Striped Magic Squares of Order 16 – Revised

This work brings striped magic squares of order 16. This revised version brings 2104 striped magic squares of order 16, while previous version was only with 348 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 Order 8×16
• Part 4: Based on Two Magic Rectangles of Order 8×16 – Upper Part with Two Magic Squares of Order 8.
• Part 5: Four Magic Squares of 8.
• Part 6: Centered With Striped Magic Square of Order 4.
• Part 7: Centered With Striped Magic Square of Order 8.
• Part 8: Centered With Striped Magic Square of Order 12
• Part 9: (a + b)²-Type Striped Magic Squares: a=12, b=4, ab=12×4 and ba=4×12

For online work click the following:

• Inder J. Taneja, Striped Magic Squares of 16 – Revised, Zenodo, September 07, 2024, pp. 1-39, https://doi.org/10.5281/zenodo.13720366.

Striped Magic Squares of Order 20

The total work contains 9 parts divided in separate categories. Total there are 2104 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:

In this part there are only 6 striped magic squares of order 16. See more in pdf file given below:

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:

Total there are 126 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 2: Based on Two Magic Rectangles of Order 2×16

Part 3: Based on Two Magic Rectangles of Order 8×16

This part brings some striped magic squares of order 16 constructed in a such a way that these are divided in two magic rectangles of orders 8×16. See below few examples:

In this case total there are 256 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 3: Based on Two Magic Rectangles of Order 8×16

Part 4: Based on Two Magic Rectangles of Order 8×16
Upper Part with Two Magic Magic Squares of Order 8

This part brings some striped magic squares of order 16 constructed in a such a way that these are divided in two magic rectangles of orders 8×16. In this case the upper part of with two striped magic squares of order 8. These two magic squares are either of same or different designs.

In this case total there are 512 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 4: Based on Two Magic Rectangles of Order 8×16 – Upper Part with Two Magic Magic Squares of Order 8

Part 5: Four Magic Squares of 8

This part brings some striped magic squares of order 16 constructed in such a way that there are four striped magic square of order 8. Below are few examples:

In this case total there are 484 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 5: Four Magic Squares of 8

Part 6: Centered With Striped Magic Square of Order 4

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 4 at the middle of magic squares of order 16. Below are few examples:

There are much more examples can be find with magic square of order 4 at the middle, but we have given below pdf file of only 15 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 6: Centered With Striped Magic Squares of Order 4

Part 7: Centered With Striped Magic Squares of Order 8

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 8 at the middle of magic squares of order 16. Below are few examples:

There are much more examples can be find with magic square of order 8 at the middle, but we have given below pdf file of only 45 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 7: Centered With Striped Magic Squares of Order 8

Part 8: Centered With Striped Magic Squares 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:

In this part there are total 220 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 8: Centered With Striped Magic Squares of Order 12

Part 9: (a+b)²-Type Striped Magic Squares:
a=12, b=4, ab=12×4 and ba=4×12

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.

In this case total there are 440 striped magic squares of order 16. See more in pdf file given below:

Pdf file of Part 7: (a+b)²-Type Striped Magic Squares

Pdf file of Complete Work

Below is a pdf file of complete work. It combines previous 9 parts given above. This file contains total 2104 striped magic squares of order 16.

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.
   • Site Link: Striped Magic Squares of Order 12 – Revised
3. Inder J. Taneja, Striped Magic Squares of 16 – Revised, Zenodo, September 07, 2024, pp. 1-39,  https://doi.org/10.5281/zenodo.13720366
   • Site Link: Striped Magic Squares of Order 16 – Revised
4. Inder J. Taneja, Striped Magic Squares of 18, Zenodo, June 13, 2024, pp. 1-34, https://doi.org/10.5281/zenodo.11629567.
   • Site Link: Striped Magic Squares of Order 18.
5. Inder J. Taneja, Striped Magic Squares of 20 – site link: