## A Sudokuwiki Resolution of Insane 475

In this post Insane 475 is taken through basic and then submitted to Andrew Stuart’s Sudokuwiki solver for advanced solving.  In the original review, the puzzle was solved by an Single Alternative Sue de Coq trial, but in this update of November 2018, it turns out that most of the solver’s results can be interpreted as variations and extensions of Sysudoku methods deemed practical for human solving.  This continues a review of the KrazyDad Insane collection found on www.krazydad.com .

We are interpreting the Sudokuwiki solver’s advanced methods, not its basic process. The solver does a number scan first, filling every cell with every value not seeing a given clue. Then it reports each elimination and confirmation to arrive at the basic candidates.

The basic trace here records a far different three stage process, avoiding the placing of many candidates that will be removed before advanced methods are even considered.

The solver finds no UR, bv scan, X-panel or coloring results.  It’s first result is a hinged AIC boomerang ANL, so we add the AIC hinges to the line marked grid for this first view of the resulting candidate field from Sysudoku basic.

Starting from 4r4c7, the chain uses the hinge at r6c4 to wink into 1 for the almost nice loop elimination.

Next is a second boomerang ANL, starting at 8r4c1 and XYing to a grouped 2-chain, with XY to 1 for the wink back in.

You could spend an hour or so looking at slink departures and possible AIC returns.

In doing so, you might have tried 7t8c1 as a starting point and noted the long chain to the 3-group in the E box, gien up on it, and moved on. We could say that the solver doesn’t, but instead, notes that the wink into ALS 123 in r59c1 creates a naked pair eliminating 2 in the boomerang target cell, and creates a boomerang ANL h a subset node.

But we won’t. The solver does no such thing. It tries dozens of  consequences of thousands of possible AIC steps, including new subsets.

In solver messages, Andrew the code writer can only report the chain links, the specific action that ended the chain and the name assigned to the goal of the code at the time.

We can do a bit better, for the human solver that Andrew and I both value. We can describe the goal in familiar human terms – the boomerang ANL – and describe the new type of AIC node uncovered here – the subset node, giving it a name related to knowledge the human solver already has. This interpretation gives the human solver something specific to look for: a weak link into one value group of an ALS  makes a weak link from every other group to any outside candidate seeing the group.

The Sudokuwiki solver currently identifies the boomerang above as a digit forcing chain which is to follow a forcing chain from each candidate of a bv until they end on the same candidate.  This won’t happen unless you advance the AIC together, keeping a list of candidates included in each. More often one of the chains reaches a contradiction or a puzzle solution first. Now you have a different puzzle.

With more than two candidates, Andrew Stuart’s forcing chain unison strategy is a cell forcing chain. Here, all three r4c5 candidates have to converge and agree by forcing chains that 2r6c6 has to go.

The practicality issue is this: How many forcing chains do you have to trace to an ending before this happens again? The Sysudoku answer is, way too many. The computer doesn’t care.

Next, the solver might have gone over the same data to arrive at a third boomerang. A human solver would more likely retrace back to find another slink into the cell of another c1 2-candidate. That is a good strategy in AIC building after any boomerang.

Sudokuwiki restarts the methods list after every action, something human solvers can’t do.

The cell forcing chain yields a critical slink for a simple pair of grouped ANL.

The solver now announces a disturbance in the force:

Two ANL combine with 3-groups for a nice loop. The grouped 3-chain sees the 3 in the blue ALS 123 in r28c1 which slinks with the 2-group, which winks out to 2r7c1, which XY’s to the 7 in ALS 379 in r8c13, which slinks to the 3-group that winks out to the 3-chain.

Next to the right,  a  pre-AIC boomerang.

Then comes a fifth boomerang starting and ending with a 2-group in the SE box, and with a boxline.

This we can label  a box boomerang, since the starting group and the ending group exist within a box, rather than a cell.

Looking at this, two single candidates  in a box can close a box boomerang if one partners in a slink crossing the box boundary. And you can substitute line, or unit, for box.

Insane 475 continues AIC building with another box boomerang. This one requires an AIC hinge, but not exactly the one originally marked.

This one suggests the remaining unit boomerang possibility, one single and one group.

This leaves a hidden single 6 in r2c1.

Next the solver applies coloring for a single trap.  It’s marked to show that the AIC building is applied after coloring. The nice loop includes a new AIC hinge.

There follows a grouped 1-chain ANL,

and a hinged confirming ANL,

to reach the collapse.

Thanks for sticking with it.

The next post date was missed because of technical problems. Then we have a Sysudoku finish to Insane 475, beginning at the first cell forcing chain.