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Palindromic Magic Square (விகடகவி மாயச் சதுரம்)

palindrome magic square

A palindrome is “a word, phrase, or sequence that reads the same backwards as forwards“, example madam

We have come up with a new idea of forming palindrome magic square with special feature of repeated numbers along the diagonals!

This is a sample 5 x 5 Palindrome Magic Square. We have also done the same for higher orders including 7 x 7, 11 x 11, and so on! Happy exploring!!

Note: விகடகவி மாயச் சதுரம் in Tamil means Palindrome Magic Square

Diabolic Magic Square

4 x 4 Diabolic Magic Square

The above 4 x 4 Magic square gives a total of 34 across all rows (horizontal), columns (vertical) and both diagonals. ( 4 + 4 + 2 = 10 methods)

Along with that, each distinctly colored 2 x 2 square will give a combined total of 34 each.

Additionally, the four corners, 4 middle numbers will give a total of 34.

We can select, 4 particular numbers and come with a total of 34 in more than 60 different ways.

Explore it for yourself and enjoy!!

Done a World’s biggest 1999 x 1999 Diamond inlaid magic square ( All numbers from 1 to 39,96,001 used) Example: 21 x 21 Diamond inlaid magic squares is given here. (With numbers 1 – 441 )

Diamond inlaid magic square is a very special magic square. It will have all odd numbers placed in the center in a Diamond shape and all even numbers distributed in four seperate triangular shape in the four corners.

In the above 21 x 21 diamond inlaid magic square, all the numbers from 1 to 441 are used. All the vertical, Horizontal and both diagonal totals are equal to 4641.

Surprisingly around the center number 221, all the diagonally opposite postioned numbers, and symetrically opposite positioned numbers will give a total of 442. There are 441 – 1 = 440 / 2 = 220. We can get it in 220 different methods.

I have done a 1999 x 1999 Diamond inlaid magic square in which all the numbers from 1 to 39,96,001 are used. All Horizontal, vertical and both diagonal totals will be 399,40,03,999. ( Three hundred ninty nine crores, forty lakhs, three thousand and nine hundred and ninety nine) or 3,994,003,999 ( Three Billion, 994 million, three thousand nine hundred and niniety nine)

Thanks to the Almighty for giving me the idea, guided me, till the final execution to make it a reality.

Encrypted sudoku

Encrypted sudoku

It is UNIQUE in the world.  A serial of sets of sudokus are formed from left to right and Name of  a great person or thing  is encrypted  using  numbers 1 to 9 repeatedly. All sudokus are full fledged sudoku with all vertical, Horizontal and each 3 x 3  small squares are filled with 1 to 9.

Unique in the world encrypted sudoku done for the famous Indian Mathematician Srinivasa Ramanujan

The name “Sririnivasa Ramanujan” is encrypted in the Sudokus.  The word  “Srinivasa” is made with continuous letters 1 to 9 repeatedly.  For example the letter “S” contins 14 square and filled with the numbers 1 to 9 and once again with 1 to 5.   The next letter ” R ” will begin with the next number 6 and filled with 6 to 9 and from 1 to 9 onwards.

Each seperate coloured 9 x 9 squares is a full fledged sudoku with all the     3 x 3 squares are filled with 1 to 9 and all horizontal and vertical lines are also filled with 1 to 9.

This an UNIQUE featured one.  Also I have done encrypted sudoku for Swami Vivekananda, Mahatma Gandhi and many more leaders.

Ramanujan Award 2016

I was awarded the Prestegious “Ramanujan Award ” in 2016 in INDIA, which is so far  awarded to two outstanding individuals in India, for their contributions in the field of Mathematics.

This award is given by the All India Ramanujan Maths Club, New Delhi. This was given at the 11th National Mathematical Convention held at Gandhi Nagar in Gujarat near to Ahmadabad on 26-11-2016.  The award was presented by the Gujarat Speaker Ramanlal Orra.

The Ramanujan Award Shield

9×54 Ramanujan sudoku

This is a variation of the popular puzzle Sudoku.

Ramanujan Sudoku 9x54
Ramanujan Sudoku 9×54

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.

Srinivasa Ramanujan – 100-by-100 Biography Magic Square

Ramanujan and Magic Squares

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

Incidentally, in the opening page of the first Ramanujan’s notebook, there begins by working out a 3 x 3 Magic Square!

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.

Srinivasa Ramanujan 100x100 biography MagicSquare
Srinivasa Ramanujan 100 x 100 biography MagicSquare

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


Sidenote

We have constructed a smaller 16 x 16 version of this Biography Magic Square with fewer details, which you can find here.

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).