11911"}],"version-history":[{"count":13,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/11911\/revisions"}],"predecessor-version":[{"id":12055,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/11911\/revisions\/12055"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/11927"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11911"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11911"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11911"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}