How many possible puzzles can be created out of the standard 9x9 grid

In summary, the conversation discusses the complexity of creating valid Sudoku puzzles and the use of permutations and combinations in the process. The first row has 9! ways to be filled, but the following rows have more restrictions due to the use of numbers in columns and 3x3 boxes. The conversation also mentions the use of Sudoku as a brain exercise and the need for consistent practice to become proficient.
  • #1
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I am trying to find out how many possible puzzles can be created out of the standard 9x9 grid.
I was never very good at permutations and combinations, so I won't get very far here...

All I can think of at the moment is that while there are [tex]9^{81}[/tex] ways to fill all the boxes with numbers from 1-9, it is much more complicated (and fewer combinations thankfully) to have valid sudoku puzzles.

For the first row, since we need the 9 numbers to go in any order, we will have 9! ways to do this. Now for the second row it becomes much more complicated because there are many restrictions we need to place, such as the same number can't be used in the same column as the row above, but we also can't have any of the same numbers in those boxes 3x3 boxes.

Any ideas?
 
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  • #3


Thanks Xitami ... good resource link. Sudoku is a new 'brain exercise' I've been trying to perform daily. As with all new things, there is certainly a science to it and it takes some consistent practice to become proficient.


http://gbgtraining.blogspot.com" [Broken]
 
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What is the standard 9x9 grid?

The standard 9x9 grid refers to a grid used in puzzle games such as Sudoku, which consists of 9 rows and 9 columns, with each row and column also containing 9 smaller squares.

How many possible puzzles can be created out of the standard 9x9 grid?

The number of possible puzzles that can be created out of the standard 9x9 grid is 6,670,903,752,021,072,936,960. This number is calculated by taking into account the number of possible combinations for each cell in the grid and applying combinatorial principles.

Is it possible to create a unique puzzle every time with the standard 9x9 grid?

Yes, it is possible to create a unique puzzle every time with the standard 9x9 grid. As mentioned before, there are trillions of possible combinations for each cell, making it highly unlikely for two puzzles to be exactly the same.

What factors affect the number of possible puzzles in the standard 9x9 grid?

The number of possible puzzles in the standard 9x9 grid is affected by the number of starting clues given, the placement of these clues, and the solving techniques used. The more starting clues there are, the fewer possible puzzles can be created.

Can the number of possible puzzles in the standard 9x9 grid be increased?

No, the number of possible puzzles in the standard 9x9 grid cannot be increased. The number is determined mathematically based on the size of the grid and the number of starting clues. However, new solving techniques may be discovered that can create different patterns within the grid, resulting in more variations of puzzles.

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