# Block-Wise Bordered Magic Squares Multiples of 18

#### ByInder J. Taneja

Jul 13, 2023

During past years author worked with block-wisebordered and block-bordered magic squares. This work make connection between block-wise and bordered magic squares. We started with block-wise bordered magic squares of orders 144 and 126. Based on these two big magic squares, the inner order magic squares multiples of 18 are studied. By inner orders we understand that magic squares of orders 108, 90, 72, etc. The construction of the block-wise bordered magic squares multiples of 18 is based on equal sum blocks of magic squares of order 18. We have taken 37 different types of magic squares of order 18. The advantage in studying block-wise bordered magic squares is that when we remove external border, still we are left with magic squares with sequential entries. It is the same property of bordered magic squares with single digits. The difference is that instead of numbers here we have blocks of equal sum magic squares of order 18. For multiples of even orders 4 to 16 see the links below:
1. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4.
2. Block-Wise Bordered Magic Squares Multiples of Magic Squares of Order 6.
3. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 8 – Revised
4. Block-Wise Bordered Magic Squares Multiples of 10 – Revised.
5. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 12 – Revised.
6. Block-Wise Bordered Magic Squares Multiples of 14 – Revised.
7. Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 16.

This work is up to order 144. Examples below are only up to order 54. The higher order examples can be seen in Excel files attached at the end. This work also can be seen as online:

Below are few examples up to order 54 studied in this work. The work is up to order 144.
The complete excel files with 37 examples in each case are given at the end for download.

#### Magic Squares of Order 18

Below are three examples of magic squares of order 18. It includes bordered, double digits, cornered magic squares, etc. The complete list of 37 magic squares of order 18 is given as pdf file for download.

### Pdf file of 37 Magic Squares of Order 18

#### Magic Squares of Order 36

Below are only 3 examples of magic squares of order 36. The others are given as pdf file.

### Pdf file of 37 Magic Squares of Order 36

#### Magic Squares of Order 54

Below are only 3 examples of magic squares of order 54. The others are given as pdf file.

### Pdf file of 37 Magic Squares of Order 54

#### Excel file of Magic Squares Multiples of 18

The excel files below for download contains magic squares multiples of order 18 from order 18 to 144. There are 37 examples in each case. These are given in four files. One with order 144. Second with order 126. Third with orders 108 and 90. The fourth with orders 72, 54, 36 and 18.

#### 195th Days of the Year: 13.07.24 – Crazy Representations and Magic Squares of Order 13

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