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2025
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| Online Access: | https://doi.org/10.5281/zenodo.14649320 |
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| author | Inder J. Taneja |
| author_facet | Inder J. Taneja |
| contents | <p>There are many ways of representing magic squares with palindromic type entries or composite forms based on pair of Latin squares. Based on palindromic and composite magic squares we have written <strong>upside-down</strong> and/or <strong>mirror looking</strong> magic squares. By <strong>upside-down</strong>, we understand that making 180 degrees rotation still we have a magic square. Applying the <strong>upside-down</strong> property, the numbers 0, 1, 2, 5, 6, 8 and 9 remains the same, where 6 becomes 9 and 9 as 6. In this case, the numbers are written in <strong>digital/special fonts</strong>. The <strong>mirror looking</strong> property is same as <strong>horizontal flip</strong>. In this case, the numbers 0, 1, 2, 5 and 8 remains the same, where 2 becomes 5 and 5 as 2. There is one more property, known by <strong>vertical flip</strong>. For simplicity, let's call it as <strong>water reflection</strong>. In this case, the numbers 0, 1, 2, 3, 5 and 8 remains the same, where 2 becomes 5 and 5 as 2. Thus the numbers 0, 1, 2 5 and 8 are available in all the three properties. The numbers those satisfy all the three properties, we call them as<strong> universal</strong>. The same is with magic squares, i.e., the magic squares containing the numbers 0, 1, 2, 5 and 8 are known by <strong>universal</strong> magic squares. Finally, in case of <strong>upside-down</strong>, the number 6 becomes 9 and 9 as 6, and in case of <strong>water reflection</strong>, the number 3 remains the same. In this paper we worked with magic squares of orders 11 to 13, satisfying one or all the above three properties. For more details see the reference list. For more details following online link of authors web-site (<a href="https://numbers-magic.com/?p=12610">3to6</a>, <a href="https://numbers-magic.com/?p=12654">7to10</a> and <a href="https://numbers-magic.com/?p=12731">11to13</a>).</p> |
| format | Recurso digital |
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| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 11 to 13 Inder J. Taneja <p>There are many ways of representing magic squares with palindromic type entries or composite forms based on pair of Latin squares. Based on palindromic and composite magic squares we have written <strong>upside-down</strong> and/or <strong>mirror looking</strong> magic squares. By <strong>upside-down</strong>, we understand that making 180 degrees rotation still we have a magic square. Applying the <strong>upside-down</strong> property, the numbers 0, 1, 2, 5, 6, 8 and 9 remains the same, where 6 becomes 9 and 9 as 6. In this case, the numbers are written in <strong>digital/special fonts</strong>. The <strong>mirror looking</strong> property is same as <strong>horizontal flip</strong>. In this case, the numbers 0, 1, 2, 5 and 8 remains the same, where 2 becomes 5 and 5 as 2. There is one more property, known by <strong>vertical flip</strong>. For simplicity, let's call it as <strong>water reflection</strong>. In this case, the numbers 0, 1, 2, 3, 5 and 8 remains the same, where 2 becomes 5 and 5 as 2. Thus the numbers 0, 1, 2 5 and 8 are available in all the three properties. The numbers those satisfy all the three properties, we call them as<strong> universal</strong>. The same is with magic squares, i.e., the magic squares containing the numbers 0, 1, 2, 5 and 8 are known by <strong>universal</strong> magic squares. Finally, in case of <strong>upside-down</strong>, the number 6 becomes 9 and 9 as 6, and in case of <strong>water reflection</strong>, the number 3 remains the same. In this paper we worked with magic squares of orders 11 to 13, satisfying one or all the above three properties. For more details see the reference list. For more details following online link of authors web-site (<a href="https://numbers-magic.com/?p=12610">3to6</a>, <a href="https://numbers-magic.com/?p=12654">7to10</a> and <a href="https://numbers-magic.com/?p=12731">11to13</a>).</p> |
| title | Upside-Down, Mirror Looking and Water Reflection Magic Squares: Orders 11 to 13 |
| url | https://doi.org/10.5281/zenodo.14649320 |