This post introduces nice loop coloring, with a very advanced nice loop. Pattern slicing has a cameo role.
On 465, the Stuart solver tries cell and line unit forcing chains, which are rejected as humanly impractical in Sysudoku. Unprepared for irregular XYZ-wings and for coloring trials, the solver is defeated by KD Insane v4, b6, n5.
With Sysudoku Advanced, Insane 465 KrazyDad claims a skirmish in our friendly difference on the necessity guessing in solving Insane puzzles. Jim’s Insane 465 brings me to a coloring trial, but one that cannot be rightly classified as a guess.
The reviewed Insane that is stingiest on the bypass, 465 gives no more clues in basic, but does allow a 7-wing on the last line marked.
That leaves a very busy grid.
The 7 candidates remaining form a cluster around three sides of the grid. The cluster expands logically to completion in the steps shown by the arrows. First, if red 7r7c7 is true, then so is 7r9c8, and that makes 7r5c9 red. Now its slink partner 7r5c7 must be orange, trapping 7r8c7. Now 7r8c9 becomes
The Stuart solver does forcing chains, but does not use them for weak links in applying methods, for the understandable reason that to do so would require extensive unproductive chain building. So why is it possible for humans? Because the human starts with the hinge and wings, and only builds a chain to connect them.
Then after AIC hinges are added, a hinge and a reversed bv allow a boomerang ANL.
This irregular 452-wing was delayed, because its victim 2r8c6 had a role in the boomerang. A grouped 4-chain attaches the 42 wing.
The Stuart solver does forcing chains, but does not use them for weak links in methods, for the understandable reason that to do so would require extensive unproductive chain building.
So why is it possible for humans? Because of human knowledge and focus. The human starts with the hinge and wings, and only builds a chain, any chain, to connect them.
Now we come to the highlight of this post, a nice loop with two ALS nodes serving as XY links. Andrew’s solver sees it, but doesn’t say anything because this nice loop has no victims.
But we appreciate nice loops for another reason. They define coloring clusters. The alternating inferences of a nice loop makes alternating coloring links. Going clockwise, the far end of each slink is green. Going counterclockwise the far ends are blue. Nice loops have a true direction, and a false direction.
The nice loop coloring cluster is a coloring network and can be mixed and merged with any other coloring. The closed loop structure means that for each wink link in the chain , there is a corresponding slink chain in the opposite direction around the loop.
But there’s more. Once the nice loop establishes the colors, X-chains branching off carry the coloring with them, as determined by the direction of their branch. This is not the case with all AIC, but for X-chains, a failure of the not-both condition to allow the coloring is the coloring.
Next, another element of POM, the pattern conflicts with the complete 7- patterns of the red/orange cluster. The only pattern slicing opportunity is the 3-panel. There is only one pink, and two olive collectors.
Tabulation is the most systematic way to examine and report conflicts.
On the pink side, red candidates conflict with two of the five patterns, while orange ones conflict with a different two. The table lists, the conflict cells. More decisively, both red and orange conflict with two of three olive patterns, leaving only the solid one, with orange.
Unfortunately, the reduction of olive patterns nets only the one orphan 3r1c8. Pink patterns provide a home for all other candidates abandoned by departing olive patterns.
For now, I’m ready to put blue on trial. In follow up, it soon confirms orange, and the following solution emerges. The true 3-pattern turns out to be the short dash pink.
To guard against multiple solutions, I test green as well. Since blue implied orange, red implies green. So I test red and green. It fails, so Insane 465 is innocent.
Next we embark on Insane 475, so if you want to get started, it’s not too soon.