{"id":17312,"date":"2025-12-21T18:15:53","date_gmt":"2025-12-21T21:15:53","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=17312"},"modified":"2025-12-26T20:28:28","modified_gmt":"2025-12-26T23:28:28","slug":"153-magic-squares-in-honor-of-the-138th-anniversary-of-s-ramanujan-with-magic-sum-1729","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=17312","title":{"rendered":"207 Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729"},"content":{"rendered":"\n<h3 class=\"wp-block-heading has-text-align-right has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-831460d0a1c7f0025c53afbd83e4b28e\">138th Birth Anniversary of S. Ramanujan,<br>December 22, 1887-April 26, 1920<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-right has-vivid-purple-color has-text-color has-link-color wp-elements-054c3950117695baa11a47d5eb42c129\">National Mathematics Day, India &#8211; December 22<\/h3>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\"><em>This work brings <strong>magic squares<\/strong> connected with S. Ramanujan&#8217;s life and with Hardy-Ramanujan number <strong>1729<\/strong>. On december 22, 2025 there is 138th aniversiory of S. Ramanujan. This work brings magic squares of orders 3 to 20 having magic sum either 1729 or multiple of 1729. Some special entries are considered such as <strong>2212, 1887, 2025<\/strong> and <strong>138. <\/strong>See below the table of total 207 magic squares according to each order.<\/em><\/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=\"824\" height=\"995\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/Table-3-20.png\" alt=\"\" class=\"wp-image-17520\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/Table-3-20.png 824w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/Table-3-20-248x300.png 248w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/Table-3-20-768x927.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/Table-3-20-535x646.png 535w\" sizes=\"(max-width: 824px) 100vw, 824px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">The whole work can be accessed at the following link:<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 42%,rgb(152,150,240) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, 207 Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729, <strong>Zenodo<\/strong>, December 27, 2025, pp. 1-77, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.18064853\">https:\/\/doi.org\/10.5281\/zenodo.18064853<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link1: <a href=\"https:\/\/numbers-magic.com\/?p=17312\">207 Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729<\/a> (new site)<\/li>\n\n\n\n<li>Site Link2: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/12\/22\/153-magic-squares-in-honor-of-the-138th-anniversary-of-s-ramanujan-with-magic-sum-1729\/\">207Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">For previous work see the following links:<\/p>\n\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729,&nbsp;<strong>Zenodo<\/strong>, December 20, 2024, pp. 1-127,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.14538297\">https:\/\/doi.org\/10.5281\/zenodo.14538297<\/a>\n<ul class=\"wp-block-list\">\n<li>Site links:\n<ul class=\"wp-block-list\">\n<li>Part 1:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2021\/12\/25\/hardy-ramanujan-number-1729-revised\/\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1<\/a>&nbsp;(old site)<br>Part 1:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=149\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 1<\/a>&nbsp;(new site)<\/li>\n\n\n\n<li>Part 2:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/12\/24\/numbers-and-magic-squares-representations-of-hardy-ramanujan-number-1729-part-2\/\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2&nbsp;<\/a>(old site)<br>Part 2:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=13751\">Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729 \u2013 Part 2<\/a>&nbsp;(new site)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-electric-grass-gradient-background has-background\"><em>See below magic squares. Most of the work is based on three types of magic squares. <br><strong>1. General Magic Squares<br>2. Single-Digit Bordered Magic Squares.<br>3. Double-Digit Bordered Magic Squares.<br>4. Cornered Magic Squares.<\/strong><\/em><br><em><br>The construction of these magic squares is based on <strong>reduced entries algebraic <\/strong>magic sqaures recently studied by the author. For details see the reference list. If any of the magic square is not found according to above table. It can be accessed at the link of the work given above.<\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 3<\/h3>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"754\" height=\"187\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/3x3-12.png\" alt=\"\" class=\"wp-image-17313\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/3x3-12.png 754w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/3x3-12-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/3x3-12-535x133.png 535w\" sizes=\"(max-width: 754px) 100vw, 754px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are two examples magic squares of order 3 with magic sum 1729. The first example is magic squares but there are f<strong>ractional entries<\/strong>. The second one is <strong>semi-magic<\/strong> having four special entreis, such as. date of birth of S. Ramanujan <strong>2212-1887<\/strong> and <strong>138th<\/strong> aniversary on <strong>2212-2025<\/strong>. <\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 4<\/h3>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"899\" height=\"221\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-12.png\" alt=\"\" class=\"wp-image-17314\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-12.png 899w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-12-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-12-768x189.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-12-535x132.png 535w\" sizes=\"(max-width: 899px) 100vw, 899px\" \/><\/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=\"810\" height=\"224\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-34.png\" alt=\"\" class=\"wp-image-17315\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-34.png 810w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-34-300x83.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-34-768x212.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/4x4-34-535x148.png 535w\" sizes=\"(max-width: 810px) 100vw, 810px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are two examples magic squares of order 4 with magic sum 1729. The first example is in two diffeernt ways. First one is pandiagonal but having decimal entries. The second way is not pandiagonal but don&#8217;t require decimal entries. The example is also written in two parts. Both are with two equal sums magic rectangles of orders 2&#215;4. Here the magic sum is 2&#215;1729. This is to avoid decimal entries. <br><\/em><br><em>Both the <em><em><strong>examples<\/strong> uses special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 5<\/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=\"1449\" height=\"253\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/5x5-123.png\" alt=\"\" class=\"wp-image-17316\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/5x5-123.png 1449w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/5x5-123-300x52.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/5x5-123-1024x179.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/5x5-123-768x134.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/5x5-123-535x93.png 535w\" sizes=\"(max-width: 1449px) 100vw, 1449px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>three<\/strong> examples magic squares of order 5 with magic sum 1729. The first example is a pandiagonal . The second example is a cornered magic square having magic square of order 3 at the upper left corner. The third example is a single-digit bordered semi-magic square <br><br><em><em>All <strong>3 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 6<\/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=\"1075\" height=\"292\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-12.png\" alt=\"\" class=\"wp-image-17317\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-12.png 1075w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-12-300x81.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-12-1024x278.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-12-768x209.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-12-535x145.png 535w\" sizes=\"(max-width: 1075px) 100vw, 1075px\" \/><\/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=\"1082\" height=\"299\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-34.png\" alt=\"\" class=\"wp-image-17318\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-34.png 1082w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-34-300x83.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-34-1024x283.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-34-768x212.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-34-535x148.png 535w\" sizes=\"(max-width: 1082px) 100vw, 1082px\" \/><\/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=\"1080\" height=\"287\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-56-1.png\" alt=\"\" class=\"wp-image-17414\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-56-1.png 1080w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-56-1-300x80.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-56-1-1024x272.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-56-1-768x204.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/6x6-56-1-535x142.png 535w\" sizes=\"(max-width: 1080px) 100vw, 1080px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are six examples magic squares of order 6 with magic sum 1729. The first example is a normal magic square of order 6. The second example is with four equal sums semi-magic squares of order 3. The third and forth examples are with magic rectangles. The fifth one is cornrered magic square of order 6. The the last example is a single-digit bordered semi-magic square of order 6.<br><br><em><em><em>All <strong>6 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/em><\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 7<\/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=\"1248\" height=\"371\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-12.png\" alt=\"\" class=\"wp-image-17321\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-12.png 1248w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-12-300x89.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-12-1024x304.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-12-768x228.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-12-535x159.png 535w\" sizes=\"(max-width: 1248px) 100vw, 1248px\" \/><\/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=\"1245\" height=\"335\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-34.png\" alt=\"\" class=\"wp-image-17322\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-34.png 1245w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-34-300x81.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-34-1024x276.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-34-768x207.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-34-535x144.png 535w\" sizes=\"(max-width: 1245px) 100vw, 1245px\" \/><\/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=\"1282\" height=\"383\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-56.png\" alt=\"\" class=\"wp-image-17323\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-56.png 1282w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-56-300x90.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-56-1024x306.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-56-768x229.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-56-535x160.png 535w\" sizes=\"(max-width: 1282px) 100vw, 1282px\" \/><\/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=\"1298\" height=\"365\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-78.png\" alt=\"\" class=\"wp-image-17324\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-78.png 1298w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-78-300x84.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-78-1024x288.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-78-768x216.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-78-535x150.png 535w\" sizes=\"(max-width: 1298px) 100vw, 1298px\" \/><\/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=\"1287\" height=\"336\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-910.png\" alt=\"\" class=\"wp-image-17325\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-910.png 1287w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-910-300x78.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-910-1024x267.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-910-768x201.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-910-535x140.png 535w\" sizes=\"(max-width: 1287px) 100vw, 1287px\" \/><\/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=\"614\" height=\"325\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-11-1.png\" alt=\"\" class=\"wp-image-17326\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-11-1.png 614w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-11-1-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/7x7-11-1-535x283.png 535w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are<strong> eleven<\/strong> examples magic squares of order 7 with magic sum 1729. The first eight examples are based on the different types of magic squares as written in the bignninig of this wotk. The last three examples are of semi-magic squares of order 7 . <br><br><em><em>All <strong>11 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/em><\/p>\n\n\n\n<p><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 8<\/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=\"1472\" height=\"370\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-12.png\" alt=\"\" class=\"wp-image-17327\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-12.png 1472w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-12-300x75.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-12-1024x257.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-12-768x193.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-12-535x134.png 535w\" sizes=\"(max-width: 1472px) 100vw, 1472px\" \/><\/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=\"750\" height=\"360\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-3.png\" alt=\"\" class=\"wp-image-17328\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-3.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-3-300x144.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-3-535x257.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/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=\"1457\" height=\"437\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-45.png\" alt=\"\" class=\"wp-image-17329\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-45.png 1457w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-45-300x90.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-45-1024x307.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-45-768x230.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-45-535x160.png 535w\" sizes=\"(max-width: 1457px) 100vw, 1457px\" \/><\/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=\"1310\" height=\"352\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-67.png\" alt=\"\" class=\"wp-image-17330\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-67.png 1310w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-67-300x81.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-67-1024x275.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-67-768x206.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-67-535x144.png 535w\" sizes=\"(max-width: 1310px) 100vw, 1310px\" \/><\/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=\"641\" height=\"359\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-8.png\" alt=\"\" class=\"wp-image-17333\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-8.png 641w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-8-300x168.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-8-535x300.png 535w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/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=\"1420\" height=\"361\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-910.png\" alt=\"\" class=\"wp-image-17332\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-910.png 1420w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-910-300x76.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-910-1024x260.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-910-768x195.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/8x8-910-535x136.png 535w\" sizes=\"(max-width: 1420px) 100vw, 1420px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>ten<\/strong> examples magic squares of order 8 with magic sum 1729. The first three examples are based on the different types of magic squares as written in the bignninig of this wotk. The examples 4 and 5 are of semi-magic square of order 8. The examples 8, 9 and 10 are little different. The examples 8 and 9 are stripled magic square of order 8. The example 10 is based on four equazl sums <strong>pandiagonal<\/strong> magic squares of order 4. The examples 9 and 10 both are <strong>pandiagonal<\/strong>. In both these examples the magic sums ie 6916=4*1729. This we have considered to avoid decimal entries. <br><br><em><em>All <strong>10 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 9<\/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=\"1464\" height=\"403\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-12.png\" alt=\"\" class=\"wp-image-17335\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-12.png 1464w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-12-300x83.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-12-1024x282.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-12-768x211.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-12-535x147.png 535w\" sizes=\"(max-width: 1464px) 100vw, 1464px\" \/><\/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=\"1579\" height=\"402\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34.png\" alt=\"\" class=\"wp-image-17336\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34.png 1579w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34-300x76.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34-1024x261.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34-768x196.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34-535x136.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-34-1536x391.png 1536w\" sizes=\"(max-width: 1579px) 100vw, 1579px\" \/><\/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=\"1580\" height=\"404\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56.png\" alt=\"\" class=\"wp-image-17337\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56.png 1580w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56-300x77.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56-1024x262.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56-768x196.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56-535x137.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-56-1536x393.png 1536w\" sizes=\"(max-width: 1580px) 100vw, 1580px\" \/><\/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=\"1579\" height=\"391\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78.png\" alt=\"\" class=\"wp-image-17338\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78.png 1579w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78-1024x254.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78-768x190.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78-535x132.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-78-1536x380.png 1536w\" sizes=\"(max-width: 1579px) 100vw, 1579px\" \/><\/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=\"1529\" height=\"402\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-910.png\" alt=\"\" class=\"wp-image-17339\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-910.png 1529w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-910-300x79.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-910-1024x269.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-910-768x202.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-910-535x141.png 535w\" sizes=\"(max-width: 1529px) 100vw, 1529px\" \/><\/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=\"1524\" height=\"400\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1112.png\" alt=\"\" class=\"wp-image-17340\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1112.png 1524w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1112-300x79.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1112-1024x269.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1112-768x202.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1112-535x140.png 535w\" sizes=\"(max-width: 1524px) 100vw, 1524px\" \/><\/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=\"1523\" height=\"391\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1314.png\" alt=\"\" class=\"wp-image-17341\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1314.png 1523w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1314-300x77.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1314-1024x263.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1314-768x197.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1314-535x137.png 535w\" sizes=\"(max-width: 1523px) 100vw, 1523px\" \/><\/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=\"1530\" height=\"402\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1516.png\" alt=\"\" class=\"wp-image-17342\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1516.png 1530w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1516-300x79.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1516-1024x269.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1516-768x202.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1516-535x141.png 535w\" sizes=\"(max-width: 1530px) 100vw, 1530px\" \/><\/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=\"1518\" height=\"399\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1718.png\" alt=\"\" class=\"wp-image-17343\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1718.png 1518w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1718-300x79.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1718-1024x269.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1718-768x202.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1718-535x141.png 535w\" sizes=\"(max-width: 1518px) 100vw, 1518px\" \/><\/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=\"1522\" height=\"402\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1920.png\" alt=\"\" class=\"wp-image-17344\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1920.png 1522w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1920-300x79.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1920-1024x270.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1920-768x203.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/9x9-1920-535x141.png 535w\" sizes=\"(max-width: 1522px) 100vw, 1522px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>twenty<\/strong> examples magic squares of order 9 with magic sum 1729. The first example is pandiagonal with 9 equal sums semi-magic squres of order 3.  The next 11 examples, i.e., from 2 to 12 are different types of magic squares as written in the bignninig of this work. The last 8 examples, i.e., from 13 to 20 are of semi-magic squares of order 9. <br><br><em>All <strong>20 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 10<\/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=\"1949\" height=\"437\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12.png\" alt=\"\" class=\"wp-image-17345\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12.png 1949w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12-300x67.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12-1024x230.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12-768x172.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12-535x120.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-12-1536x344.png 1536w\" sizes=\"(max-width: 1949px) 100vw, 1949px\" \/><\/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=\"1944\" height=\"437\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34.png\" alt=\"\" class=\"wp-image-17346\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34.png 1944w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34-300x67.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34-1024x230.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34-768x173.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34-535x120.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-34-1536x345.png 1536w\" sizes=\"(max-width: 1944px) 100vw, 1944px\" \/><\/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=\"1948\" height=\"438\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56.png\" alt=\"\" class=\"wp-image-17347\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56.png 1948w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56-300x67.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56-1024x230.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56-768x173.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56-535x120.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-56-1536x345.png 1536w\" sizes=\"(max-width: 1948px) 100vw, 1948px\" \/><\/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=\"1729\" height=\"424\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78.png\" alt=\"\" class=\"wp-image-17348\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78.png 1729w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78-1024x251.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78-768x188.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78-535x131.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-78-1536x377.png 1536w\" sizes=\"(max-width: 1729px) 100vw, 1729px\" \/><\/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=\"1791\" height=\"427\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a.png\" alt=\"\" class=\"wp-image-17352\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a.png 1791w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a-1024x244.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a-768x183.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a-535x128.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-99a-1536x366.png 1536w\" sizes=\"(max-width: 1791px) 100vw, 1791px\" \/><\/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=\"1942\" height=\"433\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011.png\" alt=\"\" class=\"wp-image-17350\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011.png 1942w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011-300x67.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011-1024x228.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011-768x171.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011-535x119.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1011-1536x342.png 1536w\" sizes=\"(max-width: 1942px) 100vw, 1942px\" \/><\/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=\"1630\" height=\"432\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213.png\" alt=\"\" class=\"wp-image-17351\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213.png 1630w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213-300x80.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213-1024x271.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213-768x204.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213-535x142.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/10x10-1213-1536x407.png 1536w\" sizes=\"(max-width: 1630px) 100vw, 1630px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>therteen<\/strong> examples magic squares of order 10 with magic sum 1729. The first 9 examples  are different types of magic squares.. The last 4 examples are of <strong>semi-magic<\/strong> squares of order 10. The example 9 is written in two different ways. One the decimal entries are only in the inner part, i.e., in magic square of order 6. The one is with decimal entries in the outer part.<br><br><em>All <strong>13 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 11<\/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=\"1975\" height=\"474\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12.png\" alt=\"\" class=\"wp-image-17353\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12.png 1975w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12-1024x246.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12-768x184.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12-535x128.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-12-1536x369.png 1536w\" sizes=\"(max-width: 1975px) 100vw, 1975px\" \/><\/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=\"1974\" height=\"474\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34.png\" alt=\"\" class=\"wp-image-17354\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34.png 1974w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34-1024x246.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34-768x184.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34-535x128.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-34-1536x369.png 1536w\" sizes=\"(max-width: 1974px) 100vw, 1974px\" \/><\/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=\"1976\" height=\"467\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56.png\" alt=\"\" class=\"wp-image-17355\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56.png 1976w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56-300x71.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56-1024x242.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56-768x182.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56-535x126.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-56-1536x363.png 1536w\" sizes=\"(max-width: 1976px) 100vw, 1976px\" \/><\/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=\"1971\" height=\"462\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78.png\" alt=\"\" class=\"wp-image-17356\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78.png 1971w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78-300x70.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78-1024x240.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78-768x180.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78-535x125.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-78-1536x360.png 1536w\" sizes=\"(max-width: 1971px) 100vw, 1971px\" \/><\/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=\"1971\" height=\"464\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910.png\" alt=\"\" class=\"wp-image-17357\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910.png 1971w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910-300x71.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910-1024x241.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910-768x181.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910-535x126.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-910-1536x362.png 1536w\" sizes=\"(max-width: 1971px) 100vw, 1971px\" \/><\/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=\"1976\" height=\"460\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112.png\" alt=\"\" class=\"wp-image-17358\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112.png 1976w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112-300x70.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112-1024x238.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112-768x179.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112-535x125.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1112-1536x358.png 1536w\" sizes=\"(max-width: 1976px) 100vw, 1976px\" \/><\/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=\"1978\" height=\"474\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314.png\" alt=\"\" class=\"wp-image-17359\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314.png 1978w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314-1024x245.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314-768x184.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314-535x128.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1314-1536x368.png 1536w\" sizes=\"(max-width: 1978px) 100vw, 1978px\" \/><\/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=\"1977\" height=\"476\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516.png\" alt=\"\" class=\"wp-image-17360\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516.png 1977w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1024x247.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-768x185.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-535x129.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1536x370.png 1536w\" sizes=\"(max-width: 1977px) 100vw, 1977px\" \/><\/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=\"1977\" height=\"476\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1.png\" alt=\"\" class=\"wp-image-17361\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1.png 1977w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1-1024x247.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1-768x185.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1-535x129.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1516-1-1536x370.png 1536w\" sizes=\"(max-width: 1977px) 100vw, 1977px\" \/><\/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=\"1973\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718.png\" alt=\"\" class=\"wp-image-17362\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718.png 1973w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718-300x71.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718-1024x242.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718-768x181.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718-535x126.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1718-1536x363.png 1536w\" sizes=\"(max-width: 1973px) 100vw, 1973px\" \/><\/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=\"1973\" height=\"467\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920.png\" alt=\"\" class=\"wp-image-17363\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920.png 1973w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920-300x71.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920-1024x242.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920-768x182.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920-535x127.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-1920-1536x364.png 1536w\" sizes=\"(max-width: 1973px) 100vw, 1973px\" \/><\/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=\"1976\" height=\"468\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122.png\" alt=\"\" class=\"wp-image-17364\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122.png 1976w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122-300x71.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122-1024x243.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122-768x182.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122-535x127.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2122-1536x364.png 1536w\" sizes=\"(max-width: 1976px) 100vw, 1976px\" \/><\/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=\"1976\" height=\"468\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324.png\" alt=\"\" class=\"wp-image-17365\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324.png 1976w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324-300x71.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324-1024x243.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324-768x182.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324-535x127.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-2324-1536x364.png 1536w\" sizes=\"(max-width: 1976px) 100vw, 1976px\" \/><\/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=\"988\" height=\"463\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-25.png\" alt=\"\" class=\"wp-image-17366\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-25.png 988w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-25-300x141.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-25-768x360.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11-25-535x251.png 535w\" sizes=\"(max-width: 988px) 100vw, 988px\" \/><\/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=\"1921\" height=\"472\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12.png\" alt=\"\" class=\"wp-image-17367\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12.png 1921w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12-1024x252.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12-768x189.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12-535x131.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-12-1536x377.png 1536w\" sizes=\"(max-width: 1921px) 100vw, 1921px\" \/><\/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=\"1929\" height=\"462\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34.png\" alt=\"\" class=\"wp-image-17368\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34.png 1929w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34-1024x245.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34-768x184.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34-535x128.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-34-1536x368.png 1536w\" sizes=\"(max-width: 1929px) 100vw, 1929px\" \/><\/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=\"1920\" height=\"464\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56.png\" alt=\"\" class=\"wp-image-17369\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56.png 1920w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56-1024x247.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56-768x186.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56-535x129.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-56-1536x371.png 1536w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/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=\"1920\" height=\"476\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78.png\" alt=\"\" class=\"wp-image-17370\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78.png 1920w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78-1024x254.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78-768x190.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78-535x133.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-78-1536x381.png 1536w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/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=\"1912\" height=\"472\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910.png\" alt=\"\" class=\"wp-image-17372\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910.png 1912w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910-1024x253.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910-768x190.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910-535x132.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-910-1536x379.png 1536w\" sizes=\"(max-width: 1912px) 100vw, 1912px\" \/><\/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=\"1923\" height=\"473\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112.png\" alt=\"\" class=\"wp-image-17373\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112.png 1923w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112-1024x252.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112-768x189.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112-535x132.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1112-1536x378.png 1536w\" sizes=\"(max-width: 1923px) 100vw, 1923px\" \/><\/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=\"1921\" height=\"476\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314.png\" alt=\"\" class=\"wp-image-17374\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314.png 1921w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314-1024x254.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314-768x190.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314-535x133.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1314-1536x381.png 1536w\" sizes=\"(max-width: 1921px) 100vw, 1921px\" \/><\/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=\"1923\" height=\"468\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516.png\" alt=\"\" class=\"wp-image-17375\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516.png 1923w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516-1024x249.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516-535x130.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1516-1536x374.png 1536w\" sizes=\"(max-width: 1923px) 100vw, 1923px\" \/><\/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=\"1915\" height=\"467\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718.png\" alt=\"\" class=\"wp-image-17377\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718.png 1915w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718-1024x250.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718-535x130.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1718-1536x375.png 1536w\" sizes=\"(max-width: 1915px) 100vw, 1915px\" \/><\/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=\"1920\" height=\"469\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920.png\" alt=\"\" class=\"wp-image-17378\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920.png 1920w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920-1024x250.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920-768x188.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920-535x131.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-1920-1536x375.png 1536w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/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=\"1915\" height=\"467\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122.png\" alt=\"\" class=\"wp-image-17379\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122.png 1915w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122-1024x250.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122-535x130.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-2122-1536x375.png 1536w\" sizes=\"(max-width: 1915px) 100vw, 1915px\" \/><\/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=\"951\" height=\"470\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-23.png\" alt=\"\" class=\"wp-image-17380\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-23.png 951w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-23-300x148.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-23-768x380.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/11x11s-23-535x264.png 535w\" sizes=\"(max-width: 951px) 100vw, 951px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>48<\/strong> examples magic squares of order 11 with magic sum 1729. The first 25 examples are different types of magic squares.. The last 23 examples are of <strong>semi-magic<\/strong> squares of order 11. <br><br>All <strong>48 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/p>\n\n\n\n<p><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 12<\/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=\"2043\" height=\"511\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12.png\" alt=\"\" class=\"wp-image-17382\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12.png 2043w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12-300x75.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12-1024x256.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12-768x192.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12-535x134.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-12-1536x384.png 1536w\" sizes=\"(max-width: 2043px) 100vw, 2043px\" \/><\/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=\"2044\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34.png\" alt=\"\" class=\"wp-image-17384\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34.png 2044w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34-300x75.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34-1024x257.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34-768x193.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34-535x134.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-34-1536x386.png 1536w\" sizes=\"(max-width: 2044px) 100vw, 2044px\" \/><\/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=\"2042\" height=\"496\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56.png\" alt=\"\" class=\"wp-image-17385\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56.png 2042w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56-1024x249.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56-535x130.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-56-1536x373.png 1536w\" sizes=\"(max-width: 2042px) 100vw, 2042px\" \/><\/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=\"2075\" height=\"505\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78.png\" alt=\"\" class=\"wp-image-17386\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78.png 2075w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78-1024x249.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78-535x130.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78-1536x374.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-78-2048x498.png 2048w\" sizes=\"(max-width: 2075px) 100vw, 2075px\" \/><\/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=\"2075\" height=\"509\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910.png\" alt=\"\" class=\"wp-image-17387\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910.png 2075w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910-300x74.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910-1024x251.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910-768x188.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910-535x131.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910-1536x377.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-910-2048x502.png 2048w\" sizes=\"(max-width: 2075px) 100vw, 2075px\" \/><\/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=\"2074\" height=\"504\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112.png\" alt=\"\" class=\"wp-image-17388\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112.png 2074w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112-1024x249.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112-535x130.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112-1536x373.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1112-2048x498.png 2048w\" sizes=\"(max-width: 2074px) 100vw, 2074px\" \/><\/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=\"963\" height=\"505\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-13-1.png\" alt=\"\" class=\"wp-image-17389\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-13-1.png 963w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-13-1-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-13-1-768x403.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-13-1-535x281.png 535w\" sizes=\"(max-width: 963px) 100vw, 963px\" \/><\/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=\"2056\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415.png\" alt=\"\" class=\"wp-image-17390\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415.png 2056w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415-300x75.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415-1024x256.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415-768x192.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415-535x133.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415-1536x383.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1415-2048x511.png 2048w\" sizes=\"(max-width: 2056px) 100vw, 2056px\" \/><\/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=\"2062\" height=\"505\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png.png\" alt=\"\" class=\"wp-image-17391\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png.png 2062w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png-1024x251.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png-768x188.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png-535x131.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png-1536x376.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1617png-2048x502.png 2048w\" sizes=\"(max-width: 2062px) 100vw, 2062px\" \/><\/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=\"2061\" height=\"496\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png.png\" alt=\"\" class=\"wp-image-17392\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png.png 2061w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png-300x72.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png-1024x246.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png-768x185.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png-535x129.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png-1536x370.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-1819png-2048x493.png 2048w\" sizes=\"(max-width: 2061px) 100vw, 2061px\" \/><\/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=\"2005\" height=\"502\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021.png\" alt=\"\" class=\"wp-image-17393\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021.png 2005w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021-300x75.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021-1024x256.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021-768x192.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021-535x134.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2021-1536x385.png 1536w\" sizes=\"(max-width: 2005px) 100vw, 2005px\" \/><\/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=\"2006\" height=\"507\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223.png\" alt=\"\" class=\"wp-image-17394\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223.png 2006w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223-300x76.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223-1024x259.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223-768x194.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223-535x135.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-2223-1536x388.png 1536w\" sizes=\"(max-width: 2006px) 100vw, 2006px\" \/><\/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=\"1130\" height=\"497\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24-1.png\" alt=\"\" class=\"wp-image-17515\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24-1.png 1130w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24-1-300x132.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24-1-1024x450.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24-1-768x338.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24-1-535x235.png 535w\" sizes=\"(max-width: 1130px) 100vw, 1130px\" \/><\/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=\"1129\" height=\"583\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25-1.png\" alt=\"\" class=\"wp-image-17516\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25-1.png 1129w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25-1-300x155.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25-1-1024x529.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25-1-768x397.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25-1-535x276.png 535w\" sizes=\"(max-width: 1129px) 100vw, 1129px\" \/><\/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=\"1473\" height=\"576\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26-1.png\" alt=\"\" class=\"wp-image-17517\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26-1.png 1473w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26-1-300x117.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26-1-1024x400.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26-1-768x300.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26-1-535x209.png 535w\" sizes=\"(max-width: 1473px) 100vw, 1473px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\">Above there are 26 examples magic squares of order 12 with magic sum 1729. The first 13 examples are different types of magic squares. The next 10, i.e., 14 to 23 examples are of  <strong>semi-magic<\/strong> squares of order 12. The last three examples are of different type. All the three examples are <strong>pandiagonal<\/strong>. The example 24 is based on 18 equal sums <strong>magic rectangles<\/strong> of order 2&#215;4. The example 25 is with 9 equal sums <strong>pandiagonal<\/strong> magic squares of order 4. The example 26 is based on 12 equal sums magic squares of order 3. The magic sums of examples 24, 25 and 26 are <strong>S<sub>12&#215;12<\/sub>:=10374=6*1729<\/strong>, <strong>S<sub>12&#215;12<\/sub>:=10374=6*1729<\/strong> and <strong>S<sub>12&#215;12<\/sub>:=20748=12*1729<\/strong> respectively. See below the sums of magic rectangles and magic squares of lower orders of examples 24, 25 and 26:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Magic Rectangles Sums for Example 24:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"546\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24a-1-1024x546.png\" alt=\"\" class=\"wp-image-17512\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24a-1-1024x546.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24a-1-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24a-1-768x410.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24a-1-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-24a-1.png 1200w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Pandiagonal Magic Square Sums of Order 4 for Example 25:<\/strong><\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"552\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25a-1-1024x552.png\" alt=\"\" class=\"wp-image-17513\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25a-1-1024x552.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25a-1-300x162.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25a-1-768x414.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25a-1-535x288.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-25a-1.png 1192w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Magic Square Sums of Order 3 for Example 26:<\/strong><\/li>\n<\/ul>\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=\"851\" height=\"207\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26a-1.png\" alt=\"\" class=\"wp-image-17514\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26a-1.png 851w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26a-1-300x73.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26a-1-768x187.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/12x12-26a-1-535x130.png 535w\" sizes=\"(max-width: 851px) 100vw, 851px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>In this case there are only two magic squares are there. In the similar way we can write sum of other magic squares of order 3 for the example 26.<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>All <strong>26 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 13<\/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=\"1099\" height=\"621\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-1.png\" alt=\"\" class=\"wp-image-17401\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-1.png 1099w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-1-300x170.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-1-1024x579.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-1-768x434.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-1-535x302.png 535w\" sizes=\"(max-width: 1099px) 100vw, 1099px\" \/><\/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=\"1127\" height=\"620\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-2.png\" alt=\"\" class=\"wp-image-17402\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-2.png 1127w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-2-300x165.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-2-1024x563.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-2-768x423.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-2-535x294.png 535w\" sizes=\"(max-width: 1127px) 100vw, 1127px\" \/><\/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=\"1130\" height=\"622\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-3.png\" alt=\"\" class=\"wp-image-17403\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-3.png 1130w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-3-300x165.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-3-1024x564.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-3-768x423.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/13x13-3-535x294.png 535w\" sizes=\"(max-width: 1130px) 100vw, 1130px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>3<\/strong> examples magic squares of order 13 with magic sum 1729. All <strong>3 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 14<\/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=\"1073\" height=\"581\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-1-1.png\" alt=\"\" class=\"wp-image-17404\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-1-1.png 1073w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-1-1-300x162.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-1-1-1024x554.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-1-1-768x416.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-1-1-535x290.png 535w\" sizes=\"(max-width: 1073px) 100vw, 1073px\" \/><\/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=\"1072\" height=\"581\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-2-1.png\" alt=\"\" class=\"wp-image-17405\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-2-1.png 1072w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-2-1-300x163.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-2-1-1024x555.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-2-1-768x416.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-2-1-535x290.png 535w\" sizes=\"(max-width: 1072px) 100vw, 1072px\" \/><\/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=\"1067\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-3-1.png\" alt=\"\" class=\"wp-image-17406\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-3-1.png 1067w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-3-1-300x162.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-3-1-1024x554.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-3-1-768x415.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-3-1-535x289.png 535w\" sizes=\"(max-width: 1067px) 100vw, 1067px\" \/><\/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=\"1123\" height=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-4-1.png\" alt=\"\" class=\"wp-image-17407\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-4-1.png 1123w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-4-1-300x155.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-4-1-1024x529.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-4-1-768x397.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/14x14-4-1-535x276.png 535w\" sizes=\"(max-width: 1123px) 100vw, 1123px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>4 <\/strong>examples magic squares of order 14 with magic sum 1729. All <strong>4 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 15<\/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=\"1152\" height=\"673\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-1.png\" alt=\"\" class=\"wp-image-17408\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-1.png 1152w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-1-300x175.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-1-1024x598.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-1-768x449.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-1-535x313.png 535w\" sizes=\"(max-width: 1152px) 100vw, 1152px\" \/><\/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=\"1713\" height=\"814\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1.png\" alt=\"\" class=\"wp-image-17417\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1.png 1713w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1-300x143.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1-1024x487.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1-768x365.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1-535x254.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/15x15-3x3-1-1-1536x730.png 1536w\" sizes=\"(max-width: 1713px) 100vw, 1713px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>2<\/strong> examples magic squares of order 15 with magic sum 1729.  First examples is based on 9 equal sums pandiagonal magic squares of order 5. The second example is based on 25 equal sums magic squares of order 3. It contains fractional entries. <\/em><br><br><em>Both the <strong>examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">Magic Squares of Order 19<\/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=\"1451\" height=\"745\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-1.png\" alt=\"\" class=\"wp-image-17411\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-1.png 1451w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-1-300x154.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-1-1024x526.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-1-768x394.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-1-535x275.png 535w\" sizes=\"(max-width: 1451px) 100vw, 1451px\" \/><\/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=\"1443\" height=\"735\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-2.png\" alt=\"\" class=\"wp-image-17412\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-2.png 1443w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-2-300x153.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-2-1024x522.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-2-768x391.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-2-535x273.png 535w\" sizes=\"(max-width: 1443px) 100vw, 1443px\" \/><\/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=\"1426\" height=\"747\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-3.png\" alt=\"\" class=\"wp-image-17413\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-3.png 1426w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-3-300x157.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-3-1024x536.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-3-768x402.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/12\/19x19-3-535x280.png 535w\" sizes=\"(max-width: 1426px) 100vw, 1426px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-pale-cyan-blue-background-color has-background\"><em>Above there are <strong>3 <\/strong>examples magic squares of order 19 with magic sum 1729. All <strong>3 examples<\/strong> use special entries, namely the date of birth of S. Ramanujan (22.12.1887) and his 138th anniversary on 22.12.2025. These contain the four numbers <strong>2212, 1887, 2025<\/strong>, and <strong>138<\/strong>. The construction of these magic squares is based on <strong>reduced-entry algebraic magic squares<\/strong> recently studied by the author. See the reference list for details.<\/em><\/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(2,3,129) 0%,rgb(255,255,255) 58%,rgb(40,116,252) 100%)\">References<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-822297a920dfdee3543a0873f2134772\">Part 1: Work on S. Ramanujan<\/h4>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 53%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Hardy-Ramanujan Number \u2013 1729, Zenodo, December 22, 2021, <strong>Zenodo<\/strong>, pp. 1-106, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.5799640.\">https:\/\/doi.org\/10.5281\/zenodo.5799640.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729, <strong>Zenodo<\/strong>, December 20, 2024, pp. 1-127, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14538297\">https:\/\/doi.org\/10.5281\/zenodo.14538297<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, 207 Magic Squares in Honor of the 138th Anniversary of S. Ramanujan with Hardy-Ramanujan Number 1729, Zenodo, December 27, 2025, pp. 1-77, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.18064853\">https:\/\/doi.org\/10.5281\/zenodo.18064853<\/a><\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Part 2: Day and Dates of the Year &#8211; 2025 in Terms of Magic Squares<\/mark><\/h4>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 53%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares of Orders 3 to 7 in Representing Dates and Days of the Year 2025, <strong>Zenodo<\/strong>, May 04, 2025, pp. 1-474, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.15338142\">https:\/\/doi.org\/10.5281\/zenodo.15338142<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=15152\">Magic Squares of Orders 3 to 7 Representing Dates and Days of the Year 2025<\/a> (new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/05\/07\/magic-squares-of-orders-3-to-7-representing-dates-and-days-of-the-year-2025\/\">Magic Squares of Orders 3 to 7 Representing Dates and Days of the Year 2025 <\/a> (old site) <\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares of Order 8 Representing Days and Dates of the Year 2025, <strong>Zenodo<\/strong>, May 04, 2025, pp. 1-134, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.15338246\">https:\/\/doi.org\/10.5281\/zenodo.15338246<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=15547\">Magic Squares of Order 8 Representing Days and Dates of the Year 2025<\/a> (new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/05\/07\/magic-squares-of-order-8-representing-days-and-dates-of-the-year-2025\/\">Magic Squares of Order 8 Representing Days and Dates of the Year 2025<\/a> (old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares of Order 9 Representing Days and Dates of the Year 2025, <strong>Zenodo<\/strong>, May 09, 2025, pp. 1-132, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.15375349\">https:\/\/doi.org\/10.5281\/zenodo.15375349<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=15629\">Magic Squares of Order 9 Representing Days and Dates of the Year 2025<\/a> (new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/05\/09\/magic-squares-of-order-9-representing-days-and-dates-of-the-year-2025\/\">Magic Squares of Order 9 Representing Days and Dates of the Year 2025<\/a> (old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares of Order 10 Representing Days and Dates of the Year 2025, <strong>Zenodo<\/strong>, May 21, 2025, pp. 1-59, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.15481738\">https:\/\/doi.org\/10.5281\/zenodo.15481738<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=15710\">Magic Squares of Order 10 Representing Dates and Days of the Year 2025 (new site)<\/a><\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/05\/21\/magic-squares-of-order-10-representing-dates-and-days-of-the-year-2025\/\">Magic Squares of Order 10 Representing Dates and Days of the Year 2025 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares of Order 12 Representing Days and Dates of the Year 2025&nbsp;<strong>Zenodo<\/strong>, June 10, 2025, pp. 1-43,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.15631884\">https:\/\/doi.org\/10.5281\/zenodo.15631884<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16068\">Magic Squares of Order 12 Representing Dates and Days of the Year 2025 (new site)<\/a><\/li>\n\n\n\n<li>Site Link:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/06\/10\/magic-squares-of-order-12-representing-dates-and-days-of-the-year-2025\/\">Magic Squares of Order 12 Representing Dates and Days of the Year 2025 (old site).<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Part 3: Reduced Entries Agebraic Magic Squares <\/mark><\/h4>\n\n\n\n<p><\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 53%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Orders 3 to 7<\/em>, <strong>Zenodo<\/strong>, September 29, 2025, pp. 1-59, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.17219769\">https:\/\/doi.org\/10.5281\/zenodo.17219769<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16158\">Reduced Entries Algebraic Magic Squares of Orders 3, 5, 7 and 9 (new site)<\/a><\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/08\/09\/reduced-entries-algebraic-pandiagonal-magic-squares-of-orders-4-to-8\/\">Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 (new site)<\/a><\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/07\/06\/reduced-entries-algebraic-magic-squares-of-orders-3-5-7-and-9\/\">Reduced Entries Algebraic Magic Squares of Orders 3, 5, 7 and 9 (old site)<\/a><\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16523\">Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 8, <strong>Zenodo<\/strong>, September 23, 2025, pp. 1-65, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.17186001\">https:\/\/doi.org\/10.5281\/zenodo.17186001<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16282\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=16282\">Reduced Entries Algebraic Magic Squares of Orders 4, 6, 8 and 10 <\/a>(new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16523\">Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8<\/a> (new site)<\/li>\n\n\n\n<li> Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16523\">Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 <\/a>(old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9<\/em>, Zenodo, August 27, 2025, pp. 1-92, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.16955571\">https:\/\/doi.org\/10.5281\/zenodo.16955571<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16572\">Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9<\/a> (new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/08\/27\/self-made-algebraic-magic-semi-magic-and-pandiagonal-magic-squares-of-order-9\/\">Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9<\/a> (old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>. <em>Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10<\/em>,&nbsp;<strong>Zenodo<\/strong>, September 18, 2025, pp. 1-112, &nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.17149185\">https:\/\/doi.org\/10.5281\/zenodo.17149185<\/a>\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16653\">Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10<\/a>&nbsp;(new site)<\/li>\n\n\n\n<li>Site Link:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/09\/18\/self-made-algebraic-magic-semi-magic-and-pandiagonal-magic-squares-of-order-10\/\">Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10&nbsp;<\/a>(old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Self-Made Algebraic Magic Squares of Order 11<\/em>, <strong>Zenodo<\/strong>, October 12, 2025, pp. 1-58, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.17330815\">https:\/\/doi.org\/10.5281\/zenodo.17330815<\/a> .\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16759\">Self-Made Algebraic Magic Squares of Order&nbsp;11<\/a> (new site)<\/li>\n\n\n\n<li>Site Link:  <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/10\/10\/self-made-algebraic-magic-squares-of-order-11\/\">Self-Made Algebraic Magic Squares of Order 11<\/a> (old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Self-Made Algebraic Semi-Magic Squares of Order 11<\/em>, <strong>Zenodo<\/strong>, October 12, 2025, pp. 1-77, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.17330822\">https:\/\/doi.org\/10.5281\/zenodo.17330822<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:  <a href=\"https:\/\/numbers-magic.com\/?p=16767\">Self-Made Algebraic Semi-Magic Squares of Order 11<\/a> (new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/10\/11\/self-made-algebraic-semi-magic-squares-of-order-11\/\">Self-Made Algebraic Semi-Magic Squares of Order 11<\/a> (old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Reduced Entries Algebraic Magic and PanMagic Squares of Order 12<\/em>,&nbsp;<strong>Zenodo<\/strong>, July 23, 2025, pp. 1-74,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.16370556\">https:\/\/doi.org\/10.5281\/zenodo.16370556<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=16149\">Reduced Entries Algebraic Magic and Panmagic Squares of Order 12<\/a> (new site)<\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/07\/24\/reduced-entries-algebraic-magicand-panmagic-squares-of-order-12\/\">Reduced Entries Algebraic Magic and Panmagic Squares of Order 12<\/a><a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/09\/18\/self-made-algebraic-magic-semi-magic-and-pandiagonal-magic-squares-of-order-10\/\">&nbsp;<\/a>(old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Reduced Entries Algebraic Semi-Magic Squares of Order 12<\/em>, Zenodo, July 23, 2025, pp. 1-60,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.15692014\">https:\/\/doi.org\/10.5281\/zenodo.15692014<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16447\">Reduced Entries Algebraic Semi-Magic Squares of Order 12<\/a> <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/09\/18\/self-made-algebraic-magic-semi-magic-and-pandiagonal-magic-squares-of-order-10\/\">&nbsp;<\/a>(old site)<\/li>\n\n\n\n<li>Site Link:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/07\/24\/reduced-entries-algebraic-semi-magic-squares-of-order-12\/\">Reduced Entries Algebraic Semi-Magic Squares of Order 12 <\/a>(old site)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\"><strong>Part 4: Agebraic Magic Squares: Double-Digits, Cornered and Striped <\/strong><\/mark><\/p>\n\n\n\n<p><\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 53%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Double-Digit Cyclic-Type Bordered Reduced Entries Algebraic Magic Squares of Orders 7 to 20,&nbsp;<strong>Zenodo<\/strong>, November 21, 2025, pp.1-37, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.17675032\">https:\/\/doi.org\/10.5281\/zenodo.17675032<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=17009\">Double-Digit Cyclic-Type Bordered Algebraic Magic Squares of Orders 7 to 20 for Reduced Entries (New Site)<\/a><\/li>\n\n\n\n<li>Site Link2:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/12\/01\/double-digit-cyclic-type-bordered-algebraic-magic-squares-of-orders-7-to-20-for-reduced-entries\/\" target=\"_blank\" rel=\"noreferrer noopener\">Double-Digit Cyclic-Type Bordered Algebraic Magic Squares of Orders 7 to 20 for Reduced Entries (Old Site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Algebraic Cyclic, Flat and Cornered Striped Magic Squares for Even Orders from 4 to 20,&nbsp;<strong>Zenodo<\/strong>, December 02, 2025, pp. 1-58,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.17793845\">https:\/\/doi.org\/10.5281\/zenodo.17793845<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link1:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=17009\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=17058\">Algebraic Cyclic, Flat and Cornered Striped Magic Squares of Even Orders from 4 to 20 (New Site).<\/a><\/li>\n\n\n\n<li>Site Link2:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/12\/02\/algebraic-cyclic-flat-and-cornered-striped-magic-squares-of-even-orders-from-4-to-20\/\">Algebraic Cyclic, Flat and Cornered Striped Magic Squares of Even Orders from 4 to 20 (Old Site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>&nbsp;Algebraic Double-Digit and Cornered Magic Squares of Odd Orders from 5 to 19,&nbsp;<strong>Zenodo<\/strong>, December 08, 2025, pp. 1-46,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.17859037\">https:\/\/doi.org\/10.5281\/zenodo.17859037<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link1: <a href=\"https:\/\/numbers-magic.com\/?p=17179\">Algebraic Double-Digit and Cornered Magic Squares of Odd Orders from 5 to 19 (new site) <\/a><\/li>\n\n\n\n<li>Site Link2: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/12\/08\/algebraic-double-digit-and-cornered-magic-squares-of-odd-orders-from-5-to-19\/\">Algebraic Double-Digit and Cornered Magic Squares of Odd Orders from 5 to 19 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>138th Birth Anniversary of S. Ramanujan,December 22, 1887-April 26, 1920 National Mathematics Day, India &#8211; December 22 This work brings magic squares connected with S. Ramanujan&#8217;s life and with Hardy-Ramanujan number 1729. On december 22, 2025 there is 138th aniversiory of S. Ramanujan. This work brings magic squares of orders 3 to 20 having magic [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":17413,"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-17312","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\/2025\/12\/19x19-3.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/17312","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=17312"}],"version-history":[{"count":12,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/17312\/revisions"}],"predecessor-version":[{"id":17539,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/17312\/revisions\/17539"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/17413"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=17312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=17312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=17312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}