{"id":16653,"date":"2025-09-17T18:41:00","date_gmt":"2025-09-17T21:41:00","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=16653"},"modified":"2025-09-19T00:28:08","modified_gmt":"2025-09-19T03:28:08","slug":"self-made-algebraic-magic-semi-magic-and-pandiagonal-magic-squares-of-order-10","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=16653","title":{"rendered":"Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10"},"content":{"rendered":"\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\">This work brings&nbsp;<strong>self-made algebraic magic<\/strong>,&nbsp;<strong>semi-magic<\/strong>&nbsp;and&nbsp;<strong>pandiagonal magic<\/strong>&nbsp;squares . By&nbsp;<strong>self-made<\/strong>&nbsp;or&nbsp;<strong>reduced<\/strong>&nbsp;or&nbsp;<strong>less entries<\/strong>, we understand that instead of normal&nbsp;<em><strong>n^2<\/strong><\/em>&nbsp;entries of a magic square order&nbsp;<em><strong>n<\/strong><\/em>, we are&nbsp;using less numbers, where the magic square is&nbsp;<strong>complete in itself<\/strong>. This is just put any integer values for the&nbsp;<strong>less&nbsp;entries<\/strong>, one will get always a magic square. Moreover, in these situations the entries are no more<strong>&nbsp;sequential<\/strong>&nbsp;numbers. These entries are&nbsp;<strong>non-sequential positive<\/strong>&nbsp; and&nbsp;<strong>negative<\/strong>&nbsp; numbers. In some cases, these may be&nbsp;<strong>decimal<\/strong>&nbsp;or&nbsp;<strong>fractional<\/strong>&nbsp;values depending on the way of chosing the&nbsp;<strong>entries<\/strong>. Sometime to avoid&nbsp;<strong>decimal<\/strong>&nbsp;or&nbsp;<strong>fractional<\/strong>&nbsp;entries we apply certain conditions. These conditions depends on the types of magic squares. The name&nbsp;<strong>self-made<\/strong>&nbsp;is not known in the literature of magic squares. It is being introduced for first time here in this work. The work is based on different types of magic squares, i.e.,&nbsp;<strong>pandiagonal<\/strong>,&nbsp;<strong>block-wise<\/strong>,&nbsp;<strong>cornered<\/strong>,&nbsp;<strong>single-digit bordered<\/strong>,&nbsp;<strong>double-digit bordered<\/strong>, etc. It is not necessary, but we worked with magic rectangles with equal width and length for the same category within a magic square. If we relax this condition, i.e., by considering only equality of width, still we have good results. For more details refer author\u2019s previous works. Previously, the author brought similar kind of work for the orders 3 to 12, specially for the for the&nbsp;<strong>dates<\/strong>&nbsp;and&nbsp;<strong>days<\/strong>&nbsp;of the year 2025, where the&nbsp;<strong>dates<\/strong>&nbsp;are few&nbsp;<strong>entries<\/strong>&nbsp;and&nbsp;<strong>days<\/strong>&nbsp;are the&nbsp;<strong>sums<\/strong>&nbsp;of magic squares. Total there are 48 magic squares, out of them 9 are just&nbsp;<strong>magic squares<\/strong>, 10 are&nbsp;<strong>semi-magic<\/strong> squares and 29 are&nbsp;<strong>pandiagonal<\/strong>&nbsp;magic squares. This work is available online at the following links:<a href=\"http:\/\/bit.ly\/47bnATN\">&nbsp;<\/a><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\">Once again, s<strong>elf-made<\/strong> means that they are complete in themselves: once you choose the entries and the magic sum, a magic square will always result. These squares can contain <strong>integer<\/strong>, <strong>decimal<\/strong>, or <strong>fractional<\/strong> values.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-blush-light-purple-gradient-background has-background\">For more details see the link given below:<br><br><strong>Inder J. Taneja<\/strong>. <em>Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10<\/em>, <strong>Zenodo<\/strong>, September 18, 2025, pp. 1-112, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.17149185\">https:\/\/doi.org\/10.5281\/zenodo.17149185<\/a><br><br>See below the details of the work<\/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(252,185,0) 0%,rgb(255,255,255) 41%,rgb(255,105,0) 100%)\">Self-Made Algebraic Magic and Sem-Magic Squares of Order 10<\/h3>\n\n\n\n<p>This part is already discussed before. See the following links:<\/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>, <strong>Inder J. Taneja<\/strong>&nbsp;\u2013 Reduced Entries Magic and Semi-Magic Squares of Orders 4, 6, 8 and 10, Zenodo, July 05, 2025, pp. 1-85,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.15814675\">https:\/\/doi.org\/10.5281\/zenodo.15814675<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16158\"><\/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:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/07\/06\/reduced-entries-algebraic-magic-squares-of-orders-3-5-7-and-9\/\">&nbsp;<\/a><a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/07\/07\/reduced-entries-algebraic-magic-squares-of-orders-4-6-8-and-10\/\">Reduced Entries Algebraic Magic Squares of Orders 4, 6, 8 and 10<\/a> (old site)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\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(252,185,0) 0%,rgb(255,255,255) 41%,rgb(255,105,0) 100%)\">Self-Made Algebraic Pandiagonal Magic Squares of Order 10<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\">Below are 29 pandiagonal magic squares of order 10. These are based on the results given above. It is divided in four parts.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-69792656d630b413fd9c2edac74b4840\">Part 1: Four Equal Sums Padiagonal Magic Squares of Order 5<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-e17ed3ba216a9c5e4cec9f1e7f9d82ce\">Result 1: 4 Equal Sum Pandiagonal Magic Squares of Order 5.<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p1.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p1.png\" alt=\"\" class=\"wp-image-12230\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>pandiagonal<\/strong> magic square of order 10 divided in four equal sums blocks of order 5. These blocks are also <strong>pandiagonal <\/strong>magic squares of order 5. The magic sum of order 10 is represented by <strong>L=2*S<\/strong>, where S is the sum of magic square of order 5. In this case, the magic sums of order 10 is always an even mumber.  <br><br>There are no conditions on the magic sum of order 5 to bring this pandiagonal magic square of order 10. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p1.png\" alt=\"\" class=\"wp-image-12231\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-74e79dab2ac20ea44e7f4d7362b8b2dc\">Part 2: Double-Digits Bordered Pandiagonal Magic Squares<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-8593128af3852f9fa0428ac6e2e8e468\">Result 2: Double-Digits Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p2.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p2.png\" alt=\"\" class=\"wp-image-12232\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>double-digit bordered pandiagonal<\/strong> magic square of order 10 having <strong>pandiagonal <\/strong>magic square of order 6 in the middle. The four magic rectangles of order 2&#215;6 are of equal width and length. We have both the magic squares of orders 10 and 6 pandiagonal. The magic sum of order 10 is given as <strong>L=(5\/3)*S<\/strong>, where <strong>S<\/strong> is the magic sum of order 6. <br><br>In order to bring this<strong> pandiagonal<\/strong> magic square of order 10 without <strong>decimal<\/strong> entries, the magic sum of order 6 should be multiple of 6. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p2.png\" alt=\"\" class=\"wp-image-12233\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-2948f6d18b94f9f81b5ad5cc20ebb2e9\">Result 3: Double-Digits Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p3.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p3.png\" alt=\"\" class=\"wp-image-12236\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>double-digit bordered pandiagonal<\/strong> magic square of order 10 having cornered <strong>pandiagonal<\/strong> magic square of order 6 in the middle. It contains a <strong>pandiagonal<\/strong> magic square of order 4 at the upper-left corner. The magic rectangles of order 2&#215;4 and 2&#215;6 are of equal width and length in each case. All the magic squares of orders 4, 6 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10 and 6 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/2)*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>=(3\/2)* M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 20.  See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p3.png\" alt=\"\" class=\"wp-image-12237\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-6ab2189bc615bf4abfd46d13ee020a6d\">Result 4: Double-Digits Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p4.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p4.png\" alt=\"\" class=\"wp-image-12238\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>double-digit bordered pandiagonal<\/strong> magic square of order 10 having <strong>single-digit pandiagonal<\/strong> magic square of order 6 with pandiagonal magic square of order 4. The four magic rectangles of order 2&#215;6 are of equal width and length. All the magic squares of orders 4, 6 and 10 are pandiagonal. The magic sums of orders 10 and 6 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/2)*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>=(3\/2)*M<\/strong>, where M is the magic sum of order 4. <br><br>In order to bring this<strong> pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p4.png\" alt=\"\" class=\"wp-image-12240\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-cfd83cd0f82a158e7a196122954b82d0\">Result 5: Double-Digits Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p5.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p5.png\" alt=\"\" class=\"wp-image-12241\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>double-digit bordered pandiagonal<\/strong> magic square of order 10 having pandiagonal magic square of order 6 with four equal sums <strong>semi-magic<\/strong> squares of order 3. The four magic rectangles of order 2&#215;6 are of equal width and length. The magic squares of orders 6 and 10 are <strong>pandiagonal <\/strong>and the blocks of order 3&#215;3 are <strong>semi-magic<\/strong>. The magic sums of orders 10 and 6 are given as <strong>L<sub>10\u00d710<\/sub> = (10\/3)*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>=2* M<\/strong>, where <strong>M<\/strong> is the <strong>semi-magic<\/strong> sum of order 3.<br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 3 should be multiple of 3. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p5.png\" alt=\"\" class=\"wp-image-12243\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-9201e7a483cf53c2387d46520972e5b8\">Result 6: Double-Digits Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p6.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p6.png\" alt=\"\" class=\"wp-image-12244\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>double-digit bordered pandiagonal<\/strong> magic square of order 10 having striped <strong>pandiagonal<\/strong> magic square of order 6 with three equal sums magic rectangles of order 2&#215;6. The four magic rectangles of order 2&#215;6 are of equal width and length. The magic squares of orders 6 and 10 are pandiagonal. The magic sums of orders 10 and 6 are given as <strong>L<sub>10\u00d710<\/sub>=5*m<\/strong> and <strong>S<sub>6\u00d76<\/sub>=3*m<\/strong>, where magic rectangle of order<strong> m x3m<\/strong>. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the width of magic rectangles of order 2&#215;6 should be multiple of 10. See below two examples: <\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p6.png\" alt=\"\" class=\"wp-image-12245\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-92ad4abe7971a4d4a7c9828247635490\">Part 3: Cornered Pandiagonal Magic Squares<\/h3>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-84e16430a17483133e3b71a75d935a1d\">Result 7: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p7.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p7.png\" alt=\"\" class=\"wp-image-12247\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>pandiagonal <\/strong>magic square of order 8 at the upper-left corner. It contains four equal sums <strong>pandiagonal<\/strong> magic squares of order 4. The two magic rectangles of order 2&#215;8 are of equal width and length. The magic squares of orders 4, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10 and 8 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/2)*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>=(3\/2)* M<\/strong>, where <strong>M <\/strong>is the magic sum of order 4. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p7.png\" alt=\"\" class=\"wp-image-12248\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-a476bd0e2fb1b59fdbe6e0acc8f7ec9f\">Result 8: Cornered Pandiagonal Magic Square of Order 10 <\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p8.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p8.png\" alt=\"\" class=\"wp-image-12250\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>pandiagonal <\/strong>magic square of order 8 at the upper-left corner. It contains eight equal sums magic rectangles of order 2&#215;4. The two magic rectangles of order 2&#215;8 are of equal width and length. The magic squares of orders 8 and 10 are pandiagonal. The magic sums of orders 10 and 8 are given as<strong> L<sub>10\u00d710<\/sub>=5*m<\/strong> and <strong>S<sub>8\u00d78<\/sub>=4*m<\/strong>, where <strong>m<\/strong> is the width of the magic rectangle of order <strong>mx2m<\/strong>. <br><br>In order to bring xthis pandiagonal magic square of order 10 without decimal entries, the width magic rectangle of order sum of order 2&#215;4 should be multiple of 2. Also the first entry, i.e., <strong>A1<\/strong>, should be multiple of 2.  See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p8.png\" alt=\"\" class=\"wp-image-12330\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-e437ac1084a8be9242da13422cb52db6\">Result 9: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p9-1.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p9-1.png\" alt=\"\" class=\"wp-image-12254\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>double-digit pandiagonal<\/strong> magic square of order 8 at the upper-left corner. It contains a pandiagonal magic square of order 4. The two magic rectangles of order 2\u00d78 are of equal length and width . The magic squares of orders 4, 8 and 10 are pandiagonal. The magic sums of orders 10, 8 and 4 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/2)* M <\/strong>and <strong>T<sub>8\u00d78<\/sub> = 2* M<\/strong>, where <strong>M<\/strong> is the magic sum of magic square of order 4.<br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p9.png\" alt=\"\" class=\"wp-image-12255\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-db87a55fb08ecc9af0eb14478393c59b\">Result 10: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p10.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p10.png\" alt=\"\" class=\"wp-image-12257\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having cornered <strong>pandiagonal<\/strong> magic square of order 8 at the upper-left corner. It contains a <strong>pandiagonal <\/strong>magic square of order 6. The two magic rectangles of orders 2\u00d76 and 2\u00d78 are of equal length and width in each case. The magic squares of orders 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8 and 6 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/3)* S<\/strong> and <strong>T<sub>8\u00d78<\/sub>=(4\/3)*S<\/strong>, where <strong>S<\/strong> is the magic sum of order 6. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 6 should be multiple of 6. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p10.png\" alt=\"\" class=\"wp-image-12258\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-6093ae10a2f30eac05c535215c168522\">Result 11: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p11.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p11.png\" alt=\"\" class=\"wp-image-12260\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having cornered <strong>pandiagonal<\/strong> magic square of orders 8 and 6 at the upper-left corners. It contains a <strong>pandiagonal<\/strong> magic square of order 4. The magic rectangles of orders 2\u00d74, 2\u00d76 and 2\u00d78 are of equal length and width in each case. The magic squares of orders 4, 6, 8 and 10 are pandiagonal. The magic sums of orders 10, 8, 6 and 4 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/2)* M<\/strong>, <strong>T<sub>8\u00d78<\/sub>=2*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>=(3\/2)*M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4.  <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p11.png\" alt=\"\" class=\"wp-image-12261\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d7e441e7b8738eae5d5ebc8c53e37495\">Result 12: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p12.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p12.png\" alt=\"\" class=\"wp-image-12263\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>cornered pandiagonal<\/strong> magic square of orders 8 and 6 at the upper-left corners. The magic square of order 6 is <strong>single-digit bordered<\/strong> <strong>pandiagonal<\/strong> with <strong>pandiagonal<\/strong> magic square of order 4 in the inner part. The magic rectangles of orders 2\u00d76 and 2\u00d78 are of equal length and width in each case. The magic squares of orders 4, 6, 8 and 10 are<strong> pandiagonal<\/strong>. The magic sums of orders 10, 8, 6 and 4 are given as <strong>L<sub>10\u00d710<\/sub>=(5\/2)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub>=2*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>=(3\/2)* M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4.<br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p12.png\" alt=\"\" class=\"wp-image-12264\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-5660ed4b53f79c40fd7931ed02c27a81\">Result 13: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p13.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p13.png\" alt=\"\" class=\"wp-image-12267\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>cornered pandiagonal<\/strong> magic square of orders 8 at the upper-left corners. The magic square of order 6 is a <strong>striped pandiagonal<\/strong>. The magic rectangles of orders 2\u00d76 and 2\u00d78 are of equal length and width in each case. The magic squares of orders 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8 and 6 are given as <strong>L<sub>10\u00d710<\/sub>:=5*m<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=5*m<\/strong> and <strong>S<sub>6\u00d76<\/sub> := 3*m<\/strong>, where <strong>m<\/strong> is the width of magic rectangle of order 2\u00d76. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the width of magic rectangles of order 2\u00d76 should be multiple of 10. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p13.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p13.png\" alt=\"\" class=\"wp-image-12266\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-9d3942c2ecd84ced3f762716a1b289df\">Result 14: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p14.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p14.png\" alt=\"\" class=\"wp-image-12269\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>single-digit pandiagonal<\/strong> magic squares of orders 6 and 8 at the upper-left corner with pandiagonal magic square of order 4 in the inner part. The magic squares of orders 4, 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8, 6 and 4 are given as <strong>L<sub>10\u00d710<\/sub>:=(5\/2)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=2*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>:=(3\/2)*M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4.<br><br>In order to bring this <strong>pandiagonal <\/strong>magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p14.png\" alt=\"\" class=\"wp-image-12270\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-377a2e9481701a884a37edab6a364f8a\">Result 15: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p15.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p15.png\" alt=\"\" class=\"wp-image-12273\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>single-digit pandiagonal<\/strong> magic squares of orders 8 at the upper-left corner with <strong>pandiagonal <\/strong>magic square of order 6 in the inner part. The magic squares of orders 6, 8 and 10 are pandiagonal. The magic sums of orders 10, 8 and 6 are given as <strong>L<sub>10\u00d710<\/sub>:=(5\/3)*S<\/strong> and <strong>T<sub>8\u00d78<\/sub>:=(4\/3)* S<\/strong>, where <strong>S<\/strong> is the magic sum of order 6. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the magic sum of order 6 should be multiple of 6. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p15.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p15.png\" alt=\"\" class=\"wp-image-12272\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-f6e52bb91edd79f359d7c830f78222b2\">Result 16: Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p16.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p16.png\" alt=\"\" class=\"wp-image-12275\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>single-digit pandiagonal<\/strong> magic squares of orders 8 at the upper-left corner with <strong>pandiagonal<\/strong> magic square of order 6 formed by four equal sums <strong>semi-magic<\/strong> squares of order 3 in the inner part . The magic squares of orders 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8 and 6 are given as <strong>L<sub>10\u00d710<\/sub>:=(10\/3)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=(8\/3)*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>:=2*M<\/strong>, where <strong>M<\/strong> is the <strong>semi-magic <\/strong>sum of order 3.<br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 3 should be multiple of 3. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p16.png\" alt=\"\" class=\"wp-image-12276\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-50684025d358733ce70eb2df309edae0\">Result 17:  Cornered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p17.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-p17.png\" alt=\"\" class=\"wp-image-12277\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>cornered pandiagonal<\/strong> magic square of order 10 having <strong>single-digit pandiagonal<\/strong> magic squares of orders 8 at the upper-left corner with pandiagonal magic square of order 6 formed by three equal sums magic rectangles of order 2\u00d76 in the inner part . The magic squares of orders 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8 and 6 are given as <strong>L<sub>10\u00d710<\/sub>:= 5*m<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=4*m<\/strong> and <strong>S<sub>6\u00d76<\/sub>:=3*m<\/strong>, where <strong>m<\/strong> is the width of magic rectangle of order 2\u00d76. <br><br>In order to bring this <strong>pandiagonal <\/strong>magic square of order 10 without decimal entries, the width of magic rectangles of order 2\u00d76 should be multiple of 10. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-p17.png\" alt=\"\" class=\"wp-image-12279\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-0ee37bdb26f9d27211b912cf180f7bce\">Part 4: Single-Digit Bordered Pandiagonal Magic Squares<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-4845f10f866d92fbf7573e2d6e59f0f1\">Result 18: Single-Digit Bordered Pandiagonal Magic Square of Order 10 <\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps1.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps1.png\" alt=\"\" class=\"wp-image-12284\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\">It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a <strong>pandiagonal<\/strong> magic square of order 8. It contains four equal sums <strong>pandiagonal<\/strong> magic square of order 4. The magic squares of orders 4, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8 and 4 are given as <strong>L<sub>10\u00d710<\/sub> :=(5\/2)*M<\/strong> and <strong>T<sub>8\u00d78<\/sub>:=2*M<\/strong>, where M is the magic sum of order 4. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps1.png\" alt=\"\" class=\"wp-image-12285\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d23703dce5d07be590065c9b8a93691e\">Result 19: Single-Digit Bordered Pandiagonal Magic Square of Order 10 <\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps2.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps2.png\" alt=\"\" class=\"wp-image-12286\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a<strong> pandiagonal<\/strong> magic square of order 8. It contains eight equal sums magic rectangles of order 2\u00d74. The magic squares of orders 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10 and 8 are given as <strong>L<sub>10\u00d710<\/sub>:=5* m<\/strong> and <strong>T<sub>8\u00d78<\/sub>:=4*m<\/strong>, where <strong>m<\/strong> is the width of magic rectangle of order m\u00d72m. <br><br>In order to bring this <strong>pandiagonal <\/strong>magic square of order 10 without decimal entries, the width of magic rectangle of order <strong>m\u00d72m<\/strong>, i.e., <strong>m<\/strong>  should be multiple of 2. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps2.png\" alt=\"\" class=\"wp-image-12288\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-0ee0bbb3e48c22cce850ca84bc2221b4\">Result 20: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps3.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps3.png\" alt=\"\" class=\"wp-image-12291\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a <strong>double-digit pandiagonal<\/strong> magic square of order 8. It contains a <strong>pandiagonal <\/strong>magic square of order 4 in the middle. The magic squares of orders 4, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8 and 4 are given as <strong>L<sub>10\u00d710<\/sub> :=(5\/2)* M <\/strong>and<strong> T<sub>8\u00d78<\/sub>:=2* M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal  entries, the magic sum of order 4 should be multiple of 8. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps3.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps3.png\" alt=\"\" class=\"wp-image-12289\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-859e119774c35ab351cc6eaee1de5176\">Result 21: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps4.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps4.png\" alt=\"\" class=\"wp-image-12292\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a <strong>cornered pandiagonal <\/strong>magic square of order 8. It contains a <strong>pandiagonal<\/strong> magic square of order 6 at the upper-left corner. The magic squares of orders 6, 8 and 10 are pandiagonal. The magic rectangles of orders 2\u00d76 are of equal width and length. The magic sums of orders 10, 8 and 6 are given as<strong> L<sub>10\u00d710<\/sub> :=(5\/3)*S<\/strong> and <strong>T<sub>8\u00d78<\/sub>:=(4\/3)*S<\/strong>, where <strong>S<\/strong> is the magic sum of order 6. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the magic sum of order 6 should be multiple of 6. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps4.png\" alt=\"\" class=\"wp-image-12293\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-8145f5402491a2ecee6eed503000482c\">Result 22: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps5.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps5.png\" alt=\"\" class=\"wp-image-12295\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a single-digit bordered pandiagonal magic square of order 10 embedded with a cornered pandiagonal magic square of order 8. It contains a pandiagonal magic square of order 6 at the upper-left corner. It is composed of 4 equal sum semi-magic squares of order 3. The magic squares of orders 6, 8 and 10 are pandiagonal. The magic rectangles of orders 2 \u00d7 6 are of equal width and length. The magic sums of orders 10, 8, 6 and 3 are given as <strong>L<sub>10\u00d710<\/sub>:=(10\/3)*M<\/strong>,  <strong>T<sub>8\u00d78<\/sub>:=(8\/3)*M<\/strong>  and <strong>S<sub>6\u00d76<\/sub>:=2*M<\/strong>, where <strong>M<\/strong> is the semi-magic sum of order 3. <br><br>In order to bring this <strong>pandiagonal <\/strong>magic square of order 10 without decimal entries, the magic sum of order 3 should be multiple of 3. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps5.png\" alt=\"\" class=\"wp-image-12296\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-5b6608fd907c23782dd2ef1ba4f70b77\">Result 23: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps6.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps6.png\" alt=\"\" class=\"wp-image-12298\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a <strong>cornered pandiagonal<\/strong> magic square of order 8. It contains a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 6 at the upper-left corner having <strong>pandiagonal<\/strong> magic square of order 4 in the middle. The magic squares of orders 4, 6, 8 and 10 are pandiagonal. The magic rectangles of orders 2\u00d76 are of equal width and length. The magic sums of orders 10, 8, 6 and 4 are given as <strong>L<sub>10\u00d710<\/sub>:=(5\/2)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=2*M<\/strong> and <strong>S<sub>6\u00d76<\/sub> =(3\/2)* M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps6.png\" alt=\"\" class=\"wp-image-12299\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b88247f691aeaadc1f520b9218610f09\">Result 24: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps7.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps7.png\" alt=\"\" class=\"wp-image-12301\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a <strong>cornered pandiagonal <\/strong>magic square of order 8 having <strong>pandiagonal <\/strong>magic square of order 6 at the upper-left corner. It is formed by three equal sums magic rectangles of order 2\u00d76. The magic squares of orders 6, 8 and 10 are<strong> pandiagonal.<\/strong> The magic sums of orders 10, 8 and 6 are given as <strong>L<sub>10\u00d710<\/sub>:=5*m<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=4*m<\/strong> and <strong>S<sub>6\u00d76<\/sub>:=3*m<\/strong>, where <strong>m<\/strong> is the width of magic rectangle of order m\u00d73m. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the width of magic rectangle of order m\u00d73m, i.e., m should be multiple of 10. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps7.png\" alt=\"\" class=\"wp-image-12302\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-82407c0ee1d02b36521c2617d4070ba9\">Result 25: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps8.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps8.png\" alt=\"\" class=\"wp-image-12304\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 embedded with a <strong>cornered pandiagonal<\/strong> magic square of orders 8 and 6. It contains a <strong>pandiagonal<\/strong> magic square of order 4 at the upper-left corner. The magic squares of orders 4, 6, 8 and 10 are all <strong>pandiagonal<\/strong>. The magic rectangles of orders 2\u00d74 and 2\u00d76 are of equal width and length in each case. The magic sums of orders 10, 8, 6 and 4 are given as <strong>L<sub>10\u00d710<\/sub>:=(5\/2)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=2* M<\/strong> and <strong>S<sub>6\u00d76<\/sub> :=(3\/2)* M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps8.png\" alt=\"\" class=\"wp-image-12305\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3c7ebe10464d48a1fe53acf5df09a942\">Result 26: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps9.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps9.png\" alt=\"\" class=\"wp-image-12310\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a single-digit bordered pandiagonal magic square of order 10 and 8 embedded with a pandiagonal magic square of order 6. The magic squares of orders 6, 8 and 10 are pandiagonal. The magic sums of orders 10, 8 and 6 are given as<strong> L<sub>10\u00d710<\/sub>:=(5\/3)*S<\/strong> and <strong>T<sub>8\u00d78<\/sub>:=(4\/3)*S<\/strong>, where S is the magic sum of order 6. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 6 should be multiple of 6. See below two examples: <\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps9.png\" alt=\"\" class=\"wp-image-12309\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-841d8013b6d981f30e3ced37a53cd0a7\">Result 27: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps10.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps10.png\" alt=\"\" class=\"wp-image-12311\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 and 8 embedded with a <strong>pandiagonal<\/strong> magic square of order 6. It contains 4 equal sums magic squares of order 3. The magic squares of orders 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8, 6 and 3 are given as <strong>L<sub>10\u00d710<\/sub> :=(10\/3)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub> :=(8\/3)*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>:=2*M<\/strong> where <strong>M<\/strong> is the magic sum of order 3. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the magic sum of order 3 should be multiple of 3.<br>See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps10.png\" alt=\"\" class=\"wp-image-12312\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d22e712ba1684a87b3ccb9c854477120\">Result 28: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps11.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps11.png\" alt=\"\" class=\"wp-image-12315\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10 and 8 embedded with a <strong>pandiagonal<\/strong> magic square of order 6. It contains 3 equal sums magic rectangles of orders 2\u00d76. The magic squares of orders 6, 8 and 10 are <strong>pandiagonal<\/strong>. The magic sums of orders 10, 8, 6 are given as <strong>L<sub>10\u00d710<\/sub>:=5*m<\/strong>, <strong>T<sub>8\u00d78<\/sub> :=4*m<\/strong> and <strong>S<sub>6\u00d76<\/sub> :=3*m<\/strong> where <strong>m<\/strong> is the width of magic rectangle of order m\u00d73m. <br><br>In order to bring this <strong>pandiagonal<\/strong> magic square of order 10 without decimal entries, the width of magic rectangle of order m \u00d7 3m should be multiple of 10. See below two examples:<\/em><\/p>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps11.png\" alt=\"\" class=\"wp-image-12316\"\/><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-c374842f3ae30243724a35bbdb15c0be\">Result 29: Single-Digit Bordered Pandiagonal Magic Square of Order 10<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps12.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/gm-10x10-ps12.png\" alt=\"\" class=\"wp-image-12319\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify has-blush-light-purple-gradient-background has-background\"><em>It is a <strong>single-digit bordered pandiagonal<\/strong> magic square of order 10, 8 and 6 embedded with a <strong>pandiagonal<\/strong> magic square of order 4. The magic squares of orders 4, 6, 8 and 10 are pandiagonal. The magic sums of orders 10, 8, 6 and 4 are given as <strong>L<sub>10\u00d710<\/sub>:=(5\/2)*M<\/strong>, <strong>T<sub>8\u00d78<\/sub>:=2*M<\/strong> and <strong>S<sub>6\u00d76<\/sub>:=(3\/2)*M<\/strong>, where <strong>M<\/strong> is the magic sum of order 4. <br><br>In order to bring this pandiagonal magic square of order 10 without decimal entries, the magic sum of order 4 should be multiple of 4. See below two examples: <\/em><\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><a href=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps12.png\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.wordpress.com\/wp-content\/uploads\/2025\/09\/m-10x10-ps12.png\" alt=\"\" class=\"wp-image-12320\"\/><\/a><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 41%,rgb(255,105,0) 100%)\">References<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3804c43aa2a7e74fb660f0157db8aca6\">Part 1: Representing Days and Date<\/h3>\n\n\n\n<ol style=\"background-color:#45c84b4f\" 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,&nbsp;<strong>Zenodo<\/strong>, May 04, 2025, pp. 1-474,&nbsp;<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:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=15152\">Magic Squares of Orders 3 to 7 Representing Dates and Days of the Year 2025<\/a>&nbsp;(new site)<\/li>\n\n\n\n<li>Site Link:&nbsp;<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&nbsp;<\/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,&nbsp;<strong>Zenodo<\/strong>, May 04, 2025, pp. 1-134,&nbsp;<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:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=15547\">Magic Squares of Order 8 Representing Days and Dates of the Year 2025<\/a>&nbsp;(new site)<\/li>\n\n\n\n<li>Site Link:&nbsp;<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>&nbsp;(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,&nbsp;<strong>Zenodo<\/strong>, May 09, 2025, pp. 1-132,&nbsp;<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:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=15629\">Magic Squares of Order 9 Representing Days and Dates of the Year 2025<\/a>&nbsp;(new site)<\/li>\n\n\n\n<li>Site Link:&nbsp;<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>&nbsp;(old site)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Magic Squares of Order 11 Representing Days and Dates of the Year 2025,&nbsp;<strong>Zenodo<\/strong>, May 31, 2025, pp. 1-94,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.15564676\">https:\/\/doi.org\/10.5281\/zenodo.15564676<\/a>\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=15857\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=15857\">Magic Squares of Order 11 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\/05\/31\/magic-squares-of-order-11-representing-dates-and-days-of-the-year-2025\/\">Magic Squares of Order 11 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 \u2013 (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<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-5cb08c3e721f742133a2b2a90034616c\">Part 2: Revised with Examples<\/h3>\n\n\n\n<ol style=\"background-color:#45c84b4f\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Reduced Entries Magic and Semi-Magic Squares of Orders 3, 5, 7 and 9,&nbsp;<strong>Zenodo<\/strong>, July 01, 2025, pp. 1-65,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.15783321\">https:\/\/doi.org\/10.5281\/zenodo.15783321<\/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:&nbsp;<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<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Reduced Entries Magic and Semi-Magic Squares of Orders 4, 6, 8 and 10, <strong>Zenodo<\/strong>, July 05, 2025, pp. 1-85,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.15814675\">https:\/\/doi.org\/10.5281\/zenodo.15814675<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16282\">Reduced Entries Algebraic Magic Squares of Orders 4, 6, 8 and 10 (new site)<\/a><\/li>\n\n\n\n<li>Site Link:&nbsp;<a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/07\/07\/reduced-entries-algebraic-magic-squares-of-orders-4-6-8-and-10\/\">Reduced Entries Algebraic Magic Squares of Orders 4, 6, 8 and 10 (olde site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Reduced Entries Algebraic Semi-Magic Squares of Order 12, <strong>Zenodo<\/strong>, 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 (new site)<\/a><\/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 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>&nbsp;\u2013 Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8,&nbsp;<strong>Zenodo<\/strong>, August 12, 2025, pp. 1-63,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.16809756\">https:\/\/doi.org\/10.5281\/zenodo.16809756<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<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:&nbsp;<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 9, <strong>Zenodo<\/strong>, August 27, 2025, pp. 1-92,&nbsp;<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:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=16572\">Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9 (new site).<\/a><\/li>\n\n\n\n<li>Site Link:&nbsp;<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 (old site)<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>. Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10, <strong>Zenodo<\/strong>, September 18, 2025, pp. 1-112, <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:\u00a0<a href=\"https:\/\/numbers-magic.com\/?p=16653\">Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10<\/a> (new site)<\/li>\n\n\n\n<li>Site Link:\u00a0<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 <\/a>(old site)<br><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>This work brings&nbsp;self-made algebraic magic,&nbsp;semi-magic&nbsp;and&nbsp;pandiagonal magic&nbsp;squares . By&nbsp;self-made&nbsp;or&nbsp;reduced&nbsp;or&nbsp;less entries, we understand that instead of normal&nbsp;n^2&nbsp;entries of a magic square order&nbsp;n, we are&nbsp;using less numbers, where the magic square is&nbsp;complete in itself. This is just put any integer values for the&nbsp;less&nbsp;entries, one will get always a magic square. Moreover, in these situations the entries are no [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":16657,"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-16653","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\/09\/GM-10x10-P2.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/16653","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=16653"}],"version-history":[{"count":3,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/16653\/revisions"}],"predecessor-version":[{"id":16666,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/16653\/revisions\/16666"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/16657"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16653"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16653"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}