A magic square is a square grid in which the numbers in each row, column and diagonal sum to the same number.

For example,

is a magic square that uses each of the numbers from \(1\) to \(16\) once.

There are many magic squares of different sizes; perhaps you have come across some. The artist Albrecht Dürer even included one in his engraving Melancholia I.

But why are magic squares about addition? Could we have a magic square where the numbers in each row, column and diagonal multiply to the same number?