This post presents a second demonstration of LPO pattern slicing, which divides patterns of a number into two disjoint sets, often extending Medusa coloring in the process.. This new coloring LPO method puts Insane 455 down with two convincing blows, after the puzzle has shrugged off the advanced sysudokie repertoire.
No more concessions were forthcoming in basic solving:
With nothing to else to the point of coloring, I’m showing, as a basic checkpoint grid, my attempt to start two clusters, and with AIC hinges. It’s looking grim as I turn to my extreme weapon, LPO, to inflict some damage somewhere.
Starting with the 4, 6 and 9 coloring at the lower left of the grid, the 4-pattern freeform enumeration is below.
Fortunately there are only two blue patterns, and these share five 4-candidates exclusively, that is to say, with no green patterns. The blue/green cluster can be extended by coloring these candidates blue. In the C box, blue patterns are limited to r5. The blue candidate in r3c5 further limits the blue C candidates to two.
No green pattern includes r6c1 because a green freeform crossing this cell cannot visit the East box. The green patterns visiting Er6 must also include r4c1. Four candidates in the C box are orphaned. Very effective.
It’s a good idea to track what else is happening on the bv map and the x-panels as pattern analysis results come in. Here, the 4-candidate coloring enables a 348-wing that failed before.
The removal in r6c1 adds a bv to the map, and enables an XY-chain ANL, leading to an SWc3 boxline removing two more candidates. This very productive pattern slicing was not enough to get anything started, so we continue with the 6 patterns, based on the expanded blue green coloring.
Starting freeforms in r8, where we have a colored slink, we discover five blue and two green patterns. Two of these can be dismissed for conflicting with the blue 4-candidate in r3c5, but there are no additional candidate eligible for coloring.
There are, however, other slinks available in the 6-panel, and therefore, additional ways to slice patterns, and expand coloring.
To illustrate with a simpler case, compare the two different sets of freeforms below, defining the same Insane 455 5-patterns.
In the right panel, with the freeforms drawn top to bottom, the same patterns are present, but they are represented differently by the freeforms. They are also colored differently, with four candidates eligible for colors. Patterns are divided into two sets, in both panels, but not the same two sets.
This suggests that we might get a different result by redrawing free forms of the 6-patterns in a new direction. I use my pink olive colors for this pink olive analysis.
Would you like a pink olive in your next martini? Here is the next best thing. In this division of 6-patterns there is only one olive pattern. It contains the blue candidate, and a 6-candidate in the same cell as the blue 4 candidate of r3c5. What does that tell us?
It tells us that the olive pattern is false. Since it is the only olive pattern, every candidate on it is off limits for pink patterns, including the blue candidate. We have already accepted the blue candidate, but since it creates a blue conflict, we reject the olive pattern that includes it. All of the olive candidates are therefore orphaned, and all of them, other than the blue candidate, can be removed. Another remarkable LPO slicing result.
Then it easily expands to force two green 1-candidates into r5, wiping out all green candidates. Blue quickly proves orange and its time to move on.
Come back next week, after trying out Insane v.4 b.6 n.5. and keep your Powerpoint crayons sharp, especially your pink and olive ones..