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

  1. May 23, 2010 #1

    Mentallic

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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?
     
  2. jcsd
  3. May 23, 2010 #2
    Last edited by a moderator: Apr 25, 2017
  4. May 27, 2010 #3
    Re: Sudoku

    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.

    Best,
    http://gbgtraining.blogspot.com" [Broken]
     
    Last edited by a moderator: May 4, 2017
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