Rich Tasks 51: 'What is your magic number?' (Birthday Magic Square)

With any given top row, we can complete a fourth-order magic square. 

Part 1

Here is a magic square made by the birthday of the famous mathematician Ramanujan. (22 December 1887)

In this magic square rows, columns and diagonals add up to 139. 

However, there are so many other patterns in this magic square. How many can you find?

Part 2

What is your magic number? Can you complete a magic square with the date of your birthday in the top row?

Write your birthday on the top row following the instructions below:

(i) Place the special date in the first row

(ii) b+c = m+p [there are many different possible values]

(iii) a+p = g+j [there are many different possible values]

(iv) m+d = f+k [there are many different possible values]

(v) b+n = g+k

(vi) c+o = f+j

(vii) a+m = h+l [there are many different possible values]

(viii) All rows, columns and diagonals must add up to the same total

Sources
- https://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-public/ramanujans_honour_magic_square.pdf
- https://nrich.maths.org/1380
- https://en.wikipedia.org/wiki/File:Magic_Square_Ramanujan.svg