Help me with Math homework?

Question

There is a 4 by 4 grid. You have the numbers 1, 2, 3, 4, 5, 6, 7, 8, -1, -2, -3, -4, -5, -6, -7, and -8. Put the numbers into the 4 by 4 grid, so that each row, column, and diagonal add up to 0.

Answer 1

This is a variation on the magic square problem... Take two matrices, one where each row, column, and diagonal add to -10 and another where they add to 10:

-9,4,-5,0

-5,0,-9,4

0,-5,4,-9

4,-9,0,-5

+

1,2,3,4

4,3,2,1

2,1,4,3

3,4,1,2

=

-8,6,-2,4

-1,3,-7,5

2,-4,8,-6

7,-5,1,-3