The New Sudoku Players' Forum

[Lummox JR]

Ack! After rereading Nick's approach to supercoloring I finally realized that he's using the same rule I am:

Actually, the only reason why we need to care about non-conjugate colors is to see if they are falsified by the conjugate ones. To check if x is falsified, we just need to do
if excludes(x,y) and excludes(x,z) and excludes(y^1,z^1) then x is false

There it is. He's saying x is a color without a conjugate, where such colors were added for each candidate after all conjugate colors were found. With this method you can use mere transitivity to eliminate a placement rather than looking for intersections as I was doing, but it's the same principle.

This means that the advanced coloring I've been doing is identical to multicoloring, supercoloring, ultracoloring, and any of the other names it's gone by. The only difference is that instead of assigning those one-off colors, I'm merely eliminating the positions where they would appear by extension of the same technique.

[Jeff]

Given the way that works, I suspect advanced coloring is the union of all forcing chain techniques.

I don't think advanced colouring cover triple implication chains.

From here, a further candidate can be removed by an wxyz-wing, a rare encounter indeed. But it still leads to nowhere.

Now that's a new one on me. I'm wondering whether I should try implementing that in my solver, or if I should figure out if there's a base logic extending XYZ-wing to a more general case.

Take a look at here.

[Lummox JR]

I don't think advanced colouring cover triple implication chains.

Hrm. I definitely haven't read anything on that subject. Presumably they're wicked difficult to find. However it wouldn't surprise me if some extension of the technique could pick these up.

The killer rule, which is the key to supercoloring and the reason they're equivalent, is that the conjugates of two mutually exclusive colors must have a combined truth value >0, eliminating any placements that intersect them. Presumably a triple-implication chain gives 3 placements a combined truth value >0, which makes possible new intersections.

The key question to ask, then, is how to take a set of exclusions and find three values that fit such a constraint.

Currently supercoloring only operates on those two exclusion rules, so a third rule would dig up new techniques as well.

[aeb]

That's the absolute limit of advanced coloring.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 56      56      2       | 38      9       34      | 1       48      7       |
 | 179     3       8       | 6       2457    12      | 245     59      259     |
 | 4       179     17      | 12578   2578    128     | 2568    35689   23568   |
 |-------------------------+-------------------------+-------------------------|
 | 1236    12678   47      | 39      2678    5       | 246     16789   12689   |
 | 256     245678  9       | 278     1       268     | 3       45678   258     |
 | 123567  125678  1357    | 4       2678    39      | 2568    156789  125689  |
 |-------------------------+-------------------------+-------------------------|
 | 12579   12579   1357    | 125     2568    1268    | 68      368     4       |
 | 135     15      1345    | 158     4568    7       | 9       2       368     |
 | 8       24      6       | 29      3       49      | 7       15      15      |
 *-----------------------------------------------------------------------------*


From here, a further candidate can be removed by an wxyz-wing, a rare encounter indeed. But it still leads to nowhere.

I happened to come across this thread since it is given as prototype example for advanced colouring, but the Sudoku was not solved in the thread. Using almost locked sets for digits 1,3,5 in the lower left hand corner a complete solution is obtained.

[Jeff]

I happened to come across this thread since it is given as prototype example for advanced colouring, but the Sudoku was not solved in the thread. Using almost locked sets for digits 1,3,5 in the lower left hand corner a complete solution is obtained.

Hi Aeb, Refer here for some of the solutions (not that the grid has multiple solutions) captured for this grid.