# 3x3 numerical puzzle

1. Dec 9, 2014

### 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!

2. Dec 9, 2014

### Staff: Mentor

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?

3. Dec 9, 2014

### Natasha1

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

4. Dec 9, 2014

### Natasha1

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

5. Dec 9, 2014

### Staff: Mentor

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.

Yes there are.

6. Dec 9, 2014

342
234
423

Thanks!

7. Dec 9, 2014

### 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?

8. Dec 9, 2014

### Joffan

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.

9. Dec 9, 2014

### Natasha1

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