How many possible games of 3x3 Sudoku are there?

Answer 1

Too many too count. 9! (since each number can only be written once) times 9 (since there are 9 squares altogether). So according to my calculations, there are approximately 3,265,920 different sudoku combinations!

Good luck completing them all.

Answer 2

Actually, it's not possible to do sudoku on a 3x3 grid. The only reason it works on a 9x9 grid is because the grid is split up into 9 3x3 squares. You can't split up a 3x3 grid like that, since 3 is a prime number.

If you mean how many possible ways are there of arranging the numbers 1 to 9 in a 3x3 grid, then the answer is 9! = 9*8*7*6*5*4*3*2*1 = 362880

If you mean 3x3 sudoku where you just put the numbers 1 to 3 in each row and column, without any kind of small square rule, then there are only 12 possibilities. This is because there are 3! = 3*2*1 = 6 possibilities for the first row, then 2 possibilities for the first digit of the second row, and after that every digit is fixed (try it!).

You can do 4x4 sudoku, with the numbers 1 to 4 in each 2x2 box, row and column. I have no idea how many possible grids there are, but we can at least find an upper bound:

If we only consider that each row must contain the digits 1,2,3,4 in some order, then there are 24 ways to arrange each row, which would give 24*24*24*24=331776 possible arrangements. Most of these would not be sudoku grids because they would have the same number more than once in a column or 2x2 box. So the number of 4x4 sudoku grids is less than that. It's possible to find (much) lower upper bounds, but I'm not even answering the original question any more, so I won't... ;-)

Answer 3

In 3X3 Sudoku, assuming I'm figuring this out correctly, each number can be placed once in any on the nine squares.

So square one can have any of 9 numbers (expressed mathematically as 9! and spoken as "nine absolute" = 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 = 362,880).

Square two can have any of 8 numbers since you can't use the first number again (expressed as 8! or "eight absolute" = 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 = 40,320).

This continues for the remaining seven squares with the possible numbers able to be used decreasing by one:

7! = 5,040 6! = 720 5! = 120 4! = 24 3! = 6

2! = 2 1! = 1

By adding all of these numbers (362,880 + 40,320 + ... + 2 + 1), you'll come up with 409,112 total possible games of 3 X 3 Sudoku.

Happy hunting!

Answer 4

1st line:
3*2*1 possibility

2nd line:
2 possibilities (since the 1st line is already decided)

3rd line:
1 possibility.

total possible 3x3 sudoku grids = 3*2*2 = 12 !!!

PS: play 9x9, at the very least.

Answer 5

well, with each 3 x 3 grid you start with the first square. There are 9 possible mumbers that can go in it, in the next square there are 8 possible numbers, in the next 7, etc. so you end up with 9x8x7x6x5x4x3x2x1. And there are 9 possible squares, so it is 9^(9x8x7x6x5x4x3x2x1). And since there are 9 of those to make up the big puzzles, it is 9 ^ to that number, so it is really big.

Answer 6

Good question, and it's not too difficult to figure out--starting with one square and noting how your choices for the subsequent ones are limited. Building it in this way, and using the counting principle, you can get to an answer. I do wonder whether you meant a 9*9 with sub-boxes of 3*3. In this case you might start with the 4*4 with sub-boxes of 4 (it's smaller so easier to get the idea with).

Answer 7

Don't know but if you really like it you can go to Barnes and Nobles, Borders or any local bookstore and get a book full of Sudoku games ranging from easy to medium to hard.

Answer 8

start with the top left and work down to the bottom right:

3x2x1
x2x1x1
x1x1x1

=12 possibilities where they are all different

but if you turn a grid upside-down or around, is it still the same?

this would bring up more possibilities

Answer 9

i would say too many i have at least 3 books of 200 sudoku's and they are all different! & there are more books in my collection so it might go on for a long time.

Answer 10

How would you play 3x3? Don't you mean 9x9. The answer is
6,670,903,752,021,072,936,960