{"id":14213,"date":"2025-01-05T13:56:34","date_gmt":"2025-01-05T16:56:34","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=14213"},"modified":"2025-01-23T02:06:12","modified_gmt":"2025-01-23T05:06:12","slug":"water-reflexive-magic-squares-order-7-to-10","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=14213","title":{"rendered":"Water Reflection Magic Squares: Orders 7 to 10"},"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 make 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 examples of this work<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 27%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Magic Squares of Order 7<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-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) 6-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 4. Magic Square with 2-Digits (3,8)<\/li>\n\n\n\n<li>Example 5. Magic Square with 2-Digits (1,3)<\/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 8<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 7. Magic Square with 3-Digits (2,3,5)<\/li>\n\n\n\n<li>Example 8. Magic Square with 2-Digits (1,3,8)<\/li>\n\n\n\n<li>Example 9. Magic Square with 3-Digits (0,3,8)<\/li>\n\n\n\n<li>Example 10. Magic Square with 3-Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 6-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 9<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 14. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 15. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 16. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 17. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 8-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 18. The Digits (3,8)<\/li>\n\n\n\n<li>Example 19. The Digits (1,3)<\/li>\n\n\n\n<li>Example 20. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 9<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 21. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 22. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 23. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 24. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 8-Digits Cell Entries<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 25. The Digits (3,8)<\/li>\n\n\n\n<li>Example 26. The Digits (1,3)<\/li>\n\n\n\n<li>Example 27. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 10<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 4-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 28. The Digits (2,3,5,8)<\/li>\n\n\n\n<li>Example 29. The Digits (1,2,3,5)<\/li>\n\n\n\n<li>Example 30. The Digits (0,2,3,5)<\/li>\n\n\n\n<li>Example 31. The Digits (0,1,3,8)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>b) 6-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 32. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 33. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 34. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 35. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>c) 8-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 36. The Digits (3,8)<\/li>\n\n\n\n<li>Example 37. The Digits (1,3)<\/li>\n\n\n\n<li>Example 38. 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>, Universal and Upside-Down Magic Squares of Orders 7 to 10, <strong>Zenodo<\/strong>, November 05, 2024, pp. 1-120, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.14041164\">https:\/\/doi.org\/10.5281\/zenodo.14041164<\/a>.<\/li>\n<\/ul>\n\n\n\n<p>This work is for the orders 7 to 10. For the previous work on orders 3 to 6 and the further works refer the links below:<\/p>\n\n\n\n<p>For the previous work on orders 3 to 13 refer the followig links:<\/p>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(244,250,200) 57%,rgb(169,184,195) 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<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><\/li>\n<\/ul>\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%)\">Magic Squares of Order 7<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b3fd78649fe4d2408410d66cfcf938a5\">a) 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-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\"><img loading=\"lazy\" decoding=\"async\" width=\"741\" height=\"393\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235.png\" alt=\"\" class=\"wp-image-14214\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235.png 741w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235-535x284.png 535w\" sizes=\"(max-width: 741px) 100vw, 741px\" \/><\/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=\"741\" height=\"393\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235w.png\" alt=\"\" class=\"wp-image-14215\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235w.png 741w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235w-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-235w-535x284.png 535w\" sizes=\"(max-width: 741px) 100vw, 741px\" \/><\/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\"><img loading=\"lazy\" decoding=\"async\" width=\"654\" height=\"398\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138.png\" alt=\"\" class=\"wp-image-14216\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138.png 654w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138-300x183.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138-535x326.png 535w\" sizes=\"(max-width: 654px) 100vw, 654px\" \/><\/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=\"654\" height=\"398\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138w.png\" alt=\"\" class=\"wp-image-14217\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138w.png 654w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138w-300x183.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-138w-535x326.png 535w\" sizes=\"(max-width: 654px) 100vw, 654px\" \/><\/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=\"651\" height=\"432\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038.png\" alt=\"\" class=\"wp-image-14218\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038.png 651w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038-300x199.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038-535x355.png 535w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/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=\"651\" height=\"432\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038w.png\" alt=\"\" class=\"wp-image-14219\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038w.png 651w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038w-300x199.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-038w-535x355.png 535w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/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> <strong>pandiagonal magic<\/strong> squares of order 7 having <strong>4-digits cells entries<\/strong> with three number combinations (2,3,5), (1, 3, 8) and, (0,3,8).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-fc76ea2193f8773edb397f7f823a4610\">b) 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-a83c9f3231fdb5ce5a7fe5f4ad508e10\">Example 4. 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=\"868\" height=\"397\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38.png\" alt=\"\" class=\"wp-image-14222\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38.png 868w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38-300x137.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38-768x351.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38-535x245.png 535w\" sizes=\"(max-width: 868px) 100vw, 868px\" \/><\/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=\"868\" height=\"397\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38w.png\" alt=\"\" class=\"wp-image-14225\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38w.png 868w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38w-300x137.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38w-768x351.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-38w-535x245.png 535w\" sizes=\"(max-width: 868px) 100vw, 868px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-878bf539e2f889843b54def44f6c99da\">Example 5. 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=\"868\" height=\"400\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13-1.png\" alt=\"\" class=\"wp-image-14228\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13-1.png 868w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13-1-300x138.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13-1-768x354.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13-1-535x247.png 535w\" sizes=\"(max-width: 868px) 100vw, 868px\" \/><\/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=\"868\" height=\"400\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13w-1.png\" alt=\"\" class=\"wp-image-14227\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13w-1.png 868w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13w-1-300x138.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13w-1-768x354.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-13w-1-535x247.png 535w\" sizes=\"(max-width: 868px) 100vw, 868px\" \/><\/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=\"867\" height=\"399\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03.png\" alt=\"\" class=\"wp-image-14224\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03.png 867w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03-300x138.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03-768x353.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03-535x246.png 535w\" sizes=\"(max-width: 867px) 100vw, 867px\" \/><\/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=\"867\" height=\"399\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03w.png\" alt=\"\" class=\"wp-image-14229\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03w.png 867w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03w-300x138.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03w-768x353.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/7x7-03w-535x246.png 535w\" sizes=\"(max-width: 867px) 100vw, 867px\" \/><\/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 7 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%)\">Magic Squares of Order 8<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b3fd78649fe4d2408410d66cfcf938a5\">a) 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-bc8cb885f5899ab1b42df3776127b628\">Example 7. Magic Square with 3-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=\"863\" height=\"461\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235.png\" alt=\"\" class=\"wp-image-14230\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235.png 863w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235-768x410.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235-535x286.png 535w\" sizes=\"(max-width: 863px) 100vw, 863px\" \/><\/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=\"863\" height=\"461\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235w.png\" alt=\"\" class=\"wp-image-14231\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235w.png 863w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235w-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235w-768x410.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-235w-535x286.png 535w\" sizes=\"(max-width: 863px) 100vw, 863px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-f783bd20a170d1862e810570bd83f673\">Example 8. Magic Square with 2-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=\"804\" height=\"497\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138.png\" alt=\"\" class=\"wp-image-14232\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138.png 804w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138-768x475.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138-535x331.png 535w\" sizes=\"(max-width: 804px) 100vw, 804px\" \/><\/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=\"804\" height=\"497\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138w.png\" alt=\"\" class=\"wp-image-14233\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138w.png 804w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138w-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138w-768x475.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-138w-535x331.png 535w\" sizes=\"(max-width: 804px) 100vw, 804px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-bd86d1ce00de5f8d61e7e342d3d5ad10\">Example 9. Magic Square with 3-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=\"801\" height=\"498\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038.png\" alt=\"\" class=\"wp-image-14236\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038.png 801w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038-300x187.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038-768x477.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038-535x333.png 535w\" sizes=\"(max-width: 801px) 100vw, 801px\" \/><\/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=\"801\" height=\"498\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038w.png\" alt=\"\" class=\"wp-image-14237\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038w.png 801w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038w-300x187.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038w-768x477.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-038w-535x333.png 535w\" sizes=\"(max-width: 801px) 100vw, 801px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-51101d946500012d0828376ce260f6f6\">Example 10. Magic Square with 3-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=\"803\" height=\"498\" src=\"http:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013.png\" alt=\"\" class=\"wp-image-14234\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013.png 803w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013-300x186.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013-768x476.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013-535x332.png 535w\" sizes=\"(max-width: 803px) 100vw, 803px\" \/><\/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=\"803\" height=\"498\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013w.png\" alt=\"\" class=\"wp-image-14235\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013w.png 803w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013w-300x186.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013w-768x476.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-013w-535x332.png 535w\" sizes=\"(max-width: 803px) 100vw, 803px\" \/><\/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 8 having <strong>4-digits cells entries<\/strong> with three numbers combinations (2,3,5), (1,3,8), (0,3,8) and, (0,1,3). The blocks of order 2&#215;4 are of equal sums as of magic square.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-fc76ea2193f8773edb397f7f823a4610\">b) 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-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=\"989\" height=\"500\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38.png\" alt=\"\" class=\"wp-image-14238\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38.png 989w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38-768x388.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38-535x270.png 535w\" sizes=\"(max-width: 989px) 100vw, 989px\" \/><\/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=\"989\" height=\"500\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38w.png\" alt=\"\" class=\"wp-image-14239\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38w.png 989w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38w-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38w-768x388.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-38w-535x270.png 535w\" sizes=\"(max-width: 989px) 100vw, 989px\" \/><\/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=\"991\" height=\"498\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13.png\" alt=\"\" class=\"wp-image-14240\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13.png 991w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13-768x386.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13-535x269.png 535w\" sizes=\"(max-width: 991px) 100vw, 991px\" \/><\/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=\"991\" height=\"498\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13w.png\" alt=\"\" class=\"wp-image-14241\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13w.png 991w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13w-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13w-768x386.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-13w-535x269.png 535w\" sizes=\"(max-width: 991px) 100vw, 991px\" \/><\/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=\"990\" height=\"499\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03.png\" alt=\"\" class=\"wp-image-14243\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03.png 990w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03-768x387.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03-535x270.png 535w\" sizes=\"(max-width: 990px) 100vw, 990px\" \/><\/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=\"990\" height=\"499\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03w.png\" alt=\"\" class=\"wp-image-14242\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03w.png 990w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03w-300x151.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03w-768x387.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/8x8-03w-535x270.png 535w\" sizes=\"(max-width: 990px) 100vw, 990px\" \/><\/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> pandiagonal magic squares of order 8 having <strong>6-digits cells entries<\/strong> with two numbers combinations (3,8), (1,3) and (0,3). These magic squares are <strong>pandiagonal<\/strong>, where blocks of order 4 are equal sum <strong>pandiagonal<\/strong> magic squares.<\/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%)\">Magic Squares of Order 9<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-60a89780fdb35a1d79d4ce75650cd8dd\">a) 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-f4bfd66400199750cf05903cbedfc3a0\">Example 14. 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=\"972\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235p-1.png\" alt=\"\" class=\"wp-image-14280\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235p-1.png 972w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235p-1-300x158.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235p-1-768x405.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235p-1-535x282.png 535w\" sizes=\"(max-width: 972px) 100vw, 972px\" \/><\/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=\"972\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235pw-1.png\" alt=\"\" class=\"wp-image-14281\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235pw-1.png 972w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235pw-1-300x158.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235pw-1-768x405.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235pw-1-535x282.png 535w\" sizes=\"(max-width: 972px) 100vw, 972px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6098df410a576854d684a7379bf49324\">Example 15. 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=\"831\" height=\"515\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138p-1.png\" alt=\"\" class=\"wp-image-14282\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138p-1.png 831w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138p-1-300x186.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138p-1-768x476.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138p-1-535x332.png 535w\" sizes=\"(max-width: 831px) 100vw, 831px\" \/><\/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=\"831\" height=\"515\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138pw-1.png\" alt=\"\" class=\"wp-image-14283\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138pw-1.png 831w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138pw-1-300x186.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138pw-1-768x476.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138pw-1-535x332.png 535w\" sizes=\"(max-width: 831px) 100vw, 831px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-15989a0f2d2d526fb95814b945f9668b\">Example 16. 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=\"836\" height=\"514\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038p-1.png\" alt=\"\" class=\"wp-image-14284\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038p-1.png 836w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038p-1-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038p-1-768x472.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038p-1-535x329.png 535w\" sizes=\"(max-width: 836px) 100vw, 836px\" \/><\/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=\"836\" height=\"514\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038pw-2.png\" alt=\"\" class=\"wp-image-14285\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038pw-2.png 836w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038pw-2-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038pw-2-768x472.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038pw-2-535x329.png 535w\" sizes=\"(max-width: 836px) 100vw, 836px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-fe7ac3543aedf42abd199510c00019ad\">Example 17. 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=\"831\" height=\"512\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013p-1.png\" alt=\"\" class=\"wp-image-14286\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013p-1.png 831w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013p-1-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013p-1-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013p-1-535x330.png 535w\" sizes=\"(max-width: 831px) 100vw, 831px\" \/><\/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=\"831\" height=\"512\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013pw-1.png\" alt=\"\" class=\"wp-image-14287\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013pw-1.png 831w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013pw-1-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013pw-1-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013pw-1-535x330.png 535w\" sizes=\"(max-width: 831px) 100vw, 831px\" \/><\/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 pandiagonal <\/strong>magic squares of order 9 having <strong>4-digits cells entries<\/strong> with 3 numbers combinations (2,3,5), (1,3,8) and (0,3,8) and (0,1,3). <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3077b9d4db17c7dbc5623348fb3d851c\">b) 8-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-8f72e780e8f1b64e7f2434038fc1c8c7\">Example 18. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"420\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38p-1024x420.png\" alt=\"\" class=\"wp-image-14256\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38p-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38p-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38p-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38p-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38p.png 1254w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"420\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38pw-1024x420.png\" alt=\"\" class=\"wp-image-14258\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38pw-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38pw-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38pw-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38pw-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38pw.png 1254w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6dab690f52ea498681e3b53fc64280d6\">Example 19. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"419\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13p-1024x419.png\" alt=\"\" class=\"wp-image-14261\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13p-1024x419.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13p-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13p-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13p-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13p.png 1257w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"419\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13pw-1024x419.png\" alt=\"\" class=\"wp-image-14262\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13pw-1024x419.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13pw-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13pw-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13pw-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13pw.png 1257w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-e1cae4021ffc549267aa7a587fcc632f\">Example 20. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"417\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03p-1024x417.png\" alt=\"\" class=\"wp-image-14259\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03p-1024x417.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03p-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03p-768x313.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03p-535x218.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03p.png 1257w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"417\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03pw-1024x417.png\" alt=\"\" class=\"wp-image-14260\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03pw-1024x417.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03pw-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03pw-768x313.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03pw-535x218.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03pw.png 1257w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/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 9 having <strong>8-digits cells entries<\/strong> with 2 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%)\">Magic Squares of Order 9<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-60a89780fdb35a1d79d4ce75650cd8dd\">a) 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-d06fcb813529fb9ebaeb3f2daec1b045\">Example 21. 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=\"970\" height=\"514\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235b.png\" alt=\"\" class=\"wp-image-14263\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235b.png 970w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235b-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235b-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235b-535x283.png 535w\" sizes=\"(max-width: 970px) 100vw, 970px\" \/><\/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=\"970\" height=\"514\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235bw.png\" alt=\"\" class=\"wp-image-14264\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235bw.png 970w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235bw-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235bw-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-235bw-535x283.png 535w\" sizes=\"(max-width: 970px) 100vw, 970px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-661d9425fe54d830c1f0b093e7060123\">Example 22. 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=\"835\" height=\"511\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138b.png\" alt=\"\" class=\"wp-image-14265\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138b.png 835w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138b-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138b-768x470.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138b-535x327.png 535w\" sizes=\"(max-width: 835px) 100vw, 835px\" \/><\/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=\"835\" height=\"511\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138bw.png\" alt=\"\" class=\"wp-image-14266\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138bw.png 835w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138bw-300x184.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138bw-768x470.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-138bw-535x327.png 535w\" sizes=\"(max-width: 835px) 100vw, 835px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-22f5f162ba6783413368852c5635763e\">Example 23. 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=\"833\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038b.png\" alt=\"\" class=\"wp-image-14267\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038b.png 833w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038b-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038b-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038b-535x329.png 535w\" sizes=\"(max-width: 833px) 100vw, 833px\" \/><\/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=\"833\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038bw.png\" alt=\"\" class=\"wp-image-14268\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038bw.png 833w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038bw-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038bw-768x473.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-038bw-535x329.png 535w\" sizes=\"(max-width: 833px) 100vw, 833px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-3e2849a9775f51ecd665bd10da2cf451\">Example 24. 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=\"834\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013b.png\" alt=\"\" class=\"wp-image-14269\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013b.png 834w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013b-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013b-768x472.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013b-535x329.png 535w\" sizes=\"(max-width: 834px) 100vw, 834px\" \/><\/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=\"834\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013bw.png\" alt=\"\" class=\"wp-image-14270\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013bw.png 834w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013bw-300x185.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013bw-768x472.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-013bw-535x329.png 535w\" sizes=\"(max-width: 834px) 100vw, 834px\" \/><\/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> bimagic squares of order 9 having <strong>4-digits cells entries<\/strong> with 3 numbers combinations (2,3,5), (1,3,8) and (0,3,8) and (0,1,3). The magic and <strong>bimagic<\/strong> sums in each case be seen in an online complete work given above.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-3077b9d4db17c7dbc5623348fb3d851c\">b) 8-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-733e31b80f44dff251076769df4e92eb\">Example 25. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"417\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38b-1024x417.png\" alt=\"\" class=\"wp-image-14271\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38b-1024x417.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38b-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38b-768x313.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38b-535x218.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38b.png 1253w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"417\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38bw-1024x417.png\" alt=\"\" class=\"wp-image-14272\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38bw-1024x417.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38bw-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38bw-768x313.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38bw-535x218.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-38bw.png 1253w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-eed3e0ba3ba2292e88cf6464b19ffd9b\">Example 26. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"419\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13b-1024x419.png\" alt=\"\" class=\"wp-image-14273\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13b-1024x419.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13b-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13b-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13b-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13b.png 1254w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"419\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13bw-1024x419.png\" alt=\"\" class=\"wp-image-14274\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13bw-1024x419.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13bw-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13bw-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13bw-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-13bw.png 1254w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-78c6e0b1121ddf5e29968a1c247dd1fe\">Example 27. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"419\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03b-1024x419.png\" alt=\"\" class=\"wp-image-14275\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03b-1024x419.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03b-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03b-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03b-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03b.png 1257w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"419\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03bw-1024x419.png\" alt=\"\" class=\"wp-image-14276\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03bw-1024x419.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03bw-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03bw-768x314.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03bw-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/9x9-03bw.png 1257w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/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> bimagic squares of order 9 having <strong>8-digits cells entries<\/strong> with 2 numbers combinations (3,8), (1,3) and (0,3). The magic and <strong>bimagic<\/strong> sums in each case be seen in an online complete work given above.<\/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%)\">Magic Squares of Order 10<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-b3fd78649fe4d2408410d66cfcf938a5\">a) 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-4c3b5b00e56bff966818f717bb47cc89\">Example 28. The Digits (2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"533\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358-1024x533.png\" alt=\"\" class=\"wp-image-14288\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358-1024x533.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358-768x400.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358-535x278.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358.png 1084w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"533\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358w-1024x533.png\" alt=\"\" class=\"wp-image-14289\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358w-1024x533.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358w-300x156.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358w-768x400.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358w-535x278.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-2358w.png 1084w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-106e87ae9283ca6eedb0602042dfa5fb\">Example 29. The Digits (1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"485\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235-1024x485.png\" alt=\"\" class=\"wp-image-14290\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235-1024x485.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235-300x142.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235-768x364.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235-535x253.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235.png 1075w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"485\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235w-1024x485.png\" alt=\"\" class=\"wp-image-14291\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235w-1024x485.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235w-300x142.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235w-768x364.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235w-535x253.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-1235w.png 1075w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-98322812520c52f14a165658de025308\">Example 30. The Digits (0, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"480\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235-1024x480.png\" alt=\"\" class=\"wp-image-14292\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235-1024x480.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235-300x141.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235-768x360.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235-535x251.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235.png 1088w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"480\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235w-1024x480.png\" alt=\"\" class=\"wp-image-14293\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235w-1024x480.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235w-300x141.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235w-768x360.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235w-535x251.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0235w.png 1088w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0c45d5cd5a7fdc792fe786a0e1d89d21\">Example 31. The Digits (0, 1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"921\" height=\"540\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138.png\" alt=\"\" class=\"wp-image-14294\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138.png 921w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138-300x176.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138-768x450.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138-535x314.png 535w\" sizes=\"(max-width: 921px) 100vw, 921px\" \/><\/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=\"921\" height=\"540\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138w.png\" alt=\"\" class=\"wp-image-14295\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138w.png 921w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138w-300x176.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138w-768x450.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-0138w-535x314.png 535w\" sizes=\"(max-width: 921px) 100vw, 921px\" \/><\/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 10 having <strong>4-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-fc76ea2193f8773edb397f7f823a4610\">b) 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-7351cf1ff490647ab24d5ac9cfe5c515\">Example 32. The Digits (2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"397\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235-1024x397.png\" alt=\"\" class=\"wp-image-14298\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235-1024x397.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235-768x298.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235-535x208.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235.png 1319w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"397\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235w-1024x397.png\" alt=\"\" class=\"wp-image-14299\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235w-1024x397.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235w-300x116.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235w-768x298.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235w-535x208.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-235w.png 1319w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-b338292b9f8f69c0b64015a609b2b9fc\">Example 33. The Digits (1, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-138-1024x466.png\" alt=\"\" class=\"wp-image-14300\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-138-1024x466.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-138-300x137.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-138-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-138-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-138.png 1123w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a915452e94d447346012e4f2a4763aac\">Example 34. The Digits (0, 3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038-1024x466.png\" alt=\"\" class=\"wp-image-14301\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038-1024x466.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038-300x136.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038.png 1119w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038w-1024x466.png\" alt=\"\" class=\"wp-image-14302\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038w-1024x466.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038w-300x136.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038w-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038w-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-038w.png 1119w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-670409ad2ecaa5090cf898fc3b63d611\">Example 35. The Digits (0, 1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013-1024x466.png\" alt=\"\" class=\"wp-image-14303\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013-1024x466.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013-300x136.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013.png 1121w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"466\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013w-1024x466.png\" alt=\"\" class=\"wp-image-14304\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013w-1024x466.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013w-300x136.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013w-768x349.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013w-535x243.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-013w.png 1121w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/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 10 having <strong>6-digits cells entries<\/strong> with 3 numbers combinations (2, 3, 5), (1, 3, 8), (0, 3, 8) and (0,1, 3).<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-d15a2831c10df8655df53d4a90bd1e2f\">c) 8-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-e703246664799eeead2fe0f77f71d35d\">Example 36. The Digits (3, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"374\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38-1024x374.png\" alt=\"\" class=\"wp-image-14307\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38-1024x374.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38-300x109.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38-768x280.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38-535x195.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38.png 1395w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"374\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38w-1024x374.png\" alt=\"\" class=\"wp-image-14308\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38w-1024x374.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38w-300x109.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38w-768x280.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38w-535x195.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-38w.png 1395w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-c3bc41e02a05fb567cb38a85e7cc8d99\">Example 37. The Digits (1, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"373\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13-1024x373.png\" alt=\"\" class=\"wp-image-14310\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13-1024x373.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13-300x109.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13-768x280.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13-535x195.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13.png 1389w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"373\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13w-1024x373.png\" alt=\"\" class=\"wp-image-14311\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13w-1024x373.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13w-300x109.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13w-768x280.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13w-535x195.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-13w.png 1389w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a3bbbd669b5cbf2c48ca1694ff0e2cbe\">Example 38. The Digits (0, 3)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"375\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03-1024x375.png\" alt=\"\" class=\"wp-image-14312\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03-1024x375.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03-768x282.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03.png 1391w\" 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-f723ed23e74b265d646e75c9fd253b22\">Water Reflection Image<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"375\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03w-1024x375.png\" alt=\"\" class=\"wp-image-14313\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03w-1024x375.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03w-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03w-768x282.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03w-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/10x10-03w.png 1391w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/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 10 having <strong>8-digits cells entries<\/strong> with 2 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><br><\/p>\n\n\n\n<p><br><\/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 make 180 degrees rotation over the above 10 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":14214,"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-14213","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\/7x7-235.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14213","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=14213"}],"version-history":[{"count":18,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14213\/revisions"}],"predecessor-version":[{"id":14799,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14213\/revisions\/14799"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/14214"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14213"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14213"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14213"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}