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1. How many possible Sudoku boards are there? That is, a 3x3 square of 3x3 blocks where (a) each block has the numbers 1-9 exactly once, and (b) each row and column of the resulting 9x9 matrix has the numbers 1-9 exactly once?

2. I'm trying to develop a game based on Sudoku. The basic premise is you start out with a 9x9 matrix of numbers and the two players keep on performing operations on the matrix until a valid Sudoku grid is created. Whoever finishes the grid wins. (The reverse, Rubik-style game is to start with a Sudoku grid or random bunch of numbers where each number appears 9 times and wind up with a matrix like

123456789

912345678

871234567...)

The original thing I had in mind would be this: start with a Sudoku grid and allow either player to transpose two rows or two columns. The uniqueness of the numbers in the rows and columns will be invariant under this transformation.

The catch is: I need a starting matrix, ending matrix, and a rule which will guarantee at least one possible solution. I don't want to make a game impossible to win.

Thanks in advance,

ACG