{"id":15002,"date":"2025-03-03T16:56:38","date_gmt":"2025-03-03T19:56:38","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=15002"},"modified":"2025-03-15T14:16:02","modified_gmt":"2025-03-15T17:16:02","slug":"striped-and-semi-striped-double-digits-bordered-magic-squares-orders-7-to-50","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=15002","title":{"rendered":"Striped and Semi-Striped Double Digits Bordered Magic Squares: Orders 7 to 50"},"content":{"rendered":"\n<p>By boarded magic squares we understand that if we remove the external border still we are left with magic squares of lower orders with sequential entries. Single digits bordered magic squares are well-known. <strong>This work is for double digits not non in the literature<\/strong>. This work is already apresented by author in another work <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Inder J. Taneja, <a href=\"https:\/\/numbers-magic.com\/?p=9988\">New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108.<\/a><\/li>\n<\/ul>\n\n\n\n<p>This above link is of only of one type, i.e. <strong>general double digits bordered magic square<\/strong>.  Below are two more types are given. Both of these are known by striped magic squres. One is opposite-type and another is circular type.  <\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 7<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1467\" height=\"328\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/7x7-3.png\" alt=\"\" class=\"wp-image-15005\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/7x7-3.png 1467w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/7x7-3-300x67.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/7x7-3-1024x229.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/7x7-3-768x172.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/7x7-3-535x120.png 535w\" sizes=\"(max-width: 1467px) 100vw, 1467px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square is <strong>general double digits bordered magic square<\/strong>. The second one is <strong>semi-striped<\/strong> magic squares, as it is constructed with <strong>equal width striped magic rectangles<\/strong> except the inner block of order 3. It is magic square of order 3. The third magic square is also <strong>semi-striped magic square<\/strong> as it is constructed with four <strong>equal sum equal width magic rectangles<\/strong>. It is <strong>semi-striped<\/strong> as the inner block is magic square of order 3. Summarizing, there are three magic squares, the first one is <strong>general double digits bordered magic square<\/strong>. The other two are <strong>semi-stripled<\/strong> magic squares. The inner blocks are <strong>magic squares of order 3<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 8<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1676\" height=\"364\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3.png\" alt=\"\" class=\"wp-image-15006\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3.png 1676w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3-300x65.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3-1024x222.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3-768x167.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3-535x116.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/8x8-3-1536x334.png 1536w\" sizes=\"(max-width: 1676px) 100vw, 1676px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square i<strong>s general double digits bordered magic square<\/strong>. The second one is <strong>striped magic square<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong>. The third magic square is also <strong>striped magic square<\/strong> as it is also constructed with <strong>equal width magic rectangles<\/strong>. Summarizing the first magic square is <strong>general double digits bordered magic square<\/strong>. The last two are <strong>striped<\/strong> <strong>double digits bordered magic squares<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 9<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"1833\" height=\"398\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3.png\" alt=\"\" class=\"wp-image-15007\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3.png 1833w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3-300x65.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3-1024x222.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3-768x167.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3-535x116.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/9x9-3-1536x334.png 1536w\" sizes=\"(max-width: 1833px) 100vw, 1833px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square is <strong>general double digits bordered magic square<\/strong>. The second one is <strong>semi-striped magic squares<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong> except the inner block of order 5. It is magic square of order 5. The third magic square is also <strong>semi-striped magic square<\/strong> as it is constructed with four equal sum equal width magic rectangles. It is also <strong>semi-striped<\/strong> as the inner block is a magic square of order 5. Summarizing, we have one magic square as <strong>general double digits bordered magic square<\/strong>. The other two as <strong>semi-striped magic square<\/strong>s.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 10<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1998\" height=\"439\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3.png\" alt=\"\" class=\"wp-image-15008\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3.png 1998w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3-300x66.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3-1024x225.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3-768x169.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3-535x118.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/10x10-3-1536x337.png 1536w\" sizes=\"(max-width: 1998px) 100vw, 1998px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square i<strong>s general double digits bordered magic square<\/strong>. The second one is <strong>striped magic square<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong>. The third magic square is also <strong>striped magic square<\/strong> as it is also constructed with four equal sum equal width magic rectangles. Summarizing the first magic square is <strong>general double digits bordered magic square<\/strong>. The last two are <strong>striped<\/strong> <strong>double digits bordered magic square<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 11<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2208\" height=\"474\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3.png\" alt=\"\" class=\"wp-image-15009\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3.png 2208w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3-300x64.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3-1024x220.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3-768x165.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3-535x115.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3-1536x330.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/11x11-3-2048x440.png 2048w\" sizes=\"(max-width: 2208px) 100vw, 2208px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square is <strong>general double digits bordered magic square<\/strong>. The second one is <strong>semi-striped<\/strong> magic squares, as it is constructed with <strong>equal width striped magic rectangles<\/strong> except the inner block of order 3. It is magic square of order 3. The third magic square is also <strong>semi-striped magic square<\/strong> as it is constructed with four <strong>equal sum equal width magic rectangles<\/strong>. It is <strong>semi-striped<\/strong> as the inner block is magic square of order 3. Summarizing, there are three magic squares, the first one is <strong>general double digits bordered magic square<\/strong>. The other two are <strong>semi-striped<\/strong> magic squares. The inner blocks are <strong>magic squares of order 3<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 12<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2439\" height=\"508\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2.png\" alt=\"\" class=\"wp-image-15016\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2.png 2439w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2-300x62.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2-1024x213.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2-768x160.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2-535x111.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2-1536x320.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3-2-2048x427.png 2048w\" sizes=\"(max-width: 2439px) 100vw, 2439px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square i<strong>s general double digits bordered magic square<\/strong>. The second one is <strong>striped magic square<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong>. The third magic square is also <strong>striped magic square<\/strong> as it is also constructed with <strong>equal width magic rectangles<\/strong>. Summarizing the first magic square is <strong>general double digits bordered magic square<\/strong>. The last two are <strong>striped<\/strong> <strong>double digits bordered magic squares<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 13<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"3112\" height=\"545\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3.png\" alt=\"\" class=\"wp-image-15011\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3.png 3112w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3-300x53.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3-1024x179.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3-768x134.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3-535x94.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3-1536x269.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/13x13-3-2048x359.png 2048w\" sizes=\"(max-width: 3112px) 100vw, 3112px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square is <strong>general double digits bordered magic square<\/strong>. The second one is <strong>semi-striped magic squares<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong> except the inner block of order 5. It is magic square of order 5. The third magic square is also <strong>semi-striped magic square<\/strong> as it is constructed with four equal sum equal width magic rectangles. It is also <strong>semi-striped<\/strong> as the inner block is a magic square of order 5. Summarizing, we have one magic square as <strong>general double digits bordered magic square<\/strong>. The other two as <strong>semi-striped magic square<\/strong>s.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 14<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2238\" height=\"1193\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3.png\" alt=\"\" class=\"wp-image-15012\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3.png 2238w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3-300x160.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3-1024x546.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3-768x409.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3-535x285.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3-1536x819.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/14x14-3-2048x1092.png 2048w\" sizes=\"(max-width: 2238px) 100vw, 2238px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square i<strong>s general double digits bordered magic square<\/strong>. The second one is <strong>striped magic square<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong>. The third magic square is also <strong>striped magic square<\/strong> as it is also constructed with four equal sum equal width magic rectangles. Summarizing the first magic square is <strong>general double digits bordered magic square<\/strong>. The last two are <strong>striped<\/strong> <strong>double digits bordered magic square<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 15<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2363\" height=\"1253\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3.png\" alt=\"\" class=\"wp-image-15013\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3.png 2363w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3-535x284.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3-1536x814.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/15x15-3-2048x1086.png 2048w\" sizes=\"(max-width: 2363px) 100vw, 2363px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square is <strong>general double digits bordered magic square<\/strong>. The second one is <strong>semi-striped<\/strong> magic squares, as it is constructed with <strong>equal width striped magic rectangles<\/strong> except the inner block of order 3. It is magic square of order 3. The third magic square is also <strong>semi-striped magic square<\/strong> as it is constructed with four <strong>equal sum equal width magic rectangles<\/strong>. It is <strong>semi-striped<\/strong> as the inner block is magic square of order 3. Summarizing, there are three magic squares, the first one is <strong>general double digits bordered magic square<\/strong>. The other two are <strong>semi-striped<\/strong> magic squares. The inner blocks are <strong>magic squares of order 3<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 16<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2493\" height=\"1321\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1.png\" alt=\"\" class=\"wp-image-15017\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1.png 2493w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1-1024x543.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1-768x407.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1-1536x814.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/16x16-3-1-2048x1085.png 2048w\" sizes=\"(max-width: 2493px) 100vw, 2493px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square i<strong>s general double digits bordered magic square<\/strong>. The second one is <strong>striped magic square<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong>. The third magic square is also <strong>striped magic square<\/strong> as it is also constructed with <strong>equal width magic rectangles<\/strong>. Summarizing the first magic square is <strong>general double digits bordered magic square<\/strong>. The last two are <strong>striped<\/strong> <strong>double digits bordered magic squares<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 17<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2627\" height=\"1389\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3.png\" alt=\"\" class=\"wp-image-15018\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3.png 2627w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3-1536x812.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/17x17-3-2048x1083.png 2048w\" sizes=\"(max-width: 2627px) 100vw, 2627px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square is <strong>general double digits bordered magic square<\/strong>. The second one is <strong>semi-striped magic squares<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong> except the inner block of order 5. It is magic square of order 5. The third magic square is also <strong>semi-striped magic square<\/strong> as it is constructed with four equal sum equal width magic rectangles. It is also <strong>semi-striped<\/strong> as the inner block is a magic square of order 5. Summarizing, we have one magic square as <strong>general double digits bordered magic square<\/strong>. The other two as <strong>semi-striped magic square<\/strong>s.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Order 18<\/h3>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2770\" height=\"1464\" src=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3.png\" alt=\"\" class=\"wp-image-15019\" srcset=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3.png 2770w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3-300x159.png 300w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3-1024x541.png 1024w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3-768x406.png 768w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3-535x283.png 535w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3-1536x812.png 1536w, https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/18x18-3-2048x1082.png 2048w\" sizes=\"(max-width: 2770px) 100vw, 2770px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">The first magic square i<strong>s general double digits bordered magic square<\/strong>. The second one is <strong>striped magic square<\/strong>, as it is constructed with <strong>equal width striped magic rectangles<\/strong>. The third magic square is also <strong>striped magic square<\/strong> as it is also constructed with four equal sum equal width magic rectangles. Summarizing the first magic square is <strong>general double digits bordered magic square<\/strong>. The last two are <strong>striped<\/strong> <strong>double digits bordered magic square<\/strong>.<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p class=\"has-background\" style=\"background:linear-gradient(135deg,rgb(238,238,238) 0%,rgb(106,235,213) 22%,rgb(125,210,27) 50%,rgb(169,184,195) 100%)\">We observe that in case of even order magic squares, the last two magic squares are stripled magic squares. In case of of odd order magic squares the last two types of magic squares are semi-striped magic squares, since there are magic squares of orders 3 or 5 as inner blocks of magic squres. <br><br>Moreover these are divided in four groups of orders as follows: <br>1. 7, 11, 15,&#8230;<br>2. 8, 12, 16,&#8230;<br>3. 9, 13, 17,&#8230;<br>4. 10, 14, 18,&#8230;<br><br>The total work is up to order 50. More examples of similar kind are given below in excel files.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">Excel file for Download<\/h3>\n\n\n\n<div class=\"wp-block-file aligncenter\"><a id=\"wp-block-file--media-2a52a1b8-622a-4cd1-a5ad-2139b38cf91c\" href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/Doble-Digits-MS-7to50.xlsx\">Doble-Digits-MS-7to50<\/a><a href=\"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/Doble-Digits-MS-7to50.xlsx\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-2a52a1b8-622a-4cd1-a5ad-2139b38cf91c\">Download<\/a><\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgba(53,6,207,0.26) 47%,rgb(255,105,0) 100%)\">References<\/h3>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(255,206,236) 0%,rgb(159,225,142) 57%,rgb(152,150,240) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, <em>Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24<\/em>,&nbsp;<strong>Zenodo<\/strong>, April, 26, 2023, pp. 1-43,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.7866956\">https:\/\/doi.org\/10.5281\/zenodo.7866956<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Two Digits Bordered Magic Squares of Orders 28 and 32<\/em>,&nbsp;<strong>Zenodo<\/strong>, April, 26, 2023, pp. 1-36,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.7866981\">https:\/\/doi.org\/10.5281\/zenodo.7866981<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Two Digits Bordered Magic Squares of Orders 10, 14, 18 and 22<\/em>,&nbsp;<strong>Zenodo<\/strong>, April, 30, 2023, pp. 1-43,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.7880931\">https:\/\/doi.org\/10.5281\/zenodo.7880931<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Two Digits Bordered Magic Squares of Orders 26 and 30<\/em>,&nbsp;<strong>Zenodo<\/strong>, April, 30, 2023, pp. 1-45,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.7880937\">https:\/\/doi.org\/10.5281\/zenodo.7880937<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Two Digits Bordered Magic Squares of Orders 36 and 40<\/em>,&nbsp;<strong>Zenodo<\/strong>, May, 04, 2023, pp. 1-41,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.7896709\">https:\/\/doi.org\/10.5281\/zenodo.7896709<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>Two Digits Bordered Magic Squares of Orders 34 and 38<\/em>,&nbsp;<strong>Zenodo<\/strong>, May 10, 2023, pp. 1-45,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.7922571\">https:\/\/doi.org\/10.5281\/zenodo.7922571<\/a>.<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, <em>New Concepts in Magic Squares: Double Digits Bordered Magic Squares of Orders 7 to 108<\/em>,&nbsp;<strong>Zenodo<\/strong>, August 09, 2023, pp. 1-30,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.8230214\">https:\/\/doi.org\/10.5281\/zenodo.8230214<\/a>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center has-background\" style=\"background:linear-gradient(135deg,rgb(6,147,227) 0%,rgb(255,255,255) 61%,rgb(155,81,224) 100%)\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-purple-color\">Striped Magic Squares<\/mark><\/h3>\n\n\n\n<ul style=\"background:linear-gradient(135deg,rgb(252,185,0) 0%,rgb(255,255,255) 45%,rgb(255,105,0) 100%)\" class=\"wp-block-list has-background\">\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of Even Orders 6, 8, 10, 12 and 14, <strong>Zenodo<\/strong>, November 10, 2023, pp. 1-34, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.10107355\">https:\/\/doi.org\/10.5281\/zenodo.10107355<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link:&nbsp;<a href=\"https:\/\/numbers-magic.com\/?p=10587\">Striped Magic Squares of Orders 4, 6, 8, 10, 12 and 14<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of 12 &#8211; Revised, <strong>Zenodo<\/strong>, September 07, 2024, pp. 1-30, <a href=\"https:\/\/zenodo.org\/records\/13725031\">https:\/\/zenodo.org\/records\/13725031<\/a>. \n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=12447\">Striped Magic Squares of Order 12 \u2013 Revised<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, 5600+ Striped Magic Squares of Order 16,&nbsp;<strong>Zenodo<\/strong>, February 05, 2025, pp. 1-52,&nbsp;<a href=\"https:\/\/doi.org\/10.5281\/zenodo.14807639\">https:\/\/doi.org\/10.5281\/zenodo.14807639<\/a>\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=11781\">5600+ Striped Magic Squares of Order 16 (new site)<\/a><\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of 18, <strong>Zenodo<\/strong>, June 13, 2024, pp. 1-34, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.11629567\">https:\/\/doi.org\/10.5281\/zenodo.11629567<\/a>. \n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=11911\">Striped Magic Squares of Order 18<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Striped Magic Squares of 20, <strong>Zenodo<\/strong>, August 24, 2024, pp. 1-37. \n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=12326\">Striped Magic Squares of Order 20<\/a>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inder J. Taneja<\/strong>, Striped and Semi-Striped Double Digits Bordered Magic Squares: Orders 7 to 50, <strong>Zenodo<\/strong>, March 13, 2025, pp. 1-30, <a href=\"https:\/\/doi.org\/10.5281\/zenodo.15021581\">https:\/\/doi.org\/10.5281\/zenodo.15021581<\/a>.\n<ul class=\"wp-block-list\">\n<li>Site Link: <a href=\"https:\/\/numbers-magic.com\/?p=15002\">Striped and Semi-Striped Double Digits Bordered Magic Squares: Orders 7 to 50 (new site)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>By boarded magic squares we understand that if we remove the external border still we are left with magic squares of lower orders with sequential entries. Single digits bordered magic squares are well-known. This work is for double digits not non in the literature. This work is already apresented by author in another work This [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":15003,"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-15002","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-magic-squares"],"jetpack_featured_media_url":"https:\/\/numbers-magic.com\/wp-content\/uploads\/2025\/03\/12x12-3.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/15002","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=15002"}],"version-history":[{"count":7,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/15002\/revisions"}],"predecessor-version":[{"id":15042,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/15002\/revisions\/15042"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/15003"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15002"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15002"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15002"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}