This work brings self-made algebraic magic squares of order 11 for reduced entries. By reduced or less entries, we understand that instead of normal n2 entries of a magic square order n, we are using less number of entries. Moreover, in these situations the entries are no more sequential numbers. These entries are non-sequential positive and negative numbers. Sometimes, we call these kind of magic squares as self-made. It means that these are complete in themselves. Just put the values of entries and choose the magic sum, we get a magic square. In some cases, there maybe decimal or fractional values of the entries depending on the types of magic squares. Different kind of magic squares are used to bring these self-made magic squares. These are of type, block-wise, cornered, single-digit bordered, double-digit bordered, etc. In some cases, the idea of magic rectangles is also applied. In each case, the magic rectangles are considered with equal width and length. For similar kind of work for different orders the readers are suggested to see author’s work given in references.
Once again, self-made means that they are complete in themselves: once you choose the entries and the magic sum, a magic square will always result. These squares can contain integer, decimal, or fractional values.
For more details see the link given below:
Inder J. Taneja, Self-Made Algebraic Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815.
Inder J. Taneja, Self-Made Algebraic Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-77, https://doi.org/10.5281/zenodo.17330822.
See below the details of the work with Examples
Self-Made Algebraic Magic Squares of Order 11
Below are 25 self-made algebraic magic squares of order 11 for reduced entries.
Result 1: Double-Digit Bordered Algebraic Magic Square of Order 11
It is a double-digit bordered magic square of order 11 embedded with a magic square of order 7. The four magic rectangles of orders 2×7 are of equal width and length. The letters T and R represents the magic squares of orders 7 and 11 respectively. See below an example.
It contains the following magic square:
Result 2: Double-Digit Bordered Algebraic Magic Square of Order 11
It is a double-digit bordered magic square of order 11 embedded with another double-digit bordered magic square of order 7 having magic squares of order 3 in the middle. The magic rectangles of orders 2×3 and 2×7 are of equal width and length in each case. The letters M, T and R represents the magic sums of orders 3, 7 and 11 respectively. See below an example.
It contains the following magic square:
Result 3: Double-Digit Bordered Algebraic Magic Square of Order 11
It is a double-digit bordered magic square of order 11 embedded with a cornered magic square of order 7 having pandiagonal magic square of order 5 in the upper-left corner. The magic rectangles of order 2×7 and 2×5 are of equal width and length in each case. The letters S, T and R represents the magic sums of orders 5, 7 and 11 respectively. See below an example.
It contains the following magic square:
Result 4: Double-Digit Bordered Algebraic Magic Square of Order 11
It is a double-digit bordered magic square of order 11 embedded with a cornered magic square of order 7 having again a cornered magic square of order 5 in the upper-left corner containing the magic square of order 3. The magic rectangles of orders 2×7, 2×5 and 2×3 are of equal width and length in each case. The letters M, S, T and R represents the magic sums of orders 3, 5, 7 and 11 respectively. See below an example.
It contains the following magic square:
Result 5: Double-Digit Bordered Algebraic Magic Square of Order 11
It is a double-digit bordered magic square of order 11 embedded with a cornered magic square of order 7 having again a single digit bordered magic square of order 5 in the upper-left corner containing a magic square of order 3. The magic rectangles of orders 2×7 and 2×5 are of equal width and length in each case. The letters M, S, T and R represents the magic sums of orders 3, 5, 7 and 11 respectively. See below an example.
It contains the following magic square:
Result 6: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of order 11 having a double-digit bordered magic square of order 7 at the upper-left corner. It contains pandiagonal magic square of order 5 in the middle. The magic rectangles of orders 2×9 and 2×5 are of equal width and length in each case. The letters S, L and R represents the magic sums of orders 5, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 7: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of order 11 having a double-digit bordered magic square of order 7 at the upper-left corner. It again contains a cornered magic square of order 5 with a magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×9 and 2×5 are of equal width and length in each case. The letters M, S, L and R represents the magic sums of orders 3, 5, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 8: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of order 11 having a double-digit bordered magic square of order 7 at the upper-left corner. It again contains a single-digit bordered magic square of order 5 with magic square of order 3 in the inner part. The magic rectangles of orders 2×9 and 2×5 are of equal width and length in each case. The letters M, S, L and R represents the magic sums of orders 3, 5, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 9: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 and 9 having a double-digit bordered magic square of order 7 at the upper-left corner. It contains the magic squares of order 3 in the middle. The magic rectangles of orders 2×3, 2×7 and 2×9 are of equal width and length in each case. The letters M, T, L and R represents the magic sums of orders 3, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 10: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11, 9 and 7 having a pandiagonal magic square of order 5 at the upper-left corner. The magic rectangles of orders 2×5, 2×7 and 2×9 are of equal width and length in each case. The letters S, T, L and R represents the magic sums of orders 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 11: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11, 9, 7 and 5 having a magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×3, 2×5, 2×7 and 2×9 are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 12: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11, 9 and 7 having a single-digit bordered magic square of order 5 at the upper-left corner. It contains magic square of order 3 in the middle. The magic rectangles of orders 2×5, 2×7 and 2×9 are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 13: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 and 9 having a magic square of order 7 at the upper-left corner. The magic rectangles of orders 2×7 and 2×9 are of equal width and length in each case. The letters T, L and R represents the magic sums of orders 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 14: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 and 9 having a single-digit bordered magic square of order 7 at the upper-left corner. It contains magic square of order 5 in the middle. The magic rectangles of orders 2×7 and 2×9 are of equal width and length in each case. The letters S, T, L and R represents the magic sums of orders 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 15: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 and 9 having a single-digit bordered magic square of order 7 at the upper-left corner. Again it contains a cornered magic square of order 5 having magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×3, 2×7 and 2×9 are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 16: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 and 9 having a single-digit bordered magic square of orders 7 and 5 at upper-left corner with magic square of order 3 in the middle. The magic rectangles of orders 2×7 and 2×9 are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 17: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a block-wise magic square of order 9 at the upper-left corner. It is composed of 9 equal sums semi-magic squares of order 3. The magic rectangles of order 2×9 are of equal width and length. The letters M, L and R represents the magic sums of orders 3, 9 and 11 respectively. In this case T:=3*M. See below an example.
It contains the following magic square:
Result 18: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner. It contains a single-digit bordered magic square of order 7 in with magic square of order 3 in the middle. The magic rectangles of orders 2×9 are of equal width and length. The letters M, T, L and R represents the magic sums of orders 3, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 19: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner with magic square of order 7 in the middle. The magic rectangles of orders 2×9 are of equal width and length. The letters T, L and R represents the magic sums of orders 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 20: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner. It contains a cornered magic squares of orders 7 and with pandiagonal magic square of order 5 at the upper-left corner. The magic rectangles of orders 2×5 and 2×9 are of equal width and length in each case. The letters S, T, L and R represents the magic sums of orders 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 21: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner. It contains a cornered magic squares of orders 7 and 5 with magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×3, 2×5 and 2×9 are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 22: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a single-digit bordered magic squares of orders 9 and 7 at the upper-left corner. It contains a cornered magic squares of orders 5 with magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×3 and 2×9 are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
Result 24: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having single-digit bordered magic squarea of ordera 9 and 7 at the upper-left corner containg pandiagonal magic square of order 5 in the middle. The magic rectangles of orders 2×9 are of equal width and length. The letters S, T, L and R represents the magic sums of orders 5, 7, 9 and 11 respectively. See below an example
It contains the following magic square:
Result 25: Cornered Algebraic Magic Square of Order 11
It is a cornered magic square of orders 11 having a single-digit bordered magic squares of orders 9, 7 and 5 with a magic square of order 3 in the middle. The magic rectangles of order 2×9 are of equal width and length. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example.
It contains the following magic square:
References
Part 1: Day and Dates of the Year – 2025 in Terms of Magic Squares
- Inder J. Taneja, Magic Squares of Orders 3 to 7 in Representing Dates and Days of the Year 2025, Zenodo, May 04, 2025, pp. 1-474, https://doi.org/10.5281/zenodo.15338142.
- Site Link: Magic Squares of Orders 3 to 7 Representing Dates and Days of the Year 2025 (new site)
- Site Link: Magic Squares of Orders 3 to 7 Representing Dates and Days of the Year 2025 (old site)
- Inder J. Taneja, Magic Squares of Order 8 Representing Days and Dates of the Year 2025, Zenodo, May 04, 2025, pp. 1-134, https://doi.org/10.5281/zenodo.15338246.
- Site Link: Magic Squares of Order 8 Representing Days and Dates of the Year 2025 (new site)
- Site Link: Magic Squares of Order 8 Representing Days and Dates of the Year 2025 (old site)
- Inder J. Taneja, Magic Squares of Order 9 Representing Days and Dates of the Year 2025, Zenodo, May 09, 2025, pp. 1-132, https://doi.org/10.5281/zenodo.15375349.
- Site Link: Magic Squares of Order 9 Representing Days and Dates of the Year 2025 (new site)
- Site Link: Magic Squares of Order 9 Representing Days and Dates of the Year 2025 (old site)
- Inder J. Taneja, Magic Squares of Order 10 Representing Days and Dates of the Year 2025, Zenodo, May 21, 2025, pp. 1-59, https://doi.org/10.5281/zenodo.15481738.
- Inder J. Taneja, Magic Squares of Order 12 Representing Days and Dates of the Year 2025 Zenodo, June 10, 2025, pp. 1-43, https://doi.org/10.5281/zenodo.15631884.
Part 2: Reduced Entries Agebraic Magic Squares
- Inder J. Taneja, Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Orders 3 to 7, Zenodo, September 29, 2025, pp. 1-59, https://doi.org/10.5281/zenodo.17219769.
- Site Link: Reduced Entries Algebraic Magic Squares of Orders 3, 5, 7 and 9 (new site)
- Site Link: Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 (new site)
- Site Link: Reduced Entries Algebraic Magic Squares of Orders 3, 5, 7 and 9 (old site)
- Site Link: Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 (old site)
- Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 8, Zenodo, September 23, 2025, pp. 1-65, https://doi.org/10.5281/zenodo.17186001.
- Site Link: Reduced Entries Algebraic Magic Squares of Orders 4, 6, 8 and 10 (new site)
- Site Link: Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 (new site)
- Site Link: Reduced Entries Algebraic Pandiagonal Magic Squares of Orders 4 to 8 (old site)
- Inder J. Taneja, Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9, Zenodo, August 27, 2025, pp. 1-92, https://doi.org/10.5281/zenodo.16955571.
- Site Link: Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9 (new site)
- Site Link: Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9 (old site)
- Inder J. Taneja. Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10, Zenodo, September 18, 2025, pp. 1-112, https://doi.org/10.5281/zenodo.17149185
- Site Link: Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10 (new site)
- Site Link: Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 10 (old site)
- Inder J. Taneja, Reduced Entries Algebraic Magic and PanMagic Squares of Order 12, Zenodo, July 23, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.16370556.
- Site Link: Reduced Entries Algebraic Magic and Panmagic Squares of Order 12 (new site)
- Site Link: Reduced Entries Algebraic Magic and Panmagic Squares of Order 12 (old site)
- Inder J. Taneja, Self-Made Algebraic Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 .
- Site Link: Self-Made Algebraic Magic Squares of Order 11 (new site)
- Site Link: Self-Made Algebraic Magic Squares of Order 11 (old site)
- Inder J. Taneja, Self-Made Algebraic Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-77, https://doi.org/10.5281/zenodo.17330822.
- Site Link: Self-Made Algebraic Semi-Magic Squares of Order 11 (new site)
- Site Link: Self-Made Algebraic Semi-Magic Squares of Order 11 (old site)
- Inder J. Taneja, Reduced Entries Algebraic Magic and PanMagic Squares of Order 12, Zenodo, July 23, 2025, pp. 1-74, https://doi.org/10.5281/zenodo.16370556.
- Site Link: Reduced Entries Algebraic Magic and Panmagic Squares of Order 12 (new site)
- Site Link: Reduced Entries Algebraic Magic and Panmagic Squares of Order 12 (old site)
- Inder J. Taneja, Reduced Entries Algebraic Semi-Magic Squares of Order 12, Zenodo, July 23, 2025, pp. 1-60, https://doi.org/10.5281/zenodo.15692014.
- Site Link: Reduced Entries Algebraic Semi-Magic Squares of Order 12 (old site)
- Site Link: Reduced Entries Algebraic Semi-Magic Squares of Order 12 (old site)