For the first time in this work, two new concepts in construction of magic square are considered: Using small blocks of magic or bordered magic rectangles. It is not always possible to write bordered magic rectangles for the non-sequential entries. In this case, the simple magic rectangles are considered. Using algebraic formula (a+b)2. The whole work contains magic squares of even … Continue reading Different Styles of Magic Squares of Orders 8 and 10 Using Bordered Magic Rectangles and the Formula (a+b)^2

# Category: Magic Squares

# Construction of Magic Squares With Blocks of Magic Rectangles

In this work, magic squares are written with equal and unequal sums blocks of magic rectangles. The magic squares studied are of orders 12, 15, 20, 21, 24, 27, 28, 30, 33, 35, 39 and 45. The equal sum blocks magic rectangles are for the magic squares of orders 12, 20, 24, 28 and 30. This lead us … Continue reading Construction of Magic Squares With Blocks of Magic Rectangles

# Different Types of Multiple Style Magic Squares of Order 30

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. The whole work can be downloaded at the following link: Inder J. Taneja, Different Types of Multiple Style Magic Squares of Order 30, Zenodo, May 01, 2022, pp. 1-40, https://doi.org/10.5281/zenodo.6515808. Below are 612 … Continue reading Different Types of Multiple Style Magic Squares of Order 30

# Different Types of Multiple Style Magic Squares of Order 28

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. In this case there are 324 magic squares of order 32. The work can be downloaded as the following link: Inder J. Taneja, Different Types of Multiple Style Magic … Continue reading Different Types of Multiple Style Magic Squares of Order 28

# Different Types of Multiple Style Magic Squares of Order 32

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. In this case there are 324 magic squares of order 32. The work can be downloaded as the following link: Inder J. Taneja, Different Types of Multiple Style Magic … Continue reading Different Types of Multiple Style Magic Squares of Order 32

# Multiple Style Different Types of Magic Squares of Order 36

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. In case of magic square of order 36, we have written total 565 magic squares of different types. The work with excel files can be downloaded as the following … Continue reading Multiple Style Different Types of Magic Squares of Order 36

# Multiple Style Different Types of Magic Squares of Order 40

Recently, author wrote different types of magic squares for even orders. These are of type block-wise, bordered, block-bordered, block-wise bordered etc. or we can say that these are mix-type magic squares. In case of magic square of order 40, we have written total 3557 magic squares of different types. The work with extra 9-pdf files can be downloaded as the following link: … Continue reading Multiple Style Different Types of Magic Squares of Order 40

# Block-Wise Bordered Magic Squares Multiples of 14

During past years author worked with block-wise, bordered 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 140 and 126. Based on these two big magic squares, the inner order magic squares multiples of 14 are studied. By inner orders we understand as the magic squares of orders 112, 98, 84, etc. … Continue reading Block-Wise Bordered Magic Squares Multiples of 14

# Block-Wise Bordered Magic Squares Multiples of 12

During past years author worked with block-wise, bordered 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 120 and 108. Based on these two big magic squares, the inner order magic squares multiples of 12 are studied. By inner orders we understand as the magic squares of orders 96, 84, 72, etc. … Continue reading Block-Wise Bordered Magic Squares Multiples of 12

# Block-Wise Bordered Magic Squares Multiples of 10

During past years author worked with block-wise, bordered 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 120 and 110. Based on these two big magic squares, the inner order magic squares multiples of 10 are studied. By inner orders we understand as the magic squares of orders 100, 90, 80, etc. … Continue reading Block-Wise Bordered Magic Squares Multiples of 10

# Block-Wise Bordered Magic Squares Multiples of 8

During past years author worked with block-wise, bordered 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 120 and 112. Based on these two big magic inner order magic squares multiples of 8 are studied. By inner orders we understand that magic squares of orders 96, 88, 80, etc. Instead of working … Continue reading Block-Wise Bordered Magic Squares Multiples of 8

# 100-Magic Squares of Order 42 With Numbers 00 to 99

During past years author worked with block-wise, block-bordered and block-wise bordered magic squares. Recently, author wrote block-wise and block-wise bordered magic sequares mutliples of 4, 6, 8, 10 and 12. Considering multiples of 6, we have two magic square with equal sums and equal digits blocks of order 6 resulting in magic square of order 42. Here we have 49 … Continue reading 100-Magic Squares of Order 42 With Numbers 00 to 99

# Magic Squares of Orders 30, 36 and 40 With 22

Order 30 Below are magic squares of order 30, 36 and 40 with 22. The magic square of order 30 is made with equal sums blocks of order 6. The blocks giving number 2 twice is made from bordered magic square of order 6. There are total 25 blocks of order 6 with equal sums … Continue reading Magic Squares of Orders 30, 36 and 40 With 22

# Magic Square of Order 40 With 22

Below is a a magic square of order 40 made from consecutive number 1 to 1600. It contains 16 equal sums bordered magic squares of order 8 and 36 equal sums pandiagonal magic squares of order 4. If we consider 16 pandiagonal magic squares of order 4 appearing in 16 bordered magic squares of order 8, then there are 52 pandiagonal magic squares of order … Continue reading Magic Square of Order 40 With 22

# Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022

During past years, author worked with magic squares in different situations. These are of digital-type, block-wise, block-bordered, bordered, creative-type, 2-digits, magic-crosses, magic letters and magic numbers, etc. The detailed study can be seen in the reference list. The magic square summing 2020, 2021 etc. are also studied with different properties. In this work, block-wise and … Continue reading Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022

# Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6

During past years author worked with block-wise, bordered 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 108 and 102. Based on these two big magic squares inner order magic squares multiples of 6 are studied. By inner order we understand that magic squares of orders 96, 90, 84, etc. Instead of … Continue reading Block-Wise Bordered Magic Squares Multiples of Magic and Bordered Magic Squares of Order 6

# Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4

During past years author worked with block-wise, bordered 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 108 and 104. Based on these two big magic squares inner order magic squares multiples of 4 are studied. By inner order we understand … Continue reading Block-Wise Bordered and Pandiagonal Magic Squares Multiples of 4

# Creative Magic Squares: Singele Digit Representations

This work brings traditional magic squares of orders 3 to 10 in terms of single digit. In this case, the magic squares are written separately for each digit, i.e., for the digits 1 to 9. This has been done for all the orders 3 to 10. In case of orders 8 and 9 there are … Continue reading Creative Magic Squares: Singele Digit Representations

# Creative Magic Squares: Single Letter Representations

This work brings magic squares of orders 3 to 10 in terms of single letter "a", where a can take any value from 1 to 9. The magic squares of orders 8 and 9 are written in two ways, i.e, one as normal magic squares and another as bimagic squares. In case of order 10, we … Continue reading Creative Magic Squares: Single Letter Representations

# Magic Squares With Perfect Square Sum of Entries: Orders 3 to 31

This work shows how to create magic squares with a perfect square number for the total sum entries. This has been done in five ways. Initially, the two ways are using entries as consecutive odd numbers and consecutive natural numbers for odd order magic squares and consecutive fraction numbers for even order magic squares. This … Continue reading Magic Squares With Perfect Square Sum of Entries: Orders 3 to 31