How to construct a Magic Square for a Given Date

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.

[table id=magic-square-for-given-date__4x4 /]

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

[table id=magic-square-for-given-date__4x4_using_alphabets /]

  1. 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.
  2. Add all the four numbers and write on the top of the square (139).
  3. Now we have to make a 4×4 magic square.
  4. Draw a empty 4×4 square and replace 22 by A, 12 by B, 19 by C and 87 by D.
  5. Now we know A,B,C and D. Rest of the values we have to find out.
  6. Count all numbers in the total 1+3+9=13. Then 1+3=4. (add all numbers and make it a single digit. Write this in the H square
  7. 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
  8. 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.
  9. 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
  10. Now in Diagonals, we know the value of A and Z . Hence the value of G+Q = 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.
  11. 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.
  12. In the second row, we know the value of E,G,H. Hence value of E=139-(E+G+H)= 139 –( 50+17+4)= 139 – 71 = 68. Write 68 in E.
  13. 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.
  14. 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
  15. 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
  16. Now add the values of W,X,Y and Z. If you get 139 is the total,

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

Enjoy Magic square for your date of Birth!!!

How to construct a 3×3 Magic Square for a Given Total

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 /]

  1. Let us do 3 x 3 magic square with Magic Sum of 63.
  2. From 63, minus 15 ( the row total of 3×3 base magic square. (63-15=48)
  3. Divide 48 by 3(since we have decided to do 3×3 magic square (48/3=16).
  4. Add one to this (16+1=17)
  5. 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).


  • 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.

How to construct 6 x 6 Magic square

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

[table id=6×6-magic-square–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 6×6 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 3×3 square to the bottommost left 3×3 squares with the numbers 35, 32, 31 and vice versa.
  6. Your 6×6 magic square is ready. All vertical, Horizontal and both diagonal totals are equal ( 111) .

How to construct a 4 x 4 magic square

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

[table id=4×4-magic-square /]

  1. Draw a 4×4 empty square.
  2. Draw two diagonals.
  3. Start counting all the squares from the top left towards right.
  4. 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)
  5. 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.
  6. 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.


How to construct an odd order magic square?

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.

  1.  Put number one in the upper middle square.
  2. Always write the next number ONE SQUARE RIGHT AND ONE SQUARE ABOVE
    • 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.
  4. 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”


Magic Squares – What are they?

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

Properties of the Magic Square:

  1. Magic squares are made in 3×3, 4×4, 5×5….etc.
  2. Generally a 3×3 magic square is filled with numbers 1 to 9 and 4×4 magic square is filled with 1 to 16,…… In general a “nxn” magic square will be filled with 1 to n2 numbers.
  3. In general in a “nxn” magic square will have “n” rows and “n” columns and n2 Small squares.
  5. A magic square done from 1 to 9, 1 to 16,… are called as Base Magic square.
  6. 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+n2 ) / 2} ……. {( 1+n2 ) divided 2}
  7. 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…
  8. We can make 3×3, 4×4, 5×5… magic squares for a particular number, and for a given space interval at our choice.
  9. Also we can make magic squares for a given number, given year or given date of birth etc.

Article in The Hindu – A number play

I was featured in The Hindu today.

Learning mathematics can be made simple. It all depends how you approach the subject. Once you bring in the fun element, then learning any subject is easy. This was the point of discussion at the ‘Fun Maths and Mind Games’ programme by T. R. Jothilingam, an expert in number games. “Why should people hate Mathematics? Is it not the subject that makes your brain active?” he asked and assured how inadequacies could be addressed to get rid of the strong dislike for the subject among students.


You can take a look at the entire article here :  Link To Article

Srinivasa Ramanujan – 16×16 Biography Magic Square

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!

Srinivasa Ramanujan 16x16 biography Magic Square
Srinivasa Ramanujan 16×16 biography Magic Square

(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.

Article in The Hindu – In pursuit of puzzles

I was featured in The Hindu today.

Is maths fun? There may be some who reply positively but it bears a dull reputation among many others. But if the numbers are interspersed in puzzles and mind games, it is sure to kindle interest amongst children. Encouraging children to approach the subject with ease is what station master T.R. Jothilingam does. He has a passion for the mind games, puzzles, Sudoku and more. He began to deal with numbers a decade ago and set up his first magic square then. As he dealt more with them he found a great satisfaction in completing them. He has set up odd number magic squares, 4×4 magic square (total 34), special magic squares, an upside down magic square (it is a magic square when turned to 180 degrees gives the same total of 24) and a Palindrome magic square (a number when read from left to right or right to left is the same).


You can take a look at the entire article here :  Link To Article

Article in Madurai Messenger – Puzzle Master Extraordinaire

I was featured in Madurai Messenger today. 

Watching kids, and particularly teenagers, giddily glowing over learning, is always a treat. Especially when what they are learning is mathematics, a subject that sometimes bears a dull reputation amongst youth. But T.R. Jothilingam brings his passion for puzzles to the front of the class, holding the attention of his eager pupils, all the way till the bell rings. Having always had a way with numbers, it was not until seeing his fi rst magic square, about ten years ago, that Jothilingam’s interest in fun maths deeply intensifi ed. “After discovering magic squares”, he explains, “I was drawn to the satisfaction I found in completing them.”


You can take a look at the entire article here :  Link To Article