{"id":11224,"date":"2023-12-25T04:37:29","date_gmt":"2023-12-25T07:37:29","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=11224"},"modified":"2024-04-29T07:20:10","modified_gmt":"2024-04-29T10:20:10","slug":"bimagic-squares-of-orders-100-110-and-121-blocks-of-orders-10-and-11","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=11224","title":{"rendered":"Bimagic Squares of Orders 100, 110 and 121: Blocks of Orders 10 and 11"},"content":{"rendered":"\n<p>Before proceeding further below are the basic formulas to check the sums of <strong>magic<\/strong> and <strong>bimagic<\/strong> squares<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Magic Sum<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"176\" height=\"88\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/S-2.png\" alt=\"\" class=\"wp-image-11140\"\/><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Bimagic Sum<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"304\" height=\"93\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/Sb-2.png\" alt=\"\" class=\"wp-image-11141\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/Sb-2.png 304w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/Sb-2-300x92.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/figure>\n<\/div>\n\n\n<p>where <strong><em>n<\/em><\/strong> is the order the magic square.<\/p>\n\n\n\n<p class=\"has-text-align-justify has-electric-grass-gradient-background has-background\">Below are <strong>bimagic squares<\/strong> of orders 100, 110 and 121. Order 100 is with blcoks of order 10. Orders 110 and 121 are with blocks of orders 11. <br><br>This work is <strong>Aale de Winkel<\/strong>&#8216;s contribution and is obtained as private communication. <br>Aale&#8217;s web-site and e-mail: <br><a href=\"https:\/\/www.magichypercubes.com\/Encyclopedia\/\">Magic Encyclopedia magic square, magic cube, magic tesseract, magic hypercube<\/a> and e-mail: &lt;aaledewinkel@magichypercubes.com&gt;. <br><br>Also this work is based on two bimagic squares of orders 10 and 11 constructed by <strong>Fredrik Jansson<\/strong> and <strong>Bogdan Golunski<\/strong> in 2004 and 2005 respectively.  For details see the links: <br>1. <a href=\"http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm<\/a><br>2. <a href=\"http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm\">http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm<\/a><br><br>Still there is one more bimagic square of order 121 constructed by author, where blocks of order 11 are <strong>pandiagonal magic squares of equal sums<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Square of Orders 10: <strong>Fredrik Jansson<\/strong> (2004)<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">Below is a bimagic squares of order&#8217;s 10 due to <strong>Fredrik Jansson<\/strong> in 2004. For details see the linik: <a href=\"http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1118\" height=\"545\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/10x10-bi-1.png\" alt=\"\" class=\"wp-image-11230\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/10x10-bi-1.png 1118w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/10x10-bi-1-300x146.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/10x10-bi-1-1024x499.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/10x10-bi-1-768x374.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/10x10-bi-1-535x261.png 535w\" sizes=\"(max-width: 1118px) 100vw, 1118px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Squares of Orders 10: <strong>Bogdan Golunski<\/strong> (2005)<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">Below is a <strong>bimagic squares<\/strong> of order 10 by <strong>Bogdan Golunski<\/strong>, Germany, Juli 2005. For details see the link: <a href=\"http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm\">http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm<\/a>. <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1312\" height=\"582\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/04\/10x10-bi-2.png\" alt=\"\" class=\"wp-image-11737\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/04\/10x10-bi-2.png 1312w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/04\/10x10-bi-2-300x133.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/04\/10x10-bi-2-1024x454.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/04\/10x10-bi-2-768x341.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2024\/04\/10x10-bi-2-535x237.png 535w\" sizes=\"(max-width: 1312px) 100vw, 1312px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<p class=\"has-text-align-justify\">There are two more <strong>bimagic squares<\/strong> of order 10 by <strong>Bogdan Golunski<\/strong>, Germany, Juli 2005 at the same link, i.e., <a href=\"http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm\">http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Square of Order 11: <strong>Fredrik Jansson<\/strong> (2004)<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">Below is a bimagic square of order 11 due to <strong>Fredrik Jansson<\/strong> in 2004. For details see the linik: <a href=\"http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm\" target=\"_blank\" rel=\"noreferrer noopener\">http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm<\/a>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1194\" height=\"577\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/11x11-bi.png\" alt=\"\" class=\"wp-image-11231\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/11x11-bi.png 1194w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/11x11-bi-300x145.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/11x11-bi-1024x495.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/11x11-bi-768x371.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/11x11-bi-535x259.png 535w\" sizes=\"(max-width: 1194px) 100vw, 1194px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Square of Order 100: Blocks of Order 10<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">Below is an excel sheet of bimagic square of order 100 constructed by <strong>Aale de Winkel<\/strong> based on bimagic squares of order 10 constructed by <strong>Fredrik Jansson<\/strong>. Blocks of order 11 are bimagic squares with different magic and bimagic sums. In this case, we have<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>S<sub>100&#215;100<\/sub>:=500050; Sb<sub>121&#215;121<\/sub>:= 3333833350<\/strong>.  <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Excel sheel of bimagic square of order 100<\/strong><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-a5aa555b-144c-4769-a266-4a8c6e25cee5\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/100x100-bi.xlsx\">100&#215;100-bi<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/100x100-bi.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a5aa555b-144c-4769-a266-4a8c6e25cee5\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Square of Order 110: Blocks of Order 11<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">Below is an excel sheet of bimagic square of order 110 constructed by <strong>Aale de Winkel<\/strong> based on bimagic squares of order 11 constructed by <strong>Fredrik Jansson<\/strong>. Blocks of order 11 are bimagic squares with different magic and bimagic sums. In this case, we have<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>S<sub>110&#215;110<\/sub>:=665555; Sb<sub>110&#215;110<\/sub>:= 5369032185<\/strong>.   <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Excel sheel of bimagic square of order 110<\/strong><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-a5aa555b-144c-4769-a266-4a8c6e25cee5\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/110x110-bi.xlsx\">110&#215;110-bi<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/110x110-bi.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a5aa555b-144c-4769-a266-4a8c6e25cee5\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Square of Order 121: Blocks of Order 11<\/h3>\n\n\n\n<p class=\"has-text-align-justify\">Below is an excel sheet of bimagic square of order 121 constructed by <strong>Aale de Winkel<\/strong> based on bimagic squares of order 11 constructed by <strong>Fredrik Jansson<\/strong>. Blocks of order 11 are bimagic squares with different magic and bimagic sums. In this case, we have<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>S<sub>121&#215;121<\/sub>:=885841; Sb<sub>121&#215;121<\/sub>:= 8646694001<\/strong>. <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Excel sheel of bimagic square of order 121<\/strong><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-a5aa555b-144c-4769-a266-4a8c6e25cee5\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/121x121-bi-1.xlsx\">121&#215;121-bi-1<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/121x121-bi-1.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-a5aa555b-144c-4769-a266-4a8c6e25cee5\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgba(69,125,61,0.35) 59%,rgb(155,81,224) 100%)\">Bimagic Square of Order 121: Blocks of Order 11<\/h3>\n\n\n\n<p>In this case, we have<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>S<sub>121&#215;121<\/sub>:=885841; Sb<sub>121&#215;121<\/sub>:= 8646694001<\/strong>, <\/p>\n\n\n\n<p class=\"has-text-align-justify\">Blocks of order 11 are <strong>pandiagonal<\/strong> and of <strong>equal sums<\/strong>, <strong>S<sub>11&#215;11<\/sub> :=80531<\/strong>. The magic squares of order 121 is also <strong>pandiagonal<\/strong>.  See below an excel sheet for the order 121.<\/p>\n\n\n\n<p><strong>Excel sheel of bimagic square of order 121<\/strong><\/p>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-66201883-062e-49fd-a7ae-37e8265eab79\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/121x121-bi.xlsx\">121&#215;121-bi<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2023\/12\/121x121-bi.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-66201883-062e-49fd-a7ae-37e8265eab79\">Download<\/a><\/div>\n\n\n\n<p class=\"has-text-align-justify\">The different between two bimagic squares of order 121 is that one is based on different magic and bimagic sums of order 11. The second is based on pandiagonal equal sums magic squares of order 11.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-very-light-gray-to-cyan-bluish-gray-gradient-background has-background\">References<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=11031\" target=\"_blank\" rel=\"noreferrer noopener\">Block-Wise Construction of Bimagic Squares: Multiples of Orders 8 and 16<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong><a href=\"https:\/\/numbers-magic.com\/?p=11090\" target=\"_blank\" rel=\"noreferrer noopener\">&nbsp;Block-Wise Construction of Bimagic Squares Multiples of 25: Orders 25, 125 and 625<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=11129\" target=\"_blank\" rel=\"noreferrer noopener\">Block-Wise Construction of Bimagic Squares Multiples of 9: Orders 9, 81 and 729<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=11142\" target=\"_blank\" rel=\"noreferrer noopener\">Block-Wise Construction of Bimagic Squares of Orders 121 and 1331<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=11168\">Bimagic Squares of Or<\/a><a href=\"https:\/\/numbers-magic.com\/?p=11168\" target=\"_blank\" rel=\"noreferrer noopener\">d<\/a><a href=\"https:\/\/numbers-magic.com\/?p=11168\">ers 256, 512 and 1024: Blocks of Order 16.<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=11186\" target=\"_blank\" rel=\"noreferrer noopener\">Bimagic Squares of Orders 200 and 1000: Blocks of Order 8<\/a><\/li>\n\n\n\n<li><strong>Inder J. Taneja,<\/strong>&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=11198\" target=\"_blank\" rel=\"noreferrer noopener\">Bimagic Squares of Orders 400, 800, 1600 and 2000: Blocks of Order 16.<\/a><\/li>\n\n\n\n<li><strong>Aale de Winkel<\/strong>, <a href=\"https:\/\/www.magichypercubes.com\/Encyclopedia\/\">Magic Encyclopedia magic square, magic cube, magic tesseract, magic hypercube<\/a>.<\/li>\n\n\n\n<li><strong>Christian Boyer<\/strong>, <a href=\"http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm\" target=\"_blank\" rel=\"noreferrer noopener\">MULTIMAGIE.COM &#8211; Bimagic squares, 10th and 11th-Order. <\/a>(Fredrik Jansson).<a href=\"http:\/\/www.multimagie.com\/English\/Bimagic10&amp;11.htm\" target=\"_blank\" rel=\"noreferrer noopener\"> <\/a><\/li>\n\n\n\n<li><strong>Bogdan Golunski<\/strong>, <a href=\"http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm\">http:\/\/www.number-galaxy.eu\/ge_html\/10x10_bi_magic_Bsp01.htm<\/a>.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Before proceeding further below are the basic formulas to check the sums of magic and bimagic squares where n is the order the magic square. Below are bimagic squares of orders 100, 110 and 121. Order 100 is with blcoks of order 10. Orders 110 and 121 are with blocks of orders 11. This work [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":11229,"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-11224","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\/2023\/12\/10x10-bi.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/11224","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=11224"}],"version-history":[{"count":5,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/11224\/revisions"}],"predecessor-version":[{"id":11741,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/11224\/revisions\/11741"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/11229"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}