{"id":14668,"date":"2025-01-19T00:06:41","date_gmt":"2025-01-19T03:06:41","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=14668"},"modified":"2025-01-23T01:54:06","modified_gmt":"2025-01-23T04:54:06","slug":"water-reflection-magic-squares-order-24","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=14668","title":{"rendered":"Water Reflection Magic Squares: Order 24"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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. This work is for orders 14 to 16. Full work can be downloaded from the following link:<\/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><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>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Below is the index of the work given below for the order 24.<\/strong><\/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>Magic Squares of Order 24: Blocks of Semi-Magic Squares of Order 3<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>a) 5-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 1. The Digits (1,2,3,5,8)<\/li>\n\n\n\n<li>Example 2. The Digits (0,2,3,5,8)<\/li>\n\n\n\n<li>Example 3. The Digits (0,1,2,3,5)<\/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. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 5. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 6. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 7. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>c) 10-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Example 8. The Digits (3,8)<\/li>\n\n\n\n<li>Example 9. The Digits (1,3)<\/li>\n\n\n\n<li>Example 10. The Digits (0,3)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Magic Squares of Order 24: Blocks of Magic Squares of Order 4<\/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 11. The Digits (1,2,3,5,8)<\/li>\n\n\n\n<li>Example 12. The Digits (0,2,3,5,8)<\/li>\n\n\n\n<li>Example 13. The Digits (0,1,2,3,5)<\/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 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>c) 10-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 24: Blocks of Order <\/strong>8\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 (1,2,3,5,8)<\/li>\n\n\n\n<li>Example 22. The Digits (0,2,3,5,8)<\/li>\n\n\n\n<li>Example 23. The Digits (0,1,2,3,5)<\/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 24. The Digits (2,3,5)<\/li>\n\n\n\n<li>Example 25. The Digits (1,3,8)<\/li>\n\n\n\n<li>Example 26. The Digits (0,3,8)<\/li>\n\n\n\n<li>Example 27. The Digits (0,1,3)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>c) 10-Digits Cell Entries:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Semi-Bimagic Squares<\/li>\n\n\n\n<li>Example 28. The Digits (3,8)<\/li>\n\n\n\n<li>Example 29. The Digits (1,3)<\/li>\n\n\n\n<li>Example 30. 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 class=\"wp-block-paragraph\">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: Orders 14 to 16.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14518\"><\/a><a href=\"https:\/\/numbers-magic.com\/?p=14561\">Water Reflection Magic Squares: Order 17 to 20.<\/a> <\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14616\">Water Reflection Magic Squares: Orders 21 to 23.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <a href=\"https:\/\/numbers-magic.com\/?p=14668\">Water Reflection Magic Squares: Order 24. (This work)<\/a>.<\/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 24: <br>Blocks of Semi-Magic Squares of Order 3<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-2975793e9cf5c4d106124282105982d5\">a) 5-Digits Cell Entries: <\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-94f95c133e9e33cd5bdfa41ada017eaf\">Example 1. The Digits (1, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1915\" height=\"835\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358.png\" alt=\"\" class=\"wp-image-14670\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358.png 1915w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358-300x131.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358-1024x446.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358-768x335.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358-535x233.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-12358-1536x670.png 1536w\" sizes=\"(max-width: 1915px) 100vw, 1915px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-7ae5fc37a4722cdcef6ba410e5c4fbb0\">Example 2. The Digits (0, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1924\" height=\"831\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358.png\" alt=\"\" class=\"wp-image-14672\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358.png 1924w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358-535x231.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-02358-1536x663.png 1536w\" sizes=\"(max-width: 1924px) 100vw, 1924px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-2592a556757f3214956c7f24e7ef9ebf\">Example 3. The Digits (0, 1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1925\" height=\"833\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235.png\" alt=\"\" class=\"wp-image-14674\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235.png 1925w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235-1024x443.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235-535x232.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-01235-1536x665.png 1536w\" sizes=\"(max-width: 1925px) 100vw, 1925px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Thus, we have three examples of <strong>semi-magic<\/strong> squares of order 24 having <strong>4-digits cells entries<\/strong> with five numbers combinations (1, 2, 3, 5, 8), (0, 2, 3, 5, 8) and (0, 1, 2, 3, 5). The internal blocks of order 3 are <strong>semi-magic<\/strong> squares with different <strong>semi-magic<\/strong> sums. The blocks of order 12 are <strong>semi-magic<\/strong> squares with equal <strong>semi-magic<\/strong> sums. <strong><em>These three examples are not water reflexive as these doesn&#8217;t give semi-magic squares after applying vertical flip.<\/em><\/strong><\/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-def3f5f15901a05d38f070bb538a8017\">Example 4. 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=\"2371\" height=\"836\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235.png\" alt=\"\" class=\"wp-image-14676\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235.png 2371w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235-300x106.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235-1024x361.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235-768x271.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235-535x189.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235-1536x542.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235-2048x722.png 2048w\" sizes=\"(max-width: 2371px) 100vw, 2371px\" \/><\/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=\"2371\" height=\"836\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w.png\" alt=\"\" class=\"wp-image-14677\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w.png 2371w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w-300x106.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w-1024x361.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w-768x271.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w-535x189.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w-1536x542.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-235w-2048x722.png 2048w\" sizes=\"(max-width: 2371px) 100vw, 2371px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-5ace58389620ebe591d92a4174ddc67c\">Example 5. 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=\"2155\" height=\"897\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138.png\" alt=\"\" class=\"wp-image-14678\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138.png 2155w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138-300x125.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138-1024x426.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138-768x320.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138-535x223.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138-1536x639.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138-2048x852.png 2048w\" sizes=\"(max-width: 2155px) 100vw, 2155px\" \/><\/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=\"2155\" height=\"897\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w.png\" alt=\"\" class=\"wp-image-14679\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w.png 2155w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w-300x125.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w-1024x426.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w-768x320.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w-535x223.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w-1536x639.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-138w-2048x852.png 2048w\" sizes=\"(max-width: 2155px) 100vw, 2155px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a31db531bcca8a26a123918e73661db8\">Example 6. 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=\"2152\" height=\"893\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038.png\" alt=\"\" class=\"wp-image-14680\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038.png 2152w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038-1024x425.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038-768x319.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038-1536x637.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038-2048x850.png 2048w\" sizes=\"(max-width: 2152px) 100vw, 2152px\" \/><\/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=\"2152\" height=\"893\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w.png\" alt=\"\" class=\"wp-image-14681\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w.png 2152w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w-1024x425.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w-768x319.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w-1536x637.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-038w-2048x850.png 2048w\" sizes=\"(max-width: 2152px) 100vw, 2152px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-5c328f6c906af427750fce8a6ebd2151\">Example 7. 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=\"2151\" height=\"894\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013.png\" alt=\"\" class=\"wp-image-14682\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013.png 2151w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013-300x125.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013-1024x426.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013-768x319.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013-1536x638.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013-2048x851.png 2048w\" sizes=\"(max-width: 2151px) 100vw, 2151px\" \/><\/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=\"2151\" height=\"894\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w.png\" alt=\"\" class=\"wp-image-14683\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w.png 2151w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w-300x125.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w-1024x426.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w-768x319.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w-1536x638.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-013w-2048x851.png 2048w\" sizes=\"(max-width: 2151px) 100vw, 2151px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Thus, we have four examples of <strong>water reflection<\/strong> <strong>semi-magic<\/strong> squares of order 24 having <strong>6-digits cells entries<\/strong> with 3 numbers combinations (2, 3, 5), (1, 3, 8), (0, 3, 8) and (0,1, 3). The internal blocks of order 3 are <strong>semi-magic<\/strong> square with different <strong>semi-magic<\/strong> sums. The blocks of order 12 are <strong>semi-magic<\/strong> squares with equal <strong>semi-magic<\/strong> sums. <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-5eb87b6132f517873c5c3b9270b9cacd\">c) 10-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-9e903b43cd383cf531350e55e6eda054\">Example 8. 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=\"2742\" height=\"981\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38.png\" alt=\"\" class=\"wp-image-14684\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38.png 2742w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1536x550.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-2048x733.png 2048w\" sizes=\"(max-width: 2742px) 100vw, 2742px\" \/><\/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=\"2742\" height=\"981\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1.png\" alt=\"\" class=\"wp-image-14685\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1.png 2742w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1-1536x550.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-38-1-2048x733.png 2048w\" sizes=\"(max-width: 2742px) 100vw, 2742px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a9bb9ccb5a076d0e443a1e986d1fd463\">Example 9. 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=\"2742\" height=\"979\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13.png\" alt=\"\" class=\"wp-image-14686\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13.png 2742w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13-768x274.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13-1536x548.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13-2048x731.png 2048w\" sizes=\"(max-width: 2742px) 100vw, 2742px\" \/><\/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=\"2742\" height=\"979\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w.png\" alt=\"\" class=\"wp-image-14687\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w.png 2742w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w-768x274.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w-1536x548.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-13w-2048x731.png 2048w\" sizes=\"(max-width: 2742px) 100vw, 2742px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-9ce7924be3408addaec1b9c47ab9d79b\">Example 10. 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=\"2746\" height=\"982\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03.png\" alt=\"\" class=\"wp-image-14688\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03.png 2746w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03-1536x549.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03-2048x732.png 2048w\" sizes=\"(max-width: 2746px) 100vw, 2746px\" \/><\/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=\"2746\" height=\"982\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w.png\" alt=\"\" class=\"wp-image-14689\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w.png 2746w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w-1536x549.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-3x3-03w-2048x732.png 2048w\" sizes=\"(max-width: 2746px) 100vw, 2746px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Above we have three examples of <strong>water reflection semi-magic<\/strong> squares of order 24 having <strong>10-digits cells entries<\/strong> with 2 numbers combinations (3, 8), (1, 3) and (0, 3). In each case, the internal blocks of order 3 are <strong>semi-magic<\/strong> squares with different <strong>semi-magic<\/strong> sums. The blocks of order 12 are <strong>semi-magic<\/strong> squares with equal <strong>semi-magic<\/strong> sums. <\/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 24<br>Blocks of Magic Squares of Order 4<\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-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-7251d1fae72eb93cf0177f882654455b\">Example 11. The Digits (1, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1914\" height=\"827\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358.png\" alt=\"\" class=\"wp-image-14692\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358.png 1914w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358-300x130.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358-768x332.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358-535x231.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-12358-1536x664.png 1536w\" sizes=\"(max-width: 1914px) 100vw, 1914px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0a05fb3759fcdb003ead3f1d4903352f\">Example 12. The Digits (0, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1928\" height=\"824\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358.png\" alt=\"\" class=\"wp-image-14694\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358.png 1928w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358-300x128.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358-1024x438.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358-768x328.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358-535x229.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-02358-1536x656.png 1536w\" sizes=\"(max-width: 1928px) 100vw, 1928px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-0f7930a4985dfaf2415c9d314f2bf1f3\">Example 13. The Digits (0, 1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1916\" height=\"827\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235.png\" alt=\"\" class=\"wp-image-14696\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235.png 1916w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235-300x129.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235-1024x442.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235-768x331.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235-535x231.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-01235-1536x663.png 1536w\" sizes=\"(max-width: 1916px) 100vw, 1916px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Thus, we have three examples of <strong>semi-magic<\/strong> squares of order 24 having <strong>4-digits cells entries<\/strong> with five numbers combinations (1, 2, 3, 5, 8), (0, 2, 3, 5, 8) and (0, 1, 2, 3, 5). The internal blocks of order 4 are magic squares with different magic sums. The blocks of order 12 are <strong>semi-magic<\/strong> squares with equal <strong>semi-magic<\/strong> sums. <strong><em>These three examples are not water reflexive as these doesn&#8217;t give semi-magic squares after applying vertical flip.<\/em><\/strong><\/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-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=\"2370\" height=\"826\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235.png\" alt=\"\" class=\"wp-image-14698\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235.png 2370w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235-300x105.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235-1024x357.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235-768x268.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235-535x186.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235-1536x535.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235-2048x714.png 2048w\" sizes=\"(max-width: 2370px) 100vw, 2370px\" \/><\/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=\"2370\" height=\"826\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w.png\" alt=\"\" class=\"wp-image-14699\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w.png 2370w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w-300x105.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w-1024x357.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w-768x268.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w-535x186.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w-1536x535.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-235w-2048x714.png 2048w\" sizes=\"(max-width: 2370px) 100vw, 2370px\" \/><\/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=\"2154\" height=\"890\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138.png\" alt=\"\" class=\"wp-image-14700\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138.png 2154w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138-1024x423.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138-768x317.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138-535x221.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138-1536x635.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138-2048x846.png 2048w\" sizes=\"(max-width: 2154px) 100vw, 2154px\" \/><\/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=\"2154\" height=\"890\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w.png\" alt=\"\" class=\"wp-image-14701\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w.png 2154w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w-1024x423.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w-768x317.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w-535x221.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w-1536x635.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-138w-2048x846.png 2048w\" sizes=\"(max-width: 2154px) 100vw, 2154px\" \/><\/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=\"2153\" height=\"892\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038.png\" alt=\"\" class=\"wp-image-14702\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038.png 2153w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038-1024x424.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038-768x318.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038-1536x636.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038-2048x848.png 2048w\" sizes=\"(max-width: 2153px) 100vw, 2153px\" \/><\/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=\"2153\" height=\"892\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w.png\" alt=\"\" class=\"wp-image-14703\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w.png 2153w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w-1024x424.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w-768x318.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w-1536x636.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-038w-2048x848.png 2048w\" sizes=\"(max-width: 2153px) 100vw, 2153px\" \/><\/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=\"2154\" height=\"893\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013.png\" alt=\"\" class=\"wp-image-14704\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013.png 2154w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013-1024x425.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013-768x318.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013-1536x637.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013-2048x849.png 2048w\" sizes=\"(max-width: 2154px) 100vw, 2154px\" \/><\/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=\"2154\" height=\"893\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w.png\" alt=\"\" class=\"wp-image-14705\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w.png 2154w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w-300x124.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w-1024x425.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w-768x318.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w-535x222.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w-1536x637.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-013w-2048x849.png 2048w\" sizes=\"(max-width: 2154px) 100vw, 2154px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Thus, we have four examples of <strong>water reflection semi-magic<\/strong> squares of order 24 having <strong>6-digits cells entries<\/strong> with 3 numbers combinations (2, 3, 5), (1, 3, 8), (0, 3, 8) and (0,1, 3). The internal blocks of order 4 are magic square with different magic sums. The blocks of order 12 are <strong>semi-magic<\/strong> squares with equal <strong>semi-magic<\/strong> sums.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-5eb87b6132f517873c5c3b9270b9cacd\">c) 10-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-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2741\" height=\"982\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1.png\" alt=\"\" class=\"wp-image-14712\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1.png 2741w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1-1024x367.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1-535x192.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1-1536x550.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38-1-2048x734.png 2048w\" sizes=\"(max-width: 2741px) 100vw, 2741px\" \/><\/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=\"2741\" height=\"982\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1.png\" alt=\"\" class=\"wp-image-14713\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1.png 2741w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1-1024x367.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1-535x192.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1-1536x550.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-38w-1-2048x734.png 2048w\" sizes=\"(max-width: 2741px) 100vw, 2741px\" \/><\/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-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2743\" height=\"981\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1.png\" alt=\"\" class=\"wp-image-14714\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1.png 2743w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1-1536x549.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13-1-2048x732.png 2048w\" sizes=\"(max-width: 2743px) 100vw, 2743px\" \/><\/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=\"2743\" height=\"981\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1.png\" alt=\"\" class=\"wp-image-14715\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1.png 2743w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1-1536x549.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-13w-1-2048x732.png 2048w\" sizes=\"(max-width: 2743px) 100vw, 2743px\" \/><\/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-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2745\" height=\"982\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1.png\" alt=\"\" class=\"wp-image-14716\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1.png 2745w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1-1536x549.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03-1-2048x733.png 2048w\" sizes=\"(max-width: 2745px) 100vw, 2745px\" \/><\/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=\"2745\" height=\"982\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1.png\" alt=\"\" class=\"wp-image-14717\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1.png 2745w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1-300x107.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1-1024x366.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1-768x275.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1-535x191.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1-1536x549.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-4x4-03w-1-2048x733.png 2048w\" sizes=\"(max-width: 2745px) 100vw, 2745px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Above we have three examples of <strong>water reflection pandiagonal<\/strong> magic squares of order 24 having <strong>10-digits cells entries<\/strong> with 2 numbers combinations (3, 8), (1, 3) and (0, 3). In each case, the internal blocks of order 4 are also <strong>pandiagonal<\/strong> magic squares with <strong>equal magic sums<\/strong>.<\/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 24: <br>Blocks 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-cc70422dbff5d611787d2a699ebc4109\">Example 21. The Digits (1, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1909\" height=\"851\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1.png\" alt=\"\" class=\"wp-image-14721\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1.png 1909w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1-300x134.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1-1024x456.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1-768x342.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1-535x238.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358-1-1536x685.png 1536w\" sizes=\"(max-width: 1909px) 100vw, 1909px\" \/><\/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=\"1909\" height=\"851\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w.png\" alt=\"\" class=\"wp-image-14722\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w.png 1909w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w-300x134.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w-1024x456.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w-768x342.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w-535x238.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-12358w-1536x685.png 1536w\" sizes=\"(max-width: 1909px) 100vw, 1909px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-b2569795ca5e95d8b8428475a1bdc4e4\">Example 22. The Digits (0, 2, 3, 5, 8)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1924\" height=\"855\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358.png\" alt=\"\" class=\"wp-image-14723\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358.png 1924w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358-300x133.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358-1024x455.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358-768x341.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358-535x238.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358-1536x683.png 1536w\" sizes=\"(max-width: 1924px) 100vw, 1924px\" \/><\/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=\"1924\" height=\"855\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w.png\" alt=\"\" class=\"wp-image-14724\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w.png 1924w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w-300x133.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w-1024x455.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w-768x341.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w-535x238.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-02358w-1536x683.png 1536w\" sizes=\"(max-width: 1924px) 100vw, 1924px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-27914a936164ce8d82d0b4d5a114b9bb\">Example 23. The Digits (0, 1, 2, 3, 5)<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1911\" height=\"854\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235.png\" alt=\"\" class=\"wp-image-14725\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235.png 1911w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235-300x134.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235-1024x458.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235-768x343.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235-535x239.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235-1536x686.png 1536w\" sizes=\"(max-width: 1911px) 100vw, 1911px\" \/><\/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=\"1911\" height=\"854\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w.png\" alt=\"\" class=\"wp-image-14726\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w.png 1911w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w-300x134.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w-1024x458.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w-768x343.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w-535x239.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-01235w-1536x686.png 1536w\" sizes=\"(max-width: 1911px) 100vw, 1911px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Thus, we have three examples of <strong>water reflection<\/strong> <strong>semi-magic<\/strong> squares of order 24 having <strong>4-digits cells entries<\/strong> with five numbers combinations (1, 2, 3, 5, 8), (0, 2, 3, 5, 8) and (0, 1, 2, 3, 5). The internal blocks of order 8 are magic squares with different magic sums. <\/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-3cf585b1fd1c6651e6f4274e5492b2ad\">Example 24. 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=\"2367\" height=\"851\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235.png\" alt=\"\" class=\"wp-image-14727\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235.png 2367w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235-300x108.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235-1024x368.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235-768x276.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235-535x192.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235-1536x552.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235-2048x736.png 2048w\" sizes=\"(max-width: 2367px) 100vw, 2367px\" \/><\/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=\"2367\" height=\"851\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w.png\" alt=\"\" class=\"wp-image-14728\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w.png 2367w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w-300x108.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w-1024x368.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w-768x276.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w-535x192.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w-1536x552.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-235w-2048x736.png 2048w\" sizes=\"(max-width: 2367px) 100vw, 2367px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-63f2f5cda5e4b009e76520ec5ad521ba\">Example 25. 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=\"2155\" height=\"883\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138.png\" alt=\"\" class=\"wp-image-14729\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138.png 2155w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138-1536x629.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138-2048x839.png 2048w\" sizes=\"(max-width: 2155px) 100vw, 2155px\" \/><\/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=\"2155\" height=\"883\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w.png\" alt=\"\" class=\"wp-image-14730\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w.png 2155w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w-1536x629.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-138w-2048x839.png 2048w\" sizes=\"(max-width: 2155px) 100vw, 2155px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-950563a4968461971f2ad0877eac0512\">Example 26. 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=\"2151\" height=\"882\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038.png\" alt=\"\" class=\"wp-image-14731\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038.png 2151w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038-1536x630.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038-2048x840.png 2048w\" sizes=\"(max-width: 2151px) 100vw, 2151px\" \/><\/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=\"2151\" height=\"882\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w.png\" alt=\"\" class=\"wp-image-14732\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w.png 2151w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w-1024x420.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w-768x315.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w-535x219.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w-1536x630.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-038w-2048x840.png 2048w\" sizes=\"(max-width: 2151px) 100vw, 2151px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-a1c80ad772510f07433547ce8d114485\">Example 27. 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=\"2154\" height=\"885\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013.png\" alt=\"\" class=\"wp-image-14733\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013.png 2154w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013-1024x421.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013-768x316.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013-535x220.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013-1536x631.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013-2048x841.png 2048w\" sizes=\"(max-width: 2154px) 100vw, 2154px\" \/><\/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=\"2154\" height=\"885\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w.png\" alt=\"\" class=\"wp-image-14734\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w.png 2154w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w-300x123.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w-1024x421.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w-768x316.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w-535x220.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w-1536x631.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-013w-2048x841.png 2048w\" sizes=\"(max-width: 2154px) 100vw, 2154px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Thus, we have four examples of <strong>water reflection semi-magic<\/strong> squares of order 24 having <strong>6-digits cells entries<\/strong> with 3 numbers combinations (2, 3, 5), (1, 3, 8), (0, 3, 8) and (0,1, 3). The internal blocks of order 8 are magic square with different magic sums. <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-luminous-vivid-orange-color has-text-color has-link-color wp-elements-5eb87b6132f517873c5c3b9270b9cacd\">c) 10-Digits Cell Entries:<\/h3>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-vivid-purple-color has-text-color has-link-color wp-elements-2e3e55c4228da1bbec1f5c5d50275f09\">Semi-Bimagic Squares<\/h2>\n\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-6f2fadfb48e4a26ec68ec99a21c3e336\">Example 28. 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=\"2906\" height=\"970\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38.png\" alt=\"\" class=\"wp-image-14735\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38.png 2906w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38-300x100.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38-1024x342.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38-768x256.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38-535x179.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38-1536x513.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38-2048x684.png 2048w\" sizes=\"(max-width: 2906px) 100vw, 2906px\" \/><\/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=\"2906\" height=\"970\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w.png\" alt=\"\" class=\"wp-image-14736\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w.png 2906w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w-300x100.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w-1024x342.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w-768x256.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w-535x179.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w-1536x513.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-38w-2048x684.png 2048w\" sizes=\"(max-width: 2906px) 100vw, 2906px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-d42651a4d0655225f00dd49cd887c602\">Example 29. 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=\"2911\" height=\"973\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13.png\" alt=\"\" class=\"wp-image-14737\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13.png 2911w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13-300x100.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13-1024x342.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13-768x257.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13-535x179.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13-1536x513.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13-2048x685.png 2048w\" sizes=\"(max-width: 2911px) 100vw, 2911px\" \/><\/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=\"2911\" height=\"973\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w.png\" alt=\"\" class=\"wp-image-14738\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w.png 2911w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w-300x100.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w-1024x342.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w-768x257.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w-535x179.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w-1536x513.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-13w-2048x685.png 2048w\" sizes=\"(max-width: 2911px) 100vw, 2911px\" \/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-ddeeae69cfa8ea67f2d0674ba0a560cb\">Example 30. 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=\"2912\" height=\"813\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03.png\" alt=\"\" class=\"wp-image-14739\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03.png 2912w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03-300x84.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03-1024x286.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03-768x214.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03-535x149.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03-1536x429.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03-2048x572.png 2048w\" sizes=\"(max-width: 2912px) 100vw, 2912px\" \/><\/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=\"2912\" height=\"813\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w.png\" alt=\"\" class=\"wp-image-14740\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w.png 2912w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w-300x84.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w-1024x286.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w-768x214.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w-535x149.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w-1536x429.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/01\/24x24-8x8-03w-2048x572.png 2048w\" sizes=\"(max-width: 2912px) 100vw, 2912px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 63%,rgb(255,105,0) 100%)\">Above we have three examples of <strong>water reflection semi-bimagic<\/strong> squares of order 24 having <strong>10-digits cells entries<\/strong> with 2 numbers combinations (3, 8), (1, 3) and (0, 3). In each case, the internal blocks of order 8 are also <strong>pandiagonal<\/strong> bimagic squares with <strong>equal magic square sums<\/strong>.<\/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 wp-block-paragraph\" 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 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><\/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","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":14670,"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-14668","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\/24x24-3x3-12358.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14668","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=14668"}],"version-history":[{"count":9,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14668\/revisions"}],"predecessor-version":[{"id":14790,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/14668\/revisions\/14790"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/14670"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14668"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14668"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14668"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}