how to make a 4x4 magic sqaure which

Question

equals 18

Answer 1

place the numbers on the main diagonals:

1 x x 4
x 6 7 x
x 10 11 x
13 x x 16

Now fill in the others, working from bottom to top, right to left:

1 15 14 4
12 6 7 9
8 10 11 5
13 3 2 16

The rows, columns and diagonals add to 34.

We want them to add to 18, which means subtracting 16 from each row. That means lower each number by 4:

-3 12 11 0
8 2 3 5
4 6 7 1
9 -1 -2 12

That's very unusual, since normally nxn magic squares are built with the numbers from 1 to n^2.

we could also have used fractions, by multiplying the original values by 18/34.