Recycle AIC Building on UHC 311

This post shows how the AIC building done by the review solvers on ultrahardcore 311 can be systematically duplicated by a human solver. The technique is a graphic one, very amenable to ©PowerPoint graphics, and slink marking of Sysudoku Basic. This and other examples will be the basis for AIC building recommendations in the Sysudoku Guide.

AIC building is a phase of Sysudoku Advanced which follows the bv scan  for Sue de Coq, WXY-wings, and XY-chains, and the X-panel analysis for X-chains, grouped X-chains, regular and finned fish, and edge limited freeform pattern analysis. After these systematic and exhaustive elimination methods, the human solver can reasonably begin AIC building, a systematic search for Alternate Inference Chains, with its many possible starting points, continuations, and terminations. Let’s look back to the post of last November 3, where solvers Sudokuwiki and Beeby immediately followed line marking.

A series of four AIC’s resulted, before the first ALS_XZ. With solvers you never see the many trial chains that do not lead to any result. Is it an overwhelming number, though? Maybe not.  Consider how the chains generated on a grid are interdependent,  restricted as they are by Sudoku placement rules. In the review, three of the four solver AIC start on the same slink.  Many segments are shared among these four.

If we set out to find every grouped, fully extended AIC without ALS nodes or 1-way branches, how many would there be?   We’ll do our top down, left to right scan for starting slinks. Eligible slinks have a wink directly to a next slink, and we can go off each end of our starting slink. Record your guess on how many distinct AIC, counting extensions and not counting extensions.

Starting off with the r1 5-slink,  we can’t leave from 5r1c2 because it doesn’t see another slink partner.  In that sense, AIC building is like lite tree building. It’s a surprise how far the AIC goes, getting into a loop but branching out to get to two possible slink terminals, but on 3, not 5.

Veteran readers know that a loop can often start a coloring cluster.

Here we realize the AIC contains  a 1-way from 3r1c2. Either terminal 3 sees the victim, and if either is false, the chain makes 5 true in the victim’s cell. In the review, Beeby made the same removal with a complex 1-way, later.

Now we shift the 3’s to mark the new slinks in NW and r1, and move on to the r1c4 slink for an AIC starter.  From the 3 it gets into the same loop, but going in the wrong direction to slink out on the 9. From 2r1c4  there’s a long branching AIC, with one branch reaching an ANL.

The second elimination in r1 generates N3, which destroys an ALS_XZ partnering ALS in the review.

Now moving on to the N 4-slink and 4r3c4, we’ll blue out past segments to put them in the background, going to black for new extensions. We get an ANL removal with each extension.

The right branch brings us to an extension to 4r8c9 which teams with our staring 4r3c6 in an ANL removing 4r8c6. Btanching off at 8r8c6 to 4rc5 removes 4r4c6.

Recycling AIC is good.

We get to do it again with a grouped extension from 5r8c1. The prior removals provide that closing slink for a confirming ANL and N4.

 A benefit of systematic AIC building is to have many AIC segments on a background layer, for  possible use later.

We’ve accounted for all the solver AIC findings. How many AIC did we have to generate? I’d say a reasonably small number.

Next week, we start a similar reverse engineering on the solvers’ ALS findings, introducing a graphics tool for systematic searching. That too, is a complexity nightmare for human searching that can be kept in bounds. The prospect is a systematic order of battle against very difficult puzzles.

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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