{"id":10071,"date":"2023-08-12T08:06:15","date_gmt":"2023-08-12T11:06:15","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=10071"},"modified":"2023-09-10T10:22:00","modified_gmt":"2023-09-10T13:22:00","slug":"cornered-magic-rectangles-in-construction-of-magic-squares-magic-squares-of-order-26","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=10071","title":{"rendered":"Different Types of Magic Rectangles in Construction of Magic Squares of Order 26"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-right wp-block-paragraph\"><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-pale-ocean-gradient-background has-background wp-block-paragraph\">This work brings magic squares in very different way. These are based on three different types of <strong>magic rectangles<\/strong>:<br><strong>1. Bordered Magic Rectangles:<br>2. Double Digits Magic Rectangles:<br>3. Cornered magic rectangles. <br><\/strong><br>First of let&#8217;s understand these magic rectangles one by one.  Removing external borders in each case still we left with lower order <strong>magic rectangles<\/strong>. See below few examples in each case.<\/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) 53%,rgb(255,105,0) 100%)\">1. Bordered Magic Rectangles<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Below are two examples of bordered magic rectangles<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-left\"><strong>Example 1. Bordered Magic Rectangle of Order 12&#215;18<\/strong><\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1141\" height=\"420\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-12x18-1.png\" alt=\"\" class=\"wp-image-10220\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-12x18-1.png 1141w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-12x18-1-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-12x18-1-1024x377.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-12x18-1-768x283.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-12x18-1-535x197.png 535w\" sizes=\"(max-width: 1141px) 100vw, 1141px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The entries according to colors are as follows:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1491\" height=\"606\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-1.png\" alt=\"\" class=\"wp-image-10221\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-1.png 1491w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-1-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-1-1024x416.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-1-768x312.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-1-535x217.png 535w\" sizes=\"(max-width: 1491px) 100vw, 1491px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">Example 2. Bordered Magic Rectangle of Order 6&#215;16<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1024\" height=\"231\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-6x16-2.png\" alt=\"\" class=\"wp-image-10226\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-6x16-2.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-6x16-2-300x68.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-6x16-2-768x173.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-6x16-2-535x121.png 535w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">The entries according to colors are as follows:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1066\" height=\"286\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-2.png\" alt=\"\" class=\"wp-image-10227\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-2.png 1066w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-2-300x80.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-2-1024x275.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-2-768x206.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/BMR-entries-2-535x144.png 535w\" sizes=\"(max-width: 1066px) 100vw, 1066px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">More details are given in author&#8217;s recent work:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\"><strong>Inder J. Taneja, <\/strong>Different Types of Magic Rectangles, <strong>Zenodo<\/strong>, September 04, 2023, pp. 1-26, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8316719\">https:\/\/doi.org\/10.5281\/zenodo.8316719<\/a>.<\/mark><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">2. Double Digits Magic Rectangles<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Below are two examples of bordered magic rectangles<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-left\"><strong>Example 1. Double Digits Magic Rectangle of Order 14&#215;20<\/strong><\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1270\" height=\"490\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-14x20-1.png\" alt=\"\" class=\"wp-image-10232\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-14x20-1.png 1270w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-14x20-1-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-14x20-1-1024x395.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-14x20-1-768x296.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-14x20-1-535x206.png 535w\" sizes=\"(max-width: 1270px) 100vw, 1270px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Except the corners, the entries <strong>entries sums<\/strong> are understood as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1022\" height=\"879\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-1-1.png\" alt=\"\" class=\"wp-image-10233\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-1-1.png 1022w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-1-1-300x258.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-1-1-768x661.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-1-1-535x460.png 535w\" sizes=\"(max-width: 1022px) 100vw, 1022px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"949\" height=\"336\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-2.png\" alt=\"\" class=\"wp-image-10234\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-2.png 949w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-2-300x106.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-2-768x272.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-2-535x189.png 535w\" sizes=\"(max-width: 949px) 100vw, 949px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-left\"><strong>Example 2. Double Digits Magic Rectangle of Order 12&#215;18<\/strong><\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1449\" height=\"421\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-12x22-2.png\" alt=\"\" class=\"wp-image-10235\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-12x22-2.png 1449w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-12x22-2-300x87.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-12x22-2-1024x298.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-12x22-2-768x223.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-12x22-2-535x155.png 535w\" sizes=\"(max-width: 1449px) 100vw, 1449px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Except the corners, the entries <strong>entries sums<\/strong> are understood as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1153\" height=\"493\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-3-1.png\" alt=\"\" class=\"wp-image-10236\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-3-1.png 1153w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-3-1-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-3-1-1024x438.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-3-1-768x328.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-3-1-535x229.png 535w\" sizes=\"(max-width: 1153px) 100vw, 1153px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"941\" height=\"268\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-4-1.png\" alt=\"\" class=\"wp-image-10237\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-4-1.png 941w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-4-1-300x85.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-4-1-768x219.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-sums-4-1-535x152.png 535w\" sizes=\"(max-width: 941px) 100vw, 941px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"951\" height=\"166\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-4x14-1.png\" alt=\"\" class=\"wp-image-10239\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-4x14-1.png 951w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-4x14-1-300x52.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-4x14-1-768x134.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DD-4x14-1-535x93.png 535w\" sizes=\"(max-width: 951px) 100vw, 951px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify wp-block-paragraph\">After reorganizing the <strong>internal magic rectangle of order 4&#215;16<\/strong>, we have the following <strong>double digits magic rectangle<\/strong>:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1544\" height=\"462\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1.png\" alt=\"\" class=\"wp-image-10238\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1.png 1544w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1-300x90.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1-1024x306.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1-768x230.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1-535x160.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/DDB-12x22-1-1536x460.png 1536w\" sizes=\"(max-width: 1544px) 100vw, 1544px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">More details are given in author&#8217;s recent work:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\"><strong>Inder J. Taneja, <\/strong>Different Types of Magic Rectangles, <strong>Zenodo<\/strong>, September 04, 2023, pp. 1-26, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8316719\">https:\/\/doi.org\/10.5281\/zenodo.8316719<\/a><\/mark><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">.<\/mark><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">3. Cornered Magic Rectangles<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Below are two examples of cornered magic rectangles<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-left\"><strong>Example 1. Cornered Magic Rectangle of Order 8&#215;12<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s consider a cornered magic rectangle of order <strong>8&#215;12<\/strong> formed by 96 sequencial entries, i.e., from 1 to 96:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"806\" height=\"323\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/MR-8x12-1.png\" alt=\"\" class=\"wp-image-10083\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/MR-8x12-1.png 806w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/MR-8x12-1-300x120.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/MR-8x12-1-768x308.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/MR-8x12-1-535x214.png 535w\" sizes=\"(max-width: 806px) 100vw, 806px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distributions in colors as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2240\" height=\"257\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1.png\" alt=\"\" class=\"wp-image-10113\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1.png 2240w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1-300x34.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1-1024x117.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1-768x88.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1-535x61.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1-1536x176.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/08\/entries-1-2048x235.png 2048w\" sizes=\"(max-width: 2240px) 100vw, 2240px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-left\"><strong>Example 2. Cornered Magic Rectangle of Order 8&#215;12<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s consider a cornered magic rectangle of order <strong>10&#215;24<\/strong> formed by 240 sequencial entries, i.e., from 1 to 240:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1680\" height=\"394\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1.png\" alt=\"\" class=\"wp-image-10244\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1.png 1680w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1-300x70.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1-1024x240.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1-768x180.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1-535x125.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/CMR-10x24-1-1536x360.png 1536w\" sizes=\"(max-width: 1680px) 100vw, 1680px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Distributions in colors as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1707\" height=\"501\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2.png\" alt=\"\" class=\"wp-image-10245\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2.png 1707w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2-300x88.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2-1024x301.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2-768x225.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2-535x157.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/entries-2-1536x451.png 1536w\" sizes=\"(max-width: 1707px) 100vw, 1707px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">More details are given in author&#8217;s recent work:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\"><strong>Inder J. Taneja, <\/strong>Different Types of Magic Rectangles, <strong>Zenodo<\/strong>, September 04, 2023, pp. 1-26, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8316719\">https:\/\/doi.org\/10.5281\/zenodo.8316719<\/a><\/mark><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-luminous-vivid-orange-color\">.<\/mark><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 42%,rgb(255,105,0) 100%)\">Based on ideas given above, we shall construct magic squares of order 22. These are constructed with <strong>four magic rectangles<\/strong>. As explained above these are of are of <strong>equal sums<\/strong>. These are made with the help of script by H. White (<a href=\"https:\/\/budshaw.ca\/Download.html\">Downloads (budshaw.ca<\/a>) &#8211; <em>NestedCornerRectangles<\/em>)). These kinds of magic squares are <strong>never seen in the history<\/strong>. There are of different styles. All the three types of magic rectangles are used to bring magic squares of order 22. See below:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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(82,199,95) 50%,rgb(65,88,208) 100%)\">Magic Squares of Order 26<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Initially below are two <strong>double digits<\/strong> and <strong>cornered magic squares<\/strong> of order 26:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1864\" height=\"973\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1.png\" alt=\"\" class=\"wp-image-10294\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1.png 1864w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1-1024x535.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1-768x401.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1-535x279.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-1-1536x802.png 1536w\" sizes=\"(max-width: 1864px) 100vw, 1864px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1867\" height=\"987\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2.png\" alt=\"\" class=\"wp-image-10295\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2.png 1867w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-2-1536x812.png 1536w\" sizes=\"(max-width: 1867px) 100vw, 1867px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">1. Bordered Magic Rectangles and <br>Magic Squares of Order 26<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-paragraph\">Below are examples of <strong>magic squares of order 26<\/strong> centered in magic squares of order 6, 10, 14 and 18 respectively. These are constructed with four equal sums <strong>bordered magic rectangles <\/strong>of orders <strong>10&#215;16, 8&#215;18, 6&#215;20<\/strong> and <strong>4&#215;22<\/strong> respectively.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1867\" height=\"990\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4.png\" alt=\"\" class=\"wp-image-10296\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4.png 1867w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-4-1536x814.png 1536w\" sizes=\"(max-width: 1867px) 100vw, 1867px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1862\" height=\"988\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30.png\" alt=\"\" class=\"wp-image-10297\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30.png 1862w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-30-1536x815.png 1536w\" sizes=\"(max-width: 1862px) 100vw, 1862px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1866\" height=\"990\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89.png\" alt=\"\" class=\"wp-image-10298\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89.png 1866w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-89-1536x815.png 1536w\" sizes=\"(max-width: 1866px) 100vw, 1866px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1864\" height=\"990\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176.png\" alt=\"\" class=\"wp-image-10299\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176.png 1864w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176-1024x544.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-176-1536x816.png 1536w\" sizes=\"(max-width: 1864px) 100vw, 1864px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">More examples are in <strong>pdf file <\/strong>attached at the end of work.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">2. Double Digits Magic Rectangles and <br>Magic Squares of Order 26<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-paragraph\">Below are examples of <strong>magic squares of order 26<\/strong> centered in magic squares of order 6, 10 and 14 respectively. These are constructed with four equal sums <strong>bordered magic rectangles <\/strong>of orders <strong>10&#215;16, 8&#215;18 <\/strong>and<strong> 6&#215;20 <\/strong>respectively.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1864\" height=\"992\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7.png\" alt=\"\" class=\"wp-image-10300\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7.png 1864w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7-1024x545.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7-768x409.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-7-1536x817.png 1536w\" sizes=\"(max-width: 1864px) 100vw, 1864px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1867\" height=\"987\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37.png\" alt=\"\" class=\"wp-image-10301\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37.png 1867w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-37-1536x812.png 1536w\" sizes=\"(max-width: 1867px) 100vw, 1867px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1865\" height=\"989\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110.png\" alt=\"\" class=\"wp-image-10302\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110.png 1865w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-110-1536x815.png 1536w\" sizes=\"(max-width: 1865px) 100vw, 1865px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">More examples are in <strong>pdf file <\/strong>attached at the end of work.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-paragraph\">In this case we don&#8217;t have magic square of order 26 <strong>centered in magic square of order 18<\/strong> having four equal sums<strong> double digits magic rectangles<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">3. Cornered Magic Rectangles and <br>Magic Squares of Order 26: First Type<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-paragraph\">Below are examples of <strong>magic squares of order 26<\/strong> centered in magic squares of order 6, 10, 14 and 18 respectively. These are constructed with four equal sums <strong>cornered magic rectangles <\/strong>of orders <strong>10&#215;16, 8&#215;18, 6&#215;20<\/strong> and <strong>4&#215;22<\/strong> respectively.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1861\" height=\"990\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11.png\" alt=\"\" class=\"wp-image-10303\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11.png 1861w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11-1024x545.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11-768x409.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-11-1536x817.png 1536w\" sizes=\"(max-width: 1861px) 100vw, 1861px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1863\" height=\"992\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49.png\" alt=\"\" class=\"wp-image-10306\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49.png 1863w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49-1024x545.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49-768x409.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-49-1536x818.png 1536w\" sizes=\"(max-width: 1863px) 100vw, 1863px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1867\" height=\"988\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126.png\" alt=\"\" class=\"wp-image-10309\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126.png 1867w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126-1024x542.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-126-1536x813.png 1536w\" sizes=\"(max-width: 1867px) 100vw, 1867px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1865\" height=\"990\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244.png\" alt=\"\" class=\"wp-image-10312\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244.png 1865w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244-1024x544.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-244-1536x815.png 1536w\" sizes=\"(max-width: 1865px) 100vw, 1865px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">3. Cornered Magic Rectangles and <br>Magic Squares of Order 26: Second Type<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-paragraph\">Below are examples of <strong>magic squares of order 26<\/strong> centered in magic squares of order 6, 10 and 14 respectively. These are constructed with four equal sums <strong>cornered magic rectangles <\/strong>of orders <strong>10&#215;16, 8&#215;18 <\/strong>and<strong> 6&#215;20<\/strong> respectively.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1869\" height=\"993\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16.png\" alt=\"\" class=\"wp-image-10304\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16.png 1869w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16-1024x544.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-16-1536x816.png 1536w\" sizes=\"(max-width: 1869px) 100vw, 1869px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1866\" height=\"990\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63.png\" alt=\"\" class=\"wp-image-10307\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63.png 1866w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-63-1536x815.png 1536w\" sizes=\"(max-width: 1866px) 100vw, 1866px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1865\" height=\"995\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151.png\" alt=\"\" class=\"wp-image-10311\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151.png 1865w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151-1024x546.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151-768x410.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-151-1536x819.png 1536w\" sizes=\"(max-width: 1865px) 100vw, 1865px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">3. Cornered Magic Rectangles and <br>Magic Squares of Order 26: Third Type<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-justify has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-paragraph\">Below are examples of <strong>magic squares of order 26<\/strong> centered in magic squares of order 6, 10 and 14 respectively. These are constructed with four equal sums <strong>cornered magic rectangles <\/strong>of orders <strong>10&#215;16, 8&#215;18 <\/strong>and<strong> 6&#215;20<\/strong> respectively.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1865\" height=\"991\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22.png\" alt=\"\" class=\"wp-image-10305\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22.png 1865w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22-1024x544.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-22-1536x816.png 1536w\" sizes=\"(max-width: 1865px) 100vw, 1865px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1865\" height=\"989\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79.png\" alt=\"\" class=\"wp-image-10308\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79.png 1865w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-79-1536x815.png 1536w\" sizes=\"(max-width: 1865px) 100vw, 1865px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1863\" height=\"989\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169.png\" alt=\"\" class=\"wp-image-10310\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169.png 1863w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169-1024x544.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169-768x408.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/MR-26x26-169-1536x815.png 1536w\" sizes=\"(max-width: 1863px) 100vw, 1863px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/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) 53%,rgb(255,105,0) 100%)\">PDF File of Magic Squares of Order 26<\/h3>\n\n\n\n<p class=\"has-text-align-justify wp-block-paragraph\">Below is a pdf file of 294 magic squares of order 26 for download.  These are constructed with 4 <strong>equal sums magic rectangles of three types<\/strong> as explained above. Magic squares numbers 1 and 2 are basic.<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/26x26.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of 26x26.\"><\/object><a id=\"wp-block-file--media-60b0ed1b-a33d-4154-ab2b-b7014de0b610\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/26x26.pdf\">26&#215;26<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/09\/26x26.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-60b0ed1b-a33d-4154-ab2b-b7014de0b610\">Download<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-blush-light-purple-gradient-background has-background\">References<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<ol class=\"has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, <a rel=\"noreferrer noopener\" href=\"https:\/\/numbers-magic.com\/?p=9406\" target=\"_blank\">Double Digits Even and Odd Orders Bordered Magic Squares<\/a>. <br>Also see: New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108, pp. 1-30, August 09, 2023, <strong>Zenodo<\/strong>. <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8230214\">https:\/\/doi.org\/10.5281\/zenodo.8230214<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 81, pp. 1-27, August 09, 2023,  <strong>Zenodo<\/strong>. <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8231157\">https:\/\/doi.org\/10.5281\/zenodo.8231157<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Different Types of Magic Rectangles, <strong>Zenodo<\/strong>, September 04, 2023, pp. 1-26, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8316719\">https:\/\/doi.org\/10.5281\/zenodo.8316719<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Different Types of Magic Rectangles in Construction of Magic Squares of Orders 14 and 18, <strong>Zenodo<\/strong>, September 10, 2023, pp. 1-32, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8331709\">https:\/\/doi.org\/10.5281\/zenodo.8331709<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Different Types of Magic Rectangles in Construction of Magic Squares of Order 22, <strong>Zenodo<\/strong>, September 10, 2023, pp. 1-36, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8331743\">https:\/\/doi.org\/10.5281\/zenodo.8331743<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Different Types of Magic Rectangles in Construction of Magic Squares of Order 26, <strong>Zenodo<\/strong>, September 10, 2023, pp. 1-39, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8331750\">https:\/\/doi.org\/10.5281\/zenodo.8331750<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Different Types of Magic Rectangles in Construction of Magic Squares of Order 30, <strong>Zenodo<\/strong>, September 10, 2023, pp. 1-44, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8331755\">https:\/\/doi.org\/10.5281\/zenodo.8331755<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Different Types of Magic Rectangles in Construction of Magic Squares of Order 34, <strong>Zenodo<\/strong>, September 10, 2023, pp. 1-49, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8331759\">https:\/\/doi.org\/10.5281\/zenodo.8331759<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Cornered Magic Squares in Construction of Magic Squares of Orders 16, 20, 24 and 28, <strong>Zenodo<\/strong>, September 10, 2023, pp. 1-35, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.8332156\">https:\/\/doi.org\/10.5281\/zenodo.8332156<\/a>.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Never seen before. This work brings magic squares in very different way. These are based on three different types of magic rectangles:1. Bordered Magic Rectangles:2. Double Digits Magic Rectangles:3. Cornered magic rectangles. First of let&#8217;s understand these magic rectangles one by one. Removing external borders in each case still we left with lower order magic [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":10312,"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-10071","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\/09\/MR-26x26-244.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/10071","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=10071"}],"version-history":[{"count":6,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/10071\/revisions"}],"predecessor-version":[{"id":10410,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/10071\/revisions\/10410"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/10312"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}