A SudokuPX grid has all of the properties of a SudokuP grid, plus diffent values along both diagonals.
I counted these some time ago, but never got around to posting the results.
These grids have far fewer PX-preserving transformations (morph options), in fact as far as I can tell we are reduced to the normal dihedral symmetries, namely transpose and rotation, so there are only 8 morph flavours, none of any interest. Perhaps blue can uncover some!
- there are 133,747,300 different SudokuPX grids (up to relabelling the digits)
- for PX-equivalence under the 8 PX-preserving transformations, we simply enumerated them explicitly and determined the number of PX-different grids as 16,724,358
- for S-equivalence, ie essentially different in the normal Sudoku-equivalence sense, we don't really know. I will leave the ED count calculation as an exercise for Serg
Given the low numbers of grids involved, and that my HS engine is currently in pieces on the garage floor, I invite blue and champagne to perhaps provide an answer to this question.
