{"id":316,"date":"2021-12-25T18:15:07","date_gmt":"2021-12-25T21:15:07","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=316"},"modified":"2023-07-22T10:35:04","modified_gmt":"2023-07-22T13:35:04","slug":"block-wise-bordered-magic-squares-multiples-of-magic-and-bordered-magic-squares-of-order-6","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=316","title":{"rendered":"Block-Wise Bordered Magic Squares Multiples of 6 – Revised"},"content":{"rendered":"\n

Revised on July 22, 2023<\/strong><\/em><\/p>\n\n\n\n

<\/p>\n\n\n\n

Recently, the author revised and improved the block-wise<\/strong> bordered<\/strong>\u00a0magic squares multiples of even number blocks<\/strong>. This means, multiples of 4, 6, 8, etc. The work is up to order 20. These works can be accessed at the following links.

1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4<\/a>.
2.\u00a0Block-Wise Bordered Magic Squares Multiples of Order 6 – Revised<\/a>.
3.\u00a0Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 8 \u2013 Revised<\/a>
4.\u00a0Block-Wise Bordered Magic Squares Multiples of 10 \u2013 Revised.<\/a>
5.\u00a0Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 12 \u2013 Revised.<\/a>
6.\u00a0Block-Wise Bordered Magic Squares Multiples of 14 \u2013 Revised.<\/a>
7.\u00a0Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16<\/a>.
8.\u00a0Block-Wise Bordered Magic Squares Multiples of 18<\/a>.
9. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 20.<\/a>

Author also worked with odd number blocks. The work is for multiples of order 3, 5, 7, 9, 11 and 13. See the links below:
1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 3<\/a>.
2. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 5 – Revised.<\/a>
3. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 7 – Revised.<\/a>
4. Block-Wise Bordered Magic Squares Multiples of 9 \u2013 Revised<\/a>.
5. Block-Wise Bordered Magic Squares Multiples of Order 11- Revised<\/a>.
6. Block-Wise Bordered Magic Squares Multiples of 13<\/a>.
7. Block-Wise Bordered Magic Squares Multiples of 15<\/a>.
8. Block-Wise Bordered Magic Squares Multiples of 17<\/a>.
9. Block-Wise Bordered Magic Squares Multiples of 19<\/a>.

The advantage in studying\u00a0block-wise bordered<\/strong>\u00a0magic squares is that when we remove external borders, still we left with magic squares with sequential entries. <\/p>\n\n\n\n

<\/p>\n\n\n\n

Recently, author also studied the double digit<\/strong>s borders resulting in interesting magic squares. These studies can be accessed at the following link:
1. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24<\/a>.
2. Two Digits Bordered Magic Squares of Orders 28 and 32<\/a>.
3. Two digits Bordered Magic Squares of Order 36.<\/a>
4. Two digits Bordered Magic Squares of Order 40.<\/a>

The work is for the order of type 4k+2, where k>1, i.e., for the orders 10, 14, 18, 22, 26, 28, 30 and 32 can be access at the following links:
1. Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22<\/a>.
2. Two digits Bordered Magic Squares o<\/a>f Orders 26 and 30<\/a>.
3. Two Digits Bordered Magic Squares of Orders 28 and 32.<\/a>

Some studies towards cornered magic squares<\/strong> are also made. See the following links:
1. Cornered Magic Squares of Orders 5 to 10<\/a>.
2. Cornered Magic Squares of Orders 11 to 13<\/a>.
3. Cornered Magic Squares of Orders 14 to 24<\/a>.<\/p>\n\n\n\n

Below are examples of bordered magic squares multiples of order 6. These examples are only for the magic squares of orders 6, 12, 18, 24, 30 and 36. In the end there are excel files<\/strong> of whole the up to order 120 multiples of 6.<\/p>\n\n\n\n

Magic Squares of Order 6<\/h4>\n\n\n\n

Below are 3 magic square of order 6. We have used these magic squares to bring bordered magic squares up to order 140 as multiples of 6.<\/p>\n\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Magic Squares of Order 12 Multiples of 6<\/h4>\n\n\n\n

Below are 3 magic square of order 12. <\/p>\n\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Magic Squares of Order 18 Multiples of 6<\/h4>\n\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Magic Squares of Order 24 Multiples of 6<\/h4>\n\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Magic Squares of Order 30 Multiples of 6<\/h4>\n\n\n\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n\n\n\n

Magic Squares of Order 36 Multiples of 6<\/h4>\n\n\n\n

<\/p>\n\n\n

\n
\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n

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\"\"<\/figure>\n<\/div>\n\n\n

<\/p>\n\n\n\n

Excel file of Whole Work for Download<\/h4>\n\n\n\n
6×6-120-6-online<\/a>Download<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"

Revised on July 22, 2023 Recently, the author revised and improved the block-wise bordered\u00a0magic squares multiples of even number blocks. This means, multiples of 4, 6, 8, etc. The work is up to order 20. These works can be accessed at the following links. 1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4.2.\u00a0Block-Wise Bordered […]<\/p>\n","protected":false},"author":1,"featured_media":9897,"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-316","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\/07\/36x36-6x6-1.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/316","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=316"}],"version-history":[{"count":5,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/316\/revisions"}],"predecessor-version":[{"id":9901,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/posts\/316\/revisions\/9901"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=\/wp\/v2\/media\/9897"}],"wp:attachment":[{"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=316"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=316"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/numbers-magic.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}