{"id":9634,"date":"2023-07-13T03:24:18","date_gmt":"2023-07-13T06:24:18","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9634"},"modified":"2023-07-13T03:24:20","modified_gmt":"2023-07-13T06:24:20","slug":"block-wise-bordered-and-pandiagonal-magic-squares-multiples-of-16","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9634","title":{"rendered":"Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16"},"content":{"rendered":"\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">During past years author worked with <strong>block-wise<\/strong>, <strong>bordered<\/strong> and <strong>block-bordered<\/strong> magic squares. This work make connection between <strong>block-wise<\/strong> and <strong>bordered<\/strong> magic squares. We started with <strong>block-wise bordered<\/strong> magic squares of orders 144 and 128. Based on these two big magic squares, the inner order magic squares multiples of 16 are studied. By inner orders we understand that magic squares of orders 112, 96, 80, etc. The construction of the <strong>block-wise bordered<\/strong> magic squares multiples of 16 is based on <strong>equal sum blocks of magic squares of order 16<\/strong>. We have taken <strong>25 different types of magic squares of order 16<\/strong>. The advantage in studying <strong>block-wise bordered<\/strong> magic squares is that when we remove external border, still we are left with magic squares with sequential entries. It is the same property of <strong>bordered<\/strong> magic squares with single digits numbers. The difference is that instead of numbers here we have blocks of equal sum magic squares of order 16. For multiples of orders 4, 6, 8, 10, 12 and 14 see the links below:<br>1.\u00a0<a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=648\" target=\"_blank\">Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4<\/a>.<br>2.\u00a0<a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=316\" target=\"_blank\">Block-Wise Bordered Magic Squares Multiples of Magic Squares of Order 6<\/a>.<br>3.\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=687\">Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 8 \u2013 Revised<\/a><br>4.\u00a0<a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=706\" target=\"_blank\">Block-Wise Bordered Magic Squares Multiples of 10 \u2013 Revised.<\/a><br>5.\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=747\">Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 12 \u2013 Revised.<\/a><br>6. <a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=812\" target=\"_blank\">Block-Wise Bordered Magic Squares Multiples of 14 \u2013 Revised<\/a><a href=\"https:\/\/numbers-magic.com\/?p=812\" target=\"_blank\" rel=\"noreferrer noopener\">.<\/a><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">This work is up to order 144. Examples below are only up to order 48. The higher order examples can be seen in<strong> Excel file attached at the end of this work<\/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(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Magic Squares of Order 16<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">Below are only three examples of magic squares of order 16. It includes <strong>bordered, double digits, cornered magic <\/strong>squares, etc. Total 25 examples are considered in this work. The other examples are either in <strong>excel file<\/strong> and <strong>pdf file<\/strong>.<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1002\" height=\"611\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-1.png\" alt=\"\" class=\"wp-image-9635\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-1.png 1002w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-1-300x183.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-1-768x468.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-1-535x326.png 535w\" sizes=\"(max-width: 1002px) 100vw, 1002px\" \/><\/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=\"1009\" height=\"621\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-5.png\" alt=\"\" class=\"wp-image-9636\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-5.png 1009w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-5-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-5-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-5-535x329.png 535w\" sizes=\"(max-width: 1009px) 100vw, 1009px\" \/><\/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=\"1002\" height=\"614\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-12.png\" alt=\"\" class=\"wp-image-9637\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-12.png 1002w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-12-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-12-768x471.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-16x16-12-535x328.png 535w\" sizes=\"(max-width: 1002px) 100vw, 1002px\" \/><\/figure>\n<\/div>\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(6,147,227) 0%,rgb(255,255,255) 47%,rgb(155,81,224) 100%)\">Pdf file of 25 Magic Squares of Order 16<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 16x16.\"><\/object><a id=\"wp-block-file--media-1c533edc-2304-424c-a1b5-7aadf5730662\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16.pdf\">16&#215;16<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-1c533edc-2304-424c-a1b5-7aadf5730662\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Magic Squares of Order 32<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">Below are only 3 examples of magic squares of order 32. The other are given in attached pdf file and in\u00a0<strong>excel file<\/strong>\u00a0given 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 loading=\"lazy\" decoding=\"async\" width=\"2313\" height=\"1164\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4.png\" alt=\"\" class=\"wp-image-9639\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4.png 2313w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4-1024x515.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4-768x386.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4-535x269.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4-1536x773.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-4-2048x1031.png 2048w\" sizes=\"(max-width: 2313px) 100vw, 2313px\" \/><\/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=\"2314\" height=\"1160\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16.png\" alt=\"\" class=\"wp-image-9640\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16.png 2314w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16-300x150.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16-1024x513.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16-768x385.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16-535x268.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16-1536x770.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-16-2048x1027.png 2048w\" sizes=\"(max-width: 2314px) 100vw, 2314px\" \/><\/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=\"2315\" height=\"1163\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22.png\" alt=\"\" class=\"wp-image-9641\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22.png 2315w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22-1024x514.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22-768x386.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22-535x269.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22-1536x772.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-22-2048x1029.png 2048w\" sizes=\"(max-width: 2315px) 100vw, 2315px\" \/><\/figure>\n<\/div>\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(6,147,227) 0%,rgb(255,255,255) 47%,rgb(155,81,224) 100%)\">Pdf file of 25 Magic Squares of Order 32<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 32x32-16x16-1.\"><\/object><a id=\"wp-block-file--media-1c533edc-2304-424c-a1b5-7aadf5730662\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-1.pdf\">32&#215;32-16&#215;16-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-1c533edc-2304-424c-a1b5-7aadf5730662\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Magic Squares of order 48<\/h3>\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=\"3073\" height=\"1560\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6.png\" alt=\"\" class=\"wp-image-9643\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6.png 3073w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6-1024x520.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6-768x390.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6-535x272.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6-1536x780.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-6-2048x1040.png 2048w\" sizes=\"(max-width: 3073px) 100vw, 3073px\" \/><\/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=\"3070\" height=\"1561\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11.png\" alt=\"\" class=\"wp-image-9644\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11.png 3070w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11-300x153.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11-1024x521.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11-768x391.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11-535x272.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11-1536x781.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-11-2048x1041.png 2048w\" sizes=\"(max-width: 3070px) 100vw, 3070px\" \/><\/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=\"3065\" height=\"1554\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19.png\" alt=\"\" class=\"wp-image-9645\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19.png 3065w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19-1024x519.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19-768x389.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19-535x271.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19-1536x779.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-19-2048x1038.png 2048w\" sizes=\"(max-width: 3065px) 100vw, 3065px\" \/><\/figure>\n<\/div>\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(6,147,227) 0%,rgb(255,255,255) 47%,rgb(155,81,224) 100%)\">Pdf file of 25 Magic Squares of Order 48<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file aligncenter\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 48x48-16x16-1.\"><\/object><a id=\"wp-block-file--media-05b267fd-bf20-4302-a790-be7b37ab5af4\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-1.pdf\">48&#215;48-16&#215;16-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-05b267fd-bf20-4302-a790-be7b37ab5af4\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Excel file for Download<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">The <strong>excel files<\/strong> below for download contains <strong>bordered magic square<\/strong> with blocks of <strong>magic squares of order 16<\/strong>.  There are 25 examples in each case. Total work is from order 16 to 144. There are three files. One is with magic squares of orders 144 and 128. The second file is with magic squares of orders 112 and 96. The third file is with orders 80, 64, 48, 32 and 16.<\/p>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-573cf448-956e-46f5-9654-057ecb9eb65e\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-144-128-online.xlsx\">16&#215;16-144-128-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-144-128-online.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-573cf448-956e-46f5-9654-057ecb9eb65e\">Download<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-0b738698-bd4a-4101-95a9-8830e02066be\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-112-96-online.xlsx\">16&#215;16-112-96-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-112-96-online.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-0b738698-bd4a-4101-95a9-8830e02066be\">Download<\/a><\/div>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-4da3f586-871c-408c-b95f-fe83fadbc0f6\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-80-16-online.xlsx\">16&#215;16-80-16-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-80-16-online.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4da3f586-871c-408c-b95f-fe83fadbc0f6\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(254,205,165) 0%,rgb(255,255,255) 16%,rgb(254,45,45) 50%,rgb(255,255,255) 79%,rgb(107,0,62) 100%)\">Pandiagonal Magic Squares Multiples of Order 16<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">Below are <strong>pandiagonal <\/strong>magic squares from orders 16 to 144 multiples of 16. These are formed by equal sum <strong>pandiagonal<\/strong> magic squares of order 4. In the end there is an <strong>excel file<\/strong> of all the <strong>pandiagonal<\/strong> magic squares for download. <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Pandiagonal Magic Squares of Order 16<\/h3>\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=\"1020\" height=\"616\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-pan.png\" alt=\"\" class=\"wp-image-9650\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-pan.png 1020w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-pan-300x181.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-pan-768x464.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-pan-535x323.png 535w\" sizes=\"(max-width: 1020px) 100vw, 1020px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Pandiagonal Magic Square of Order 32<\/h3>\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=\"2346\" height=\"1162\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan.png\" alt=\"\" class=\"wp-image-9651\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan.png 2346w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan-1024x507.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan-768x380.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan-535x265.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan-1536x761.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/32x32-16x16-pan-2048x1014.png 2048w\" sizes=\"(max-width: 2346px) 100vw, 2346px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Pandiagonal Magic Square of Order 48<\/h3>\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=\"3197\" height=\"1555\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan.png\" alt=\"\" class=\"wp-image-9652\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan.png 3197w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan-300x146.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan-1024x498.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan-768x374.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan-535x260.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan-1536x747.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/48x48-16x16-pan-2048x996.png 2048w\" sizes=\"(max-width: 3197px) 100vw, 3197px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(255,203,112) 0%,rgb(255,255,255) 21%,rgb(199,81,192) 50%,rgb(255,255,255) 64%,rgb(65,88,208) 100%)\">Excel file for Download<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">The excel file below for download contains <strong>pandiagonal<\/strong> magic squares multiples of order 16 from order 16 to 144.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<div class=\"wp-block-file\"><a id=\"wp-block-file--media-4d43cae4-6bb7-443b-bee0-a58ffc302f37\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-144-16-pandiagonal.xlsx\">16&#215;16-144-16-pandiagonal<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/16x16-144-16-pandiagonal.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4d43cae4-6bb7-443b-bee0-a58ffc302f37\">Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>During past years author worked with block-wise, bordered and block-bordered magic squares. This work make connection between block-wise and bordered magic squares. We started with block-wise bordered magic squares of orders 144 and 128. Based on these two big magic squares, the inner order magic squares multiples of 16 are studied. By inner orders we [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":9641,"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-9634","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\/07\/32x32-16x16-22.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/9634","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=9634"}],"version-history":[{"count":1,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/9634\/revisions"}],"predecessor-version":[{"id":9654,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/9634\/revisions\/9654"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/9641"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9634"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9634"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}