{"id":9655,"date":"2023-07-13T08:55:51","date_gmt":"2023-07-13T11:55:51","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9655"},"modified":"2024-05-24T02:14:47","modified_gmt":"2024-05-24T05:14:47","slug":"block-wise-bordered-magic-squares-multiples-of-18","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9655","title":{"rendered":"Block-Wise Bordered Magic Squares Multiples of 18"},"content":{"rendered":"\n

During past years author worked with block-wise<\/strong>, bordered<\/strong> and block-bordered<\/strong> magic squares. This work make connection between block-wise<\/strong> and bordered<\/strong> magic squares. We started with block-wise bordered<\/strong> magic squares of orders 144 and 126. Based on these two big magic squares, the inner order magic squares multiples of 18 are studied. By inner orders we understand that magic squares of orders 108, 90, 72, etc. The construction of the block-wise bordered<\/strong> magic squares multiples of 18 is based on equal sum blocks<\/strong> of magic squares of order 18. We have taken 37 different types of magic squares of order 18<\/strong>. The advantage in studying block-wise bordered<\/strong> magic squares is that when we remove external border, still we are left with magic squares with sequential entries. It is the same property of bordered<\/strong> magic squares with single digits. The difference is that instead of numbers here we have blocks of equal sum magic squares of order 18. For multiples of even orders 4 to 16 see the links below:
1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4<\/a>.
2. Block-Wise Bordered Magic Squares Multiples of Magic Squares of Order 6<\/a>.
3. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 8 \u2013 Revised<\/a>
4. Block-Wise Bordered Magic Squares Multiples of 10 \u2013 Revised. <\/a>
5. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 12 \u2013 Revised.<\/a>
6. Block-Wise Bordered Magic Squares Multiples of 14 \u2013 Revised<\/a>.
7. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16<\/a>.<\/p>\n\n\n\n

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    This work is up to order 144. Examples below are only up to order 54. The higher order examples can be seen in Excel files<\/strong> attached at the end. This work also can be seen as online:
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      Below are few examples up to order 54 studied in this work. The work is up to order 144.
      The complete excel files with 37 examples in each case are given at the end for download. <\/strong><\/p>\n\n\n\n

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

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      Below are three examples of magic squares of order 18. It includes bordered, double digits, cornered magic squares, etc. The complete list of 37 magic squares of order 18 is given as pdf file<\/strong> for download.<\/p>\n\n\n\n

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      Pdf file of 37 Magic Squares of Order 18<\/h3>\n\n\n\n

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