{"id":9424,"date":"2023-06-17T17:07:30","date_gmt":"2023-06-17T20:07:30","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9424"},"modified":"2023-06-17T18:06:45","modified_gmt":"2023-06-17T21:06:45","slug":"different-digits-magic-squares-and-magic-sums-number-patterns","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9424","title":{"rendered":"Different Digits Magic Squares and Magic Sums Number Patterns"},"content":{"rendered":"\n

Magic squares are generally constructed using sequential or consecutive numbers such as 1, 2, …, n^2. Here in this work, we shall write magic squares using nonconsecutive different digits numbers<\/strong>. This work, we have done for the magic squares of orders 5, 7, 8, 9 and 10. As commonly, the entries are not in a sequential way, but each cell is with different digits. Also, all the entries in a magic square are with different numbers. The aim is to write in such a way that in each case as the number of digits in cells increases, we get number patterns with magic sums<\/strong>, i.e., these sums are in symmetrical way. In case of orders 8 and 9, the magic squares considered are pan diagonal<\/strong>. In case of order 9, there are examples of bimagic squares<\/strong>, while in case of order 8 there are examples where, we have bimagic<\/strong> only in rows sums. In both these cases, there are interesting number patterns<\/strong> with bimagic sums<\/strong>. See below the table of number patterns<\/strong> for the different orders and digits that we worked in this paper:<\/p>\n\n\n\n

\"DD-Table\"<\/figure>\n\n\n\n

From the table, we observe that still, we don’t have magic squares with 3 digits in each cell for the magic squares of orders 7 and 10.<\/strong> Magic squares of orders 4 and 6 are not dealt here, as in case of order 4, we have only two possibilities, i.e., for the digits 3 and 4, and for the magic squares of order 6, we have results for the digits 5 and 6, but for the case of 4 digits, it becomes semi-magic square. For details see author’s previous work<\/a>. The bimagic sums patterns<\/strong> are for the orders 8 and 9. In case of order 8, it is only in rows.

Below are links of author’s works for download:
1. Multi-Digits Magic Squares<\/a> (old work)
2. Different Digits Magic Squares and Number Patterns<\/a> (new work)

Below are examples written separately in each case:<\/p>\n\n\n\n

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