Maths and Magic: The Magic Square

Ever since I was a child, I have been fascinated by Mathematics. I was baffled by the subject and often wondered how someone could come up with the theorems and formulae that we studied in school. While others considered it difficult, I always felt it was beautiful. It must be because numbers always aroused my curiosity and I had enormous fun playing with them.

That’s what it was for me – play! I think it was in the 6th grade that I first came across a number puzzle in a magazine. The puzzle was a grid of numbers with some empty spaces to fill in. The rule was to fill in all the empty spaces with non-repeating numbers, such that the sum of numbers along the rows, columns and diagonals was the same.

It was a captivating puzzle and I was hooked on to it every time. I felt like a genius when I could complete the puzzle and the numbers turned out to be correct. The magazine published the answers a week later in the next issue, and I always waited impatiently to check my answers against theirs. Sometimes, the magazine also ran competitions where anyone could send in their answers and win prizes. Although I solved the puzzle every week, I never sent in any of my answers. The allurement of solving the puzzle was prize enough for me, I guess!

It was only much later during my College education that I learned that these puzzles were a Mathematical concept called Magic Squares and the common sum is the “Magic constant”. Here is an example of a Magic Square, with the first nine numbers of the decimal system. The magic constant is 15.

table 1

When I entered into teaching, these Magic squares continued to hold fascination because I learned how to create them. Today, when I work with students and teachers at NumberNagar, Magic squares come in as a handy tool to inspire them on the magical quality of Maths. A simple concept like addition can take on a challenging twist when set into the context of Magic squares.

I continue to search for interesting Magic squares to tickle my curiosity and to keep my interest levels high. In my recent pursuits, I have come across a Magic square in a work of art – Durer’s Melencolia.

magic Math.png

This Magic Square has the magic constant, 34. This piece of art is a tribute and testimony to the fact that learning is all-rounded, and subjects don’t have to be segregated as rigorously as we do today. Who knows which child might get inspired to do Math by looking at Art! Or who might get inspired to do Art by looking at Maths!

There is another Magic square that has caught my attention and intrigues me every time I look at it – the Ramanujan’s Magic Square. The magic constant in this square is 139. The special features of the Ramanujan’s Magic Square are:

  • The first row of numbers is Ramanujan’s date of birth
  • In addition to every row, column and diagonals adding up to 139, there are other groups of four numbers that add up to 139 also (those coloured with the same colour).

One example is shown below.

table 2.png

The personal aspect of using one’s date of birth inspired me to create one of my own. I created my own personal date of birth Magic Square and the magic constant for my square is 129. I could also find the additional groups of four numbers that add up to the magic constant.



Every time I look at this Magic Square, I admire the genius of Ramanujan for having thought of such a magnificent way of engaging with numbers. I have always wondered how it must have been for him, when he was playing with numbers in his mind.

Aren’t you now thinking of creating your own date of birth Magic Square? Go ahead! Give it a try, that’s the magic of Maths.

May the magic be with you!

-Sriraghavan S M, Co-Founder and President – Customer Relationship, BrainSTARS

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