## An Insane 445 March to the Bridge

In this revised post, difficult line marking leaves a semi-monster. It is whittled down to a final coloring bridge by unconventional sysudokie techniques. The review puzzle, Insane volume 4, book 4, number 5, with thousands more, is available at www.krazydad.com .

Basic sysudoku basic solving,

gets you to the candidates grid:

On this grid, the preponderance of candidates {12367} is striking.

In late 2015, I posted a protest against applying “WXYZ-wing”  to another set of methods I prefer to label as the Bent N-Set family. This revision was prompted by the mission to find examples of this family.

On the first scan, I found a 5781-wing with no victims, and an as yet unverified Single Alternate SdC , Wr5 = Wr5=8(6+7)(1+2)+182.

The failed WXYZ-wing also qualified as other Bent N-Set family members, the 4-BARN, and a BNS-1. But that doesn’t get it any victims, because nobody sees all the Z = 1 candidates.

As often happens, however, the failed 5781-wing was overlaid by an APE, this one quite effective.  APE r9c13 = 17+57+71, removes 8-candidate, yielding SW8 and S8 clues and removing SW 7-candidates by boxline.

Probing a little more, it turns out that several other related methods achieve the same result.

There is a 3-BARN and BNS-1 creating a pair of toxic 8’s, and you can divide the bent 3-set two ways to get equivalent ALS 1-8’s. Which of these to call it is not much of an issue.

Now looking back at the SASdC, it’s SdC removal would create more bent 4-sets, and that might justify using a less than obvious trial result.

It turns out the 2r5c3 alone forces two 2’s in the Center box. The Sue de Coq is verified and the removals in r4c3 can be made.

They enable a BNS-1 with remainder numbers {12} and {267}, toxic for 2r4c4, but along comes an irregular 172-wing that does the same thing with the newly created bv as a wing, courtesy of a grouped forcing chain.

Such a grouped forcing chain can protect  the name of the WXYZ-wing, when it creates a wing that no bent technique can duplicate.

Following the SOB, the growing bv crop doesn’t connect into a productive XY rail. The 15 UR can’t be easily dismissed, and we move on to the X-panel, where a 6-chain ANL removes one, and the chain extends to remove another.

The panels then bog down, except for possible pattern restrictions, but first, we get out the crayons. I just add clusters until the bv field is covered. I have, blue/green, red/orange, violet/yellow and plum/aqua. What are the interactions?

In c5, not(green & plum) => blue or aqua.

In c8 this creates a bridge trap. 2r5c8 sees both blue and aqua.

Now in r5, the remaining two 2’s demand that blue is plum and aqua is green, a cluster merge. Then I notice that the aqua-green 1’s drive all 1’s from the NW box. The merged blue cluster soon confirms orange and violet, and we get a colorful solution

Four down without a guess!  Hold on, that Single Alternate Sue de Coq trial is based on SdC logic, and can be confirmed by eye . The fact that my feeble eyes had to use a trial trace has nothing to do with it!

But I have a foreboding  that the Insane collection is setting me up, and my surfing wave may be about to break over sharp rocks. The Insane review continues next week with Insane 455. Look it up on KrazyDad, work out the basics and be prepared to drag me out!