A magic square is a square array of numbers consisting of the distinct positive integers $1, 2, ..., n^2$ arranged such that the sum of the $n$ numbers in any horizontal, vertical, or main diagonal line is always the same number
I was wondering if the numbers of magic squares of order $n$ is still a conjecture (For a general $n$) ?
And I have some elementary questions regarding the magic squares.
(1) What is the smallest $n$ for a magic square ?
I guess for $n=1$ we just have one $1 \times 1$ matrix $[1]$
(2)And for $n=2$ , They don't exists !! (right)
(3)For $n=3$ we have 8 different magic squares and so on.
Now my question is, after $n=3,4$ The numbers of magic squares grows rapidly, and I want to know if there is a systematic way to get those numbers or does it remain to be a conjecture ?
Is there some interesting applications where those magic squares are used ?
I have a project to do on combinatorics and I was thinking of considering this (what do you guys think ?)
It will be interesting to try some code and algorithms on it too.
I would also love if someone knows a good resource or papers on those magic squares.