{"id":9326,"date":"2023-06-12T01:20:33","date_gmt":"2023-06-12T04:20:33","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=9326"},"modified":"2023-06-14T04:22:48","modified_gmt":"2023-06-14T07:22:48","slug":"odd-order-magic-squares-order-21","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=9326","title":{"rendered":"Magic Squares of Order 21"},"content":{"rendered":"\n

Recently, author worked with cornered Magic Squares based on two-by-two divisions. These works can be accessed at the following links:
1. Inder Jeet Taneja, Cornered Magic Squares of Orders 5 to 10<\/a>
2. Inder Jeet Taneja, Cornered Magic Squares of Orders 11 to 13<\/a>
3. Inder Jeet 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. Two Digits Bordered Magic Squares Multiples of 4: Orders 8 to 24<\/a>.
2. Two Digits Bordered Magic Squares of Orders 28 and 32<\/a>.
3. Two digits Bordered Magic Squares of Order 36.<\/a>
4. 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. Two digits Bordered Magic Squares of Orders 10, 14, 18 and 22<\/a>.
2. Two digits Bordered Magic Squares of Orders 26 and 30<\/a>.
3. Two digits Bordered Magic Squares of Order 34<\/a>.
4. Two digits Bordered Magic Squares of Order 38<\/a>. <\/a><\/p>\n\n\n\n

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This work is for magic square of order 21. It includes four type of magic squares:
1. Traditional centered magic squares.<\/strong>
2. Bordered magic squares with magic squares of order 3<\/strong>.
3. Double digits bordered magic squares.<\/strong>
4. Cornered magic squares.<\/strong>
Double digits and cornered magic squares can also be constructed using software, the reader can follow H. White’s site: Magic Squares<\/a>. Also, the cornered magic squares can be rotated in all the four directions again by using software from H. White’s site.

For the previous work on odd orders from 3 to 19 see the following links:
1. Inder J. Taneja, Odd Order Magic Squares: Orders 3 to 15<\/a>.
2. Inder J. Taneja, Odd Order Magic Squares: Orders 17 and 19.<\/a>

To have better idea, pdf file<\/strong> of total 218 magic squares of order 21 is also attached for download.<\/p>\n\n\n\n

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Magic Squares of Order 21<\/h3>\n\n\n\n

As explained above, the construction of magic squares of order 21 are of four types. Below are examples of each case.<\/p>\n\n\n\n

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1. Traditional Centered Magic Squares<\/h3>\n\n\n\n

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2. Bordered Magic Squares with Magic Squares of Order 3<\/h3>\n\n\n\n

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Above there are only three examples. More examples are in pdf file <\/strong>attached at the end of this work. These are from number 44 to 108.<\/p>\n\n\n\n

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3. Double Digits Bordered Magic Squares<\/h3>\n\n\n\n

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Above there are only three examples. More examples are in pdf file <\/strong>attached at the end of this work. These are from number 6 to 43.<\/p>\n\n\n\n

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4. Cornered Magic Squares<\/h3>\n\n\n\n

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Above there are only four examples. More examples are in pdf file <\/strong>attached at the end of this work. These are from number 109 to 218.<\/p>\n\n\n\n

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Pdf file of All Examples for Download<\/h3>\n\n\n\n

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