FINALLY, in my original posting I suggested that "m" (the difference
between the number of candidates and the number of cells) could be
greater than 1, but then I retracted that. Now I put it in again.
Consider the simple cell
{168}
I suggest that that's "almost almost locked." If it were "16" or "18" or "68"
it would be almost locked. This is almost that.
If forcing 2 weak links to an almost-locked set causes a logical
inconsistency, then I suggest that passing 3 weak links to an
almost-almost-locked set also forces a logical inconsistency.
That is, in general, we might say a set of cells is "(almost)m-locked"
where m=1 is bennys's idea. But m could be larger. {168} would be
an example of an (almost)2-locked set.
How could that play into logical testing?
Well, all you need is something like this:
- Code: Select all
1....1
/ \\
2*...2--A B==6
6 \ // .
\ 8....8 .
\ .
---------------6
The starred 2 can be eliminated.
Having it TRUE would force both A1 and A8 TRUE, but
they are weakly linked to B, which by themselves would
force B to be 6. But we have an end-around here -- very
common in Sudoku -- via a short 3D chain consisting of
a conjugate pair and a 2-valued cell.
Now, the fact is, in all Sudoku the solution is right there. One simply
needs to find it. Like a maze for which we (presumably) know that there
is an exit and a way to it. I can write a very simple program to solve
a maze. The rule is this: always turn left. The result, of course, is a lot of
backtracking (literally). But you get out of the maze.
The same is true for Sudoku. If you don't want to use backtracking,
though, there are tricks. We call them methods. I suggest that if you
look at any Sudoku puzzle, all cells will be (almost)n-locked. (That's
pretty obvious, of course.) The logic is all there, too, though. SOME
route like this will indicate that ALL non-solution candidates can be
eliminated. The entire thing could be stated in terms of
(almost)n-locked sets.
At some point I hope to introduce almost-locked sets in Sudoku Assistant.
(http://www.stolaf.edu/people/hansonr/sudoku). It's not terribly difficult --
the machinery is all there to find them -- but I've spent far too long on this
thought already. Someday....
