{"id":12875,"date":"2024-10-10T18:34:41","date_gmt":"2024-10-10T21:34:41","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=12875"},"modified":"2024-10-17T14:10:06","modified_gmt":"2024-10-17T17:10:06","slug":"rubik-style-universal-and-upside-down-cubes-using-magic-squares","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=12875","title":{"rendered":"Universal and Upside-down Magic Cubes"},"content":{"rendered":"\n<p>This work bring <strong>magic cubes<\/strong> with six sides as magic squares of orders 3, 4, 5, 7 to 8. Most of the magic squres are with different magic sums. These examples brings only <strong>universal<\/strong> and or <strong>upside-down<\/strong> magic cubes. By<strong> universal<\/strong> we understand that when the magic square is <strong>180<sup>o<\/sup> rotatable<\/strong> and are <strong>mirror looking<\/strong>, while in case of <strong>upside-down<\/strong> the magic squares are only 180<sup>o<\/sup> rotatable. <\/p>\n\n\n\n<p>The readers can also access the following links to download the whole work<\/p>\n\n\n\n<ul class=\"wp-block-list has-blush-light-purple-gradient-background has-background\">\n<li><strong>Inder J. Taneja, <\/strong>Magic Cubes Based on Magic Squares, <strong>Zenodo<\/strong>, October 17, 2024, pp. 1-63, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13924915\">https:\/\/doi.org\/10.5281\/zenodo.13924915<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site link: <a href=\"https:\/\/numbers-magic.com\/?p=12775\">Magic Cubes Based on Magic Squares<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja, <\/strong>Universal and Upside-Down Magic Cubes, <strong>Zenodo<\/strong>, October 17, 2024, pp. 1-38, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.13947425\">https:\/\/doi.org\/10.5281\/zenodo.13947425<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=12875\">Universal and Upside-down Magic Cubes<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-background has-link-color wp-elements-d4fcbe3e84020f5d5532d77fe4f79146\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 60%,rgb(113,206,126) 100%)\">Universal and Upside-down Magic Cubes Order 3<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 1.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Univesal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>semi-magic<\/strong> squares of order 3<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img fetchpriority=\"high\" decoding=\"async\" width=\"812\" height=\"363\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-1.png\" alt=\"\" class=\"wp-image-13106\" style=\"width:751px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-1.png 812w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-1-300x134.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-1-768x343.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-1-535x239.png 535w\" sizes=\"(max-width: 812px) 100vw, 812px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 3-digits, 2, 5 and 8. All the blocks of order 3&#215;3 are semi-magic with equal semi-magic sum, i.e.,  <\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>3&#215;3<\/sub>(1)=S<sub>3&#215;3<\/sub>(2)=S<sub>3&#215;3<\/sub>(3)=S<sub>3&#215;3<\/sub>(4)=S<sub>3&#215;3<\/sub>(5)=S<sub>3&#215;3<\/sub>(6):=16665. <\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"585\" height=\"519\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-1.png\" alt=\"\" class=\"wp-image-13063\" style=\"width:351px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-1.png 585w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-1-300x266.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-1-535x475.png 535w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"590\" height=\"513\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-1.png\" alt=\"\" class=\"wp-image-13064\" style=\"width:348px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-1.png 590w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-1-300x261.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-1-535x465.png 535w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is readable in any position, i.e., <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 2.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Univesal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>semi-magic<\/strong> squares of order 3<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"788\" height=\"309\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-4-1.png\" alt=\"\" class=\"wp-image-13123\" style=\"width:763px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-4-1.png 788w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-4-1-300x118.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-4-1-768x301.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-4-1-535x210.png 535w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 3-digits, 0, 2 and 5. All the blocks of order 3&#215;3 are <strong>semi-magic<\/strong> with equal s<strong>emi-magic<\/strong> sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>3&#215;3<\/sub>(1)=S<sub>3&#215;3<\/sub>(2)=S<sub>3&#215;3<\/sub>(3)=S<sub>3&#215;3<\/sub>(4)=S<sub>3&#215;3<\/sub>(5)=S<sub>3&#215;3<\/sub>(6):=7777<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"541\" height=\"402\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-4.png\" alt=\"\" class=\"wp-image-13073\" style=\"width:395px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-4.png 541w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-4-300x223.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-4-535x398.png 535w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"540\" height=\"392\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-4.png\" alt=\"\" class=\"wp-image-13074\" style=\"width:382px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-4.png 540w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-4-300x218.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-4-535x388.png 535w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is readable in any position, i.e., <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong>.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 3.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>semi-magic<\/strong> squares of order 3<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"364\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-2.png\" alt=\"\" class=\"wp-image-13107\" style=\"width:777px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-2.png 819w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-2-300x133.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-2-768x341.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-2-535x238.png 535w\" sizes=\"(max-width: 819px) 100vw, 819px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 3-digits, 1, 6 and 9. All the blocks of order 3&#215;3 are semi-magic with equal semi-magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>3&#215;3<\/sub>(1)=S<sub>3&#215;3<\/sub>(2)=S<sub>3&#215;3<\/sub>(3)=S<sub>3&#215;3<\/sub>(4)=S<sub>3&#215;3<\/sub>(5)=S<sub>3&#215;3<\/sub>(6):=17776. <\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"613\" height=\"524\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-3.png\" alt=\"\" class=\"wp-image-13071\" style=\"width:361px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-3.png 613w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-3-300x256.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-3-535x457.png 535w\" sizes=\"(max-width: 613px) 100vw, 613px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"610\" height=\"510\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-3.png\" alt=\"\" class=\"wp-image-13072\" style=\"width:362px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-3.png 610w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-3-300x251.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-3-535x447.png 535w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is <strong>upside-down<\/strong>, i.e, 180 degrees rotation, still we can read each magic square.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 4.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>semi-magic<\/strong> squares of order 3<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"814\" height=\"365\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-3.png\" alt=\"\" class=\"wp-image-13125\" style=\"width:817px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-3.png 814w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-3-300x135.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-3-768x344.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T3x3-3-535x240.png 535w\" sizes=\"(max-width: 814px) 100vw, 814px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 3-digits, 6, 8 and 9. All the blocks of order 3&#215;3 are semi-magic with equal semi-magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>3&#215;3<\/sub>(1)=S<sub>3&#215;3<\/sub>(2)=S<sub>3&#215;3<\/sub>(3)=S<sub>3&#215;3<\/sub>(4)=S<sub>3&#215;3<\/sub>(5)=S<sub>3&#215;3<\/sub>(6):=25553. <\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"526\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-2.png\" alt=\"\" class=\"wp-image-13068\" style=\"width:371px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-2.png 611w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-2-300x258.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA3x3-2-535x461.png 535w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"616\" height=\"516\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-2.png\" alt=\"\" class=\"wp-image-13069\" style=\"width:366px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-2.png 616w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-2-300x251.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB3x3-2-535x448.png 535w\" sizes=\"(max-width: 616px) 100vw, 616px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is <strong>upside-down<\/strong>, i.e, 180 degrees rotation, still we can read each magic square.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-background has-link-color wp-elements-bdc5532095d16267bd5b68e5fa3f4d45\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 60%,rgb(113,206,126) 100%)\">Magic Cubes with Magic Squares of Order 4<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 1.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>magic <\/strong>squares of order 4:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1206\" height=\"480\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-1.png\" alt=\"\" class=\"wp-image-13127\" style=\"width:1010px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-1.png 1206w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-1-300x119.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-1-1024x408.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-1-768x306.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-1-535x213.png 535w\" sizes=\"(max-width: 1206px) 100vw, 1206px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 4-digits, 1, 6, 8  and 9. All the blocks of order 4&#215;4 are magic squares with equal magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>4&#215;4<\/sub>(1)=S<sub>4&#215;4<\/sub>(2)=S<sub>4&#215;4<\/sub>(3)=S<sub>4&#215;4<\/sub>(4)=S<sub>4&#215;4<\/sub>(5)=S<sub>4&#215;4<\/sub>(6):=26664. <\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"791\" height=\"681\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-1.png\" alt=\"\" class=\"wp-image-13067\" style=\"width:533px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-1.png 791w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-1-300x258.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-1-768x661.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-1-535x461.png 535w\" sizes=\"(max-width: 791px) 100vw, 791px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"786\" height=\"665\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-1.png\" alt=\"\" class=\"wp-image-13070\" style=\"width:532px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-1.png 786w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-1-300x254.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-1-768x650.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-1-535x453.png 535w\" sizes=\"(max-width: 786px) 100vw, 786px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is readable <strong>upside-down<\/strong> position.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 2.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Universal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>magic <\/strong>squares of order 4:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1208\" height=\"480\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-2.png\" alt=\"\" class=\"wp-image-13128\" style=\"width:1046px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-2.png 1208w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-2-300x119.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-2-1024x407.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-2-768x305.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-2-535x213.png 535w\" sizes=\"(max-width: 1208px) 100vw, 1208px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 4-digits, 1, 2, 5 and 8. All the blocks of order 4&#215;4 are magic squares with equal magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>4&#215;4<\/sub>(1)=S<sub>4&#215;4<\/sub>(2)=S<sub>4&#215;4<\/sub>(3)=S<sub>4&#215;4<\/sub>(4)=S<sub>4&#215;4<\/sub>(5)=S<sub>4&#215;4<\/sub>(6):=17776. <\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"790\" height=\"682\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-2.png\" alt=\"\" class=\"wp-image-13077\" style=\"width:546px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-2.png 790w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-2-300x259.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-2-768x663.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-2-535x462.png 535w\" sizes=\"(max-width: 790px) 100vw, 790px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"786\" height=\"667\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-2.png\" alt=\"\" class=\"wp-image-13079\" style=\"width:540px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-2.png 786w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-2-300x255.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-2-768x652.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-2-535x454.png 535w\" sizes=\"(max-width: 786px) 100vw, 786px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is universal, i.e., it is readable as <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong> position.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 3.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Universal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>magic <\/strong>squares of order 4:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1047\" height=\"425\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-3a.png\" alt=\"\" class=\"wp-image-13112\" style=\"width:1019px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-3a.png 1047w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-3a-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-3a-1024x416.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-3a-768x312.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T4x4-3a-535x217.png 535w\" sizes=\"(max-width: 1047px) 100vw, 1047px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 4-digits, 0, 2, 5 and 8. All the blocks of order 4&#215;4 are magic squares with equal magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>4&#215;4<\/sub>(1)=S<sub>4&#215;4<\/sub>(2)=S<sub>4&#215;4<\/sub>(3)=S<sub>4&#215;4<\/sub>(4)=S<sub>4&#215;4<\/sub>(5)=S<sub>4&#215;4<\/sub>(6):=16665. <\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<br><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"730\" height=\"592\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-3.png\" alt=\"\" class=\"wp-image-13080\" style=\"width:494px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-3.png 730w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-3-300x243.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA4x4-3-535x434.png 535w\" sizes=\"(max-width: 730px) 100vw, 730px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"723\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-3.png\" alt=\"\" class=\"wp-image-13081\" style=\"width:499px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-3.png 723w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-3-300x239.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB4x4-3-535x427.png 535w\" sizes=\"(max-width: 723px) 100vw, 723px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is universal, i.e., it is readable as <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong> position.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-background has-link-color wp-elements-4648f0f68f76cfe36a90a52aec72f319\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 60%,rgb(113,206,126) 100%)\">Magic Cubes with Magic Squares of Order 5<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 1.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-side Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>pandiagonal <\/strong>magic squares of order 5<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1558\" height=\"598\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1.png\" alt=\"\" class=\"wp-image-13113\" style=\"width:1058px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1.png 1558w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1-300x115.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1-1024x393.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1-768x295.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1-535x205.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-1-1536x590.png 1536w\" sizes=\"(max-width: 1558px) 100vw, 1558px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 4-digits, 1, 6, 8 and 9. All the blocks of order 5&#215;5 are <strong>pandiagonal<\/strong> magic squares with different magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>5&#215;5<\/sub>(1):=34352, S<sub>5&#215;5<\/sub>(2):=35653, S<sub>5&#215;5<\/sub>(3):=35540, S<sub>5&#215;5<\/sub>(4):=35640, S<sub>5&#215;5<\/sub>(5):=35552 and S<sub>5&#215;5<\/sub>(6):=34353<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"828\" height=\"581\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-1.png\" alt=\"\" class=\"wp-image-13084\" style=\"width:644px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-1.png 828w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-1-300x211.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-1-768x539.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-1-535x375.png 535w\" sizes=\"(max-width: 828px) 100vw, 828px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"823\" height=\"576\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-1.png\" alt=\"\" class=\"wp-image-13085\" style=\"width:643px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-1.png 823w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-1-300x210.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-1-768x538.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-1-535x374.png 535w\" sizes=\"(max-width: 823px) 100vw, 823px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is readable <strong>upside-down<\/strong> position.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 2.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Universal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>pandiagonal <\/strong>magic squares of order 5<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1305\" height=\"523\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-2.png\" alt=\"\" class=\"wp-image-13114\" style=\"width:1068px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-2.png 1305w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-2-300x120.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-2-1024x410.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-2-768x308.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-2-535x214.png 535w\" sizes=\"(max-width: 1305px) 100vw, 1305px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 4-digits, 0, 2, 5 and 8. All the blocks of order 5&#215;5 are pandiagonal magic squares with different magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>5&#215;5<\/sub>(1):=15953, S<sub>5&#215;5<\/sub>(2):=25250, S<sub>5&#215;5<\/sub>(3):=25457, S<sub>5&#215;5<\/sub>(4):=25157, S<sub>5&#215;5<\/sub>(5):=25553 and S<sub>5&#215;5<\/sub>(6):=25553.<\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1077\" height=\"673\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-3.png\" alt=\"\" class=\"wp-image-13089\" style=\"width:660px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-3.png 1077w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-3-300x187.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-3-1024x640.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-3-768x480.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-3-535x334.png 535w\" sizes=\"(max-width: 1077px) 100vw, 1077px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1077\" height=\"679\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-3.png\" alt=\"\" class=\"wp-image-13090\" style=\"width:644px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-3.png 1077w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-3-300x189.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-3-1024x646.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-3-768x484.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-3-535x337.png 535w\" sizes=\"(max-width: 1077px) 100vw, 1077px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p>Above magic cube is <strong>universal,<\/strong> i.e., it is readable as <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong> position.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 3.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Universal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>pandiagonal <\/strong>magic squares of order 5<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1559\" height=\"594\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3.png\" alt=\"\" class=\"wp-image-13115\" style=\"width:1046px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3.png 1559w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3-300x114.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3-1024x390.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3-768x293.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3-535x204.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T5x5-3-1536x585.png 1536w\" sizes=\"(max-width: 1559px) 100vw, 1559px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 4-digits, 1, 2, 5 and 8. All the blocks of order 5&#215;5 are pandiagonal magic squares with different magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>5&#215;5<\/sub>(1):=17064, S<sub>5&#215;5<\/sub>(2):=26361, S<sub>5&#215;5<\/sub>(3):=26568, S<sub>5&#215;5<\/sub>(4):=26268, S<sub>5&#215;5<\/sub>(5):=26664 and S<sub>5&#215;5<\/sub>(6):=17061.<\/mark><\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"924\" height=\"576\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-2.png\" alt=\"\" class=\"wp-image-13086\" style=\"width:660px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-2.png 924w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-2-300x187.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-2-768x479.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA5x5-2-535x334.png 535w\" sizes=\"(max-width: 924px) 100vw, 924px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"919\" height=\"579\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-2.png\" alt=\"\" class=\"wp-image-13087\" style=\"width:644px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-2.png 919w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-2-300x189.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-2-768x484.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB5x5-2-535x337.png 535w\" sizes=\"(max-width: 919px) 100vw, 919px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is <strong>universal<\/strong>, i.e., it is readable as <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong> position.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-background has-link-color wp-elements-f516ef99f34327c408208f795d5ca972\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 60%,rgb(113,206,126) 100%)\">Magic Cubes with Magic Squares of Order 7<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 1.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Universal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>pandiagonal <\/strong>magic squares of order 7<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1978\" height=\"725\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1.png\" alt=\"\" class=\"wp-image-13116\" style=\"width:1111px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1.png 1978w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1-300x110.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1-1024x375.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1-768x281.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1-535x196.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-1-1536x563.png 1536w\" sizes=\"(max-width: 1978px) 100vw, 1978px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 5-digits, 0, 1, 2, 5 and 8. All the blocks of order 7&#215;7 are <strong>pandiagonal<\/strong> magic squares with different magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>7&#215;7<\/sub>(1):=27472, S<sub>7&#215;7<\/sub>(2):=27449, S<sub>7&#215;7<\/sub>(3):=27449, S<sub>7&#215;7<\/sub>(4):=27471, S<sub>7&#215;7<\/sub>(5):=25171 and S<sub>7&#215;7<\/sub>(6):=27371<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n\n<p>Above magic cube is <strong>universal<\/strong>, i.e., it is readable as <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong> position.<\/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=\"680\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-1-1024x680.png\" alt=\"\" class=\"wp-image-13092\" style=\"width:662px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-1-1024x680.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-1-300x199.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-1-768x510.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-1-535x355.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-1.png 1275w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"685\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-1-1024x685.png\" alt=\"\" class=\"wp-image-13094\" style=\"width:664px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-1-1024x685.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-1-300x201.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-1-768x513.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-1-535x358.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-1.png 1267w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 2.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>pandiagonal <\/strong>magic squares of order 7<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"2344\" height=\"939\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2.png\" alt=\"\" class=\"wp-image-13117\" style=\"width:1119px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2.png 2344w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2-300x120.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2-1024x410.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2-768x308.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2-535x214.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2-1536x615.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-2-2048x820.png 2048w\" sizes=\"(max-width: 2344px) 100vw, 2344px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 5-digits, 2, 5, 6, 8 and 9. All the blocks of order 7&#215;7 are <strong>pandiagonal<\/strong> magic squares with different magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>7&#215;7<\/sub>(1):=47470, S<sub>7&#215;7<\/sub>(2):=47463, S<sub>7&#215;7<\/sub>(3):=47463, S<sub>7&#215;7<\/sub>(4):=47475, S<sub>7&#215;7<\/sub>(5):=46775 and S<sub>7&#215;7<\/sub>(6):=47975<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n\n<p><\/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=\"739\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-3-1024x739.png\" alt=\"\" class=\"wp-image-13097\" style=\"width:670px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-3-1024x739.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-3-300x216.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-3-768x554.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-3-535x386.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-3.png 1173w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"797\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-3-1024x797.png\" alt=\"\" class=\"wp-image-13098\" style=\"width:670px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-3-1024x797.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-3-300x233.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-3-768x598.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-3-535x416.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-3.png 1082w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Above <strong>magic cube is<\/strong> readable as <strong>upside-down.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 3.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six <strong>pandiagonal <\/strong>magic squares of order 7<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1787\" height=\"728\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3.png\" alt=\"\" class=\"wp-image-13118\" style=\"width:1103px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3.png 1787w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3-300x122.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3-1024x417.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3-768x313.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3-535x218.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T7x7-3-1536x626.png 1536w\" sizes=\"(max-width: 1787px) 100vw, 1787px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 5-digits, 0, 1, 6, 8 and 9. All the blocks of order 7&#215;7 are <strong>pandiagonal<\/strong> magic squares with different magic sum, i.e.,<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>7&#215;7<\/sub>(1):=36360, S<sub>7&#215;7<\/sub>(2):=36417, S<sub>7&#215;7<\/sub>(3):=42060, S<sub>7&#215;7<\/sub>(4):=36367, S<sub>7&#215;7<\/sub>(5):=42067 and S<sub>7&#215;7<\/sub>(6):=37067<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/p>\n\n\n\n<p><\/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=\"748\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-2-1024x748.png\" alt=\"\" class=\"wp-image-13095\" style=\"width:669px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-2-1024x748.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-2-300x219.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-2-768x561.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-2-535x391.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA7x7-2.png 1152w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"747\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-2-1024x747.png\" alt=\"\" class=\"wp-image-13096\" style=\"width:672px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-2-1024x747.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-2-300x219.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-2-768x560.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-2-535x390.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB7x7-2.png 1150w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Above <strong>magic cube is<\/strong> readable as <strong>upside-down.<\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-luminous-vivid-orange-color has-text-color has-background has-link-color wp-elements-d431e5d4519b4a89c0f43995bfae065b\" style=\"background:linear-gradient(135deg,rgb(202,248,128) 0%,rgb(255,255,255) 60%,rgb(113,206,126) 100%)\">Magic Cubes with Magic Squares of Order 8<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 1.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six magic squares of order 8<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1850\" height=\"824\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1.png\" alt=\"\" class=\"wp-image-13119\" style=\"width:1154px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1.png 1850w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1-300x134.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1-1024x456.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1-768x342.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1-535x238.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-1-1536x684.png 1536w\" sizes=\"(max-width: 1850px) 100vw, 1850px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 5-digits, 0, 1, 6, 8 and 9. The First four magic squares are of equal magic sums, and the last two are also of equal magic sums. See below;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>8&#215;8<\/sub>(1):=44238, S<sub>8&#215;8<\/sub>(2):=44238, S<sub>8&#215;8<\/sub>(3):=44238, S<sub>8&#215;8<\/sub>(4):=44238, S<sub>8&#215;8<\/sub>(5):=44244 and S<sub>8&#215;8<\/sub>(6):=44244<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/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=\"674\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-1-1024x674.png\" alt=\"\" class=\"wp-image-13099\" style=\"width:644px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-1-1024x674.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-1-300x198.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-1-768x506.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-1-535x352.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-1.png 1300w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"674\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-1-1024x674.png\" alt=\"\" class=\"wp-image-13100\" style=\"width:648px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-1-1024x674.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-1-300x198.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-1-768x506.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-1-535x352.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-1.png 1300w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Above <strong>magic cube is<\/strong> readable as <strong>upside-down.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 2.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Upside-down Magic Cube<\/mark><\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six magic squares of order 8<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1959\" height=\"994\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2.png\" alt=\"\" class=\"wp-image-13120\" style=\"width:1152px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2.png 1959w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2-300x152.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2-1024x520.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2-768x390.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2-535x271.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-2-1536x779.png 1536w\" sizes=\"(max-width: 1959px) 100vw, 1959px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 5-digits, 2, 5, 6, 8 and 9. The First four magic squares are of equal magic sums, and the last two are also of equal magic sums. See below;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>8&#215;8<\/sub>(1):=55146, S<sub>8&#215;8<\/sub>(2):=55146, S<sub>8&#215;8<\/sub>(3):=55146, S<sub>8&#215;8<\/sub>(4):=55146, S<sub>8&#215;8<\/sub>(5):=55136 and S<sub>8&#215;8<\/sub>(6):=55136<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/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=\"580\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-2-1024x580.png\" alt=\"\" class=\"wp-image-13102\" style=\"width:698px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-2-1024x580.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-2-300x170.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-2-768x435.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-2-535x303.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-2.png 1436w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"586\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-2-1024x586.png\" alt=\"\" class=\"wp-image-13101\" style=\"width:698px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-2-1024x586.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-2-300x172.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-2-768x439.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-2-535x306.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-2.png 1432w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Above <strong>magic cube is<\/strong> readable as <strong>upside-down.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Example 3.<\/mark> <mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Universal Magic Cube<\/mark><\/h3>\n\n\n\n<p>Let&#8217;s consider the following six magic squares of order 8<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1875\" height=\"729\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3.png\" alt=\"\" class=\"wp-image-13121\" style=\"width:1154px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3.png 1875w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3-300x117.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3-1024x398.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3-768x299.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3-535x208.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/T8x8-3-1536x597.png 1536w\" sizes=\"(max-width: 1875px) 100vw, 1875px\" \/><\/figure>\n<\/div>\n\n\n<p>The above six magic squares are constucted using only 5-digits, 0, 1, 6, 8 and 9. The First four magic squares are of equal magic sums, and the last two are also of equal magic sums. See below;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">S<sub>8&#215;8<\/sub>(1):=32046, S<sub>8&#215;8<\/sub>(2):=24846, S<sub>8&#215;8<\/sub>(3):=24918, S<sub>8&#215;8<\/sub>(4):=32118, S<sub>8&#215;8<\/sub>(5):=32118 and S<sub>8&#215;8<\/sub>(6):=32094<\/mark>.<\/p>\n\n\n\n<p>Magic cube is composed with six magic squares representing front and back.  First three magic squares represent the front part and the last three represent the back part. See below:<\/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=\"525\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3-1024x525.png\" alt=\"\" class=\"wp-image-13103\" style=\"width:646px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3-1024x525.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3-300x154.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3-768x393.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3-535x274.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3-1536x787.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TA8x8-3.png 1581w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"560\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3-1024x560.png\" alt=\"\" class=\"wp-image-13104\" style=\"width:650px;height:auto\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3-1024x560.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3-300x164.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3-768x420.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3-535x293.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3-1536x840.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/10\/TB8x8-3.png 1580w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Above magic cube is <strong>universal<\/strong>, i.e., it is readable as <strong>upside-down<\/strong> and\/or <strong>mirror looking<\/strong> position.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This work bring magic cubes with six sides as magic squares of orders 3, 4, 5, 7 to 8. Most of the magic squres are with different magic sums. These examples brings only universal and or upside-down magic cubes. By universal we understand that when the magic square is 180o rotatable and are mirror looking, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":13106,"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-12875","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\/2024\/10\/T3x3-1.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/12875","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=12875"}],"version-history":[{"count":29,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/12875\/revisions"}],"predecessor-version":[{"id":13172,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/12875\/revisions\/13172"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/13106"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12875"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12875"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}