A Boomer Inspired Pattern Trial in 495

In the original review, KrazyDad Insane 495 was an example of Limited Pattern Overlay, but eluded a decisive solution by LPO. In this update, Stuart’s Sudokuwiki “runs out of known strategies”, but makes some spectacular plays, including an ALS boomerang suggesting a new type of pattern trial.

Looking at the basic trace, the contrast with the solver’s basic technique is stark. An unresolved 3-fill in the bypass, numbered slink lists in box marking, the order of line fills, the naked triple as a basic discovery, and finally, a line marking and closing history, it all speaks of a systematic process expressly designed for human abilities.

The contrast is also evident in comparing the Sysudoku line marked grid with the Sudokuwiki first step candidate display and in following the solver’s path to the first advanced effect.





That first advanced effect is another reminder of other disagreements with my often acknowledged mentor Andrew Stuart. It is a Bent Almost Restricted n-Set, or BARN of size 4 in the bent region Nr3, which Sudowiki identifies as a WXYZ-wing. There is justification, in that when you pick the one 3-candidate cell as a hinge, an ALS in the formation supports two of the three wings of the classic WXYZ.

In coding complex operations, covering multiple methods with unifying code is a good practice. To support human mastery of Sudoku, however, strong and simple definitions based on a small number of consistent principles is more important. To this end, the classic hinge and wing definition of the WXYZ need not be stretched, because the BARN and its equivalent, Hanson’s Bent Naked n-Set 1, cover this elimination  in a more fundamental way.

Unlike the last few Insanes, 495 has several advanced moves from the X-panel, before AIC building.  First,  a grouped 3-chain ANL. Note the c2 slink defined by grouping. It could be spotted in line marking  to go with the r3 line slink.

Next is a grouped 5-chain ANL extended two more nodes, in red, to a second one.

The removal in r7c1 permits a simple AIC boomerang from r1c2 with an XY move to a 2-chain.





AIC building comes after X-panels and the inspection for easy freeform starting lines, so I’m surprised by an Sudokuwiki announcement that 5r7c5 and 5r9c9 are orphans.



Then I notice how, starting at r9c9, a northbound freeform is restricted to a single candidate for the first 5 lines. You have to see how three boxes have to be satisfied in each bank. After coercion like this, eligible columns  and ending cells have to be in short supply.

Take a moment to confirm that freeforms starting from the other three sides are much less restricted.

Drawing in the freeform up to r5, two columns need a crossing on r4. You can’t march through Sudowiki’s algorithm for each panel, but you can spot and follow up on such restrictions as they get more and more promising.

The case for human spotting of the r7c5 orphan is harder to make. To justify it, once known, is a different matter. Exclude candidates in the same box first. Skip r6c4 and there’s no crossing in the C box. Choose  r6c4, and you have to cross r1 in two places. Let’s say finding the one is incentive for searching out the other.

The orphans do help out.  As in the salvaged slink in the grouped ANL to the left.



And the North slink now closing the grouped ANL on the right.

Now we put together two Sudokwiki findings in a simple grouped 8-chain, extended by a grouped 5-chain to an ALS 8 group terminal.




One of those eliminations proves to be redundant, when  AIC building provides


another one of those almost nice loops, with an ALS 8-group and one of its members at the terminals of the slink chain. It’s another ALS boomerang! The 8 value group of ALS 358 is toxic.



Then after this stem winder grouped AIC boomerang, Sudokuwiki  declares itself “out of known strategies”, its time to look for Sysudoku moves outside of the solver’s human methods repertoire. That means inference chain XYZ, advanced coloring, pattern analysis, limited pattern overlay and trials.



Updating  the XYZ map and the X-panels, the most decisive threat to 495 seems to be freeform restriction on the 8-panel similar to the productive one suggested by the solver on the 5-panel.

We decide on a trial of the pink freeforms on the 8-panel. It will determine the 8-clue on r6 left open by the ALS boomerang.  It is likely to be decisive, since it would remove the 13 orphans olive orphans shown here. And if it reaches a  contradiction, the three pink candidates are removed, and a new C8 is placed, removing two more.

Here is the grid as the trial starts. A trace of the trial follows. First causes are the candidates of the three pink patterns, and the bv partners of orphans. In a trial trace, effects are marked line by line, in order to reach the contradiction in the lowest level of inference.

In this case there is no contradiction and the trial generates the solution.

It turns out that the true pattern is represented by the freeform ending in dotted lines. The competition between pink patterns requires no attention.

Next up is Insane v4, b.10, n5, i.e. 4X5.

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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