{"id":9215,"date":"2023-06-10T04:08:15","date_gmt":"2023-06-10T07:08:15","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9215"},"modified":"2023-06-10T13:50:04","modified_gmt":"2023-06-10T16:50:04","slug":"odd-order-magic-squares-orders-3-to-15","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9215","title":{"rendered":"Odd Order Magic Squares: Orders 3 to 15"},"content":{"rendered":"\n

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Recently, author worked with cornered Magic Squares based on two-by-two divisions. These works can be accessed at the following links:
1. Inder J. Taneja, Cornered Magic Squares of Orders 5 to 10<\/a>
2. Inder J. Taneja, Cornered Magic Squares of Orders 11 to 13<\/a>
3. Inder J. Taneja, Cornered Magic Squares of Orders 14 to 24<\/a><\/p>\n\n\n\n

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Also, the author worked on even order<\/strong> double digits bordered magic squares<\/strong>. This works starts from order 8 and goes up to order 40. See below the links:

The work for order of type 4k, k=1, 2, 3, … i.e., for orders 8, 12, 16, 20, 24, 28, 32, 36 and 40:
1. Inder J. Taneja, Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24<\/a>.
2. Inder J. Taneja, Two Digits Bordered Magic Squares of Orders 28 and 32<\/a>.
3. Inder J. Taneja, Two digits Bordered Magic Squares of Order 36.<\/a>
4. Inder J. Taneja, Two digits Bordered Magic Squares of Order 40<\/a>.

The work is for the order of type 4k+2, k=1, 2, 3, …, i.e., for the orders 10, 14, 18, 22, 26, 30, 34 and 38:
1. Inder J. Taneja, Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22<\/a>.
2. Inder J. Taneja, Two digits Bordered Magic Squares of Orders 26 and 30<\/a>.
3. Inder J. Taneja, Two digits Bordered Magic Squares of Order 34<\/a>.
4. Inder J. Taneja, Two digits Bordered Magic Squares of Order 38<\/a>. <\/a><\/p>\n\n\n\n

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This work is for the odd order magic squares. The work includes three type of magic squares:
1. Traditional centered magic squares.
2. Double digits bordered magic squares.
3. Cornered magic squares.
To construct double digits and cornered magic squares using software, the reader can follow H. White’s site: Magic Squares<\/a>
This work is for orders 3 to 15. To have better idea, pdf files<\/strong> of magic squares of order 13 and 15 are also attached with this work.<\/p>\n\n\n\n

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Magic Square of Order 3<\/h3>\n\n\n\n

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Magic Square of Order 5<\/h3>\n\n\n\n

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Magic Square of Order 7<\/h3>\n\n\n\n

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Magic squares 1 and 2 are traditional centered magic squares<\/strong>. Magic square 3 is double digits bordered magic square<\/strong>. Magic squares 4, 5 and 6 are cornered magic squares<\/strong>. It includes as traditional magic squares of order 5.<\/p>\n\n\n\n

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Magic Square of Order 9<\/h3>\n\n\n\n

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Magic squares 1 and 2 are traditional centered magic squares. Magic squares 3, 4 and 5 are double digits bordered magic squares. Magic squares 6, 7, 8, 9, 10 and 11 are cornered magic squares. It includes as traditional as well as double digits magic squares of order 7.<\/p>\n\n\n\n

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Magic Square of Order 11<\/h3>\n\n\n\n

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Magic squares 1, 2 and 3 are traditional centered magic squares<\/strong>. Magic squares 3, 4, 5, 6, 7, 8 and 9 are double digits bordered magic squares<\/strong>. Magic squares 10 to19 are cornered magic squares<\/strong>. It includes as traditional as well as double digits magic squares of order 9.<\/p>\n\n\n\n

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Magic Square of Order 13<\/h3>\n\n\n\n

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There are total 31 magic squares of order 13. Out of them first four are traditional centered magic squares<\/strong>. Magic squares 5, 6, 7 and 8 are double digits bordered magic squares<\/strong>. Magic squares 9 to 31 are cornered magic squares<\/strong>. These cornered magic squares include as traditional<\/strong> as well as double digits<\/strong> magic squares of orders, 5, 7, 9 and 11.<\/p>\n\n\n\n

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Pdf file for download
Magic Squares of Order 13<\/mark><\/h3>\n\n\n\n