Mike Barker wrote:As far as the elimination the discontinuity is as shown. As you know, the start and end nodes share a house, but cannot be linked together. This can allow "4" to be eliminated from r6c7 (if one existed) and "2" from r3c7. For this reason I prefer the way I wrote the loop, but both ways are valid.

I arrived at my "advanced coloring" perspective via

Myth Jellies's

POM vulnerable pairs after having read numerous posts by

Lummox JR on the Programmer's Forum. You might find the MJ thread -- only 3 pages -- an interesting read.

In brief, the technique finds pure bilocation chains with a discontinuity. One chain segment has an even number of links and all other segments have an odd number of conjugate (strong) links. A segment has conjugate links for one digit only, and digits may re-occur in non-adjacent segments. Then the colored digit at each end of the even-length segment (and all similarly colored digits in that segment) may be excluded. Of course, since it's a conjugate chain, excluding just one will exclude the others consequentially.

Mike Barker wrote:The last two [edit: strong links] are disjoint and the connection is shown with a weak link. Since this does not involve a bivalue or ALS, I considered this to be part of connecting the strong links so valid for coloring.

That's definitely less restrictive for the odd-length segments and I think I can incorporate that into my solver with little difficulty.

Mike Barker wrote:In the same manner I would consider an X-wing (which is a special form of advanced coloring) to be composed of 2 disjoint strong links. This may be confusing and I can modify my description if it is an issue.

I only take issue with considering an x-wing as

any form of advanced coloring. It is "multi-coloring" in the sense of multiple chains -- only one link in each of two chains, in this case -- of a

single digit. "Advanced coloring" and "super-coloring" always involve chains of

multiple digits AFAIK.