Solve 3x3 Numerical Puzzle: Can it Be Done?

  • #1
493
8
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
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
Is there only one solution to this problem. Is the centre square 2?
 
  • #4
I just can't do this... There are no numbers that can go in the middle and satisfy this problem
 
  • #5
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.
 
  • #6
Got the answer

342
234
423

Thanks!
 
  • #7
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
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.
 
  • #9
Gosh how do you guys work all this out! Brainy!
 

Suggested for: Solve 3x3 Numerical Puzzle: Can it Be Done?

Replies
18
Views
545
Replies
6
Views
1K
Replies
4
Views
783
Replies
8
Views
852
Replies
4
Views
1K
Replies
25
Views
495
Replies
6
Views
2K
Replies
6
Views
512
Replies
5
Views
475
Back
Top