Moschopulus wrote:Does almost every grid have automorphism group of order 1?

Yes... the vast majority of them do, and this is to be expected. This will be true in the mathematically precise sense of the phrase "almost every" in that the proportion of grids with k^2 rows and columns with trivial automorphism group will tend to 1 as k tends to infinity. [I am just restricting to the square case to avoid ambiguity about what the "boxes" are, but it will be true for any sensible version]

The exact numbers for the regular Sudoku with 9 rows/columns were computed as part of the enumeration of equivalence classes of grids:

http://www.shef.ac.uk/~pm1afj/sudoku/sudgroup.html

Cheers

Gordon