Why Is There Only One Type of 3x3 Magic Square?

A magic square is a square array of positive integers such that the sums of the numbers in each row, each column, and both main diagonals are the same.

And the number of integers along one side (n) is called the order of the magic square.

n = 1

It is trivial though it is a magic square by definition.

n = 1 is trivial

n = 2

It cannot be constructed. Try a few, and you will see.

Some trials to make n = 2 magic square (and failed)

n = 3

This is the example of n = 3 magic square.

n = 3 magic square

From now on, we will show that this is the only n=3 magic square.

Note, however, that the rotated and flipped ones are considered the same. The orientation of numbers that have become difficult to see due to rotation or flipping should be…