Colouring Troubleshooting

gaby · Posted: Mon Oct 17, 2005 9:50 pm Post subject:

Ruud, the missing conjugate in box 3 isn't coloured because it doesn't intersect in any way with any of the other conjugates. Should I make it colour every conjugate in the set?
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Ruud · Site Admin

Lummox JR · Posted: Mon Oct 17, 2005 11:16 pm Post subject:

Lummox JR · Posted: Mon Oct 17, 2005 11:37 pm Post subject:

Ruud, I'd been meaning to get back to this post from yesterday, since it's got an interesting insight:

Ruud · Site Admin

Thanks for the feedback.

I brought this up because I wanted to see how far I could go to bring the coloring technique upto the same level as the template checker. Since the latter does not know what other digits are involved, the conclusions it draws must be solely based upon the distribution of cells that allow that digit (btw I call them vacancies in my program, in line with candidates for digits that can fill them)

Now since I've dug a little deeper into coloring, the eliminations made by the template checker make a lot more sense to me. Where coloring stops at the intersections, I can go just a little further and see how it has come to those eliminations.

To stay within the same effective range as the template checker, I cannot add any logic that would include other digits, so I would have to stick to hidden singles (single vacancies sounds better) and vacancies locked in line-box intersections (pointing pairs). As you suggested, a spare set of colors could be used to perform these "what if a were true" and "what if b were true" scenarios.

I still consider this logic, because the premise is simple: either a or b contains that digit. It's just how far you are willing to go extrapolating from that premise.

Another issue, now I've got your attention, has been haunting me the last couple of days, and I would appreciate some feedback.

My solver, like probably most other solvers, will take care of an XY-Wing by eliminating the Z-digit from the peers shared by the XZ and YZ cells.

A more interesting approach would be to consider XZ and YZ a conjugate pair for the Z digit. The solver has an excellent tool to exploit conjugate pairs to the max: multicoloring. Even if the pair would not eliminate any candidates by itself, it can still be used in a coloring scheme.

It is certainly not hard to implement. I already have a method that hunts XY-wings. The only thing I need to change is not to draw conclusions immediately, but to add the XZ and YZ cells as an extra conjugate pair to coloring. The coloring method would deal with the immediate eliminations, but can also link it to other pairs, make exclusions, etc.

Actually, this idea excites me even more than extended coloring.

Ruud.

gaby · Posted: Tue Oct 18, 2005 10:04 am Post subject:

I nailed the problem in the end. It was a hangover from the colour contradiction detection. Previously it scanned for all light coloured clashses and all dark coloured clashes, and it was changed to work on a single colour at a time, but I hadn't changed the candidate removal part of that system, so it was still removing all of the dark colours, not just the dark yellow colours. Now 'tis fixed. Just have to make it colour the rest of the conjugates, to see what happens.
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Nick70 · Posted: Tue Oct 18, 2005 12:11 pm Post subject:

Lummox JR · Posted: Tue Oct 18, 2005 5:32 pm Post subject:

Indeed, when using the color set system you have conjugates b!{CD} and E!{CD}, hence b=E. When using extended colors in this way, this simple rule will do:

If a color or set of colors A is the conjugate of two other colors or sets B and C, B=C. If B is a color and C a set, one and only one of C's members is true if B is true, and vice-versa; if B is false, none of C's members are true, and vice-versa. If B and C are both sets, either they will each have one true member or their members will all be false.