I need to determine a set of numbers in this configuration:
123
456
789
The sum of 3 numbers cannot equal the sum of 3 numbers either left, right, up, down, or diagonally.
e.g.
4+5+6 == 7+5+3 == 15 is acceptable
7+2+9 == 3+6+9 == 18 is not acceptable
How can I determine what set of numbers will meet this criteria?
A magic $3\times 3$-square is
$$\pmatrix{6&1&8\\7&5&3\\2&9&4}$$
Upto symmetries, this is overmore the only possibility.