{"id":10016,"date":"2023-08-09T02:54:32","date_gmt":"2023-08-09T05:54:32","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=10016"},"modified":"2025-01-28T15:33:57","modified_gmt":"2025-01-28T18:33:57","slug":"new-concepts-in-magic-squares-cornered-magic-squares-from-order-5-to-81","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=10016","title":{"rendered":"New Concepts in Magic Squares: Cornered Magic Squares from Order 5 to 108"},"content":{"rendered":"\n<p class=\"has-text-align-right\"><strong><em><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Never seen before.<\/mark><\/em><\/strong><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\">By boarded magic squares we understand that if we remove the external border still, we are left with magic squares of lower orders with sequential entries. Single digits bordered magic squares are well-known. This work brings ver different types of bordered magic squares but are of <strong>corner-type<\/strong>, known by <strong>cornered magic squares<\/strong>. Instead of removing the whole border, here we remove only last row and column. By doing so, we still left with lower order cornered magic squares. This work is up to order 81. We start with order 5. <br><br>Lower order cornered magic suares (up to order 23) can be calculated using software by Harry While: <a href=\"https:\/\/budshaw.ca\/Download.html\">Downloads (budshaw.ca)<\/a>. <br><br>During past days author did few works in this direction. These are as follows:<\/p>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li>Inder J. Taneja, Cornered Magic Squares of Order 6, <strong>Zenodo<\/strong>, May 23, 2023, pp. 1-23, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.7960679\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.7960679<\/a>. <br>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=8923\">Cornered Magic Squares of Order 6<\/a>.<br><\/li>\n\n\n\n<li>Inder J. Taneja, Cornered Magic Squares of Orders 5 to 13, <strong>Zenodo<\/strong>, June 03, 2023, pp. 1-71, <a rel=\"noreferrer noopener\" href=\"https:\/\/doi.org\/10.5281\/zenodo.8000467\" target=\"_blank\">https:\/\/doi.org\/10.5281\/zenodo.8000467<\/a>.<br>Site Links: <br>1. <a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=9010\" target=\"_blank\">Cornered Magic Squares of Orders 5 to 10<\/a>.<br>2. <a href=\"https:\/\/numbers-magic.com\/?p=9073\">Cornered Magic Squares of Orders 11 to 13<\/a>.<\/li>\n\n\n\n<li>Inder J. Taneja, Cornered Magic Squares of Orders 14 to 24, <strong>Zenodo<\/strong>, June 03, 2023, pp. 1-39, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8000471\">https:\/\/doi.org\/10.5281\/zenodo.8000471<\/a>.<br>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=8923\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=9138\">Cornered Magic Squares of Orders 14 to 24<\/a>.<br><\/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(252,185,0) 0%,rgb(255,255,255) 36%,rgb(255,105,0) 100%)\">Corned Magic Squares: <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Orders 5 to 30<\/mark><\/h3>\n\n\n\n<p class=\"has-blush-light-purple-gradient-background has-background\">Below are examples of cornered magic squares of orders 5 to 30. The total work is up to order 81. Most of the work is done manually. For the complete work see the<strong> excel file<\/strong> attached at the end.<\/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=\"1305\" height=\"406\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c5-6-7.png\" alt=\"\" class=\"wp-image-14842\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c5-6-7.png 1305w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c5-6-7-300x93.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c5-6-7-1024x319.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c5-6-7-768x239.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c5-6-7-535x166.png 535w\" sizes=\"(max-width: 1305px) 100vw, 1305px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1128\" height=\"496\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c8-9.png\" alt=\"\" class=\"wp-image-14843\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c8-9.png 1128w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c8-9-300x132.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c8-9-1024x450.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c8-9-768x338.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c8-9-535x235.png 535w\" sizes=\"(max-width: 1128px) 100vw, 1128px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1526\" height=\"585\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c10-11-1.png\" alt=\"\" class=\"wp-image-14846\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c10-11-1.png 1526w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c10-11-1-300x115.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c10-11-1-1024x393.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c10-11-1-768x294.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c10-11-1-535x205.png 535w\" sizes=\"(max-width: 1526px) 100vw, 1526px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1940\" height=\"673\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a.png\" alt=\"\" class=\"wp-image-14879\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a.png 1940w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a-300x104.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a-1024x355.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a-768x266.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a-535x186.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c12-13a-1536x533.png 1536w\" sizes=\"(max-width: 1940px) 100vw, 1940px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1084\" height=\"715\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c14.png\" alt=\"\" class=\"wp-image-14848\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c14.png 1084w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c14-300x198.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c14-1024x675.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c14-768x507.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c14-535x353.png 535w\" sizes=\"(max-width: 1084px) 100vw, 1084px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1149\" height=\"749\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c15.png\" alt=\"\" class=\"wp-image-14850\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c15.png 1149w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c15-300x196.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c15-1024x668.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c15-768x501.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c15-535x349.png 535w\" sizes=\"(max-width: 1149px) 100vw, 1149px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1220\" height=\"785\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c16.png\" alt=\"\" class=\"wp-image-14851\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c16.png 1220w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c16-300x193.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c16-1024x659.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c16-768x494.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c16-535x344.png 535w\" sizes=\"(max-width: 1220px) 100vw, 1220px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1354\" height=\"824\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs18.png\" alt=\"\" class=\"wp-image-14876\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs18.png 1354w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs18-300x183.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs18-1024x623.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs18-768x467.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs18-535x326.png 535w\" sizes=\"(max-width: 1354px) 100vw, 1354px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1284\" height=\"846\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c17.png\" alt=\"\" class=\"wp-image-14852\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c17.png 1284w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c17-300x198.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c17-1024x675.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c17-768x506.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c17-535x353.png 535w\" sizes=\"(max-width: 1284px) 100vw, 1284px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1353\" height=\"887\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c18.png\" alt=\"\" class=\"wp-image-14853\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c18.png 1353w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c18-300x197.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c18-1024x671.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c18-768x503.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c18-535x351.png 535w\" sizes=\"(max-width: 1353px) 100vw, 1353px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1418\" height=\"932\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c19.png\" alt=\"\" class=\"wp-image-14854\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c19.png 1418w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c19-300x197.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c19-1024x673.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c19-768x505.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c19-535x352.png 535w\" sizes=\"(max-width: 1418px) 100vw, 1418px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1495\" height=\"971\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c20.png\" alt=\"\" class=\"wp-image-14855\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c20.png 1495w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c20-300x195.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c20-1024x665.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c20-768x499.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c20-535x347.png 535w\" sizes=\"(max-width: 1495px) 100vw, 1495px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1557\" height=\"1014\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2.png\" alt=\"\" class=\"wp-image-14881\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2.png 1557w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2-300x195.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2-1024x667.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2-768x500.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2-535x348.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c21-2-1536x1000.png 1536w\" sizes=\"(max-width: 1557px) 100vw, 1557px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1627\" height=\"1047\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22.png\" alt=\"\" class=\"wp-image-14858\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22.png 1627w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22-300x193.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22-1024x659.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22-768x494.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22-535x344.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c22-1536x988.png 1536w\" sizes=\"(max-width: 1627px) 100vw, 1627px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1695\" height=\"1091\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23.png\" alt=\"\" class=\"wp-image-14859\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23.png 1695w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23-300x193.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23-1024x659.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23-768x494.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23-535x344.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c23-1536x989.png 1536w\" sizes=\"(max-width: 1695px) 100vw, 1695px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1684\" height=\"1135\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24.png\" alt=\"\" class=\"wp-image-14860\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24.png 1684w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24-300x202.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24-1024x690.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24-768x518.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24-535x361.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c24-1536x1035.png 1536w\" sizes=\"(max-width: 1684px) 100vw, 1684px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1829\" height=\"1182\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25.png\" alt=\"\" class=\"wp-image-14861\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25.png 1829w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25-300x194.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25-1024x662.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25-768x496.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25-535x346.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c25-1536x993.png 1536w\" sizes=\"(max-width: 1829px) 100vw, 1829px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1894\" height=\"1225\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26.png\" alt=\"\" class=\"wp-image-14862\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26.png 1894w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26-300x194.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26-1024x662.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26-768x497.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26-535x346.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c26-1536x993.png 1536w\" sizes=\"(max-width: 1894px) 100vw, 1894px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2189\" height=\"1280\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27.png\" alt=\"\" class=\"wp-image-14863\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27.png 2189w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27-300x175.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27-1024x599.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27-768x449.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27-535x313.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27-1536x898.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c27-2048x1198.png 2048w\" sizes=\"(max-width: 2189px) 100vw, 2189px\" \/><\/figure>\n<\/div>\n\n\n<p>For more examples see the excel files below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2485\" height=\"1326\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28.png\" alt=\"\" class=\"wp-image-14864\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28.png 2485w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28-1024x546.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28-768x410.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28-1536x820.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c28-2048x1093.png 2048w\" sizes=\"(max-width: 2485px) 100vw, 2485px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2818\" height=\"1367\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29.png\" alt=\"\" class=\"wp-image-14866\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29.png 2818w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29-300x146.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29-1024x497.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29-768x373.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29-535x260.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29-1536x745.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c29-2048x993.png 2048w\" sizes=\"(max-width: 2818px) 100vw, 2818px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2513\" height=\"1411\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30.png\" alt=\"\" class=\"wp-image-14867\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30.png 2513w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30-300x168.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30-1024x575.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30-768x431.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30-535x300.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30-1536x862.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/c30-2048x1150.png 2048w\" sizes=\"(max-width: 2513px) 100vw, 2513px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-blush-light-purple-gradient-background has-background\">Excel files for Download<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>File 1: Cornered Magic Squares: Orders 5 to 81.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-23e43716-a946-4e5a-81bc-31cdff32ded5\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/Cornered-5to81-online.xlsx\">Cornered-5to81-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/Cornered-5to81-online.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-23e43716-a946-4e5a-81bc-31cdff32ded5\">Download<\/a><\/div>\n\n\n\n<p><strong>File 2: Cornered Semi-Magic Squares: Orders 82 to 108.<\/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) 36%,rgb(255,105,0) 100%)\">Striped Cornered Magic Squares: <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">Orders 6 to 20<\/mark><\/h3>\n\n\n\n<p>By striped magic squares we understand that the magic squares constructed magic rectangles with equal width orders, i.e., <strong>2xn<\/strong>, where <strong>n=4, 6, 8, &#8230; <\/strong>See below few examples<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1003\" height=\"410\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs6-8.png\" alt=\"\" class=\"wp-image-14870\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs6-8.png 1003w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs6-8-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs6-8-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs6-8-535x219.png 535w\" sizes=\"(max-width: 1003px) 100vw, 1003px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1463\" height=\"550\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs10-12.png\" alt=\"\" class=\"wp-image-14871\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs10-12.png 1463w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs10-12-300x113.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs10-12-1024x385.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs10-12-768x289.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs10-12-535x201.png 535w\" sizes=\"(max-width: 1463px) 100vw, 1463px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1063\" height=\"654\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs14.png\" alt=\"\" class=\"wp-image-14872\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs14.png 1063w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs14-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs14-1024x630.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs14-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs14-535x329.png 535w\" sizes=\"(max-width: 1063px) 100vw, 1063px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1215\" height=\"672\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs16x16.png\" alt=\"\" class=\"wp-image-14873\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs16x16.png 1215w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs16x16-300x166.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs16x16-1024x566.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs16x16-768x425.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs16x16-535x296.png 535w\" sizes=\"(max-width: 1215px) 100vw, 1215px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1374\" height=\"903\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs20x20.png\" alt=\"\" class=\"wp-image-14874\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs20x20.png 1374w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs20x20-300x197.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs20x20-1024x673.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs20x20-768x505.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/cs20x20-535x352.png 535w\" sizes=\"(max-width: 1374px) 100vw, 1374px\" \/><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Never seen before. By boarded magic squares we understand that if we remove the external border still, we are left with magic squares of lower orders with sequential entries. Single digits bordered magic squares are well-known. This work brings ver different types of bordered magic squares but are of corner-type, known by cornered magic squares. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":10034,"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-10016","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\/08\/c-26.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/10016","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=10016"}],"version-history":[{"count":6,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/10016\/revisions"}],"predecessor-version":[{"id":14882,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/10016\/revisions\/14882"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/10034"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}