Fill a 3x3 square with the numbers from 1 to 9, so the four sides and the two diagonals share the same sum, which is to be as large as possible.
Well, to make the sum the largest, obviously the greater number goes to the corner, thus
9 _ 8
_ _ _
7 _ 6
Then, it is just filling up the remainders:
9 1 8
2 3 4
7 5 6
I am not sure if this is the largest possible, the is 18.