[Someone]

I would not call what the GP describes as ”guess and check”, but as “backtracking”.

That is just making logic observations, using the grid as a memory aid (“let’s see, if foo is a 1 and bar is a 2, then that’s a 7, and then that must be a 4, and that a 3, and then we hit a dead end, so the claim “this is a 1 and this is a 2” in’s true. Maybe foo is a 1 and bar is a 3? No, that’s clearly incorrect. Maybe foo is a 1 and bar is a 4? Etc)

I think human Sudoku solving is different, though. Humans don’t do a depth-first search, but a breadth-first one for paths that soon lead to being able to fill in some squares. Experienced solvers probably have heuristics for finding them.

I think I would rate the difficulty of a puzzle by the ¿average? depth needed in such a depth-first search to permanently place a new digit in a new cell, with correction factors for the number of paths at that depth that do that and the number of cells to fill in.

[olliej]

Generally if a puzzle requires bifurcation it’s considered to be at least partially broken.

The setter is expected to have made it so that determining each cell can be done without simply seeing if a choice eventually succeeds. Of course exactly how many steps to count as bifurcation is fairly nebulous.