Striped Magic Squares of Order 20

This work brings striped magic squares of order 20. Before we proceed further below examples of 9 stripes used in whole the work.

Striped Magic Rectangles

Below are examples of magic rectangles used in this work. These are orders 2×4 to 2×20 used in this work. Since all these are of equal width, we call them stripes.

Whole the work on striped magic squares of order 20 are always among above 9 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 20. 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 20
• Part 2: Two Magic Squares of Order 8 at Corners
• Part 3: Four Magic Squares of Order 8 at Corners
• Part 4: Centered With Striped Magic Square of Order 4
• Part 5: Centered With Striped Magic Square of Order 8
• Part 6: Centered With Striped Magic Square of Order 12
• Part 7: (a + b)²-Type Striped Magic Squares: a=12, b=8, ab=12×8 and ba =8×12
• Part 8: Centered With Striped Magic Square of Order 16
• Part 9: (a + b)²-Type Striped Magic Squares: a=16, b=4, ab=16×4 and ba=4×16

For online work click the following:

• Inder J. Taneja, Striped Magic Squares of 20, Zenodo, August 24, 2024, pp. 1-37,

Striped Magic Squares of Order 20

The total work contains 9 parts divided in separate categories. Total there are 8042 striped magic squares of order 20.

Part 1: General and Cornered Striped Magic Squares of Order 20

This part is with striped magic squares of order 20. This part brings some magic squares of order 20 made in a general way. Some them include striped cornered, striped double digits bordered, etc. Below are few examples:

In this case total there are 266 striped magic squares of order 20. See more in pdf file given below:

Pdf file of Part 1

Part 2: Two Magic Squares of Order 8 at Corners

This part brings some striped magic squares of order 20 made in a such a way that there are two magic squares of order 8 at oposite corners. Below are few examples:

In this case total there are 550 striped magic squares of order 20. See more in pdf file given below:

Pdf file of Part 2: Cornered With 2 Striped Magic Squares of Order 8

Part 3: Four Magic Squares of Order 8 at Corners

This part brings some striped magic squares of order 20 made in a such a way that there are four striped magic squares of order 8 at each corner. Below are few examples:

In this case total there are 484 striped magic squares of order 20. See more in pdf file given below:

Pdf file of Part 3: Cornered With 4 Striped Magic Squares of Order 8

Part 4: Centered With Striped Magic Square of Order 4

This part brings some striped magic squares of order 20 made in a such a way that there is a striped magic square of order 4 at the centered. Below are few examples:

In this case total there are 91 striped magic squares of order 20. See more in pdf file given below:

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

Part 5: Centered With Striped Magic Square of Order 8

This part brings some striped magic squares of order 20 made in a such a way that there is a striped magic square of order 8 at the centered. Below are few examples:

In this case total there are 135 striped magic squares of order 20. See more in pdf file given below:

Pdf file of Part 5: Centered With Striped Magic Squares of Order 8

Part 6: Centered With Striped Magic Square of Order 12

This part brings some striped magic squares of order 20 made in a such a way that there is a striped magic square of order 12 at the centered. Below are few examples:

In this case total there are 288 striped magic squares of order 20. See more in pdf file given below:

Pdf file of Part 6: Centered With Striped Magic Squares of Order 12

Part 7: (a+b)²-Type Striped Magic Squares:
a=12, b=8, ab=12×8 and ba=8×12

This part brings some striped magic squares of order 20. These are made by using the algebraic formula (a+b)², where a=12, b=8, ab=12×8 and ba=8×12. In this case there are 72 magic squares of order 12, 9 magic squares of order 8. There are 8 different way are considered to write ab or ba. Considering the product 72x9x8 = 5184, there are 5184 different ways of writing stripled magic squares of order 20 by use of the algebraic formula (a+b)². Below are few examples.

In this case total there are 5184 striped magic squares of order 20. See more in pdf file given below:

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

Part 8: Centered With Striped Magic Square of Order 16

This part brings some striped magic squares of order 20 made in a such a way that there is a striped magic square of order 16 at the centered. Below are few examples:

In this case total there are 348 striped magic squares of order 20. See more in pdf file given below:

Pdf file of Part 8: Centered With Striped Magic Squares of Order 16

Part 9: (a+b)²-Type Striped Magic Squares:
a=16, b=4, ab=16×4 and ba=4×16

This part brings some striped magic squares of order 20. These are made by using the algebraic formula (a+b)², where a=16, b=4, ab=16×4 and ba=4×16. In this case there are 348 magic squares of order 16, 1 magic squares of order 4. There are 2 different way are considered to write ab or ba. Considering the product 348x1x2 = 696, there are 696 different ways of writing striped magic squares of order 20 by use of the algebraic formula (a+b)². Below are few examples.

In this case total there are 696 striped magic squares of order 20. There are 677 semi-magic squares. By simple calculations we can change them to magic squares. It shall be done late on. See more in pdf file given below:

Pdf file of Part 9: (a+b)²-Type Striped Magic Squares

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.
   • Site Link: Striped Magic Squares of Orders 4, 6, 8, 10, 12 and 14
2. Inder J. Taneja, Striped Magic Squares of 16, Zenodo, May 16, 2024, pp. 1-22,  https://doi.org/10.5281/zenodo.11205510.
   • Site Link: Striped Magic Squares of Order 16. 
3. 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.
4. Inder J. Taneja, Striped Magic Squares of 20, Zenodo,
   • Site Link: Striped Magic Squares of Order 20.