Insane 425 Introduces the Boomerang

This post checkpoints a stunning XYZ 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(ANL).

One of the toxic set members is blue, but that doesn’t mean the other is green. One of them is true, but both of them could be, making both blue and making blue true.


These removals made possible a wildly irregular 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.

In such cases, the small rounded squares serve to identify the 3 member toxic set.








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


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.

The starting signal is a slink emerging  from a cell of several other values to launch an AIC. If a slink terminal of the growing chain sees one of the other candidates in the starting cell, an almost nice loop has been found which eliminates that candidate.

Using the ANL above as an example, as the 2-slink leaving r1c4 does an XY transition to a 3-chain, we’re watching for a wink at the 2, 6 or 7  candidates of r1c4. When the AIC hinge of r6c9 allows a transition to 7, we’re not going to miss the slink with 7r1c9.

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. The starting slink partner is 1r8c7.

Marking AIC hinges by grouped slinks can be helpful.  Here, the premarked hinge at r8c5 was redrawn.

The boomerang parade paves the way for coloring and 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

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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