The word “RAMANUJAN” occupied 89 cells and numbers 1 to 9 are used 9 times each and the balance filled with 1 to 8. 8 along with the properties of NORMAL SUDOKU.

1) The entire word “RAMANUJAN” is first written using 119 squares (or cells).
2) Numbers 1 to 9 are filled inside each of these letters.
3) In total, the numbers 1 to 9 are written 13 times and the remaining cells are filled with 1 and 2.
4) We then take each Sudoku of 9 x 9 individually and fill them. The total number of squares that are covered for the word/letter are filled 1 to 9, the adjacent Sudoku (in the right) will commence with the numbers next to the last with 1 to 9 till it fills in the alphabet in that 9 x 9 Sudoku, and the next word/letter will start with the filled number.
For example, the first sudoku contains 20 squares, that are filled with 1 to 9 two times and the balance with 1 & 2. Hence the next Sudoku will commence with 3 to 9, 1 to 9, and so on.

The word “RAMANUJAN” occupied 89 cells and numbers 1 to 9 are used 9 times each and the balance filled with 1 to 8. 8 along with the properties of NORMAL SUDOKU.

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

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.