{"id":648,"date":"2022-02-10T21:07:23","date_gmt":"2022-02-11T00:07:23","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=648"},"modified":"2023-10-27T01:23:49","modified_gmt":"2023-10-27T04:23:49","slug":"block-wise-bordered-and-pandiagonal-magic-squares-multiples-of-4","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=648","title":{"rendered":"Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4"},"content":{"rendered":"\n<p class=\"has-text-align-justify\">During past years author worked with&nbsp;<strong>block-wise<\/strong>,&nbsp;<strong>bordered<\/strong>&nbsp;and&nbsp;<strong>block-bordered<\/strong>&nbsp;magic squares. This work make connection between&nbsp;<strong>block-wise<\/strong>&nbsp;and&nbsp;<strong>bordered<\/strong>&nbsp;magic squares. We started with&nbsp;<strong>block-wise bordered<\/strong>&nbsp;magic squares of orders 108 and 104. Based on these two big magic squares inner order magic squares multiples of 4 are studied. By inner order we understand that magic squares of orders 100, 96, 92, etc. Instead of working in decreasing order, we worked with increasing orders, such as, orders 4, 8, 12, etc. The construction of the&nbsp;<strong>block-wise bordered<\/strong>&nbsp;magic squares multiples of 4 is based on equal sum blocks of&nbsp;<strong>pandiagonal<\/strong>&nbsp;magic squares of order 4. The&nbsp;<strong>block-wise bordered<\/strong>&nbsp;magic squares studied are not&nbsp;<strong>pandiagonal<\/strong>. Redistributing the same blocks in each case, we get<strong>&nbsp;pandiagonal<\/strong>&nbsp;magic squares of order 4, 8, 12, etc. This work is only for the multiples of order 4. The further multiples, such as multiples, 6, 8, 10, etc.  can be seen at the following link:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Inder J. Taneja, <a href=\"https:\/\/numbers-magic.com\/?p=9414\">Multiple Orders Bordered Magic Squares<\/a><\/li>\n<\/ul>\n\n\n\n<p>The above link give bordered magic squares up to order 20.<\/p>\n\n\n\n<p class=\"has-text-align-justify\"><em><strong>Examples given below are only up to order 48. Higher orders examples can be seen in Excel file attached with the work. The total work is up to order 108.<\/strong><\/em><\/p>\n\n\n\n<p>Below are the links of the work:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Bordered Magic Squares Multiples of 4<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Inder J. Taneja, Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4.\u00a0<strong>Zenodo<\/strong>, August 31, 2021, pp. 1-148,\u00a0<a href=\"https:\/\/doi.org\/10.5281\/zenodo.5347897\">https:\/\/doi.org\/10.5281\/zenodo.5347897<\/a>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Pandiagonal Magic Squares Multiples of 4<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, <strong>Zenodo<\/strong>, January 31, 2019, pp. 1-17,  <a href=\"https:\/\/doi.org\/10.5281\/zenodo.2554288\">https:\/\/doi.org\/10.5281\/zenodo.2554288<\/a>.<\/li>\n\n\n\n<li>Inder J. Taneja, A Simplified Procedure to Construct Pandiagonal Magic Squares Multiples of 4  (Revised), <strong>Zenodo<\/strong>, August 10, 2023, pp. 1-27, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8236754\">https:\/\/doi.org\/10.5281\/zenodo.8236754<\/a>.<\/li>\n<\/ul>\n\n\n\n<p>Excel files for download are given at the end of each part.<\/p>\n\n\n\n<p class=\"has-text-align-justify\">Below are some examples studied in the work. The total work is up to order 108. The example below are only up to order 48. The examples are given in two blocks:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>First Block: <\/strong>Block-wise bordered magic squares from order 12 to 48;<\/li>\n\n\n\n<li><strong>Second Block:<\/strong> Pandiagonal Magic Squares from orders 4 to 48.<\/li>\n\n\n\n<li>Higher orders are already in attached excel files.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-background\" id=\"first-block-block-borderd-magic-squares\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(255,255,255) 48%,rgb(155,81,224) 100%)\">Block-Bordered Magic Squares<\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Magic Squares of Orders 4 and 8<\/h3>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img fetchpriority=\"high\" decoding=\"async\" width=\"275\" height=\"206\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/4x4-p.png\" alt=\"\" class=\"wp-image-10639\" style=\"aspect-ratio:1.3349514563106797;width:275px;height:auto\"\/><\/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=\"541\" height=\"398\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/8x8-m.png\" alt=\"\" class=\"wp-image-10640\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/8x8-m.png 541w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/8x8-m-300x221.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/8x8-m-535x394.png 535w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 12<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"801\" height=\"591\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/12x12-m.png\" alt=\"\" class=\"wp-image-10641\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/12x12-m.png 801w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/12x12-m-300x221.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/12x12-m-768x567.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/12x12-m-535x395.png 535w\" sizes=\"(max-width: 801px) 100vw, 801px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 16<\/h4>\n\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=\"1062\" height=\"783\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/16x16-m.png\" alt=\"\" class=\"wp-image-10642\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/16x16-m.png 1062w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/16x16-m-300x221.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/16x16-m-1024x755.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/16x16-m-768x566.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/16x16-m-535x394.png 535w\" sizes=\"(max-width: 1062px) 100vw, 1062px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 20<\/h4>\n\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=\"1131\" height=\"836\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/20x20-m.png\" alt=\"\" class=\"wp-image-10643\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/20x20-m.png 1131w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/20x20-m-300x222.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/20x20-m-1024x757.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/20x20-m-768x568.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/20x20-m-535x395.png 535w\" sizes=\"(max-width: 1131px) 100vw, 1131px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 24<\/h4>\n\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=\"1519\" height=\"1118\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/24x24-m.png\" alt=\"\" class=\"wp-image-10644\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/24x24-m.png 1519w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/24x24-m-300x221.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/24x24-m-1024x754.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/24x24-m-768x565.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/24x24-m-535x394.png 535w\" sizes=\"(max-width: 1519px) 100vw, 1519px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 28<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1778\" height=\"1307\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m.png\" alt=\"\" class=\"wp-image-10646\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m.png 1778w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m-300x221.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m-1024x753.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m-768x565.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m-535x393.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/28x28-m-1536x1129.png 1536w\" sizes=\"(max-width: 1778px) 100vw, 1778px\" \/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 32<\/h4>\n\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=\"2020\" height=\"1488\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m.png\" alt=\"\" class=\"wp-image-10649\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m.png 2020w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m-300x221.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m-1024x754.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m-768x566.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m-535x394.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/32x32-m-1536x1131.png 1536w\" sizes=\"(max-width: 2020px) 100vw, 2020px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 36<\/h4>\n\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=\"2009\" height=\"1523\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1.png\" alt=\"\" class=\"wp-image-10682\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1.png 2009w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1-300x227.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1-1024x776.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1-768x582.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1-535x406.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/36x36-m-1-1536x1164.png 1536w\" sizes=\"(max-width: 2009px) 100vw, 2009px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 40<\/h4>\n\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=\"2237\" height=\"1659\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m.png\" alt=\"\" class=\"wp-image-10651\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m.png 2237w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m-300x222.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m-1024x759.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m-768x570.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m-535x397.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m-1536x1139.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/40x40-m-2048x1519.png 2048w\" sizes=\"(max-width: 2237px) 100vw, 2237px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 44<\/h4>\n\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=\"2458\" height=\"1816\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m.png\" alt=\"\" class=\"wp-image-10653\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m.png 2458w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m-300x222.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m-1024x757.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m-768x567.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m-535x395.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m-1536x1135.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/44x44-m-2048x1513.png 2048w\" sizes=\"(max-width: 2458px) 100vw, 2458px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Block-Wise Bordered Magic Square of Order 48<\/h4>\n\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=\"2213\" height=\"1643\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m.png\" alt=\"\" class=\"wp-image-10654\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m.png 2213w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m-300x223.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m-1024x760.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m-768x570.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m-535x397.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m-1536x1140.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-m-2048x1520.png 2048w\" sizes=\"(max-width: 2213px) 100vw, 2213px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pdf file for Download<\/h4>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-08af5dd2-4d43-4cae-ace3-69ac7de3966b\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/bordered-108x108-104x104-4.xlsx\">bordered-108&#215;108-104&#215;104-4<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/bordered-108x108-104x104-4.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-08af5dd2-4d43-4cae-ace3-69ac7de3966b\">Download<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-background\" id=\"first-block-block-borderd-magic-squares\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(255,255,255) 48%,rgb(155,81,224) 100%)\">Pandiagonal Magic Squares Multiples of 4<\/h2>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Orders 4 and 8<\/h4>\n\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=\"270\" height=\"246\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-4x4-1.png\" alt=\"\" class=\"wp-image-10658\"\/><\/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=\"563\" height=\"427\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-8x8-1.png\" alt=\"\" class=\"wp-image-10659\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-8x8-1.png 563w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-8x8-1-300x228.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-8x8-1-535x406.png 535w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 12<\/h4>\n\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=\"795\" height=\"605\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-12x12-1.png\" alt=\"\" class=\"wp-image-10660\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-12x12-1.png 795w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-12x12-1-300x228.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-12x12-1-768x584.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-12x12-1-535x407.png 535w\" sizes=\"(max-width: 795px) 100vw, 795px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 16<\/h4>\n\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=\"1356\" height=\"772\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-16x16-1.png\" alt=\"\" class=\"wp-image-10661\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-16x16-1.png 1356w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-16x16-1-300x171.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-16x16-1-1024x583.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-16x16-1-768x437.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-16x16-1-535x305.png 535w\" sizes=\"(max-width: 1356px) 100vw, 1356px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 20<\/h4>\n\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=\"1518\" height=\"908\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-20x20-1.png\" alt=\"\" class=\"wp-image-10662\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-20x20-1.png 1518w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-20x20-1-300x179.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-20x20-1-1024x613.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-20x20-1-768x459.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-20x20-1-535x320.png 535w\" sizes=\"(max-width: 1518px) 100vw, 1518px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 24<\/h4>\n\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=\"1889\" height=\"1124\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1.png\" alt=\"\" class=\"wp-image-10663\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1.png 1889w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1-300x179.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1-1024x609.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1-768x457.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1-535x318.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-24x24-1-1536x914.png 1536w\" sizes=\"(max-width: 1889px) 100vw, 1889px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 28<\/h4>\n\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=\"2462\" height=\"1292\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1.png\" alt=\"\" class=\"wp-image-10664\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1.png 2462w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1-1024x537.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1-768x403.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1-535x281.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1-1536x806.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-28x28-1-2048x1075.png 2048w\" sizes=\"(max-width: 2462px) 100vw, 2462px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 32<\/h4>\n\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=\"3088\" height=\"1459\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1.png\" alt=\"\" class=\"wp-image-10665\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1.png 3088w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1-300x142.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1-1024x484.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1-768x363.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1-535x253.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1-1536x726.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-32x32-1-2048x968.png 2048w\" sizes=\"(max-width: 3088px) 100vw, 3088px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 36<\/h4>\n\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=\"2929\" height=\"1330\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1.png\" alt=\"\" class=\"wp-image-10666\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1.png 2929w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1-300x136.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1-1024x465.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1-1536x697.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-36x36-1-2048x930.png 2048w\" sizes=\"(max-width: 2929px) 100vw, 2929px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 40<\/h4>\n\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=\"3405\" height=\"1645\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1.png\" alt=\"\" class=\"wp-image-10667\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1.png 3405w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1-300x145.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1-1024x495.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1-768x371.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1-535x258.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1-1536x742.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-40x40-1-2048x989.png 2048w\" sizes=\"(max-width: 3405px) 100vw, 3405px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 44<\/h4>\n\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=\"3125\" height=\"1615\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1.png\" alt=\"\" class=\"wp-image-10668\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1.png 3125w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1-300x155.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1-1024x529.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1-768x397.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1-535x276.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1-1536x794.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/pan-44x44-1-2048x1058.png 2048w\" sizes=\"(max-width: 3125px) 100vw, 3125px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pandiagonal Magic Squares of Order 48<\/h4>\n\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=\"2216\" height=\"1645\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p.png\" alt=\"\" class=\"wp-image-10669\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p.png 2216w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p-300x223.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p-1024x760.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p-768x570.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p-535x397.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p-1536x1140.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/48x48-p-2048x1520.png 2048w\" sizes=\"(max-width: 2216px) 100vw, 2216px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 52%,rgb(113,206,126) 100%)\">Pdf file of Pandiagonal Magic Squares Multiples of  4: Orders 4 to 108<\/h4>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-650671d8-7129-4130-a78d-28e7d9082c59\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/Pan-4k-4to108.xlsx\">Pan-4k-4to108<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/10\/Pan-4k-4to108.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-650671d8-7129-4130-a78d-28e7d9082c59\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>During past years author worked with&nbsp;block-wise,&nbsp;bordered&nbsp;and&nbsp;block-bordered&nbsp;magic squares. This work make connection between&nbsp;block-wise&nbsp;and&nbsp;bordered&nbsp;magic squares. We started with&nbsp;block-wise bordered&nbsp;magic squares of orders 108 and 104. Based on these two big magic squares inner order magic squares multiples of 4 are studied. By inner order we understand that magic squares of orders 100, 96, 92, etc. Instead of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":651,"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-648","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\/2022\/02\/16x16-m.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/648","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=648"}],"version-history":[{"count":11,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/648\/revisions"}],"predecessor-version":[{"id":10685,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/648\/revisions\/10685"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/651"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}