This work brings striped magic squares of order 16. This revised version brings 5641 striped magic squares of order 16, while previous version was only with 2104 striped magic squares.

Striped Magic Rectangles

Below are examples of magic rectangles used in this work. These are orders 2×4 to 2×16 used in this work. Since all these are of equal width, we call them stripes.

Whole the work on striped magic squares of order 16 are always among above 7 types of magic rectangles, where the width is always same. The change is only in length. According to the order of the stripes the entries are different but the sums are always same.

Below are few examples of striped magic squares of order 16. Due to high quantity of magic squares these are divided in 9 parts given as follows:

  • Part 1: General and Cornered Striped Magic Squares of Order 16.
  • Part 2: Based on Two Magic Rectangles of Order 2×16.
  • Part 3: Based on Two Magic Rectangles of Orders 6×8 and 8×10
  • Part 4: Based on Magic Rectangles of Different Orders
  • Part 5: Based on Magic Rectangles of Different Orders
  • Part 6: Based on Magic Rectangles of Different Orders
  • Part 7: Based on Magic Rectangles of Different Orders
  • Part 8: Based on Magic Rectangles of Different Orders
  • Part 9: Based on Magic Rectangles of Different Orders 8×16
  • Part 10: Based on Magic Rectangles of Different Orders 8×16
  • Part 11: Different Combinations of Magic Squares of Orders 8
  • Part 12: Centered With Striped Magic Squares of Orders 4 and 8.
  • Part 13: Centered With Striped Magic Square of Order 12
  • Part 14: (a + b)2-Type Striped Magic Squares

For online work click the following:

The total work contains 14 parts divided in separate categories. Total there are 5641 striped magic squares of order 16.

Part 1: General, Double Digits and Cornered Striped Magic Squares of Order 16

This part brings some magic squares of order 16 made in a general way. Some them include striped cornered, striped double digits bordered, etc. Below are few examples:

There are total 6 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 1

Part 2: Based Two Magic Rectangles of Order 2×16

This part brings some striped magic squares of order 16 a such a way that these two magic rectangles are either at beginnig or at the end. The middle part are magic rectangles of order 12×16 resulting in striped magic squares of order 16. See below few examples:

There are total 126 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 2

Part 3: Based on Two Magic Rectangles of Orders 6×8 and 8×10

This part brings some striped magic squares of order 16 constructed with the help of four
magic rectangle, where two of them are of orders 6×8 and another two are of orders 10×8.
See below few examples

There are total 1232 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 3

Part 4: Based on Magic Rectangles of Different Orders

This part is very much similar to part 3. See below few examples.

There are total 396 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 4

Part 5: Based on Magic Rectangles of Different Orders

This part brings some striped magic squares of order 16. It is also very much similar to parts 3 and 4. See below few examples.

There are total 792 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 5

Part 6: Based on Magic Rectangles of Different Orders

This part brings some striped magic squares of order 16. It is also very much similar to parts 3, 4 and 5. See below few examples.

There are total 317 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 6

Part 7: Based on Magic Rectangles of Different Orders

This part brings some striped magic squares of order 16. It is also very much similar to parts 3, 4, 5 and 6. See below few examples.

There are total 396 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 7

Part 8: Based on Magic Rectangles of Different Orders

This part brings some striped magic squares of order 16. It is also very much similar to parts 3, 4, 5, 6 and 7. See below few examples.

There are total 414 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 8

Part 9: Magic Rectangles of Order 8×16

This part brings some striped magic squares of order 16. It is based on magic rectangles of
Order 8×16 and different combinations of magic squares of Order 8. See below few examples.

There are total 512 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 9

Part 10: Magic Rectangles of Order 8×16

This part brings some striped magic squares of order 16. It is based on magic rectangles of
Order 8×16. See below few examples

There are total 247 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 10

Part 11: Different Combinations of Magic Squares of Order 8

This part brings some striped magic squares of order 16. It is based on different combinations of magic squares of order 8.

There are total 484 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 11

Part 12: Centered With Striped Magic Square of Orders 4 and 8

This part brings some striped magic squares of order 16 constructed in a such a way that
there are a striped magic square of orders 4 and 8 are at the middle of magic squares of order 16. Below are few examples.

There are total 60 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 12

Part 13: Centered With Striped Magic Square of Order 12

This part brings some striped magic squares of order 16 constructed in a such a way that
there is a striped magic square of order 12 at the middle of magic squares of order 16. Below are few examples.

There are total 220 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 13

Part 14: (a+b)2-Type Striped Magic Squares

This part brings some striped magic squares of order 16 constructed in such a way that it follows the algebraic formula (a+b)2, where a=12, b=4, ab=12×4 and ba=4×12. Below are few examples.

There are total 440 striped magic squares in this part. The complete work is given below as a pdf file.

Pdf file of Part 14

References

  1. Inder J. Taneja, Striped Magic Squares of Even Orders 6, 8, 10, 12 and 14, Zenodo, November 10, 2023, pp. 1-34, https://doi.org/10.5281/zenodo.10107355.
  2. Inder J. Taneja, Striped Magic Squares of 12 – Revised, Zenodo, September 07, 2024, pp. 1-30,  https://doi.org/10.5281/zenodo.13725031.
  3. Inder J. Taneja, Inder J. Taneja, 5600+ Striped Magic Squares of Order 16, Zenodo, February 05, 2025, pp. 1-52, https://doi.org/10.5281/zenodo.14807639
  4. Inder J. Taneja, Striped Magic Squares of 18, Zenodo, June 13, 2024, pp. 1-34, https://doi.org/10.5281/zenodo.11629567.
  5. Inder J. Taneja, Striped Magic Squares of 20 – site link:

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