Solve 3x3 Numerical Puzzle: Can it Be Done?

In summary, the conversation discusses a mathematical problem involving placing numbers in a 3 x 3 square so that any line of three numbers adds up to 9 in any direction. The participants discuss different strategies and solutions, with some confusion and excitement about the possibilities. Ultimately, it is determined that there is only one solution to the problem, with some variations through rotations and reflections.
  • #1
Natasha1
493
9
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!
 
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  • #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
Natasha1 said:
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.

Natasha1 said:
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
Mark44 said:
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!
 

Related to Solve 3x3 Numerical Puzzle: Can it Be Done?

1. Can a 3x3 numerical puzzle always be solved?

Yes, a 3x3 numerical puzzle can always be solved as long as it follows the basic rules of a standard numerical puzzle. These rules include using numbers 1-9 only once in each row, column, and 3x3 sub-grid, and ensuring that the puzzle has only one unique solution.

2. How do you approach solving a 3x3 numerical puzzle?

The best approach to solving a 3x3 numerical puzzle is to start with the easiest clues and use logic and deduction to fill in the remaining numbers. It is helpful to look for patterns and eliminate possibilities in rows, columns, and sub-grids. It is also important to keep track of the numbers already used in each row, column, and sub-grid.

3. Are there any strategies or techniques for solving a 3x3 numerical puzzle?

Yes, there are various strategies and techniques that can be used to solve a 3x3 numerical puzzle. Some common techniques include scanning for potential numbers, marking off numbers that are already used in each row, column, and sub-grid, and using the "process of elimination" to narrow down possibilities for each empty cell. There are also more advanced techniques such as "X-wing" and "swordfish" that can be used for more challenging puzzles.

4. How long does it typically take to solve a 3x3 numerical puzzle?

The time it takes to solve a 3x3 numerical puzzle can vary greatly depending on the difficulty level and the individual's experience and solving techniques. Some people may be able to solve a 3x3 numerical puzzle in a matter of minutes, while others may take longer, especially for more challenging puzzles.

5. Are there any tips for beginners to improve their skills in solving 3x3 numerical puzzles?

Yes, some tips for beginners include starting with easier puzzles and gradually increasing the difficulty level, practicing regularly to improve logic and deduction skills, and trying out different solving techniques to find what works best. It can also be helpful to use online resources or apps that provide step-by-step guides or allow for the use of hints and tips while solving the puzzles.

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