In one post, the 10th ultrahardcore review puzzle is wrapped, but not without an introduction of something new in Systematic Sudoku. Ordinarily advanced steps begin in line marking, and lite coloring is introduced.
In line marking Stefan Heine’s ultrahardcore 399, the Sysudoku marking of line slinks pays off on the third line.
On r3, the 6-slink doesn’t match the one on r9 for a 6-wing, but the alignment on one column signals a 6-chain known as a skyscraper. The weak link doesn’t depend on column 5 being filled.
The X-chain can’t identify all victims until their rows are filled. So, like we do with X-wings, we leave the skyscraper on the grid until the remaining rows are filled.
The skyscraper claims a victim 6r7c8 when c8 is finally marked,
This time it didn’t matter, because the 6-wing on columns c6 and c7 removes that victim before r7 is filled on the close
Sudokuwiki and Beeby, like most solvers, do X-wings and X-chains after basic because they number scan all candidates around the givens first, before searching for anything. Beeby finds the skyscraper first, and notes it as a Sashimi 6-wing. Now in advanced mode, they continue to fight it out in the notes on what they’re finding.
Sudokuwiki’s APE becomes Beeby’s ALS_87.
Then Sudokuwiki digit forcing chain Sysudoku boomer from 9r7c8 is duplicated by an eyebrow raising Beeby ALS_31.
Sudokuwiki’s dfc grouped ANL is Beeby’s grouped 1-way.
And a Beeby grouped ALS-wing is described as another digit forcing chain.
The solvers disagree on how to start the boomer, and Beeby takes the longer path
In this Sudokuwiki APE, the blue ALS excludes 41 and 43; the green ALS, 47 and 48.
Beeby’s ALS_34 mixes the ALS a little differently.
Both solvers hang up after Beeby’s second ALS ANL
But an extensive slink network is left behind to support two clusters.
Sysudoku reader Dove Mittelman suggests the marking of candidates in a “lite” color if they are true when the color is true. These “lite” candidates work in coloring traps. A candidate that sees a lite candidate or group and the opposite color is false regardless of the true color.
I mark lite candidates with arrows because I already use lighter shades for visibility.
Note above that lite candidates are those slinked with full colored candidates of a different value. Lite traps require seeing opposite color candidate, full or lite, of the same value. Lite green 3, 5, and 9 candidates have no blue trap partners. Lite green 7r6c8 does have a matching lite blue 7r3c1, but no 7 candidate sees them both.
I’ll come back after the review when I have examples where lite coloring is productive.
Although lite coloring fails in this case, when green generates many lite candidates, that makes it a good choice for a color trial. Full color traps and an orange wrap in c2 come quickly, confirming green and red.
The solution in colors:
Next, we start on the two extra ultras, with UHC 443.