I've recently turned my attention to the particular case of Sudoshiki, aka "Sudoku Inequality".

This is basically Futoshiki on a 9x9 grid, but with the added condition that the solution is a valid Sudoku grid.

I have been investigating p(U), ie the probability of a randomly generated grid having a unique solution. A grid has a unique solution in Futoshiki if and only if the corresponding set of clues ("<", ">") for every adjacent pair (ie: fully-specified ) uniquely corresponds to that grid.

For normal Futoshiki, ie: random latin squares of size 9, we have previously estimated p(U) = approx 1%. (see here)

But early testing of Sudoshiki grids suggests that p(U) for these cases is more like 30% !!

The only caveat is that I can't guarantee that my random Sudoku grid generator gives a uniformly distributed sample. Does anybody have access to the "full catalog" (5,472,730,538 classes) of Sudoku grids?

Or could anyone supply a sizeable sample thereof? Say a million or so?