Category Archives: recreational math

How to make the Number puzzle

Some of my friends asked about the procedure for doing the above puuzzle.

Just look into the pattern closely for two or three times.

All yellow numbers are written on clockwise and the blue squares are filled with anti clockwise.

Now check the total of two blue squares and in between yellow square.

Adjust some the numbers in the begining to come at the total correctly.


Now let the required total be 2025.

Deduct 369 from the 2025, you will get 1656

Since the total 369 is the addition of 3 squares, divide 1656 by 3, you will get 552.

Now add 552 in all the squares. the total of two blue squares and in between yellow square. you will get 2025

The format 1 to 210 will give a total of 369 and you have added 3 x 552, you will get 369 + 1656 = 2025.

Circular Number Puzzle from 1 to 1000 A Unique way– Part Three

In continuation of the number puzzles, a new puzzle was done by me on 8-2-2022.

All numbers from 1 to 1000 are utilised in this puzzle and any three continuous squares ( two brown squares and one Blue square in between will give the same total of 1752 at any given point.

I thank the Almighty for giving me the idea, conducted me, guided me to complete the NEW BIGGEST CIRCULAR NUMBER PUZZLE.

Number puzzle — A unique way (Part Two) Honoring The great Indian Mathematician Srinivasa Ramanujan’s 135th Birth Anniversary in a Unique way

The entire world is celebrating the 135th Birth year of the famous Indian Mathematician Srinivasa Ramanaujan. On this occassion we proudly submit a new idea/ puzzle that gives a total of 135

In the above puzzle, count any three successive (two blue squares and one brown square in between) throughout the round, you will get 135

Concept, Design and execution by T.R.Jothilingam, Retired Railway Station Superintendent, Madurai, South India.

Receipient of Ramanujan Award in India in 2016.

Done Five Maths World Records in Sept 2017

Got First place in a worldwide puzzle contest in 2014

Got “Top 100 Maths Genius Award in December 2017

Number Puzzle – A new way

Recently I had an opportunity to see a Heptagonal Puzzle done by the Famous Mathematician Henry Dudeney (1847 – 1930).

It is a puzzle with seven sides and each meeting point and the middle of the line are placed with some numbers. The numbers are so arranged that any two numbers on two continuous points and one middle number betwwen them will always give a total of 26.

As a puzzle lover it attracted me to expand this puzzle in a bigger way.

In my first attempt after so many trail and errors I made my first puzzle with numbers 1 to 22 with total of 40

Then I expanded it from 1 to 46 with a total of 82

Now I made a Biggest one successfully with all numbers from 1 to 210 with a total of 369, and it is in a zig zag form with the same concept.

Hope you can enjoy and get some idea and enjoy Maths in a easy way.

Best of luck, kindly go through my website

Finding the DAY for any given DATE

Finding the DAY for any given DATE

1) Let the given date is 14-7-2021.

2) The formula is [ K + { (M-2) x 2.6 – 0.2 } + C/4 + D/4 +D-2C] divided by 7

3) Where K is the date M is the month C is the century D is the last two digit of the year

4) [ 14 + { (7-2) x 2.6 – 0.2} + 20/4 + 21/4 + 21 – 40 }] divided by 7

if M – 2 is zero or -1 ( Feb or Jan) , less one from the year ( D ) and add 12 months to month M.

Drop all the residuals/fractions in all cases and take the whole number only

5) [ 14 + 12.8 + 5 + 5 + 21 – 40] divided by 7

6) {14 + 12 + 5 + 5 + 21 – 40) divided by 7

7) 17 / 7 = 2 and 3/7

If the reminder comes ZERO, it is SUNDAY. 1/7 means MONDAY, 2/7 means Tuesday, 3/7 means WEDNESDAY, 4/7 means THURSDAY, 5/7 means FRIDAY AND 6/7 means SATURDAY.

Hence 14-7-2021 is Wednesday .

9) Try for other dates also.

By T.R.Jothilingam,Retd.Railway Station Supt., Madurai



There are so many other mind boggling games in the Chess Board, other than playing chess.

Some of the puzzles are given below

In a 8 x 8 Chess Board, you can put a maximum of 8 Queens ( each one is to be treated with the power of QUEEN).

One of the position is given below. There are 8 Queens available and check and satisfy by yourself that they are not cutting each other .

Believe. There are 92 different methods available. Try by yourself to find out more methods. Enjoy the new experience

64 knight(Horse) movement in a chess board. It is one of the hardest puzzles that can be solved by the Human Brain.

It is very tough to do, but it is possible.

Draw a 8 x 8 squares in a paper with Ballpoint pen and start writing 1,2,3 etc with a pencil. Start number one anywhere and continue the next number in a knight move method, till you are reaching 64.

See the magical thing in the picture given below. In the outer ring all the diagonally opposite numbers are having a difference of 6. Also in the second inner ring also the diagonally opposite numbers are giving a difference of 6 excepting 10 and 64

Some of my students ( Eighth Standard – 13 years) in Madurai have done more than 10 different methods. You can find infinite ways of doing this. Best wishes.


There are eight pieces available in the first row of the Chess Board.

They are One King, One Queen, two Bishop (camel) and two Knight (Horse) and two Rook (Elephant).

With these Eight pieces, when placed in some proper positions, they will guard all the sixty four squares with their own power. Please check and satisfy by yourself.

Once again, there are so many different methods available. Try to do it more and more methods

64 King move in a chess Board and 8 x 8 Magic square

In the following chess board, one King starts from number one and make 64 moves and completes his journey without any break.

Finally, if you add the numbers it will give a total of 260 in all vertical, Horizontal and both diagonals. Yes. It is a 8 x 8 Magic square also.

Try for other methods also.

Puzzling number Puzzles

There are many different kinds of puzzles for entertainment as well as to improve our knowledge as well.

In the above You have to write all numbers from 1 to 9 in the same arrangement and you can put any mathematical symbol as you know.

The result of the final format must be 100.

Remember. There are 320 different methods available.

Some of the solutions are given here for easy understanding.

Hope you will be finding this puzzle is very challenging and enjoyable.

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!


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


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


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).