{"id":18266,"date":"2026-03-20T23:15:37","date_gmt":"2026-03-21T02:15:37","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=18266"},"modified":"2026-04-12T23:22:21","modified_gmt":"2026-04-13T02:22:21","slug":"beauty-of-magic-squares-3888-multiple-order-bordered-magic-squares-of-order-108-2","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=18266","title":{"rendered":"Beauty of Magic Squares: 3240 Multiple Order Bordered Magic Squares of Order 108 – Part 2"},"content":{"rendered":"\n

During past years author worked with block-wise<\/strong> bordered<\/strong> magic squares multiples of even and odd number blocks. This means, multiples of 3, 4, 5, 6, etc. These works can be accessed at the following links. <\/p>\n\n\n\n

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  1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 3<\/a><\/li>\n\n\n\n
  2. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4<\/a>.<\/li>\n\n\n\n
  3. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 5<\/a>.<\/li>\n\n\n\n
  4. Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6<\/a>.<\/li>\n\n\n\n
  5. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 7<\/a>.<\/li>\n\n\n\n
  6. Block-Wise Bordered Magic Squares Multiples of 8<\/a>.<\/li>\n\n\n\n
  7. Block-Wise Bordered Magic Squares Multiples of 9<\/a>.<\/li>\n\n\n\n
  8. Block-Wise Bordered Magic Squares Multiples of 10<\/a>.<\/li>\n\n\n\n
  9. Block-Wise Bordered Magic Squares Multiples of 11<\/a>.<\/li>\n\n\n\n
  10. Block-Wise Bordered Magic Squares Multiples of 12<\/a>.<\/li>\n\n\n\n
  11. Block-Wise Bordered Magic Squares Multiples of 13.<\/a><\/li>\n\n\n\n
  12. Block-Wise Bordered Magic Squares Multiples of 14<\/a>.<\/li>\n\n\n\n
  13. Block-Wise Bordered Magic Squares Multiples of 15.<\/a><\/li>\n\n\n\n
  14. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16.<\/a><\/li>\n\n\n\n
  15. Bordered Magic Squares Multiples of 17.<\/a><\/li>\n\n\n\n
  16. Block-Wise Bordered Magic Squares Multiples of 18.<\/a><\/li>\n\n\n\n
  17. Bordered Magic Squares Multiples of 19.<\/a><\/li>\n\n\n\n
  18. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 20.<\/a><\/li>\n<\/ol>\n\n\n\n

    The advantage in studying block-wise bordered<\/strong> magic squares is that when we remove external borders, still we are left with magic squares with sequential entries. The bordered<\/strong> magic squares also have the same property. The difference is that instead of numbers here we have blocks of magic squares.<\/p>\n\n\n\n

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

    In previous work there are also 3240 multiple order bordered magic squares of order 108. It is done by considering double border of magic squares of order 9 ovedr magic square of order 72. In this work instead of double border of order 9, we have considered a border of magic squares of order 18 obrt the magic squares of order 72. See the figure above where the upper border is of magic square of order 18. <\/strong><\/em><\/p>\n\n\n\n

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

    This work bring magic squares, based on multiple order magic squares in the same magic squares. This means same magic square contains borders of order 3, 4, 5, etc. It can be accessed at the following link:

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

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

    This work brings brodered magic squares<\/strong> in such a way that in the beginning there is magic square of order 12 with different sums magic squares of order 3. The further borders are magic squares of orders 4, 5, 6, 7, and 8 resulting in multiple order bordered magic squares of order 72. Considering again a border of magic squares of order 18, we get multiple order bordered magic squares of order 108<\/strong>. The even order borders are with magic squares, such as of orders 4, 6, 8 and 18 are with equal sums magic squares<\/strong>. The odd order borders of orders 5 and 7 are with different sums magic squares. <\/strong><\/p>\n\n\n\n

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

    See below the details of above multiple order bordered magic squares of order 108:<\/strong><\/p>\n\n\n\n

    <\/p>\n\n\n

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

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

    See below the details of above multiple order bordered magic squares.<\/p>\n\n\n\n