A Trials Experiment with Golden Nugget


This post and the next illustrate the ability of an LPO pattern trial and Sue de Coq verification trials to penetrate the candidate fog of an extreme puzzle, thus allowing advanced methods to solve it.  The subject in this case is the forum darling known as The Golden Nugget.  It’s a timely follow up on the trial techniques demonstrated in the review of the KrazyDad Insane collection.

I was very pleased to receive some thoughtful questions from  Maija Ingelin on trial and error solving of hard puzzles.  The comment, and my reply, are on the About page.  Relevant here is the fact that extreme puzzles tend to absorb a series of guessing probes without offering back decisive progress.  This saddles the human solver with an intolerable backtracking burden, although a computer backtracking algorithm handles it easily.  The human solver’s defense, illustrated well in the KrazyDad  review, is to logically construct multiple candidate trial probes, with decisive alternatives.  The review featured probes using cluster colors, nice loop coloring, Sue de Coq verification, AIC and pattern slicing on moderately extreme puzzles.

Super extremes like Golden Nugget I consider to be impractical for human solving. But I can show  that multiple candidate trials can get the human solver in the door, and keep backtracking to a practical minimum.  The basic  and advanced solving techniques of this blog, and an ample supply of patience,  can then be sufficient for victory.

So we begin with the line marked candidate grid for Golden Nugget.  If you want to do the basic solving, just copy the Calibri big numbers and have at it. Box marking is easy, but line marking is hell.  Looking at the result, it’s pretty clear what I mean by the fog of candidates, isn’t it?

Nug LMTo really come to grips with the fog of candidates, just map them out on the X-panel.  Basic solving produced no clues, and not a single bv cell!  A paltry number of slinks, so put away the crayons.  No AIC hinges. I tried enumerating ALS, but that’s hopeless.  OK, that’s enough, I’m invoking  LPO.

I thought the 2-panel offered some hope for orphans, and did the freeform analysis below.

Nug 2-orphansFreeforms from r9c7 look to be the most restricted, but are too numerous for conflict analysis. The second panel highlights uncovered candidates.  I then try to cover these with patterns from the remaining r9 candidates.  Unfortunately, I succeed.

Just to investigate how the trial of a pattern effects the candidate fog, I put on trial the first five candidates of the blue freeforms, namely r9c7, r7c4, r6c3, r4c8 and r3c9.

Nug nt sdc 1The effect is good. A naked triple is created, and we now have three bv!   Wow!

One of the bv sets up a potential Sue de Coq, namely

Cr3=9(3+5)(1+7) +197.

The test for (3+5) missing is a second level, but if it fails, we have the Sue de Coq eliminations

The trial is for   r9c7 = 2, etc.  and Cr3 = 197.  After this marking,

Nug 2 marking

the grid was clear Nug 197 swordenough for a 7-chain, a swordfish, and an ordinary 378-wing.

Nug nt sdc 2

 

 

 

 

 

 

 

The bv and uncluttered grid supported two clusters, but  there were no traps, bridges, or wraps. Then I found another potential SdC in

SWr9 = (3+8)(5+6)

+3(5+6)(6+5).

We’re in for a third tier trial.

 

 

Nug 197 trial        The marking for Wr9=3(5+6)(6+5) starts with a naked triple 147 in c7, and forces two 7’s in c1.

Nug sdc 3That leaves us with the verified Sue de Coq  SWr9 = (3+8)(5+6), which extends the red/orange cluster.

Not bad.  Slow progress, but remember what we’re dealing with.

 

 

 

 

 

Nug 197 xy and sdc 4Continuing on the second tier,  we find a small XY-chain on our bv map, and notice that the removal triggers a potential Sue de Coq:  NWr3 = 3(6+4)(7+1)+713.

How about if you pick it up there and see how far you can go with the r9c7=2 trial in the Nugget.  If it’s not a surprise, I’ll be surprised.

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About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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