Having worked on a variety of special Magic squares ourselves, we could not think of a greater tribute to Srinivasa Ramanujan than this!

Summary

This is one of the biggest number puzzles we have done so far! This Biography Magic Square summarizes the important events that happened in the life of Sri Srinivasa Ramanujan.

The important dates in the life of Srinivasa Ramanujan were compiled from various sources. These dates were taken two digits at a time, representing either the date of the month or the month or the first/second half of the four-digit year. As an example, Ramanujan’s date-of-birth 22-12-1887, is taken as four separate entries as 22 12 18 and 87. In short, Ramanujan’s entire life history is reproduced here, from his birth to till date in Ramanujan-style.

Construction

Important dates from Ramanujan’s life were collected and these were then arranged horizontally in a row, from left to right. This row would form the top row of this biography magic square. The rest of the magic square is constructed after assembling this row.

This magic square has the properties of a conventional magic square, namely the sum of the entries along each row/column/diagonal sum up to the same magic-sum 2183.

It has these additional properties:
– starting from left to right, or, from top to bottom, we have embedded magic squares of orders 4 x 4 , 8 x 8, 12 x 12, 16 x 16, 20 x 20, and then in increased orders of 25 x25, 30 x 30, 36 x 36, 42 x 42, 49 x 49, 56 x 56, 64 x 64, 72 x 72, 81 x 81, 90 x 90, and finally 100 x 100. This is thus a cascade of magic-squares-inside-a-magic-sqaure!

Thus the total 100 x 100 Ramanujan Biography Magic square will contain the following 184 smaller magic squares of sizes as listed below:

Size of Magic Square Number of such Magic Squares Total Entries

4 x 4 Magic squares 25 25 ( 4 x 4 ) = 400 squares

5 x 5 Magic squares 20 20 ( 5 x 5 ) = 500 squares

6 x 6 Magic squares 24 24 ( 6 x 6 ) = 864 squares

7 x 7 Magic squares 28 28 ( 7 x 7 ) = 1372 squares

8 x 8 Magic squares 32 32 ( 8 x 8 ) = 2048 squares

9 x 9 Magic squares 36 36 ( 9 x 9 ) = 2916 squares

10 x 10 Magic squares 19 19 (10 x 10 ) = 1900 squares

Total 184 (Different sized squares) 10,000 Squares

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 4×4 magic square.

Draw a empty 4×4 square and replace 22 by A, 12 by B, 19 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. Then 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 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.

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. Hence 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. If you 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….

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

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.

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:

Magic squares are made in 3×3, 4×4, 5×5….etc.

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.

In general in a “nxn” magic square will have “n” rows and “n” columns and n2 Small squares.

After filling all columns, 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+n2 ) / 2} ……. {( 1+n2 ) 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 3×3, 4×4, 5×5… magic squares for a particular number, and for a given space interval at our choice.

Also we can make magic squares for a given number, given year or given date of birth etc.