Lite Coloring

Medusa Coloring is used extensively in Sysudoku, with clusters being identified early and often bringing a wrap, when 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 links 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 progress toward a wrap is delayed.  

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, or merge of clusters, 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 of lite coloring was brought to my attention by Sysudoku reader Dov Mittelman, and to my knowledge, it is original with Dov. The rationale and systematic implementation details of the posts and this Guide page originate with Sysudoku.

The definition above doesn’t tell us how to identify the lite color candidates. They come in a branching sequence, starting with full color candidate. We’ll refer to this branching sequence as a lite tree of the color of it’s starting candidate, the root.  The tree grows by pairs of weak and strong links. With any color candidate, full or lite, on the tree, identify slink partners of any value, seen by that candidate. They are false when the starting candidate is true. And for each one, its slink partner is color lite in the root color, simply because it is true when the seen partner is false. The color lite marking procedure generates a lite tree of lite candidates of the root color. Don’t include  candidates of the root’s opposing color in the lite tree. Instead, use them to generate trees of lite candidates of the opposing color. It isn’t necessary to include a candidate in more than one tree of the same root color.

Our first example of lite coloring is from 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.

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 wink/slink pair to the next lite candidate.

Start 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 tree to 8r1c2, it’s OK for blue lite 8 to claim yellow r5c2 is also blue lite. But that doesn’t mean yellow is blue. It means that yellow becomes true when blue is confirmed to be true.

Note how Sysudoku cell corner slink marking points out the slink partners, directly assisting color lite marking.

A lite coloring trap

The other blue candidate 4r8c5 claims red 6r7c9 as blue lite! That enables any red candidate to act as blue lite in a trap. Here 6r7c9 acts as blue lite to make 4r9c9 blue lite. Since 1r9c1 is green lite, 4r9c3, which sees blue lite and green lite, is false. 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 6r7c5 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.  That means red is blue and orange is green. Lite coloring can merge clusters.

A lite confirmation and a lite wrap

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 from the confirmation N1 to blue 3r7c5 and a green wrap:

We don’t see it here, but a lite coloring wrap occurs when lite coloring trees from opposing colors meet on a candidate of another full color. The full color is confirmed, and its opposite is false. No need to wait for a lite color to be confirmed.   For example, if 1r3c6 had been purple, purple would be confirmed and yellow wrapped.

A wrap to watch for

Next, a caution and a quick wrap from Manuel Castillo’s Only Extreme 347 and the post of January 26, 2021. After many cluster building eliminations two lite trees appear.

Blue lite 9r4c1 and green lite 9r8c2 create trap 9s and confirm 9r8c2. But that doesn’t confirm green. The trap doesn’t depend on either color being true.

In fact, when the smoke clears, green 6r9c6 is still in place. The follow released a green lite tree which wraps back to re-enter r1c8. Hmmm.

Several more examples of lite coloring come from an update of KrazyDad Insane 425 in the post of February 2, 2021. Red and blue are merged when blue and green cluster candidates participate in a red/green bridge. Red candidates wink at green ones, which naturally slink at blue ones. When red is true, blue is true.

After the cluster merge, lite trap and a lite confirmation.

Then at the end, a different wrap, as two green lite trees put competing candidates in the same box.