Hanson’s Polarity ANL

This post reviews the section of Bob Hanson’s Sudoku Assistant report titled Almost- Locked Ranges. It presents an effective solving idea, but with hazy definitions and a confusing name. Here I identify this idea as a familiar one in the Sysudoku repertoire, with spotting methods much more consistent with human solving.

Hanson ALR 1As usual, Bob leaves the definition of his “almost-locked range” to examples. His first one is built on the r6c9 removal from this distribution of 6 candidates:

The “almost-locked range” is identified as the intersection of r6 and c9. There is an ER change of direction from c9, enabling 6r6c9 to see both colors of the cluster. Unfortunately for this demonstration, there is already an obvious trap (light blue diamonds added) that confirms r5c7, making the ANL through r6c9 and the shortcut slink superfluous.

The idea of Bob’s removal is worth considering whenever any extensive AIC is constructed. Outside candidates seeing a member candidate directly may also have a forcing chain to a member of opposite polarity. That is the relevant idea!

But why does Bob describe the r6c9 intersection, in this case, a coloring trap on steroids, as an “almost-locked range”? “Range” was earlier used in the label “row/column range checking”, which could as well be called line checking. The section of that title was actually about boxline restrictions. In this example, it seems to be about line/line restrictions, and the ER periscope type of vision. My use of ER has been supplanted by the more general grouped forcing chain vision, which I found to be easily represented in a more explicit and consistent way.

So I’m going forward with the theory that Bob’s “almost-locked range” is a combination of direct and ER or forcing chain vision of toxic polarities.

Sudo FrankenBob’s next “almost-locked range” example is the Franken Fish, which I analyzed in a post of 8/05/12, based on Andrew Stuart’s reporting. It’s certainly a good example of a 90 degree change of inference direction, but it’s not an ALR. In the Franken Fish, or SudoPod?, a slink forces one of two aligned groups(x’s) to be have a true candidate x. This forces one of the aligned groups A or B to have a true candidate x. A candidate in any red cell sees a true candidate from every possible combination true candidates.

But the winks don’t work the other way. The red cell candidates only force contradictions, not a polarity. Another mislabeling.

Next in the report is Bob’s enumeration of 15 possible configurations of the ALR. They are the empty rectangle(ER) box configurations I have reported on, distinguishing incoming and outgoing directions by red and blue colors. This enumeration confirms that the “almost-locked ranges” is all about seeing both polarities of AIC’s, by direct and ER vision. So instead of “almost-locked range”, let’s call the general version of this toxic set elimination method the “polarity ANL” method. “Polarity” is a concept in common with Bob’s strong link chains and my coloring clusters. In the Sudoku inference notation the ALR becomes an almost nice loop (ANL), with the removed candidate between the adjacent winks.

Hanson tlink 1Now let’s examine Bob’s four examples, as transcribed for sysudokie readers. In Sysudoku diagrams, I’ll use the burnt orange coloring for the removal and the targeted link.

From the puzzle top1465 #250, 1r1c3 sees both partners of a naked pair. Along with the naked pair r4np15, it is probably the ER path in the N box, along with the direct wink, that signals a possible polarity ANL.


Hanson PANL 3In Bob’s second example, from top95 #20, the grouping of the ER box trades in two winks for a slink.

Hanson PANL 4






In the third polarity ANL example, did I miss something, or did Bob use a forcing chain instead of an ER box? I got the image, but I couldn’t find my magnifying glass. If so, I can give Bob credit for forcing chain vision in the ALR, although he never mentions that, or any other form of AIC.


Hanson PANL 5Bob’s last example, from impossible520, #517, is not self evident. Five 9-candidates have been mystically removed from the completion field by Sudoku Assistant, the ones in the red font. These removals create bv and allow a blue green cluster to spread into the 8-candidates. The ER periscope allows the green 8-candidates to see each other. But this is not a polarity ANL. It’s a color wrap!   Blue is true, and green candidates must go.

It makes a big dent in impossible 517, but it’s a different animal . No targeted polarity difference. The only element in common with examples 1 – 3 is the ER box, and the previous abandons that. I’m sure I’ve done this kind of color wrap, but if not, here it is.

And so, what Bob’s “almost-locked range” really is, remains a mystery. But I’m entirely satisfied with Hanson’s idea, which he illustrates, but does not adequately define, in his SA report.

Three of Bob’s examples of targeted polarities were single slinks. This suggests looking around each new slink and naked pairs for an AIC closing the loop. This distraction in the basic solving process isn’t practical.  Instead of scanning outside candidates for those creating polarity clashes, I have a better alternative. That is, in the advanced solving stage, to expand the polarities of AIC loops and clusters by AIC extensions with X-panel analysis and coloring. Then the polarity ANL manifest themselves as X-panel ANL and as color traps. An example is the nice loop cluster of KrazyDad Insane v.4, b.6, n.5 in the Insane review.

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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