{"id":8838,"date":"2023-05-09T15:04:41","date_gmt":"2023-05-09T18:04:41","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=8838"},"modified":"2023-05-10T21:02:36","modified_gmt":"2023-05-11T00:02:36","slug":"two-digits-bordered-magic-squares-of-order-34","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=8838","title":{"rendered":"Two digits Bordered Magic Squares of Order 34"},"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. <a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=8687\" target=\"_blank\">Two digits Bordered Magic Squares of Order 40<\/a>.<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>3. Two digits Bordered Magic Squares of Order 34 (This work).<br><br>In this work we shall give two digits bordered magic squares of order 34. As explained in previous works below is <strong>digit-wise classification<\/strong> of bordered magic squares:<\/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><strong>Single Digit:<\/strong> <\/strong>Bordered magic squares based on single digit.<\/li>\n\n\n\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.<\/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 34 and 38, Zenodo, May 10, 2023, pp. 1-45, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.7922571\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.7922571<\/a>.<br><br>Below are few examples along with <strong>pdf file<\/strong> of order 34 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 34<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"2468\" height=\"1229\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1.png\" alt=\"\" class=\"wp-image-8840\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1.png 2468w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1-1024x510.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1-1536x765.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-1-2048x1020.png 2048w\" sizes=\"(max-width: 2468px) 100vw, 2468px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"2466\" height=\"1225\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2.png\" alt=\"\" class=\"wp-image-8841\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2.png 2466w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2-1024x509.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2-1536x763.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-2-2048x1017.png 2048w\" sizes=\"(max-width: 2466px) 100vw, 2466px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"2470\" height=\"1223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3.png\" alt=\"\" class=\"wp-image-8842\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3.png 2470w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3-1024x507.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3-768x380.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3-535x265.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3-1536x761.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-3-2048x1014.png 2048w\" sizes=\"(max-width: 2470px) 100vw, 2470px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2469\" height=\"1225\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4.png\" alt=\"\" class=\"wp-image-8843\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4.png 2469w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4-1024x508.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4-768x381.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4-535x265.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4-1536x762.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-4-2048x1016.png 2048w\" sizes=\"(max-width: 2469px) 100vw, 2469px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2466\" height=\"1228\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440.png\" alt=\"\" class=\"wp-image-8844\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440.png 2466w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440-1024x510.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440-1536x765.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-440-2048x1020.png 2048w\" sizes=\"(max-width: 2466px) 100vw, 2466px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2471\" height=\"1227\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584.png\" alt=\"\" class=\"wp-image-8845\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584.png 2471w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1024x508.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-768x381.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1536x763.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-2048x1017.png 2048w\" sizes=\"(max-width: 2471px) 100vw, 2471px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2471\" height=\"1227\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1.png\" alt=\"\" class=\"wp-image-8846\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1.png 2471w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1-1024x508.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1-768x381.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1-1536x763.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-584-1-2048x1017.png 2048w\" sizes=\"(max-width: 2471px) 100vw, 2471px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2465\" height=\"1226\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730.png\" alt=\"\" class=\"wp-image-8847\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730.png 2465w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730-1024x509.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730-1536x764.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-730-2048x1019.png 2048w\" sizes=\"(max-width: 2465px) 100vw, 2465px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2469\" height=\"1228\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825.png\" alt=\"\" class=\"wp-image-8848\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825.png 2469w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825-1024x509.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825-1536x764.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-825-2048x1019.png 2048w\" sizes=\"(max-width: 2469px) 100vw, 2469px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2467\" height=\"1226\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854.png\" alt=\"\" class=\"wp-image-8849\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854.png 2467w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854-1024x509.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854-1536x763.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-854-2048x1018.png 2048w\" sizes=\"(max-width: 2467px) 100vw, 2467px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2469\" height=\"1228\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878.png\" alt=\"\" class=\"wp-image-8850\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878.png 2469w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878-1024x509.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878-1536x764.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-878-2048x1019.png 2048w\" sizes=\"(max-width: 2469px) 100vw, 2469px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2471\" height=\"1230\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924.png\" alt=\"\" class=\"wp-image-8851\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924.png 2471w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924-1024x510.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924-1536x765.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-924-2048x1019.png 2048w\" sizes=\"(max-width: 2471px) 100vw, 2471px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2469\" height=\"1228\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929.png\" alt=\"\" class=\"wp-image-8852\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929.png 2469w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929-1024x509.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929-768x382.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929-535x266.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929-1536x764.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34-929-2048x1019.png 2048w\" sizes=\"(max-width: 2469px) 100vw, 2469px\" \/><\/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 34<\/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\/34x34.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 34x34.\"><\/object><a id=\"wp-block-file--media-b2137614-f244-4a3c-b23c-928228e4d094\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34.pdf\">34&#215;34<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/05\/34x34.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-b2137614-f244-4a3c-b23c-928228e4d094\">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":8852,"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-8838","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\/34x34-929.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/8838","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=8838"}],"version-history":[{"count":3,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/8838\/revisions"}],"predecessor-version":[{"id":8897,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/8838\/revisions\/8897"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/8852"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}