{"id":8687,"date":"2023-05-04T02:43:32","date_gmt":"2023-05-04T05:43:32","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=8687"},"modified":"2023-05-07T00:24:14","modified_gmt":"2023-05-07T03:24:14","slug":"two-digits-bordered-magic-squares-of-order-40","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=8687","title":{"rendered":"Two digits Bordered Magic Squares of Order 40"},"content":{"rendered":"\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\">For the first time in history, this the author worked with <strong>two digits bordered magic squares<\/strong> multiples of 4. These are from orders 8 to 40. These can be accessed at the following links:<br>1. <a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=8493\" target=\"_blank\">Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24<\/a>.<br>2. <a href=\"https:\/\/numbers-magic.com\/?p=8551\">Two Digits Bordered Magic Squares of Orders 28 and 32<\/a>.<br>3. <a href=\"https:\/\/numbers-magic.com\/?p=8669\">Two digits Bordered Magic Squares of Order 36.<\/a><br>4. Two digits Bordered Magic Squares of Order 40. (This work)<br><br>The work is for the order of type 4k+2, where k&gt;1, i.e., for the orders 10, 14, 18, 22, 26 and 30 can be access at the following links:<br>1. <a href=\"https:\/\/numbers-magic.com\/?p=8583\">Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22<\/a>.<br>2. <a href=\"https:\/\/numbers-magic.com\/?p=8629\">Two digits Bordered Magic Squares of Orders 26 and 30<\/a>.<br><br>In this work we shall give two digits bordered magic squares of order 40. As explained in previous works below is <strong>digit-wise classification<\/strong> of bordered magic squares:<\/p>\n\n\n\n<p><strong>Single Digit:<\/strong> Bordered magic squares based on single digit.<\/p>\n\n\n\n<ul class=\"has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-list\">\n<li><strong>Two Digits:<\/strong> Bordered magic squares based on magic rectangles of order 2xk (k=4, 8, 12, &#8230;). <\/li>\n\n\n\n<li><strong>Three Digits:<\/strong> Bordered magic squares based on magic squares of order 3: <\/li>\n\n\n\n<li><strong>Four Digits:<\/strong> Bordered magic squares based on magic squares of order 4. <\/li>\n\n\n\n<li><strong>Five Digits:<\/strong> Bordered magic squares based on magic squares of order 5 (appearing soon).<\/li>\n\n\n\n<li><strong>Six Digits:<\/strong> Bordered magic squares based on magic squares of order 6, etc.<br><br>The work can also be accessed at the following link:<br><\/li>\n<\/ul>\n\n\n\n<ul class=\"has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, Two digits Bordered Magic Squares of Orders 36 and 40, <strong>Zenodo<\/strong>, May 04, pp. 1-41, 2023, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.7896709\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.7896709<\/a>.<br>Below are few examples along with <strong>pdf file<\/strong> of order 40 for download.<br><\/li>\n<\/ul>\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) 13%,rgb(255,255,255) 30%,rgb(255,105,0) 100%)\">Two Digits Bordered Magic Square of Order 40<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"3500\" height=\"1722\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1.png\" alt=\"\" class=\"wp-image-8790\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1.png 3500w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1-1536x756.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-1-1-2048x1008.png 2048w\" sizes=\"(max-width: 3500px) 100vw, 3500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"3500\" height=\"1726\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1.png\" alt=\"\" class=\"wp-image-8791\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1.png 3500w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1-1024x505.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1-768x379.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1-535x264.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1-1536x757.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-20-1-2048x1010.png 2048w\" sizes=\"(max-width: 3500px) 100vw, 3500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"3496\" height=\"1722\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1.png\" alt=\"\" class=\"wp-image-8792\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1.png 3496w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1-535x264.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1-1536x757.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-86-1-2048x1009.png 2048w\" sizes=\"(max-width: 3496px) 100vw, 3496px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3504\" height=\"1728\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1.png\" alt=\"\" class=\"wp-image-8794\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1.png 3504w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1-1024x505.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1-768x379.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1-535x264.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1-1536x757.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-265-1-2048x1010.png 2048w\" sizes=\"(max-width: 3504px) 100vw, 3504px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3503\" height=\"1728\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1.png\" alt=\"\" class=\"wp-image-8795\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1.png 3503w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1-1024x505.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1-768x379.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1-535x264.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1-1536x758.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-308-1-2048x1010.png 2048w\" sizes=\"(max-width: 3503px) 100vw, 3503px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3495\" height=\"1722\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1.png\" alt=\"\" class=\"wp-image-8796\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1.png 3495w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1-1024x505.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1-535x264.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1-1536x757.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-343-1-2048x1009.png 2048w\" sizes=\"(max-width: 3495px) 100vw, 3495px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3500\" height=\"1722\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1.png\" alt=\"\" class=\"wp-image-8797\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1.png 3500w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1-1536x756.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-374-1-2048x1008.png 2048w\" sizes=\"(max-width: 3500px) 100vw, 3500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3501\" height=\"1720\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1.png\" alt=\"\" class=\"wp-image-8798\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1.png 3501w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1-300x147.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1-1024x503.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1-768x377.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1-1536x755.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-399-1-2048x1006.png 2048w\" sizes=\"(max-width: 3501px) 100vw, 3501px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3499\" height=\"1721\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1.png\" alt=\"\" class=\"wp-image-8799\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1.png 3499w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1-1536x755.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-424-1-2048x1007.png 2048w\" sizes=\"(max-width: 3499px) 100vw, 3499px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3501\" height=\"1723\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1.png\" alt=\"\" class=\"wp-image-8800\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1.png 3501w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1-1536x756.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-476-1-2048x1008.png 2048w\" sizes=\"(max-width: 3501px) 100vw, 3501px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3501\" height=\"1722\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1.png\" alt=\"\" class=\"wp-image-8801\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1.png 3501w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1-1536x755.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-493-1-2048x1007.png 2048w\" sizes=\"(max-width: 3501px) 100vw, 3501px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3503\" height=\"1725\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2.png\" alt=\"\" class=\"wp-image-8802\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2.png 3503w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2-1024x504.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2-768x378.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2-535x263.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2-1536x756.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40-505-2-2048x1009.png 2048w\" sizes=\"(max-width: 3503px) 100vw, 3503px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\">Pdf file for Download: Order 40<\/h3>\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\/2023\/05\/40x40.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 40x40.\"><\/object><a id=\"wp-block-file--media-102beff5-d6b9-4dd2-a440-d9feeb52fad3\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40.pdf\">40&#215;40<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/40x40.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-102beff5-d6b9-4dd2-a440-d9feeb52fad3\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>For the first time in history, this the author worked with two digits bordered magic squares multiples of 4. These are from orders 8 to 40. These can be accessed at the following links:1. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24.2. Two Digits Bordered Magic Squares of Orders 28 and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":8702,"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-8687","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\/2023\/05\/40x40-505-1.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/8687","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=8687"}],"version-history":[{"count":3,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/8687\/revisions"}],"predecessor-version":[{"id":8803,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/8687\/revisions\/8803"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/8702"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8687"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8687"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}