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?
To 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.
Freeforms 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.
The 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,
the grid was clear 
enough for a 7-chain, a swordfish, and an ordinary 378-wing.
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.
The marking for Wr9=3(5+6)(6+5) starts with a naked triple 147 in c7, and forces two 7’s in c1.
That 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.
Continuing 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.
