## Sue de Coq Trials of Insane 475

In this post , a reader’s checkpoint affirms that Insane 465 is free of multiple solutions.  Then Insane 475 is taken through basic and advanced solving stages.  A new form of two dimensional trace is introduced that is particularly suitable for conducting and documenting trials.  This continues a review of the KrazyDad Insane collection found on www.krazydad.com .

I trust you your Labor Day weekend was delightful.  This post was scheduled ahead of time and I spent mine at the beach.

Let’s continue first with Insane 465. Your trial of the tan nodes of the Insane 465 nice loop should begin this way.

Going back to revise my X-panels and bv map,  I found that a 3-wing had appeared, and that triggered a 489-wing with a victim seeing one wing via a forcing chain.

Following up, I had one more removal before trying red and orange, an ordinary 456-wing .  Both failed on the last few cells so Insane 465 is proved honest.  Chalk one up for the KrazyDad Insane collection.

That is, unless one of my alert readers discovers a path to the solution without the nice loop trial.  Could happen.

That brings the order of business to IN 475, that is, Insane v.4, b.7, n.5.  The basic traces are simple because very little is accomplished.

The first advanced discovery can be shown on the line marked grid.  In the SdC chute Nr3, alternative (4+5) could be missing, but for either

7(4+5)(6+9) or 967, the 9-candidate of r2c4 is removed, leaving two more boxline removals in the NW box.

Sneaky.

Next,  there is the potential Sue de Coq, Wc1 = 4(1+2)(3+8), where 1 and 2 could be missing.  This isn’t the case, but the trial of  Wc1 = 834 is a long and tedious job, and I thought it would be a very good thing to show that here,  how different this trial is from the easy bv number guessing more justly labeled as trial and error.  I wanted to illustrate graphically on the grid, in the sysudoku spirit of logic discovery,  the shortest  logical route to a contradiction.

This problem led me to a new form of trace.  No, don’t groan yet.  This is really neat.  It requires a different algorithm for conducting the marking, with different and sometimes strange winners in the cause and effect contests.  But it produces a trace that is simply followed top to bottom and left to right! And the tracing solver can then graphically document the shortest logical route to a contradiction.

The 2-d traces of earlier posts document depth first marking.  They are read left to right, but with a confusing habit of bouncing up and down.  Their advantage is that they follow up more immediately on the most recent markings,  favoring the human inclination to do just that.  But when a trial reaches a contradiction, the shortest route is difficult to recover from the2-d trace.

So maybe you’d like to see what I’m so worked up about?

Well first, the depth first marking order.  As before, we list all effects of a new cause immediately.  in a list, those on the same number are listed first.  The difference is that we do not follow up on the effects as causes until we have followed up  on all the effects remaining on that level, and on all the effects to the left of these effects on the next level.  As we write a list, this means that we have to push trace events at earlier levels to the right to make room for the effects not yet recorded on the current level.

You have my permission to come back and read this paragraph several times as you read through the following trial trace and the corresponding graphical representation of its shortest path.  In effect, the marking moves in breadth first order, distributing a tree of effects across the page or screen.  Moving down the tree directly to the contradiction gives the shortest inference path to the contradiction, sometimes with the assistance of later clues at the same level.  This route reveals the elegance of the result. The overall size of the tree still indicates the complexity of the effort involved.

See if you can interpret the chain graphics and trace down the tree to the question marks where SW and NW 1-candidates (circled) are placed in the same column.

Applying the verified Sue de Coq of Wc1 gives us the four removals shown at the left,

After these removals, we have another potential Sue de Coq in Sc6, with Sc6 = 9(2+5)(4+7), but with 2 and 5 possibly missing.  The trial of Sc6 = 9(naked pair 47) is equally long and tedioius, but we verify the SdC and remove a 5-candidate from r7c4 and 2 and 5 from r7c5.

The SdC’s have added a few bv, but there are still no XY-chains. I also get no x-chains or fish on the X-panels, and coloring allows only an anemic blue / green cluster.  The only action is this long AIC chain producing no toxic set (ANL) removals.

The LPO panels are also unpromising, either too many patterns, or too few and disconnected between numbers.

But wait! A possible crack in the armor appears in the 3-pattern  pink olive freeform enumeration at left.  There are only two pink patterns, both exclusively including the 3-candidates in r5c9 and r1c7. Several 3-candidates are included only in olive patterns, and one more only in pink patterns.  Opportunity knocks in that the long AIC chain virtually determines the contents of r1c9.  If the 4-candidate is true, every candidate reached by a slink of the chain is true. And only the pink patterns remain.

I think this situation is similar to the Sue de Coq alternative analysis and the nice loop coloring analysis for which the Insanes required trials.  We must put the AIC chain on trial, starting with the reluctant “guess”, that r1c9 = 4.  I’ll leave it up to you to sin first, with a checkpoint from me in the next post.

As if that weren’t enough, you could also look at the basic solving of Insane 485.  We’re going  there next time.