# Different Types of Magic Squares of Order 14

#### ByInder J. Taneja

Sep 18, 2022

Revised in December 06, 2023
Total 4101 Magic Squares of Order 14

This work brings magic squares of orders 14. It unifies most of the previous works. Different types of constructions are considered. These includes, bordered, magic rectangles, double digits bordered, cornered, etc. It is summarized as the following points:

1. Boarded magic squares.
2. Bordered magic rectangles.
3. Algebraic formula (a+b)2.
4. Double digits bordered magic squares.
5. Cornered magic squares.
6. Striped Magic Squares

Just as an idea below are links of the works magic squares using the special aspects as double digits, corner, striped etc.

This work brings different types of magic squares of order 14. It is a revised version of the author’s previous work. Below are examples of magic squares of order 14. Total there are 4101 examples, but only few are given below. To simplify we have divided the whole work in 10 parts. Below are explanations of each parts with separate pdf files of magic squares of order 14. Most of the work is done manually, and magic squares are adjusted one by one.

In the end there is a pdf file for download of 4101 magic squares of order 14. The work can also be seen online at the following link:

Inder J. Taneja, Different Types of Magic Squares of Order 14, Zenodo, November 18, 2023, pp. 1-35, https://doi.org/10.5281/zenodo.10153249.

This work brings magic squares of orders 14. It unifies most of the previous works. Different types of constructions are considered. These includes, bordered, magic rectangles, double digits bordered, cornered, etc. It is summarized as the following points:

1. Boarded magic squares.
2. Bordered magic rectangles.
3. Algebraic formula (a+b)2.
4. Double digits bordered magic squares.
5. Cornered magic squares.
6. Bordered with Magic Squares of Order 12.

### Magic Squares of Order 14

Below are few examples of magic squares of order 14. These are divided in different parts. We have separated these magic squares in 10 parts.

### Part 1. General or Mix Type Magic Squares

This part give some general magic square of order 14. Below are only 6 examples. The examples are in a pdf file attached below:

### Part 2. Magic Square of Order 6 in the Middle

This part give some magic square of order 14 written in different ways. All these magic squares magic square of order 6 is in the middle. There are different choices of magic squares of order 6. Below are only 6 examples. The other examples are in a pdf file attached below:

### Part 3. (a+b)2-Type, where a=8 and b=6

This part give some magic square of order 14 based on the algebraic formula (a+b)2. Here a=8 and b=6. Since there are many possibilities of writing magic squares of orders 8 and 6, this give different magic squares of order 14. The complete pdf file is attached. Moreover, the magic rectangle of type axb or bxa are also taken in different forms. Below are only 6 examples. The examples are in a pdf file attached below:

### Part 4. (a+b)2-Type, where a=8 and b=6: Closed Form – I

This part give magic squares of order 14 based on the algebraic formula (a+b)2. Here it is applied in little different way. We have taken in three different ways a magic rectangle of order 6×14. Also different forms of magic rectangle of order 6×8 are taken. Different types of magic squares of order 8 are considered to bring magic squares of order 14. See below few examples. The complete work is given as pdf file attached below:

### Part 5. (a+b)2-Type, where a=8 and b=6: Closed Form – II

This part is very much similar to previous part. Here instead of considering magic rectangles of order 6×14, we have considered two different magic rectangles of order 6×10 and 6×4 covering the space of magic rectangles of order 6×14. The rest of work is similar to previous part. See below few examples. The complete work is given as pdf file attached below:

### Part 6. Double Digits Embedded With Magic Squares of Order 10

This part is based on double digit magic squares. To bring magic squares of order 14, we have embedded it with magic squares of order 10. The idea of double digits magic square is given above in a reference list. See below few examples. The complete work is given as pdf file attached below:

### Part 7. Cornered Magic Squares

This part is brings cornered magic squares of order 14. These are of nested type. It allows us to write magic squares up to order 14 in the beginning. It is done after some adjustment. More details on cornered magic squares are given in a reference list given in the beginning of the work. See below few examples. The complete work is given as pdf file attached below:

### Part 8. (a+b)2-Type, where a=10 and b=4: Open Form

This part give some magic square of order 14 based on the algebraic formula (a+b)2. Here a=10 and b=4. It is written in two different way. One call as open form, where we have used magic square of order 4 at the corner. The other two are magic rectangles of order 4×10. Since we have many magic squares of order 10. Replacing different forms of magic square of order 10, we get magic square of order 14. See below few examples. The complete work is given as pdf file attached below.

### Part 9. (a+b)2-Type, where a=10 and b=4: Closed Form

This part give some magic square of order 14 based on the algebraic formula (a+b)2. Here a=10. Instead considering b=4, we have considered directly the magic rectangles of order 4×10. Two of them are complete magic rectangles of order 4×10 and the third is combination of magic rectangles of orders 4×10 and 4×4. Since we have many magic squares of order 10. Replacing different forms of magic square of order 10, we get magic square of order 14. See below few examples. The complete work is given as pdf file attached below.

### Part 10. Bordered Magic Squares: Embedded with Magic Squares of Order 12

This part is very much similar to double digits bordered magic squares. Here instead of border of double digits, we have single digit border. The inner part is replaced by magic squares of order 12. See below few examples. The complete work is given as pdf file attached below:

### Pdf File of 3584 Magic Squares of Order 14 for Download

Below is a list of previous works. These shall be revised including all the new types of constructions of magic squares.

1. Inder J. Taneja, Different Types of Magic Squares of Orders 6, 8, 10 and 12, Zenodo, November 07, 2023, pp. 1-41, https://doi.org/10.5281/zenodo.10080859.
a) Different Types of Magic Squares of Order 12.
b) Different Types of Magic Squares of Orders 6, 8 and 10.
2. Inder J. Taneja, Different Types of Magic Squares of Order 14, Zenodo, November 18, 2023, pp. 1-35, https://doi.org/10.5281/zenodo.10153249.
3. Inder J. Taneja, Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-63, https://doi.org/10.5281/zenodo.7320116.
4. Inder J. Taneja, Different Styles of Magic Squares of Order 18 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.7320131.
5. Inder J. Taneja, Different Styles of Magic Squares of Order 20 Using Bordered Magic Rectangles, Zenodo, November 14, 2022, pp. 1-88, https://doi.org/10.5281/zenodo.7320877.