{"id":13242,"date":"2024-10-22T23:05:09","date_gmt":"2024-10-23T02:05:09","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=13242"},"modified":"2024-11-05T14:56:23","modified_gmt":"2024-11-05T17:56:23","slug":"universal-and-upside-down-magic-squares-of-order-21","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=13242","title":{"rendered":"Universal and Upside-Down Magic Squares of Order 21"},"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 and bimagic squares of order 16. 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 as universal<\/strong> magic square. By mirror looking<\/strong>, we understand that putting in front of mirror, still we see the image as a magic square. In case of mirror looking<\/strong>, writing as digitais fonts<\/strong>, 2 becoms 5 and 5 as 2. In case of upside-down<\/strong>, 6 becomes 9 and 9 as 6. <\/p>\n\n\n\n

This work brings examples in different categories of entries. These are divided in three parts. In each part we worked with blocks of magic squares of orders 7 and 3. The order 7 magic squares are always pandigonal<\/strong> and the order 3 are always semi-magic<\/strong> squares.<\/p>\n\n\n\n

    \n
  1. 4-Digits Cell Entries<\/strong>\n