This post tells the story in the solving of Krazy Dad Insane v4, b1, n5, as reported in updated Sysudoku posts of 7/13/13 and 7/20/13. It’s one way that coloring and pattern analysis work together.
Important features of Sysudoku Basic are illustrated on the first screen. Always included is a complete basic trace in a very compact format. This service is not duplicated elsewhere.
The first grid shows a large number of bypass clues, with very few pencil marks. The 5-wing occurs on the second line marking. How was it spotted? In marking c2, the 5’s are placed at the Southwest corner, marking a line slink. Form the corresponding habit: when you mark a line slink, look for a parallel one.
Now what happens? No immediate victim, but the fish icons remain and prevent the addition of the pencil marks added, then removed by many other solvers, human and computer.
Next is the line marked grid, where you can see the completed candidate field. If it doesn’t look like yours, then maybe you should look at what else happened to all those pencil marks. And what it means to have the marks placed in the cells as they are. Is this coded information to be used in advanced solving?
Also on the first grid, the first advanced method beyond the 5-wing is in evidence, a blue/green cluster.
The most significant figure of the post, however is this pair of panels. Patterns and coloring come together here. The 5-panel has the very simple blue/green cluster. Freeforms are not required to show that the cluster marks two 5 patterns.
Then the 7-panel jumps out at you as being very limited in patterns as well. A quick freeform analysis with r9 as a starting row divides the 7-patterns, three from r9c2 and one from r9c4. Now we mix in a little overlay, some LPO. The 5 and 7 patterns overlay without conflict, except in coloring. There is only one way for slinked 7’s to overlay colors consistently with the 5 coloring. All of the 7-candidates are compatible with all of the 5-candidates. Of course the coloring added to the 5-cluster is limited to the compatible coloring links of the 7-panel.
The benefit of expanding a cluster is to trap candidates and confirm one color. Here is the expanded cluster as the trap sequence begins.
The traps carry KD 415 past the first Sudokuwiki advanced move, but not to a solution.
Instead, three irregular XYZ-wings are found in the growing bv field to continue the blue/green expansion to a wrap of green, and a collapse.
Here is the first of these, a 376-wing where the weak link attaching the 36 wing is a grouped 3-chain. A systematic way to spot these without extensive searching is noted in the bv scan section of The Guide. An important element is the use of an XYZ map to limit consideration to the cell set that can form an XYZ-wing, without regard to cell location. Then for each possible set, you concentrate on building the necessary connecting forcing chains as winks.
The 367 hinge is placed on the map only because the bv 67 and 36 are on it. With the easy wink to wing 76, we are motivated to find a forcing chain to 36 on the grid.
On very difficult puzzles, it would be worthwhile to return to your XYZ map at the AIC building stage, when more types of wing attachments are available.
The second XYZ-wing is a regular XYZ wing, an occurrence more rare than an irregular one. The third XYZ makes up for it. One wing is attached by forcing chain, and the victim sees one toxic set member by forcing chain.
Finally, please be patient with the ads and with the Sysudoku practice of leaving something for readers to try, and backing them up next post. The latter is why the finish of KD 415 was held for the next post.