{"id":920,"date":"2022-03-02T19:51:54","date_gmt":"2022-03-02T22:51:54","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=920"},"modified":"2022-03-02T19:51:58","modified_gmt":"2022-03-02T22:51:58","slug":"creative-magic-squares-singele-digit-representations","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=920","title":{"rendered":"Creative Magic Squares: Singele Digit Representations"},"content":{"rendered":"\n<p class=\"has-text-align-justify\">This work brings traditional magic squares of orders 3 to 10 in terms of&nbsp;<strong>single digit<\/strong>. In this case, the magic squares are written separately for each digit, i.e., for the digits 1 to 9. This has been done for all the orders 3 to 10. In case of orders 8 and 9 there are two possibilities, i.e, one as normal magic squares and another as&nbsp;<strong>bimagic<\/strong>&nbsp;squares. In case of magic square of order 10, two different ways are written. One as a general magic square without any block. Another as&nbsp;<strong>block-bordered<\/strong>&nbsp;magic squares with inner magic square of order 8. Again the inner magic square can be written in two ways, i.e., one just&nbsp;<strong>pandiagonal<\/strong>&nbsp;and another&nbsp;<strong>pandiagonal<\/strong>&nbsp;and&nbsp;<strong>bimagic<\/strong>. In case of&nbsp;<strong>single digit<\/strong>&nbsp;the representations of numbers are not uniform. Writing in terms of single letter&nbsp;<em><strong>\u201ca\u201d<\/strong><\/em>, we can get uniformity in representations of numbers. It is done in&nbsp;<a href=\"https:\/\/inderjtaneja.com\/2021\/07\/28\/creative-magic-squares-single-letter-representations\/\" target=\"_blank\" rel=\"noreferrer noopener\">another work<\/a>.<\/p>\n\n\n\n<p>The whole work can be downloaded at the folloiwng link:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Inder J. Taneja, Creative Magic Squares: Single Digit Representations, <strong>Zenodo<\/strong>, March 25, 2021, pp. 1-165,\u00a0<a href=\"http:\/\/doi.org\/10.5281\/zenodo.4637121\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/doi.org\/10.5281\/zenodo.4637121<\/a><\/li><\/ul>\n\n\n\n<p>Below are Examples of Magic Squares of Orders 3 to 10.<\/p>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 3<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-3x3-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-3x3-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8655\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-3x3-d1.png?w=960&amp;h=\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-3x3-d2.png?w=4500&amp;h=\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 4<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-4x4-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-4x4-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8659\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"1002\" data-id=\"923\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1-1024x1002.png\" alt=\"\" class=\"wp-image-923\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1-1024x1002.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1-600x587.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1-300x293.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1-768x751.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1-535x523.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d1.png 1475w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"981\" height=\"1024\" data-id=\"922\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-981x1024.png\" alt=\"\" class=\"wp-image-922\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-981x1024.png 981w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-600x626.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-287x300.png 287w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-768x802.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-535x559.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2-1471x1536.png 1471w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-4x4-d2.png 1473w\" sizes=\"(max-width: 981px) 100vw, 981px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 5<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-5x5-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-5x5-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8662\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-2 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"983\" height=\"1024\" data-id=\"925\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-983x1024.png\" alt=\"\" class=\"wp-image-925\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-983x1024.png 983w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-600x625.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-288x300.png 288w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-768x800.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-535x558.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1-1474x1536.png 1474w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d1.png 1637w\" sizes=\"(max-width: 983px) 100vw, 983px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"989\" height=\"1024\" data-id=\"924\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-989x1024.png\" alt=\"\" class=\"wp-image-924\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-989x1024.png 989w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-600x621.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-290x300.png 290w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-768x795.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-535x554.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2-1484x1536.png 1484w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-5x5-d2.png 1639w\" sizes=\"(max-width: 989px) 100vw, 989px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 6<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-6x6-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-6x6-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8665\"\/><\/a><\/figure><\/div>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-3 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1020\" data-id=\"927\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-1024x1020.png\" alt=\"\" class=\"wp-image-927\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-1024x1020.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-300x300.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-100x100.png 100w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-600x597.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-150x150.png 150w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-768x765.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-535x533.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-256x256.png 256w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1-1536x1529.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d1.png 1637w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1011\" data-id=\"926\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-1024x1011.png\" alt=\"\" class=\"wp-image-926\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-1024x1011.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-100x100.png 100w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-600x592.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-300x296.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-768x758.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-535x528.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2-1536x1516.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-6x6-d2.png 1632w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 7<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-7x7-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-7x7-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8669\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-4 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1024\" data-id=\"928\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-1000x1024.png\" alt=\"\" class=\"wp-image-928\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-1000x1024.png 1000w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-600x615.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-293x300.png 293w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-768x787.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-535x548.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1-1499x1536.png 1499w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d1.png 1638w\" sizes=\"(max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"980\" height=\"1024\" data-id=\"929\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-980x1024.png\" alt=\"\" class=\"wp-image-929\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-980x1024.png 980w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-600x627.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-287x300.png 287w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-768x803.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-535x559.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2-1469x1536.png 1469w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-7x7-d2.png 1635w\" sizes=\"(max-width: 980px) 100vw, 980px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 8: Pandiagonal<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-8x8-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-8x8-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8672\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-5 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"888\" data-id=\"932\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-1024x888.png\" alt=\"\" class=\"wp-image-932\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-1024x888.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-600x521.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-300x260.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-768x666.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-535x464.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1-1536x1333.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d1.png 1631w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"839\" data-id=\"930\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-1024x839.png\" alt=\"\" class=\"wp-image-930\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-1024x839.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-600x492.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-300x246.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-768x630.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-535x439.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2-1536x1259.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d2.png 1637w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1007\" height=\"1024\" data-id=\"931\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-1007x1024.png\" alt=\"\" class=\"wp-image-931\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-1007x1024.png 1007w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-600x610.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-295x300.png 295w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-768x781.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-535x544.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3-1510x1536.png 1510w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-d3.png 1633w\" sizes=\"(max-width: 1007px) 100vw, 1007px\" \/><\/figure>\n<\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Magic Square of Order 8: Pandiagonal and Bimagic<\/h2>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-8x8-ex2.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-8x8-ex2.png?w=1024\" alt=\"\" class=\"wp-image-8677\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-6 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"843\" data-id=\"933\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-1024x843.png\" alt=\"\" class=\"wp-image-933\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-1024x843.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-600x494.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-300x247.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-768x632.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-535x440.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1-1536x1264.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db1.png 1638w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"941\" height=\"1024\" data-id=\"935\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2-941x1024.png\" alt=\"\" class=\"wp-image-935\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2-941x1024.png 941w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2-600x653.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2-276x300.png 276w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2-768x836.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2-535x582.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db2.png 1209w\" sizes=\"(max-width: 941px) 100vw, 941px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"901\" height=\"1024\" data-id=\"934\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3-901x1024.png\" alt=\"\" class=\"wp-image-934\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3-901x1024.png 901w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3-600x682.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3-264x300.png 264w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3-768x873.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3-535x608.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-8x8-db3.png 1256w\" sizes=\"(max-width: 901px) 100vw, 901px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 9: Pandiagonal<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-9x9-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-9x9-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8684\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-7 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"748\" data-id=\"936\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1-1024x748.png\" alt=\"\" class=\"wp-image-936\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1-1024x748.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1-600x438.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1-300x219.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1-768x561.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1-535x391.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d1.png 1330w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"766\" data-id=\"937\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2-1024x766.png\" alt=\"\" class=\"wp-image-937\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2-1024x766.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2-600x449.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2-300x224.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2-768x575.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2-535x400.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d2.png 1326w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"880\" data-id=\"938\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3-1024x880.png\" alt=\"\" class=\"wp-image-938\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3-1024x880.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3-600x516.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3-300x258.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3-768x660.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3-535x460.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-d3.png 1329w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 9: Bimagic<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-9x9-ex2.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-9x9-ex2.png?w=1024\" alt=\"\" class=\"wp-image-8688\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-8 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"781\" data-id=\"941\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1-1024x781.png\" alt=\"\" class=\"wp-image-941\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1-1024x781.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1-600x458.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1-300x229.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1-768x586.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1-535x408.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db1.png 1325w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"760\" data-id=\"940\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2-1024x760.png\" alt=\"\" class=\"wp-image-940\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2-1024x760.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2-600x445.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2-300x223.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2-768x570.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2-535x397.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db2.png 1328w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"970\" data-id=\"939\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3-1024x970.png\" alt=\"\" class=\"wp-image-939\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3-1024x970.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3-600x568.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3-300x284.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3-768x727.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3-535x507.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-9x9-db3.png 1324w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Magic Square of Order 10<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-10x10-ex1.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-10x10-ex1.png?w=1024\" alt=\"\" class=\"wp-image-8693\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-9 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"808\" data-id=\"944\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1-1024x808.png\" alt=\"\" class=\"wp-image-944\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1-1024x808.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1-600x473.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1-300x237.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1-768x606.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1-535x422.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d1.png 1328w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"793\" data-id=\"942\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2-1024x793.png\" alt=\"\" class=\"wp-image-942\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2-1024x793.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2-600x465.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2-300x232.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2-768x595.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2-535x414.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d2.png 1376w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"979\" data-id=\"943\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3-1024x979.png\" alt=\"\" class=\"wp-image-943\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3-1024x979.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3-600x574.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3-300x287.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3-768x734.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3-535x512.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-d3.png 1322w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"alignwide wp-block-heading\">Bordered Magic Square of Order 10<\/h3>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-10x10-ex2.png?w=1024\"><img decoding=\"async\" src=\"https:\/\/inderjtaneja.files.wordpress.com\/2021\/07\/sd-10x10-ex2.png?w=1024\" alt=\"\" class=\"wp-image-8697\"\/><\/a><\/figure>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-1 is-cropped wp-block-gallery-10 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"781\" data-id=\"947\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1-1024x781.png\" alt=\"\" class=\"wp-image-947\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1-1024x781.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1-600x458.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1-300x229.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1-768x586.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1-535x408.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db1.png 1331w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"774\" data-id=\"945\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2-1024x774.png\" alt=\"\" class=\"wp-image-945\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2-1024x774.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2-600x454.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2-300x227.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2-768x580.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2-535x404.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db2.png 1327w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"780\" data-id=\"946\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3-1024x780.png\" alt=\"\" class=\"wp-image-946\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3-1024x780.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3-600x457.png 600w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3-300x229.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3-768x585.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3-535x408.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2022\/03\/sd-10x10-db3.png 1333w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p>Author\u2019s work on single digits for natural numbers can be seen at<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Inder J. Taneja, <a href=\"https:\/\/inderjtaneja.com\/2017\/08\/21\/single-digit-representation-of-natural-numbers\/\" target=\"_blank\" rel=\"noreferrer noopener\"><a href=\"https:\/\/inderjtaneja.com\/2017\/08\/21\/single-digit-representation-of-natural-numbers\/\">Single Digit Representation of Natural Numbers 1 to\u00a010000<\/a><\/a><\/li><li>Inder J. Taneja, Single Digits <a href=\"https:\/\/inderjtaneja.com\/2019\/01\/01\/single-letter-representations-of-numbers-from-1-to-20000\/\" target=\"_blank\" rel=\"noreferrer noopener\">Representations of Natural Numbers from 1 to 20000<\/a>, <\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This work brings traditional magic squares of orders 3 to 10 in terms of&nbsp;single digit. In this case, the magic squares are written separately for each digit, i.e., for the digits 1 to 9. This has been done for all the orders 3 to 10. In case of orders 8 and 9 there are two [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":948,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3],"tags":[],"class_list":["post-920","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\/2022\/03\/sd-3x3-d1.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/920","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=920"}],"version-history":[{"count":2,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/920\/revisions"}],"predecessor-version":[{"id":949,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/920\/revisions\/949"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/948"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=920"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=920"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=920"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}