Insane 425 Introduces the Boomerang

This post checkpoints a finish on Insane 415 and demonstrates a cluster merge by LPO with Insane 425, as part of a review of KrazyDad’s Insane collection on .  A spotting technique is explained and named for a type of AIC Almost Nice Loop. The post was updated in November 2018.

Did you find something on the grid of a tamed Insane 415 of last post? Here are two rare items, an ordinary 349-wing and a simple XY chain almost nice loop.







These removals made possible a wild ER made 564-wing. The 46 wing is attached to the hinge via a forcing chain, and the removed 4-candidate sees the other wing via a grouped forcing chain.





The removal is decisive , as the blue/green cluster expands to force two green 4-candidates in r9, proving




One down, ten to go in my quest to walk the Insane tightrope without  guessing.

Moving on to Insane 425, it’s a cooperative bypass and box marking.  Line marking, not so much.





The fill strings tell it like it is.




The limited supply of bv explains the lack of bv scan and XY-chain opportunities.  But XYZ steps up in the form of an irregular 173-wing. The 37 wing is attached by ER forcing chain.  Then both victims use two merging forcing chains to “see” the 3-candidate of that wing

What a headache it would be to cover this type of irregular XYZ-wing in a computer  code.  Does anybody else even write about them?  Yet with the reasonable aid of the XYZ map explained in the Guide, we can all do it. At base, it is “follow your nose” logic.  It doesn’t require anything but focused attention to lay out a chain from candidate to candidate, as directed by the XYZ map.

In Insane 425 the Guide project has brought an unexpected bonus. The Insane collection is being updated, because it offers many outstanding examples combining coloring with pattern analysis.  The update includes a rework of each solution, with a check for omissions by Andrew Stuart’s solver. This is not the bonus, but the solver did uncover this indecisive 1-chain ANL that I had missed.


The bonus is an unsung type of AIC ANL illustrated here. It is found by computer solvers by traversing  a huge tree of possibilities completely out of reach of a human solver. But it can be defined in a way that makes human searching practical.

At the AIC stage, where chains are built on added AIC hinges, the starting signal is a slink emerging into an AIC from a cell of several other values. If a slink terminal of the growing chain sees one of the starting cell’s other candidates, an almost nice loop has been found to eliminate that candidate.

To give this type of ANL an identity, and to honor the Sudoku writers from down under, let’s call it the AIC boomerang. That fits, but there is another way to stumble across an AIC boomerang as you build an AIC. Every odd candidate, there is a new slink terminal. If you reach a repeated slink terminal, you have a possible regular ANL. But if it’s any slink value terminal in a cell of a candidate winking at the beginning terminal, it’s a boomerang.

It’s not very far to the next AIC boomerang in Insane 425. Two cells over, terminal 6 gets its turn and hops a ride on the same chain.





That allows a 4-chain to extended on each end into a grouped AIC for some boxline eliminations.






Then it happens again.


Another boomerang. This time, in a wind tunnel. The terminal seeing 7r8c7 is a group.

All of this paves the way for pattern analysis, to be explored next time.

To set the stage, here are two very limited clusters with a common value 3. These clusters have freeform starting edge r6 that suggests coloring restrictions on patterns. If you’ve reached X-Panel Pattern Analysis in the Guide, you might want to do a freeform panel on your own.



About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
This entry was posted in Extreme Solving, KrazyDad, Puzzle Reviews and tagged , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s