I've since extended my program to what I call "level 2" --
propagating forcing constraints a bit further:
If a digit in a _row_ can only appear in 2 or 3 positions
within the same 3x3 block, then that digit is eliminated from
the rest of the block. If the digit can appear in multiple
blocks, then we can't eliminate it.
Ditto for columns.
For blocks, the rule is more complicated. If a digit can
only appear within a single row or column within a block,
then it can be eliminated from the rest of the row or column,
respectively.
These new rules, together with the previous set of forcing rules,
appears sufficient to solve the LATimes Sudoku's called
"Moderate", while the previous set of rules were sufficient
for those called "Gentle".
However, my "level 2" is not sufficient for LATimes "Diabolical",
nor for the Sudoku's in "Sudoku Genius".
It would appear that the LATimes _does_ have a precise definition of
what it means to be "Gentle" (~ level 1), "Moderate" (~ level 2),
and "Diabolical".
Since "level 2" appears to be exhausting the notion of what
can be done with only local rules & "force fields" (the information
propagating on rows, columns & blocks), I would suggest that level 2
captures the notion of "non-backtracking".
---
BTW, I mentioned that my bit representation produced "surprises"
in that some squares "accidentally" produced singleton sets. However,
because these singletons were "accidental", they didn't get a chance
to propagate their "first-class" status and suppress the same digit
in rows, columns and blocks. While this problem is automatically fixed
by level 2, this constraint really belongs to level 1, and so my level
1 program has to have an extra check just for this constraint. "The
representation giveth, and the representation taketh away."
