by 
NOYFB
ANSWERS: 3
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Per my calculations there are just under 749,000,000,000,000,000 possible puzzles. That does not include the possible combinations that at a reasonable 20 cells could be pre-displayed. That would add about as many zeros...
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There are 'only' 6670903752021072936960 valid Sudoku 9x9 grids. http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf
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Double click on the small image in my original answer to expand it. Then look at the contents of each cell and the notes describing. What you will see is that in the first cell, I chose the top-left for convenience, you can choose any one of 9 numbers, then in the second cell, there are only 8 numbers available, because you've already chosen one. Similarly, in each subsequent cell there is one less number available. That means that there are 9x8x7x6x5x4x3x2x1=362880 possible ways just to select the first row. Then going back to first cell in the second row, we've already chosen 3 numbers in the first zone. That means there are 6 numbers available for the first cell, 5 for the second, 4 for the third. Continue in this way for each cell and you will get what I have shown in the picture, and if you multiple them all out, you get the astronomical number I came up with. I chose to start in one corner, but the logic is valid in any combination since multiplication is commutative, i.e 4x3x2 is the same as 3x2x4.
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