{"id":9675,"date":"2023-07-13T14:28:43","date_gmt":"2023-07-13T17:28:43","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9675"},"modified":"2023-07-13T14:30:37","modified_gmt":"2023-07-13T17:30:37","slug":"block-wise-bordered-and-pandiagonal-magic-squares-multiples-of-20","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9675","title":{"rendered":"Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 20"},"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 140 and 120. 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 100, 80, etc. The construction of the <strong>block-wise bordered<\/strong> magic squares multiples of 20 is based on <strong>equal sum blocks of magic squares of order 20<\/strong>. We have taken <strong>57 different types of magic squares of order 20<\/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, 14, 16 and 18 see the links below:<br>1.&nbsp;<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.&nbsp;<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.&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=687\">Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 8 \u2013 Revised<\/a><br>4.&nbsp;<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.&nbsp;<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><br>7. <a href=\"https:\/\/numbers-magic.com\/?p=9634\">Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16<\/a>.<br>8. <a href=\"https:\/\/numbers-magic.com\/?p=9655\">Block-Wise Bordered Magic Squares Multiples of 18<\/a>.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><\/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 140. Examples below are only up to order 60. 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 20<\/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 20. It includes <strong>bordered, double digits, cornered magic <\/strong>squares, etc. Total 57 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=\"1231\" height=\"751\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-3.png\" alt=\"\" class=\"wp-image-9676\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-3.png 1231w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-3-300x183.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-3-1024x625.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-3-768x469.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-3-535x326.png 535w\" sizes=\"(max-width: 1231px) 100vw, 1231px\" \/><\/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=\"1224\" height=\"752\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-16.png\" alt=\"\" class=\"wp-image-9677\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-16.png 1224w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-16-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-16-1024x629.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-16-768x472.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-16-535x329.png 535w\" sizes=\"(max-width: 1224px) 100vw, 1224px\" \/><\/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=\"1226\" height=\"756\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-29.png\" alt=\"\" class=\"wp-image-9678\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-29.png 1226w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-29-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-29-1024x631.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-29-768x474.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-20x20-29-535x330.png 535w\" sizes=\"(max-width: 1226px) 100vw, 1226px\" \/><\/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 57 Magic Squares of Order 20<\/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\/20x20.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 20x20.\"><\/object><a id=\"wp-block-file--media-1c533edc-2304-424c-a1b5-7aadf5730662\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20.pdf\">20&#215;20<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20.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 40<\/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 40. The other are given in attached pdf file and in&nbsp;<strong>excel file<\/strong>&nbsp;given 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=\"2864\" height=\"1431\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4.png\" alt=\"\" class=\"wp-image-9680\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4.png 2864w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4-300x150.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4-1024x512.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4-768x384.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4-535x267.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4-1536x767.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-4-2048x1023.png 2048w\" sizes=\"(max-width: 2864px) 100vw, 2864px\" \/><\/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=\"2865\" height=\"1437\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17.png\" alt=\"\" class=\"wp-image-9681\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17.png 2865w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17-300x150.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17-1024x514.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17-768x385.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17-535x268.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17-1536x770.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-17-2048x1027.png 2048w\" sizes=\"(max-width: 2865px) 100vw, 2865px\" \/><\/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=\"2866\" height=\"1433\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37.png\" alt=\"\" class=\"wp-image-9682\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37.png 2866w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37-300x150.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37-1024x512.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37-768x384.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37-535x268.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37-1536x768.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-20x20-37-2048x1024.png 2048w\" sizes=\"(max-width: 2866px) 100vw, 2866px\" \/><\/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 57 Magic Squares of Order 40<\/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\/40x40.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 40x40.\"><\/object><a id=\"wp-block-file--media-1c533edc-2304-424c-a1b5-7aadf5730662\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40.pdf\">40&#215;40<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40.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 60<\/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=\"2802\" height=\"1126\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14.png\" alt=\"\" class=\"wp-image-9684\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14.png 2802w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14-300x121.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14-1024x412.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14-768x309.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14-535x215.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14-1536x617.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-14-2048x823.png 2048w\" sizes=\"(max-width: 2802px) 100vw, 2802px\" \/><\/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=\"2805\" height=\"1123\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24.png\" alt=\"\" class=\"wp-image-9685\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24.png 2805w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24-300x120.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24-1024x410.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24-768x307.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24-535x214.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24-1536x615.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-24-2048x820.png 2048w\" sizes=\"(max-width: 2805px) 100vw, 2805px\" \/><\/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=\"2803\" height=\"1123\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41.png\" alt=\"\" class=\"wp-image-9686\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41.png 2803w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41-300x120.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41-1024x410.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41-768x308.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41-535x214.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41-1536x615.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-20x20-41-2048x821.png 2048w\" sizes=\"(max-width: 2803px) 100vw, 2803px\" \/><\/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 57 Magic Squares of Order 60<\/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\/60x60.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 60x60.\"><\/object><a id=\"wp-block-file--media-05b267fd-bf20-4302-a790-be7b37ab5af4\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60.pdf\">60&#215;60<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60.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 57 examples in each case. Total work is from order 20 to 140. There are two files. One is with magic squares of orders 140 and 120. The second file is with magic squares of orders 100, 80, 60, 40 and 20. <\/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\/20x20-140-120-online.xlsx\">20&#215;20-140-120-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-140-120-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\/20x20-100-20-online.xlsx\">20&#215;20-100-20-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-100-20-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<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 20<\/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 20 to 120 multiples of 20. These are formed by magic squares of orders 4 and 5. The magic squares of order 4 are <strong>pandiagonal<\/strong> and of <strong>equal sums<\/strong>. The magic squares of order 5 are also <strong>pandiagonal<\/strong> but with <strong>different sums<\/strong>. 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 20<\/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=\"1250\" height=\"751\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-pan.png\" alt=\"\" class=\"wp-image-9690\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-pan.png 1250w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-pan-300x180.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-pan-1024x615.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-pan-768x461.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-pan-535x321.png 535w\" sizes=\"(max-width: 1250px) 100vw, 1250px\" \/><\/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=\"1251\" height=\"755\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-5x5-pan.png\" alt=\"\" class=\"wp-image-9691\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-5x5-pan.png 1251w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-5x5-pan-300x181.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-5x5-pan-1024x618.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-5x5-pan-768x464.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-5x5-pan-535x323.png 535w\" sizes=\"(max-width: 1251px) 100vw, 1251px\" \/><\/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 40<\/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=\"2900\" height=\"1434\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan.png\" alt=\"\" class=\"wp-image-9692\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan.png 2900w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan-1024x506.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan-768x380.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan-535x265.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan-1536x760.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-4x4-pan-2048x1013.png 2048w\" sizes=\"(max-width: 2900px) 100vw, 2900px\" \/><\/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=\"2898\" height=\"1429\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan.png\" alt=\"\" class=\"wp-image-9693\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan.png 2898w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan-1024x505.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan-768x379.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan-535x264.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan-1536x757.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/40x40-5x5-pan-2048x1010.png 2048w\" sizes=\"(max-width: 2898px) 100vw, 2898px\" \/><\/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 60<\/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=\"2847\" height=\"1104\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan.png\" alt=\"\" class=\"wp-image-9694\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan.png 2847w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan-1024x397.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan-768x298.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan-535x207.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan-1536x596.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-4x4-pan-2048x794.png 2048w\" sizes=\"(max-width: 2847px) 100vw, 2847px\" \/><\/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=\"2849\" height=\"1104\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan.png\" alt=\"\" class=\"wp-image-9695\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan.png 2849w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan-1024x397.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan-768x298.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan-535x207.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan-1536x595.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/60x60-5x5-pan-2048x794.png 2048w\" sizes=\"(max-width: 2849px) 100vw, 2849px\" \/><\/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 contain <strong>pandiagonal<\/strong> magic squares multiples of order 20 from order 20 to 120.<\/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\/20x20-120-20-pan-online.xlsx\">20&#215;20-120-20-pan-online<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/07\/20x20-120-20-pan-online.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 140 and 120. 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":9677,"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-9675","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\/20x20-20x20-16.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/9675","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=9675"}],"version-history":[{"count":2,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/9675\/revisions"}],"predecessor-version":[{"id":9698,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/9675\/revisions\/9698"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/9677"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9675"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9675"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9675"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}