Lite Coloring

Medusa Coloring is used extensively in Sysudoku, with clusters being identified early and often bringing a wrap, a cluster color coming into conflict with itself, with the opposing color being recognized as true.  

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 their lite  color becomes known to be true. Take the blue/green cluster seen so frequently here. A candidate is said to be blue lite if it becomes blue when blue is recognized as true. If it is marked as blue lite, it can be useful before blue is known to be true. The most frequent example is the coloring trap. A blue lite candidate can work with a green or green lite candidate in a trap. When blue is known to be true, green will be known to be false. The certainty that blue or green will become true is enough for us to remove the blue lite victim now.

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 explanation and implementation details of the posts and this Guide page originate with Sysudoku.

The definition of lite coloring doesn’t tell us how to identify the lite color candidates. The key is what candidate becomes false when the lite color becomes true. The slink partners of that candidate take on the lite color.  A chain of lite colorings starts with a full color candidate, but chain links can be lite. Lite coloring trees grow just like full Medusa coloring trees.

Given the nature of the lite coloring trees, the natural way to mark lite coloring is to draw arrows from the lite colored candidate to the newly lite colored slink partners of the turned off candidate, skipping the turned off candidate.

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.

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.

But it took some hard AIC building to get here.

Pattern Slice Solution

An easier DIY  path to a KD Insane 425 solution starts with pattern slicing in the Guide’s Sysudoku Advanced/Pattern Slicing. The pink olivepattern slink translates to this blue/green cluster. A typical lite trap occurs as lite trees are started.

7r2c7 sees full blue 3 and lite green 7.

The blue lite tree from2r2c3 brings lite blue traps with lite green 7r1c9. The new naked pair 26 brings a naked pair 79.

The lite green tree from 1r2c7 brings lite green 6r8c7 and the lite blue tree 3r6c3 brings lite blue4r8c3 to trap 6r8c3, confirming the group 6r9c13, which traps 9r9c6.

Now something new in lite coloring that can apply to regular coloring as well.

Blue creates naked triple 279 in r8, and 16 in r8c7.  Green creates naked triple 467 in the SE box, and 67 in r8c7. 

Regardless of the cluster color, a 6 candidate and only a 6 candidate, is left in r8c7. The cluster has spoken. It’s a value intersection.

The follow up leaves lots of bv and slinks for a new red/orange cluster. Note that trace ends without a coloring wrap. That may be typical of the coloring value intersection.

The red orange cluster squeezes blue 3r6c3 out, for a wrap.

The red orange expansion wraps orange in r5.

for an easy DIY green red solution of KrazyDad 425.