This is a DIAMOND Magic-Square wherein all the ODD-numbers are inside the Diamond shape. (Magic-Total is 65)

[table id=diamond_inlaid_5x5 /]

This is a DIAMOND Magic-Square wherein all the ODD-numbers are inside the Diamond shape. (Magic-Total is 65)

[table id=diamond_inlaid_5x5 /]

The above is a 30 x 30 Magic Squares inside a Magic Square

This is a special construction of a Magic Square wherein we start with a small Magic Square (centermost one in the figure) and added rows and columns around it, ensuring that we have a Magic Square at each stage. This Magic Square has been color-coded to make the Magic Squares clearer.

From the center Yellow coloured is a 4 x 4 Magic square with a total of 1802 in all vertical, Horizontal and in both diagonals. When combininng with the blue coloured sqauare, that 6 x 6 will give a totl of 2703. Further it will expand to 8 x 8 , 10 x 10 etc… and finally it will become 30 x 30 with a grand total of 13515.

**I have done this Magic squares inside the magic square from 5 x 5, 6 x 6, 7 x 7, …….198 x 198, 199 x 199 and 200 x 200. In the 200 x 200 Magic squares inside a magic square all the numbers from 1 to 40,000 are used and the row total will be 4,00,00,100. Also I am planning to do it upto 1500 x 1500. **

*Definitely, it is a gift given to me by Almighty. I thank the Almighty for giving me the idea, guided me to work, and helped me to complete it with much difficulties. *

This is a special Magic Square called as the SWASTIKA Magic Square. All odd numbers are inside the SWASTIKA SYMBOL. (The Magic-Total is 65)

[table id=swastika-5×5 /]

You can find more special Magic-Squares here

Let us do magic square to the date of Birth of our Greatest Indian Mathematician Sri Srinivasa Ramanujan.

His date of Birth is 22nd Dec 1887. The following is a Date-Of-Birth Magic Square with a Magic Total 139.

**By following the given method we can do hundreds of, thousands of, millions of Date of Birth Magic Squares for any given date.**

The following is a table with variables, which we will use in the explanation

- Write the date in the top row first square, month in the second square and year in two parts in the third and fourth square.
- Add all the four numbers and write on the top of the square (139).
- Now we have to make a 4 x 4 magic square.
- Draw a empty 4 x 4 square and replace
**22 by A, 12 by B, 18 by C and 87 by D.** - Now we know
**A,B,C and D**. Rest of the values we have to find out. - Count all numbers in the total
**1+3+9=13.**Once again count**1+3=4.**(add all numbers and make it a single digit.**Write this in the H square** - Now add
**B+C ( 12 + 18 =30)**. Divide**30 into two parts. i.e 14 and 16.**Write**14 in W**square and**16 in the Z square** - By using the properties of Magic square, i.e all vertical, Horizontal and both Diagonal totals are equal, we are going to solve this Magic Square.
- In the Fourth vertical column, we know the values of
**D,H,Z.**we have to find Out the value of S. Hence**S = 139 – (D+H+Z) = 139 — ( 87+4+16) = 139 – 107 = 32.****This is the value of S. Write 32 in the S square** - Now in Diagonals, we know the value of
**A and Z .**Hence the value of**F + R = 139 – (22 + 16) = 139-38= 101. Divide it into two parts 50 and 51**and write it in the F and R squares.**F = 50 and R = 51.** - In another diagonal, we know the value of D and W . Hence the value of
**G+Q = 139 – (87 + 14) = 139-101= 38.**Divide it into two parts 17 and 21 and write it in the F and R squares.**G = 17 and Q = 21.** - In the second row, we know the value of
**E,G,H. H**ence value of**E=139-(E+G+H)= 139 –( 50+17+4)= 139 – 71 = 68. Write 68 in E.** - In the third row, we know the value of
**Q,R,S.**Hence value of**P=139-(Q+R+S)= 139 –(21+51+32)= 139 – 104 = 35. Write 35 in P.** - Now in the second vertical column, we know the values of
**B,F,Q.**Hence value of**X = 139 – (12+50+21) = 139- 83 = 56. Write 56 in X** - Now in the third vertical column, we know the values of
**C,G,R.**Hence value of**X = 139 – (18+17+51) = 139- 86 = 53. Write 53 in Y** - Now add the values of W,X,Y and Z. You will get 139 is the total.

Hurray!!! **MAGIC SQUARE FOR 22-12-1887 IS READY**

**In step number 10, we have divided 101 into 50 and 51. Instead it can be divided into q and 101 or 1 and 100 or 2 and 99 etc. etc… Interestingly we can divide it as -1 and 102 or -2 and 103 or -3 ans 104 etc. While dividing each number, if the numbers are slightly changed, we can get a new Magic square. **

**Hence we can make hundreds of, thousands of, millions of date of birth magic squares for any given date**

**Enjoy Magic square for your date of Birth!!! In various methods….**

Let the given Number be 63. We will get to the following 3 X 3 Magic-Total 63.

[table id=construct-magic-square-for-given-total-63__3x3 /]

- Let us do 3 x 3 magic square with Magic Sum of 63.
- From 63, minus 15 ( the row total of 3×3 base magic square. (63-15=48)
- Divide 48 by 3(since we have decided to do 3×3 magic square (48/3=16).
- Add one to this (16+1=17)
- Now start constructing a 3 x 3 magic square with 17 as the beginning number and (Top row middle – Just in the place of 1).

Note:

- For constructing 3×3 magic square -15, then divide by 3, then add 1.
- For constructing 4×4 magic square -34, then divide by 4, then add 1. and
- For constructing 5×5 magic square -65, then divide by 5, then add 1.

While dividing by 3 or 4 or 5, if any fraction comes, put that fraction in all the squares. You should not delete or make it decimal.

Here is a 6 x 6 Magic Square with Magic-Total 111

1)Draw a 6 x 6 empty square.

2)Draw a bold line after the third square, Horizontally and vertically.

3).Now the 6 x 6 magic square will be divided into four 3 x 3 Magic squares.

4) Start filling the 3 x 3 magic square on the top left with numbers 1 to 9. and top right from 19 to 27, bottom left with 28 to 36 and bottom right with 10 to 18.

5) Now exchange the numbers 8,5,4 from the top left 3 x 3 square to the bottommost left 3 x 3 squares with the numbers 35, 32, 31 and vice versa.

6) Your 6 x 6 magic square is ready. All vertical, Horizontal and both diagonal totals are equal ( 111) .

As per the instructions given in step no. 4, the numbers 35,32,31 will be available in the down magic square in place of 8,5,4

The FINAL FORMAT OF 6 X 6 IS GIVEN ABOVE. This will be after exchanging numbers 8,5,4 and replacee them by 35,32,31 and vice versa

This is a 4 x 4 Magic Square with Magic-Total 34

[table id=4×4-magic-square /]

- Draw a 4×4 empty square.
- Draw two diagonals.
- Start counting all the squares from the top left towards right.
- Now start writing numbers 1 to 16, count all squares and write numbers ONLY IN THE BLANK SQUARES (2,3,5,8,9,12,14,15 are to be written)
- Now start writing number from the bottom most right square towards left, count all squares, BUT WRITE NUMBERS ONLY IN THE SQUARES HAVING DIAGONAL LINES ONLY (1,4,6,7,10,11,13 AND 16) ARE TO BE WRITTEN.
- Magic square 4×4 is ready.

**Note: This method is applicable only for 4×4 magic square. For 6×6, 8×8 there are separate methods available. **

**This is a 3 X 3 Magic square with Magic-Total 15**

[table id=3×3-magic-square__total-15 /]

We will discuss the construction of this, step-by-step.

- Put number one in the upper middle square.
- Always write the next number ONE SQUARE RIGHT AND ONE SQUARE ABOVE
- AND WHEN IT GOES:
- Beyond boundary in the upper side, write it vertically down most square.
- Beyond the boundary in the right side, write it in the horizontally leftmost Square.
- When the square is already filled with a number, just step-down one square vertically below.

- And after the Top right square always write the next number one square vertically below.

With these simple steps you can make any biggest “ODD NUMBER MAGIC SQUARE IN THE WORLD”

These steps are useful ONLY FOR ODD NUMBER MAGIC SQUARE AND WILL NOT BE USEFUL FOR EVEN NUMBER MAGIC SQUARES.

Magic squares are a set of numbers filled in a 3 x 3, 4 x 4,… squares and after filling it, all the vertical, Horizontal and both diagonal totals are equal.

**Properties of the Magic Square:**

- Magic squares are made in 3 x 3, 4 x 4, 5 x 5….etc.
- Generally a 3 x 3 magic square is filled with numbers 1 to 9 and 4 x 4 magic square is filled with 1 to 16,…… In general a “n x n” magic square will be filled with 1 to n square numbers.
- In general in a “n x n” magic square will have “n” rows and “n” columns and n square Small squares.
- After filling all squares ALL VERTICAL, ALL HORIZONTAL AND BOTH DIAGONAL THE TOTALS ARE EQUAL.
- A magic square done from 1 to 9, 1 to 16,… are called as Base Magic square.
- The total of a row/column of a Base Magic Square will be “First number plus the Last number added together, divided by two, and then multiplied by the Number of rows”. i.e. {( 1 + n square ) / 2} ……. {( 1 + n square ) divided 2}
- Generally natural numbers 1,2,3,… are used for forming the magic squares and we can use fractions, zero, negative numbers and squares, cubes etc etc…
- We can make 3 x 3, 4 x 4, 5 x 5… upto infinite. Magic squares for a particular number, particular size and for a given space interval is at our choice.
- Also we can make magic squares for a given number, given year or given date of birth etc.

This Biography Magic Square summarizes the important events that in the life of Sri Srinivasa Ramanujan.

**How it was constructed:**

Important dates in the life of Ramanujan were taken, two digits at a time, representing either the date or the month or the first or second part of the four-digit year. As an example, Ramanujan’s birth-day 22-12-1887 is taken in four separate entries as 22 12 18 87. These were then laid out in the top of the Magic Square, in the first column. Then, a complete Magic Square was built on top of these numbers, with the following additional feature : each square indicated by a separate color (in this case, there are 4 such 4×4 sub-sqaures), which are magic squares themselves!

(Download Ramanujan_16x16_biography_Magic_Square in excel format).

This is a smaller version of the 100-by-100 and 125-by-125 biography magic squares that we have constructed.

This was earlier published in an article “*A Unique Novel Homage to the Great Indian Mathematician*” in the March 2013 (Volume 23, Pg 146-147) Mathematics Newsletter published by the Ramanujan Mathematics Society. (download free).

If you find this interesting, you could construct your own! If you want some help, drop a mail to me at contact[at]jollymaths[dot]com.