This four-by-four Magic Square uses all the integers from -7 to 8. Complete the square. More Magic Squares!

Question

This four-by-four Magic Square uses all the integers from -7 to 8. Complete the square.

This is what has been given so far:

-7 _ _ _

_ -2 _ +1

_ _ +3 _

+5 _ _ _

Please Help. Thank you

Answer 1

So, first of all, magic squares are still valid when:

They are rotated,

and

All numbers are added to a same number (the number can be negative)

Therefore, given that the normal 1-16 magic square will be:

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

After rotation, you get:

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

and adding each number by -8, you get:

+5 0 -4 -7
-5 +2 -2 +7
-8 +3 -1 +6
+8 -3 +1 -4

which is the final answer!