Solve 3x3 Numerical Puzzle: Can it Be Done?

[Natasha1]

1. In a 3 x 3 square, place the numbers 2,2,2,3,3,3,4,4,4 in it so that when any line of three numbers is added up in any direction (including diagonally) the total is always 9.

2. I have tried for hours, can anyone tell me if this problem is actually possible?

The best I get is when I do

234
342
423

And only get one diagonal of 4s which you can also do with only 3s or 2s. Any help would be truly welcomed. Thank you!

 

[jedishrfu]

Start with the center square and think what number can be placed there so that the two diagonals and middle row and middle column can sum to 9 with the same number?

 

[Natasha1]

Is there only one solution to this problem. Is the centre square 2?

 

[Natasha1]

I just can't do this... There are no numbers that can go in the middle and satisfy this problem

 

[Mark44]

Is there only one solution to this problem. Is the centre square 2?

It took me about 4 tries, but I came up with two solutions, and there are probably four or maybe more. I don't have 2 in the center.

I just can't do this... There are no numbers that can go in the middle and satisfy this problem

Yes there are.

 

[Natasha1]

Got the answer

342
234
423

Thanks!

 

[Natasha1]

In my head only 4, 3 and 2 made 9... Ahhh basic! Forgot the 3, 3, 3.

Has anyone got any other combinations by pure interest?

 

[Joffan]

It took me about 4 tries, but I came up with two solutions, and there are probably four or maybe more. I don't have 2 in the center.

Excluding rotations, I think there's only one. With rotations, four, and allowing reflections makes no difference.

There must be at least one 3 in every line (9 is odd), which forces the diagonal of 3s, and the rest is determined by your next number placement.

 

[Natasha1]

Gosh how do you guys work all this out! Brainy!