This is a variation of the popular puzzle Sudoku.
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.
Srinivasa Ramanujan had a special affinity toward numbers. His taxi-cab number (1729) incident is popular. A Mathematician without parallel, he made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. His works have been collected and analyzed throughout the world
Having worked on a variety of special Magic squares ourselves, we could not think of a greater tribute to Srinivasa Ramanujan than this!
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.
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
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).
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.
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
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 /]
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 /]
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.
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.