# TR Jothilingam magic square maths puzzles

# In pursuit of puzzles

LALITHASAI

Is maths fun? There may be some who reply positively but it bears a dull reputation among many others. But if the numbers are interspersed in puzzles and mind games, it is sure to kindle interest amongst children. Encouraging children to approach the subject with ease is what station master T.R. Jothilingam does. He has a passion for the mind games, puzzles, Sudoku and more. He began to deal with numbers a decade ago and set up his first magic square then. As he dealt more with them he found a great satisfaction in completing them. He has set up odd number magic squares, 4×4 magic square (total 34), special magic squares, an upside down magic square (it is a magic square when turned to 180 degrees gives the same total of 24) and a Palindrome magic square (a number when read from left to right or right to left is the same).

**Square inside a square**

His latest is a huge magic square inside a magic square. Explains Mr. Jothilingam: It contains 1–900 numbers arranged in 30×30 squares giving a grand total of 13,515 when added vertically, diagonally and horizontally. The uniqueness of this square is that it is similar to the whorl of a flower. When you remove the outermost line of numbers it becomes a 28×28 magic square. Similarly, as we remove line by line we will move into the innermost whorl (when it becomes a 4×4 magic square – total of the numbers will be 1802). Every time we remove a whorl the total diminishes by 901.

What exactly are these magic squares? “It is a square array of numbers consisting of distinct positive integers arranged in such a way that the sum of the numbers in any direction is always the same number _ magic constant.”

**Unususal shapes**

The math wizard has also created unusual shapes using these squares. Year 2012 has been declared as the Year of Mathematics. As a homage to the great Indian mathematician Ramanujan he has created the ‘Ramanujan Biography magic square’.

Jothilingam says: From top left towards right the important dates in the life of Ramanujan was taken in double digits representing either the date or month or the first or second part of the day. Then his date of birth is taken in four separate squares. I have also formed two separate 100×100 Ramanujan Biography magic squares with all the important dates, years in the life of Ramanujan from his birth to demise and later too.

All the 100 squares of two digits will have a total 2183 and 2179. From top left towards right onwards or from top to bottom onwards the magic squares will be of orders 4×4, 8×8, 12×12, 16×16, 20×20 and then in increased orders of 25×25, 30×30, 36×36, 42×42, 49×49, 56×56, 64×64, 72×72, 81×81, 90×90 and finally100x100.

Forming unique Sudoku puzzles is another creation of his. He has names encrypted into sudoku puzzles. Called Éncrypted Sudoku, an array of numbers has a name hidden in them.

**Novel puzzle**

The novel puzzle contains a number of square fields with numbers repeated in a particular order according to the encrypted name. For instance, the word ‘The’ has been encrypted using 28 numbers repeated in the sequence 1-9, 1-9, 1-9 and 1. Similarly ‘Hindu’ has been encrypted using 45 numbers and filled with 1-9 numbers five times. It is a full-fledged Sudoku obeying all its properties. (Normally every Sudoku has 3×3 small squares, each vertical, horizontal line are formed with 1-9 numbers.

He has created Sudokus with 10,000; 14,641; 50,625 and a mega 1,60,000 squares.

Jothilingam’s creations include hand finger multiplication, solving various kinds of chess puzzles and so on. He is ably assisted by T.J. Ramnath Babu, B. Tech in National Institute of Technology, Tiruchy and T.J. Raghunath Babu, engineering in Guindy Engineering College, Anna University (he was a first rank holder in all collegiate competition conducted by Microsoft company in SRM University for program designing in 2008 and 2009).

Jothilingam has also conducted programmes in Jaya TV, Podhigai, and delivered guest lectures in various colleges.

He conducts classes in more than 100 schools and colleges in Tamil Nadu, Karnataka and Kerala.

His aim is to enter the Guiness Book of World Records. He also plans to release a book on Fun Maths and Mind Games in simplified language.

To know about his brain stimulating concepts, mail tojothi@gmail.comor contact 94428 10486.

**T.R. Jothilingam has set up odd number magic squares, 4×4 magic square, etc.**