{"id":15857,"date":"2025-05-31T01:50:51","date_gmt":"2025-05-31T04:50:51","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=15857"},"modified":"2025-06-02T11:11:09","modified_gmt":"2025-06-02T14:11:09","slug":"magic-squares-of-order-11-representing-dates-and-days-of-the-year-2025","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=15857","title":{"rendered":"Magic Squares of Order 11 Representing Dates and Days of the Year 2025"},"content":{"rendered":"\n

This work brings dates<\/strong> and days<\/strong> of the year 2025 in terms of magic squares of order 11 for the months of June, September and November 2025<\/strong>. It is based on reduced entries<\/strong> magic squares of order 11. In this work we have considered ten types of magic squares of order 11<\/strong>. The details are as given below:<\/p>\n\n\n\n

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  1. The first type<\/strong> is a double-digit bordered<\/strong> magic square of order 11 embedded with cornered magic square of order 7. The internal magic square of order 7 contains a pandiagonal<\/strong> magic square of order 5 and two equal sums magic rectangles of order 2×5. The external parte is with four equal sums magic rectangles of order 2×7.
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  2. The second type<\/strong> is a cornered<\/strong> magic square of order 11, where the magic squares of order 9, 7 and 5 are in the left upper corner. The magic rectangles of orders 2×5, 2×7 and 2×9 are of equal width and length for each case.
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  3. The third type<\/strong> is a cornered magic square of order 11 with double-digit bordered<\/strong> magic square of order 9 at the upper left corner embedded with a pandiagonal<\/strong> magic square of order 5. The four magic rectangles of orders 2\u00d75 are of equal width and length. The two magic rectangles of orders 2×9 are also of equal width and length.
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  4. The forth type<\/strong> is a cornered<\/strong> magic square of order 11 with single-digit bordered<\/strong> magic square of order 9 at the upper left corner embedded with cornered magic square of order 7. It contains two equal sums magic rectangles<\/strong> of order 2×5 and a pandiagonal <\/strong>magic square of order 5. The magic rectangles of order 2×9 are also of equal width and length. Even though the magic square of order 9 is semi-magic <\/strong>at one diagonal, but it allows to write a magic square of order 11.
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  5. The fifth type<\/strong> is also a cornered<\/strong> magic square of order 11 with single digit bordered magic square of order 7 at the upper left corner embedded with magic square of order 5. The magic square of order 9 is also a part of cornered magic square of order 11. The magic rectangles<\/strong> of orders 2×7 and 2×9 are of equal sums in each case. Even though the magic square of order 7 is semi-magic<\/strong> but still we have orders 9 and 11 as magic squares.
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  6. The sixth type<\/strong> is also a cornered<\/strong> magic square of order 11 with single-digit bordered<\/strong> magic square of order 9 at the upper left corner embedded with magic squares of orders 5 and 7. The magic square of order 5 is pandiagonal<\/strong>. The two magic rectangles<\/strong> of order 2\u00d79 are of equal width and length. Even though the we have a semi-magic<\/strong> square at one diagonal of order 9, but still the order 11 is a magic square.
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  7. The seventh type<\/strong> is a double-digit bordered<\/strong> magic square of order 11 embedded with double digits magic squares of order 7. The internal part is a magic square of order 3. The four magic rectangles<\/strong> of orders 2\u00d73 and 2\u00d77 in each case are of equal width and length<\/strong>. To avoid fractional entries<\/strong> the difference between the sums of magic squares is considered as multiple of 4. Moreover, the magic sum of magic squares of order 3 is considered as multiple of 3<\/strong>, otherwise it gives decimal entries. In this case, an alternative approach<\/strong> based on width of magic rectangles is also suggested.
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  8. The eight type<\/strong> is a cornered<\/strong> magic square of order 11, where the magic squares of orders 3, 5, 7 and 9 are at the left upper corner<\/strong> of magic square of order 11. In each case the magic rectangles of orders 2×3, 2×5, 2×7 and 2×9 are of equal width and length. Here also to avoid fractional and decimal entries the width of magic rectangles is considered multiples of 2 and magic sum of order 3 should is considered as multiple of 3<\/strong>.
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  9. The ninth type<\/strong> is a cornered<\/strong> magic square of order 11, where at upper left corner there is a double-digit bordered<\/strong> magic square of order 7 embedded with magic square of order 3. In this case the four magic rectangles<\/strong> of order 2×3 are of equal width and length. It also contains a magic square of order 9. The magic rectangles of orders 2×7 and 2×9 are also of equal width and length in each case. Again here to avoid fractional values, the magic sum of order 3 should be multiple of 3<\/strong>.
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  10. The tenth type<\/strong> is a cornered<\/strong> magic square of order 11, where at upper left corner there is a single-digit bordered<\/strong> magic square of order 9 embedded with double-digit bordered<\/strong> magic square of order 7. It also contains magic square of order 3. In this case the four magic rectangles<\/strong> of order 2×3 are of equal width and length. The two magic rectangles<\/strong> of order 2×9 are also of equal width and length. Even though the magic square of order 9 is a semi-magic<\/strong> at one diagonal, but still we have order 11 as a magic square.
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  11. The eleventh type<\/strong> is a cornered<\/strong> magic square of order 11, where at upper left corner there is a single-digit bordered<\/strong> magic square of order 7 embedded with magic square of orders 3. In this case the two magic rectangles of order 2×7 are of equal width and length. The magic rectangles of order 2×9 are also of equal width and length. Even though the magic square of order 7 is semi-magic<\/strong> at one diagonal, but still we have order 11 as a magic square. In order to have order 7 as a magic square, we must have the condition M\/5=S\/7, where M and S are sum of magic squares of orders 5 and 7.
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  12. The twelfth type<\/strong> is a cornered<\/strong> magic square of order 11, where at upper left corner there is a single-digit bordered<\/strong> magic square of order 9 embedded with magic square of orders 3. In this case the two magic rectangles of order 2×9 are of equal width and length. Even though the magic square of order 9 is semi-magic<\/strong> at one diagonal, but still we have order 11 as a magic square. In order to have order 9 as a magic square, we must have the condition M\/5=S\/7=T\/9.<\/li>\n<\/ol>\n\n\n\n

    The pdf files of whole the work are given at the end. The whole work with details can be accessed at the following link:<\/p>\n\n\n\n