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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?

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    What i sthe significance of 7+2+9? – 2017-02-23
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    Hard to guess what you want. Do you want to create a magic $3\times 3$-square ? – 2017-02-23
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    **Hagen** - 7+2+9 is just an example using the numbers I gave (1-9). They are not significant other than showing this configuration is disqualifying. **Peter** - I think this is exactly what I was looking for. – 2017-02-23

1 Answers 1

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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.