Multiples of fun

T.N. Mahesh’s study is a small room made smaller by a clutter of boards. Most of these vinyl panels depict magic squares with missing numbers. He explains, “These are magic square puzzles that I carry to schools. By solving them, students get to understand the beauty of magic squares.” Not a peripatetic teacher, Mahesh however looks for opportunities to promote the subject. And he compels attention for what is an impressively original work in the field. After scaling up 4x4 magic squares to 8x8, he creates puzzles out of them.

Mahesh has worked on all the 880 magic squares of the order-4 that are classified into 12 groups. Out of them, he has chosen around a hundred to create puzzles. “Scaling up each of the hundred to an 8x8 magic square in 25 different ways, I create a wide range of puzzles,” says Mahesh. “Technically, I can scale up each of the 880 magic squares of the order-4 using 25 methods and churn out countless puzzles. But I stick to certain groups (out of the 12) because they make more challenging puzzles than the others.”

Mahesh has a professionally designed website — magicsquarepuzzles.com – where he posts these puzzles for free. He holds a copyright for the method with which he derives his puzzles, and it is titled “The Mimic Method & The Game Magic Square Puzzles”.

It’s remarkable that Mahesh is not a trained mathematician and serves as a development officer with the Life Insurance Corporation of India. A love for numbers bloomed when he was helping his mother, Indira Narasinga Rao, write a book, Magic of Magic Squares (2007), which discusses the dynamics of odd-order and even-order magic squares. Indira made it to the Limca Book of Records in 2001, for scaling up a 4x4 magic square that is found in the Hindu almanac, to a 1000 x 1000 magic square.

His mother’s achievement served as inspiration, but Mahesh did not follow her trail. He has evolved his own style, which includes taking up double even-order magic squares. All of Mahesh’s scaled-up magic squares are divisible by the numbers 2 and 4. “I can create 12x12, 16x16 and other magic squares that are divisible by ‘2’ and ‘4’, up to infinity,” says Mahesh. “It’s logically possible, but not practical. Paper and screen size are among considerations that keep me focused on 8x8 magic square puzzles.”

There is another reason. Mahesh believes unwieldy magic square puzzles can be a put-off. “These puzzles hone skills of logic and arithmetic. For this reason, they have to be made interesting,” says the 45-year-old recreational mathematician.

Keeping with this line of reasoning, he has made a 50-minute film, titled Magic Square Puzzle.