A magic square is a square divided into smaller squares, each of which must be filled with a whole number so that the sum of the numbers in each row, column and main diagonal is equal to the same amount.

In the example in the picture, all of the rows, columns, and main diagonals add up to the number \(15\). In fact, any \(3 \times 3\) magic square, filled with the numbers \(\{1,2,3,4,5,6,7,8,9\}\) will have its rows, columns and main diagonals sum to \(15\).

You can make magic squares of any size: \(2\times 2\), \(3 \times 3\), \(4 \times 4\), \(5 \times 5\) and so on.