 # A Magic Square of order four in Ramanujan’s Honour

An equation for me has no meaning, unless it expresses a thought of God.

Srinivasa Ramanujan

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National Mathematics Day is observed annually on December 22nd to mark the anniversary of the eminent mathematician Srinivasa Ramanujan’s birth. His contribution to the subject does not require any introduction.

A square matrix can tell us so many things and even show us some magic. In this blog post let us consider the magic square due to this legendary mathematician, which uses Ramanujan’s birthday (December 22, 1887) to fill the cells in the top row. The first number 22 represents the date (of his birth), the second number 12 is the month (of his birth), and the third and fourth numbers together 1887 is the year (of his birth). The magic square is here.

## Few Notable Properties

(a) The sum of the row elements in each row is equal to 139. For example,

22 + 12 + 18 + 87 = 139

88 + 17 + 9 + 25 = 139

10 + 24 + 89 + 16 = 139

19 + 86 + 23 + 11 = 139

(b) The sum of the column elements in each column is equal to 139. For example,

22 + 88 + 10 + 19 = 139

12 + 17 + 24 + 86 = 139

18 + 9 + 89 + 23 = 139

87 + 25 + 16 + 11 = 139

(c) The sum of the diagonal elements is also equal to 139. For example,

22 + 17 + 89 + 11 = 139 (green)

19 + 24 + 9 + 87 = 139 (light blue)

(d) The sum of the corner elements is also equal to 139. For example,

22 + 87 + 11 + 19 = 139

(e) The sums of the numbers in the two sets of like coloured cells are again the same number 139. For example,

12 + 18 + 86 + 23 = 139 (yellow)

88 + 10 + 25 + 16 = 139 (purple)

(f) The sums of the numbers in the two sets of like coloured cells are again the same number 139. For example,

12 + 88 + 23 + 16 = 139 (yellow)

18 + 10 + 86 + 25 = 139 (blue)

(g) The sum of the numbers in the four central cells is again 139. For example,

17 + 9 + 89 + 24 = 139

(h) The sums of the numbers in the like-coloured 2 × 2 blocks are all 139. For example,

22 + 12 + 17 + 88 = 139 (light blue)

18 + 87 + 25 + 9 = 139 (orange)

89 + 16 + 11 + 23 = 139 (olive green)

10 + 24 + 86 + 19 = 139 (green)

(i) The sums of the numbers in the like-coloured 2 × 2 blocks are also 139. For example,

88 + 17 + 24 + 10 = 139 (gray)

9 + 25 + 16 + 89 = 139 (lime)

## Explanation

A closer look at the below 4 × 4 matrix will show that there is really no magic in the above magic square. Consider the given one and look at the elements that belong to the same colour box. What are your thoughts?

Clearly, the given matrix looks like this. What we all need to know is the first row of elements. Considering the first row elements as DD, MM, CC and YY, the above matrix can be written as

It is easy to see why the above magic observations work on this matrix. Using the same idea as above, you can create another birthday magic square easily. All you need to do is to choose the matrix elements accordingly. In fact, you can build such magic squares for anybody’s date of birth (even yours).

Your suggestions are eagerly and respectfully welcome! See you soon with a new mathematics blog that you and I call Math1089 – Mathematics for All!“.

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