{"id":14126,"date":"2025-01-05T00:02:07","date_gmt":"2025-01-05T03:02:07","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=14126"},"modified":"2025-01-23T02:04:32","modified_gmt":"2025-01-23T05:04:32","slug":"water-reflexive-magic-squares-order-3-to-6","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=14126","title":{"rendered":"Water Refletion Magic Squares: Order 3 to 6"},"content":{"rendered":"\n<p>This work brings more concepts in magic squares. In past we studied a lot of upside-down and mirror looking magic squares. These are based some kind of digital\/special fonts. To understand better let&#8217;s consider the following 10 digits from 0 to 9:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-1024x90.png\" alt=\"\" class=\"wp-image-14128\" style=\"width:699px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-d.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-9bb23a63a92f5e66e4d5ab76f26113f0\">Upside-down<strong> (180 degrees rotation)<\/strong><\/h4>\n\n\n\n<p>Let&#8217;s consider 180 degrees rotation over the above 10 digits, we get<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-1024x90.png\" alt=\"\" class=\"wp-image-14130\" style=\"width:691px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dr.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>We observe that the numbers 0, 1, 2, 5, 6, 8 and 9 are still there. The difference is that 6 becomes 9.<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-6254d61d65daf44d6885af59f4408f5c\">Mirror Looking (Horizontal Flip)<\/h4>\n\n\n\n<p>Let&#8217;s see how these numbers can seen in mirror:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-1024x90.png\" alt=\"\" class=\"wp-image-14129\" style=\"width:698px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dm.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>We observe that the numbers 0, 1, 2, 5 and 8 are still there. In this case the numbers 2 and 5 interchanges, i.e., 2 becomes 5 and 5 as 2.<\/p>\n\n\n\n<p>In general there are two kinds of flips, i.e.,<strong> horizontal flip<\/strong> and <strong>vertical filp<\/strong>. See the image below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"278\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/flip.png\" alt=\"\" class=\"wp-image-14131\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/flip.png 354w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/flip-300x236.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-right\">Source: <a href=\"https:\/\/www.mathsisfun.com\/definitions\/vertical-flip.html\">https:\/\/www.mathsisfun.com\/definitions\/vertical-flip.html<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-bf7d1a8f7075e9d1cc6bb9fb0b25506a\">Water Reflection (Vertical Flip)<\/h4>\n\n\n\n<p>Making vertical flip over the digits 0 to 9, we get<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"90\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-1024x90.png\" alt=\"\" class=\"wp-image-14132\" style=\"width:700px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-1024x90.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-300x27.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-768x68.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw-535x47.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/numbers-dw.png 1109w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>We observe the numbers 0, 1, 2, 3, 5 and 8 remains the same. The numebrs 0, 1, 2, 5 and 8 are already in mirror looking except the number. That&#8217;s why we call these numbers as <strong>universal<\/strong> numbers. Here also 2 becomes 5 and 5 as 2. Thus using <strong>vertical flip<\/strong>, we get an extra number as 3. Let&#8217;s call the operation as <strong>water reflection<\/strong>. This means that the numbers 0, 1, 2, 3, 5 and 8 are <strong>water reflexive<\/strong>. <\/p>\n\n\n\n<p>The aim this work is write magic squares based on the numbers 0, 1, 2, 3, 5 and 8, where 3 is always there, i.e., making combinations of 3 with the numbers 0, 1, 2, 5 and 8.  Below is an index of the example covered in this work<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 38%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Magic Squares of Order 3<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 2-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 1. Magic Square with 3-Digits (0,1,3)<\/li>\n\n\n\n<li>Example 2. Magic Square with 3-Digits (0,3,8)<\/li>\n\n\n\n<li>Example 3. Magic Squares with 3-Digits (1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 4-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 4. Magic Square with 2-Digits (1,3)<\/li>\n\n\n\n<li>Example 5. Magic Square with 2-Digits (3,8)<\/li>\n\n\n\n<li>Example 6. Magic Square with 2-Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 4<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 2-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 7. Magic Square with 4-Digits (2,3,5,8)<\/li>\n\n\n\n<li>Example 8. Magic Square with 4-Digits (1,3,5,8)<\/li>\n\n\n\n<li>Example 9. Magic Square with 4-Digits (0,2,3,5)<\/li>\n\n\n\n<li>Example 10. Magic Square with 4-Digits (0,1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 4-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 11. The Digits (3,8)<\/li>\n\n\n\n<li>Example 12. The Digits (1,3)<\/li>\n\n\n\n<li>Example 13. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 5<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 5-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 14. The Digits (1,2,3,5,8)<\/li>\n\n\n\n<li>Example 15. The Digits (0,2,3,5,8)<\/li>\n\n\n\n<li>Example 16. The Digits (0,1,2,3,5)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 4-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 17. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 18. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 19. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 20. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>c) 6-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 21. The Digits (3,8)<\/li>\n\n\n\n<li>Example 22. The Digits (1,3)<\/li>\n\n\n\n<li>Example 23. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 6<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 6-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 24. The Digits (3,8)<\/li>\n\n\n\n<li>Example 25. The Digits (1,3)<\/li>\n\n\n\n<li>Example 26. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>References<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Full work can be downloaded from the following link:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Inder J. Taneja<\/strong>, Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 3 to 6, <strong>Zenodo<\/strong>, January 07, 2025, pp. 1-93, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14607070\">https:\/\/doi.org\/10.5281\/zenodo.14607070<\/a>.<\/li>\n<\/ul>\n\n\n\n<p>For further work on orders 7 to 16 follow the links below:<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(203,242,199) 47%,rgb(113,206,126) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja, <\/strong><a href=\"https:\/\/numbers-magic.com\/?p=14126\">Water Reflection Magic Squares: Order 3 to 6<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14213\">Water Reflection Magic Squares: Order 7 to 10.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14339\">Water Reflection Magic Squares: Order 11 to 13.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14518\">Water Reflection Magic Squares: Order 14 to 16<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14561\">Water Reflection Magic Squares: Orders 17 to 20.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14616\">Water Reflection Magic Squares: Orders 21 to 23.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=14668\">Water Reflection Magic Squares: Order 24.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>,&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=14749\">Water Reflection Magic Squares: Order 25.<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(42,222,179) 53%,rgb(155,81,224) 100%)\">Magic Squares of Order 3<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3eeaf5a250fc3e78b1e247748c6bf37c\">a) 2-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-d5e8ff53cf27fd0b312d43ed58f471ed\">Example 1. Magic Square with 3-Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"192\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-013.png\" alt=\"\" class=\"wp-image-14133\" style=\"width:204px;height:auto\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"192\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-013w-1.png\" alt=\"\" class=\"wp-image-14138\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a5f44eeca7b5bf78bb3d1d9713aaf6b8\">Example 2. Magic Square with 3-Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"192\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-038.png\" alt=\"\" class=\"wp-image-14137\" style=\"width:204px;height:auto\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"192\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-038w.png\" alt=\"\" class=\"wp-image-14139\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-e7209a665b8a4aa36e72eae5cba0fb9f\">Example 3. Magic Squares with 3-Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"201\" height=\"192\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-138.png\" alt=\"\" class=\"wp-image-14135\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"201\" height=\"192\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-138w.png\" alt=\"\" class=\"wp-image-14140\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflexive<\/strong> <strong>semi-magic<\/strong> squares of order 3 having <strong>2-digits cells entries<\/strong> with three number combinations (0,1,3), (0, 3, 8) and, (1,3,8). In this case, we <strong>semi-magic<\/strong> squares of order 3.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-9263a1dbce8facd8987da2b46f073d50\">b) 4-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-33921f4002f987d1f4e41469b41eba81\">Example 4. Magic Square with 2-Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"178\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-13.png\" alt=\"\" class=\"wp-image-14143\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"178\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-13w.png\" alt=\"\" class=\"wp-image-14146\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-c4330aa616f254d3f1193ae4e1bd4ad5\">Example 5. Magic Square with 2-Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"178\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-38.png\" alt=\"\" class=\"wp-image-14142\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"286\" height=\"178\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-38w.png\" alt=\"\" class=\"wp-image-14144\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-63fb683c81d5017b810e06ac6fbe9ed2\">Example 6. Magic Square with 2-Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"182\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-03.png\" alt=\"\" class=\"wp-image-14141\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"182\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/image.png\" alt=\"This image has an empty alt attribute; its file name is 3-3x3-03w.png\" class=\"wp-image-14148\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflexive<\/strong> <strong>semi-magic<\/strong> squares of order 3 having <strong>4-digits cells entries<\/strong> with two number combinations (1,3), (3, 8) and, (0,3). In this case, we <strong>semi-magic<\/strong> squares of order 3.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(42,222,179) 53%,rgb(155,81,224) 100%)\">Magic Squares of Order 4<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3eeaf5a250fc3e78b1e247748c6bf37c\">a) 2-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-8ec1f89b521e60860d8b621567b07dda\">Example 7. Magic Square with 4-Digits (2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"226\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-2358.png\" alt=\"\" class=\"wp-image-14161\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-2358.png 311w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-2358-300x218.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"226\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-2358w.png\" alt=\"\" class=\"wp-image-14165\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-2358w.png 311w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-2358w-300x218.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-9945215dfcb4c9ae075de8633a8a56f6\">Example 8. Magic Square with 4-Digits (1,3,5,8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-1235.png\" alt=\"\" class=\"wp-image-14162\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-1235.png 307w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-1235-300x218.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-1235w.png\" alt=\"\" class=\"wp-image-14166\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-1235w.png 307w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-1235w-300x218.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-e9b7509836612cb75234ba1d91b66263\">Example 9. Magic Square with 4-Digits (0, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"306\" height=\"223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-0235.png\" alt=\"\" class=\"wp-image-14163\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-0235.png 306w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-0235-300x219.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"306\" height=\"223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-0235w.png\" alt=\"\" class=\"wp-image-14167\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-0235w.png 306w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-0235w-300x219.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-c0050c18f8ca43943990952a01e2bafb\">Example 10. Magic Square with 4-Digits (0, 1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-0138.png\" alt=\"\" class=\"wp-image-14164\" style=\"width:299px;height:auto\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"293\" height=\"223\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/3-3x3-0138w.png\" alt=\"\" class=\"wp-image-14168\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflexive<\/strong> magic squares of order 4 having <strong>2-digits cells entries<\/strong> with four numbers combinations (2,3,5,8), (1,2,3,5), (0,2,3,5) and, (0,1,3,8). <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-9263a1dbce8facd8987da2b46f073d50\">b) 4-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-da077d56b7cfa21d65a3396a242df0b2\">Example 11. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"406\" height=\"252\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-38.png\" alt=\"\" class=\"wp-image-14169\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-38.png 406w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-38-300x186.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"406\" height=\"252\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-38w.png\" alt=\"\" class=\"wp-image-14173\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-38w.png 406w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-38w-300x186.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-8dcecaba86242b4eef91c0759bca8f7d\">Example 12. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"411\" height=\"253\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-13-1.png\" alt=\"\" class=\"wp-image-14171\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-13-1.png 411w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-13-1-300x185.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"411\" height=\"253\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-13w.png\" alt=\"\" class=\"wp-image-14174\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-13w.png 411w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-13w-300x185.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-b15a144995985d1f1ec766804502f718\">Example 13. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"250\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-03.png\" alt=\"\" class=\"wp-image-14172\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-03.png 407w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-03-300x184.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"250\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-03w.png\" alt=\"\" class=\"wp-image-14175\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-03w.png 407w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/4x4-03w-300x184.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflexive<\/strong> magic squares of order 4 having <strong>4-digits cells entries<\/strong> with two numbers combinations (3,8), (1,3) and (0,3). In this case, the magic squares are <strong>pandiagonal<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(42,222,179) 53%,rgb(155,81,224) 100%)\">Magic Squares of Order 5<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-621b74c0715e70e5ac4876266596be56\">a) 5-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-f72a762b3c13bed31d5a088ef6314c6c\">Example 14. The Digits (1, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"284\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-12358.png\" alt=\"\" class=\"wp-image-14178\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-12358.png 385w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-12358-300x221.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"284\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-12358w.png\" alt=\"\" class=\"wp-image-14181\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-12358w.png 385w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-12358w-300x221.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-89e34293dea8e59748f6ea78615442f2\">Example 15. The Digits (0, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"284\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-02358.png\" alt=\"\" class=\"wp-image-14179\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-02358.png 368w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-02358-300x232.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading alignwide has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-ff6e03382a0f07791f17659f9710773a\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"284\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-02358w.png\" alt=\"\" class=\"wp-image-14182\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-02358w.png 368w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-02358w-300x232.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-8e16ebddd51e45abf88b22813ec2da0f\">Example 16. The Digits (0, 1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"283\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-01235.png\" alt=\"\" class=\"wp-image-14180\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-01235.png 383w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-01235-300x222.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading alignwide has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-ff6e03382a0f07791f17659f9710773a\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"283\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-01235w.png\" alt=\"\" class=\"wp-image-14183\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-01235w.png 383w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-01235w-300x222.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflexive<\/strong> magic squares of order 5 having <strong>2-digits cells entries<\/strong> with five numbers combinations (1,2,3,5), (0,2,3,5) and (0,1,2,5). In this case, the magic squares are <strong>pandiagonal<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-9af06514e148167842f30c07b763200f\">b) 4-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a8f64753458d329920cbc391ff56c3b3\">Example 17. The Digits (2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"537\" height=\"286\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235.png\" alt=\"\" class=\"wp-image-14187\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235.png 537w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235-535x285.png 535w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading alignwide has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-ff6e03382a0f07791f17659f9710773a\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"537\" height=\"286\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235w.png\" alt=\"\" class=\"wp-image-14189\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235w.png 537w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235w-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-235w-535x285.png 535w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-3c4c287301d5c054afa1a1b93afe3e18\">Example 18. The Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"470\" height=\"292\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-138.png\" alt=\"\" class=\"wp-image-14185\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-138.png 470w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-138-300x186.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"470\" height=\"292\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-138w.png\" alt=\"\" class=\"wp-image-14190\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-138w.png 470w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-138w-300x186.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-3e15b678b6cb09c1b2adc36e69823dd3\">Example 19. The Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"288\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-038.png\" alt=\"\" class=\"wp-image-14186\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-038.png 467w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-038-300x185.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"288\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-038w.png\" alt=\"\" class=\"wp-image-14191\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-038w.png 467w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-038w-300x185.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-3619d5ffcf27a4e35c904d9e488ab69b\">Example 20. The Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"470\" height=\"290\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-013.png\" alt=\"\" class=\"wp-image-14188\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-013.png 470w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-013-300x185.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"470\" height=\"290\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-013w.png\" alt=\"\" class=\"wp-image-14192\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-013w.png 470w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-013w-300x185.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have four examples of <strong>water reflexive<\/strong> magic squares of order 5 having <strong>4-digits cells entries<\/strong> with three numbers combinations (2,3,5), (1,3,8), (0,3,8) and (0,1, 3). In this case, the magic squares are <strong>pandiagonal<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-da529aea76bcb38ff4654ca16d5441e1\">c) 6-Digits Cell Entries<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-dc99b8d46bd499902ab9acc1311044e1\">Example 21. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"315\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38.png\" alt=\"\" class=\"wp-image-14193\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38.png 622w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38-535x271.png 535w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"315\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38w.png\" alt=\"\" class=\"wp-image-14199\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38w.png 622w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38w-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-38w-535x271.png 535w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-e3ca5684213c857bd15e021583890adc\">Example 22. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"624\" height=\"315\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13.png\" alt=\"\" class=\"wp-image-14194\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13.png 624w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13-535x270.png 535w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"624\" height=\"315\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13w.png\" alt=\"\" class=\"wp-image-14197\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13w.png 624w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13w-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-13w-535x270.png 535w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-aa269ecd8dc62c880f1885fd7586ac18\">Example 23. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"627\" height=\"316\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03.png\" alt=\"\" class=\"wp-image-14195\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03.png 627w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03-535x270.png 535w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"627\" height=\"316\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03w.png\" alt=\"\" class=\"wp-image-14198\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03w.png 627w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03w-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/5x5-03w-535x270.png 535w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflexive<\/strong> <strong>pandiagonal<\/strong> magic squares of order 5 having <strong>6-digits cells entries<\/strong> with two numbers combinations (3,8), (1,3) and (0,3). In this case, the magic squares are <strong>pandiagonal<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(42,222,179) 53%,rgb(155,81,224) 100%)\">Magic Squares of Order 6<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-8d524e11f2c4b1bc44f3d10af8095dd1\">a) 6-Digits Cell Entries:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-590a8cfb4b83706f29f4494ecaf1f7b9\">Example 24. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"378\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38.png\" alt=\"\" class=\"wp-image-14204\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38-535x270.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"378\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38w.png\" alt=\"\" class=\"wp-image-14207\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38w.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38w-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-38w-535x270.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-c24dfe40e05ebc8d8d7f6a9451689e4e\">Example 25. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"375\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13.png\" alt=\"\" class=\"wp-image-14205\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13-300x150.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13-535x268.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"375\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13w.png\" alt=\"\" class=\"wp-image-14208\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13w.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13w-300x150.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-13w-535x268.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0a76f82c4dfecf89abd42289a9ef9593\">Example 26. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"372\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03.png\" alt=\"\" class=\"wp-image-14206\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03-535x265.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-purple-color has-text-color has-link-color wp-elements-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"750\" height=\"372\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03w.png\" alt=\"\" class=\"wp-image-14209\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03w.png 750w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03w-300x149.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/6x6-03w-535x265.png 535w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 49%,rgb(152,150,240) 100%)\">Thus, we have three examples of <strong>water reflexive<\/strong> magic squares of order 6 having <strong>6-digits cells entries<\/strong> with two numbers combinations (3,8), (1,3) and (0,3) .<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(212,193,193) 22%,rgb(18,184,20) 57%,rgb(237,212,212) 74%,rgb(113,206,126) 100%)\">References<\/h3>\n\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(255,255,255) 51%,rgb(152,150,240) 100%)\">Below are references of complete project in 8 parts for the orders 3 to 25. Mainly, it includes three things: <strong>Upside-down, Mirror Looking<\/strong> and <strong>Water Reflection<\/strong> properties of magic squares.<\/p>\n\n\n\n<ol class=\"wp-block-list has-light-green-cyan-to-vivid-green-cyan-gradient-background has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 3 to 6<\/em>, <strong>Zenodo<\/strong>, January 07, 2025, pp. 1-93, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14607070\">https:\/\/doi.org\/10.5281\/zenodo.14607070<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12610\">Universal and Upside-Down Magic Squares of Order 3 to 6 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14126\">Water Reflexive Magic Squares: Order 3 to 6 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/09\/30\/universal-and-upside-down-magic-squares-of-order-3-to-6\/\">Universal and Upside-Down Magic Squares of Order 3 to 6 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/11\/water-reflexive-magic-squares-order-3-to-6\/\">Water Reflexive Magic Squares: Order 3 to 6 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 7 to 10<\/em>, <strong>Zenodo<\/strong>, January 07, 2025, pp. 1-171, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14607071\">https:\/\/doi.org\/10.5281\/zenodo.14607071<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12654\">Universal and Upside-Down Magic Squares of Orders 7 to 10 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14213\">Water Reflexive Magic Squares: Order 7 to 10 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/09\/30\/universal-and-upside-down-magic-squares-of-orders-7-to-10\/\">Universal and Upside-Down Magic Squares of Orders 7 to 10 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/11\/water-reflexive-magic-squares-order-3-to-6\/\"><\/a><a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/11\/water-reflexive-magic-squares-order-7-to-10\/\">Water Reflexive Magic Squares: Order 7 to 10 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 11 to 13<\/em>, <strong>Zenodo<\/strong>, January 15, 2025, pp. 1-146, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14649320\">https:\/\/doi.org\/10.5281\/zenodo.14649320<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12731\">Universal and Upside-Down Magic Squares of Orders 11 to 15 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14339\">Water Reflection Magic Squares: Order 11 to 13 (new site).<\/a> <\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/07\/universal-and-upside-down-magic-squares-of-orders-11-to-15\/\">Universal and Upside-Down Magic Squares of Orders 11 to 15 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-11-to-13\/\">Water Reflection Magic Squares: Orders 11 to 13 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 14 to 16<\/em>, <strong>Zenodo<\/strong>, January 15, 2024, pp. 1-140, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14649519\">https:\/\/doi.org\/10.5281\/zenodo.14649519<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13138\">Universal and Upside-Down Magic and Bimagic Squares of Order 16 (new site) <\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13138\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14518\">Water Reflection Magic Squares: Order 14 to 16 (new site).<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/16\/universal-and-upside-down-magic-and-bimagic-squares-of-order-16\/\">Universal and Upside-Down Magic and Bimagic Squares of Order 16 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-14-to-16\/\">Water Reflection Magic Squares: Orders 14 to 16 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 17 to 20<\/em>, Zenodo, January 17, 2025, pp. 1-86, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14676293\">https:\/\/doi.org\/10.5281\/zenodo.14676293<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13186\">Universal and Upside-Down Magic Squares of Order 20 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13186\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14561\">Water Reflection Magic Squares: Orders 17 to 20 (new site)<\/a>.<\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/23\/universal-and-upside-down-magic-and-bimagic-squares-of-order-16-2\/\">Universal and Upside-Down Magic Squares of Order 20 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-17-to-20\/\">Water Reflection Magic Squares: Orders 17 to 20 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 21 to 23<\/em>, <strong>Zenodo<\/strong>, January 20, 2025, pp. 1-83,  <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14688709\">https:\/\/doi.org\/10.5281\/zenodo.14688709<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13242\">Universal and Upside-Down Magic Squares of Order 21 (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13242\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14616\">Water Reflection Magic Squares: Orders 21 to 23 (new site).<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/23\/10984\/\">Universal and Upside-Down Magic Squares of Order 21 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-orders-21-to-23\/\">Water Reflection Magic Squares: Orders 21 to 23 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 24<\/em>, <strong>Zenodo<\/strong>, Janeiro 20, 2025, pp. 1-150, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14700325\">https:\/\/doi.org\/10.5281\/zenodo.14700325<\/a>\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13299\">Universal and Upside-Down Magic Squares of Order 24 (new site)<\/a><\/li>\n\n\n\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=14668\">Water Reflection Magic Squares: Order 24 (new site)<\/a>.<\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/29\/universal-and-upside-down-magic-squares-of-order-24\/\">Universal and Upside-Down Magic Squares of Order 24 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-order-24\/\">Water Reflection Magic Squares: Order 24 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Upside-Down, Mirror Looking and Water Reflection Magic Squares: Order 25<\/em>, <strong>Zenodo<\/strong>, January 21, 2025, pp. 1-79, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14715162\">https:\/\/doi.org\/10.5281\/zenodo.14715162<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=13336\">Universal and Upside-Down Magic and Bimagic Squares of Order 25 (new site) <\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=14749\">Water Reflection Magic Squares: Order 25. (new site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2024\/10\/30\/universal-and-upside-down-magic-and-bimagic-squares-of-order-25\/\">Universal and Upside-Down Magic and Bimagic Squares of Order 25 (old site)<\/a><\/li>\n\n\n\n<li>Site link: <a href=\"https:\/\/inderjtaneja.wordpress.com\/2025\/01\/23\/water-reflection-magic-squares-order-25\/\">Water Reflection Magic Squares: Order 25 (old site)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This work brings more concepts in magic squares. In past we studied a lot of upside-down and mirror looking magic squares. These are based some kind of digital\/special fonts. To understand better let&#8217;s consider the following 10 digits from 0 to 9: Upside-down (180 degrees rotation) Let&#8217;s consider 180 degrees rotation over the above 10 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":14174,"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-14126","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\/01\/4x4-13w.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14126","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=14126"}],"version-history":[{"count":18,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14126\/revisions"}],"predecessor-version":[{"id":14798,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14126\/revisions\/14798"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/14174"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}