{"id":12654,"date":"2024-09-29T23:32:27","date_gmt":"2024-09-30T02:32:27","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=12654"},"modified":"2024-11-06T12:48:20","modified_gmt":"2024-11-06T15:48:20","slug":"universal-and-upside-down-magic-squares-of-orders-7-to-10","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=12654","title":{"rendered":"Universal and Upside-Down Magic Squares of Orders 7 to 10"},"content":{"rendered":"\n

There are many ways of representing magic squares with palindromic type entries. Also, we can write magic squares in the composite forms based on pair of Latin squares. This paper works with magic squares of order 3 to 6. By upside-down<\/strong>, we understand than by making 180o<\/sup> it remains same. When the magic square is of both type, i.e., upside-down<\/strong> and mirror looking<\/strong>, we call it an universal<\/strong> magic square. By mirror looking we understand that putting in front of mirror, still we see the image as a magic square. In case of mirror looking, writing as digitais fonts<\/strong>, 2 becoms 5 and 5 as 2. In case of upside-down, 6 becomes 9 and 9 as 6.

The magic squares of order 9, we have considered in two different situations. One as bimagic<\/strong> and another as pandiagonal<\/strong>. In case of order 8, we considered the situations with pandiagonal<\/strong> and bimagic<\/strong>. For complete work for the orders 3 to 25, the readers can access the links given in the references at the end. This work can be accessed online at the following link:<\/p>\n\n\n\n