Lite Coloring

Medusa Coloring is used extensively in Sysudoku Advanced, with clusters being identified early and often being the climax of the solution path. One color comes into conflict with itself and the opposing color is recognized as true. Segments of a cluster’s slink network often provides shortcut AIC in other elimination or confirming methods.

Coloring clusters can be used in trials, but when they are, it is because all regular systematic methods have failed. Lite coloring is a way to extend coloring when one or more clusters are developed, but a trial is contemplated.  

The idea of lite coloring is to identify candidates able to act as candidates of a color, not because they are within the cluster, but because they will become that color when it becomes known to be true. We use the term color lite, defined by

Such a candidate can participate in a coloring trap or bridge, before that knowledge is gained, because the trap or bridge depends only on the knowledge that one of the two opposing colors of the cluster is true. The concept begs for a clear illustration, which will follow, but first let me credit  Sysudoku reader Dov Mittelman with the lite coloring idea, and claim that to my knowledge, it is original with Dov, and by way of announcement, Sysudoku.

The full Sysudoku solution path is in the post, Lite Coloring in a Red Russel Special, of January 5, 2021. The Red Russel Special is my title for the puzzle submitted to the now defunct Players forum, now replaced by the EnjoySudoku forum, by “Red” Russel, and highlighted in 2020. Besides the full debut of Lite Coloring the Red Russel Special also illustrates four X-wings in line marking, and a beautiful hidden quad.

The definition doesn’t tell us how to identify the lite color candidates. They come in a sequence. With any color candidate, full or lite, identify slink partners seen by that candidate. They are false when the starting candidate is true. And in each case, the slink partner is color lite in the starting color. The color lite marking procedure is to generate a branching tree of lite  candidates of the starting color. Naturally, the root of the tree is a full color candidate. The sequence does not include candidates of the opposing color, which generate branching sequences of lite candidates of the opposing color.

Lite Color Marking

The four X-wings leave three small and isolated slink networks, marked as blue/green, red/orange/ and purple/yellow clusters.

In Sysudoku, we draw arrows to mark lite candidates.  The arrow stands for a wink to a candidate seen by color candidate and slink to its slink partner.

Starting with blue 4r3c1. If true it erases 5, 6, and 7, and no other 4’s, except the green ones. Only 6 is a slink partner, and its slink partner is blue lite. It is blue when blue is known to be true.

Continuing the lite sequence from blue 4r3c1, it’s OK for blue lite 8 to claim yellow r5c2 is also blue lite. But that doesn’t mean yellow is blue. It becomes blue only when blue is confirmed to be true.

The Sysudoku cell corner slink marking directly assists color lite marking.

A lite coloring trap

The other blue candidate 4r8c5 claims red 6r7c9 as blue lite! A red candidate can act as blue lite in a trap. It does that, making 4r9c9 blue lite. Since 1r9c1 is green lite, 4r9c3 which sees blue lite and green lite in r9, is false. Red 6r7c9 is red, but blue lite 4r9c9 is not necessarily blue, but for sure, blue or green is true, so blue lite 4r9c3 or green lite 4r9c3 is true. The trap works.

A lite coloring bridge

But there is something else.  Blue makes 3r7c5 true and that forces orange candidate to be false when blue becomes true. But orange and red are opposing cluster colors. If any orange candidate is false, they all are, and all red candidates are true. So now, red is true when blue is true.  Red is blue and orange is green. Lite coloring can merge cluster colors.

Let’s merge the red/orange cluster with the blue/green cluster and re-mark the red/orange lite sequences  as new blue/green lite sequences.

1r3c6 is blue lite and green lite. It wins either way .

6r1c7 sees green in the NE box and lite blue 6r1c1.

3r6c7 sees green lite 3r1c7 in c7 and blue lite in the East box.

It’s a short follow up to blue 3r7c5 and a green wrap:

Now green lite sequences disappear, and blue lites become blue clues. Including yellow 7r5c2. Yellow 7’s are confirmed as blue, and the purple 7’s they see are removed.

The Red Russel Special is easily solved from there. It also succumbs to the hidden quad, as is demonstrated in the January 5, 2021 post.

We don’t see it in the Special, but a lite coloring wrap occurs when lite coloring chains from opposing colors meet on a candidate of another full color. The full color is true, and its opposite is false. No need to wait for a lite color to be confirmed. One of the opposing lite colors is true. We don’t know which, but we do know the candidate is true, so its color prevails, regardless.