The anti-magic square?

Question

2 9 4
7 5 3
6 1 8

The above shows a magic square which I'm sure most of you are familiar with. It uses the numbers 1 to 9 in a 3x3 grid in a manner that the three rows and the three columns together with the two diagonals. each add up to 15.

Now can you place these same numbers in such a way to form an anti-magic square so that the total in every direction is different? And if you're feeling very clever, can you create this anti-magic square in such a way that NONE of the totals is 15?

Answer 1

There are lots of choices... here's a few that avoid 15:

1 2 9
4 3 7
6 8 5

1 3 5
8 2 6
4 9 7

1 2 9
5 3 6
4 8 7

1 2 7
3 4 5
9 8 6

1 2 7
3 6 9
8 5 4

etc.

Note, these aren't "antimagic squares" in the formal definition. They are heterosquares. For a true antimagic square of order 3, all the sums would have to be consecutive integers. An exhaustive computer search of all the combinations found there was no 3 by 3 antimagic square with these properties (differing consecutive sums).

Answer 2

1 6 2
7 5 8
3 9 4

Answer 3

Another option

1 3 9
4 6 8
5 7 2

Answer 4

5 3 1
2 9 8
4 6 7

1st row = 9
2nd row = 19
3rd row = 17
1st column = 11
2nd column = 18
3rd column = 16

Diagonals = 14 and 21