I've just finished with a Sudoku I've been constructing for a while. It is excellent, it is perfect in any way! So I want to sell it somewhere. Not just once but in so many variations as possible in order to squeeze as much money out of it as I can.
I've noticed that it stays as brilliant, even if you interchange any line within a third horizontally or vertically, also if you interchange any third horizontally or vertically. You can turn it upside down, mirror it, rotate it and surely a lot of other manipulations too. And all these new combinations stems of the original Sudoku. And all new combinations you can sell as if it was a new one (if you're careful and not sell all of them to the same place).
Now, the question is (puzzle if you like):
How many variations can you produce from the same original Sudoku ?
4 global rotations. Blocks can be interchanged along block rows and columns, 6^2. Within each block rows can be interchanged 6 times and there are three blocks so 6^3. Similarly with columns. This gives:
4* (6^8) = 6,718,464 different puzzles.
You might also try permuting the numbers (1 -> 2, 2->3 etc.) for an extra factor of 9!, but I think that this over-counts.