A Nakex 83 BARN Challenge

Nakamoto 83 earns its Extreme badge by an extremely tough Basic, and resistance to anything short of AIC building. It ends with an expanding cluster, accelerated by a series of BARNs. This post brings you to the first one, and leaves it to you to find the rest, before the March 10 post.

The line marked grid is evidence of the extremely tough basic phase, with many long line fill lists and cells of four and five candidates.

The basic trace reports no concessions.

Heavy lifting continues as Nakex 83 requires immediate AIC building. Here is AIC boomer 1 turned confirming ANL, from 2r1c3. It ties 2 and 3-chains together with AIC winks.





A second confirming ANL follows the same spotting pattern, two converging slinks, starting as a boomerang from 3r3c1.





After the follow up



the naked pair C47 removes two 7’s from the C box, the aligned triple W7t removes 7r8c2, and an XY ANL removes two 4’s.




Now, starting from the new 7-slink in the r5s57 pair, an ALS node and XY segment lead back to the starting 7 for a nice loop.

Nakex 83 is showing that boomer search is a basis for all AIC building, and there is good reason to keep up with bv scanning data.



a budding cluster nets a trap, and an XY ANL, to which Sudokuwiki adds a BARN.

For newcomers, a BARN is a Bent Almost Restricted n-set.









An n-set is n cells containing only n values. In this and most cases, n = 4. “Restricted” here means confined to one unit, box or line. “Almost” refers to one of the values being bent to share two units, a bent region. In a BARN the bent value is toxic. It  includes a true value.

From here, Nakamoto Extreme 83 finishes with coloring expansions and traps, generating a series of three more BARNs and two shortcut ANL. Using Sudokuwiki, I missed out on finding them, but you don’t have to. It’s laid out next week.




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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8 Responses to A Nakex 83 BARN Challenge

    • Sudent says:

      Thanks for sharing your opinions on Sysudoku, and your alternative approach to Nakamoto Extreme 83.
      With its publication here, hopefully there will be comments comparing the two approaches.
      As to your opinions:
      Sysudoku is not written for Sudoku geniuses or experts. Rather, it is intended as a personal account providing an entry for the rest of us into advanced Sudoku.
      I didn’t coin “strong link” and “weak link”. I only shortened them for emphasis and frequent use. Do you speak for the Sudoku world?
      My “patented Notation from Hell”, the basic trace, is compact enough to be published for every review puzzle. It allows beginners to follow every step of Sysudoku basic, which is itself designed to avoid clutter in basic solving. Trace readers provide rationale which clutters other notations, itself an aid to learning. Instructions are given, but any expert can follow the basic trace by filling a grid, without instruction.
      Your “each little obvious coloring” is actually a quickly applied representation of a color link network, a color link being a combined weak and strong link. Coloring cluster expansions are not “ impenetrable”.

      • abdlomax says:

        Thanks. Of course you did not coin “strong link” and “weak link,” I was merely pointing out that the terms are counter-intuitive, and did not blame you for that. I wrote: “But sysudoku did not create this mess, which simply acts as a barrier to newcomers.” There are many such barriers, created over the years by many authors.

        I disagree about your notation not being “cluttered.” Compared to what I use, it’s very, very cluttered, and “showing every step” of solving creates what I call “impenetrable” documentation, not well designed for pedagogy. I’ve been considering how to show the detailed process, but the reality is that people will not understand coloring if they don’t play with it, so I’m not sure there would be much benefit. I would use video or a slide show.

      • Sudent says:

        Good to know we share the goal. I’d like to know what the weak and strong labels run counter to, for you. I think the terms fit in this sense. The conclusion of the strong link inference is the confirmation of a candidate, a placement. The conclusion of the weak link inference is an elimination, a generally lesser result.

        Also, we may be referring to different things by ‘notation’, I took your reference to be to my basic traces, which are very busy because they document detailed basic solving. You and most of the writing community defer Wayne Gould’s basic solving andstart with a full set of candidates generated mechanically from the givens. That’s real clutter. You probably are saying my link marking by cell placement is just introducing clutter. But no, it earns and records information that you use intuitively, but find hard to teach to beginners. AI went through a stage of that, the Expert System.

        Just admit that you record the same information twice in the keypad positioning of candidates by value and by cell position. That’s obviously inefficiently redundant. I claim you’re all missing something, but are way too expert to read Sysudoku Basic traces and learn what it is. But no matter, you can all skip the traces and spot the critical slinks unaided. Talent beats engineering.

        Do we both mean the same thing by “coloring”?

      • abdlomax says:

        Quite a lot to address. Notation. First about candidate notation. I developed my methods with ink on paper, and independently invented priority notation of box doubles. That’s parsimonious, only adding in additional candidates when needed, making pairs visible before they become hidden. Then I add in box triples, watching for patterns, then higher counts, until eventually the puzzle is solved or the candidate notation is complete.

        I do not use small numbers, but dots in phone position, so what I do is not redundant. However, redundancy is not necessarily “inefficient.” The eye recognizes patterns faster than it can read numbers, and can see positions in a wider range of vision than it can read numbers. So in that basic solving, I make only these marks inside the puzzle: dots for candidates, X over a dot for an eliminated candidate, and I diagonally chamfer the corner of locked multiples, with the corner matching in the set. Easy to see and never gets in the way later.

        People are used to what they are used to. When I work on a puzzle (from Reddit) that has sequential, non-positional notation, it is much more work for me to see patterns than with positional.

        Now, most solving I do is responding to questions and for that I use Hodoku, and while I miss the easy early solving from limiting notation to box doubles, the reliability of autofill and the availability of very clear and highly useful candidate highlighting more than makes up for that. So, yes, that could seem to be “clutter,” and when I’m working in ink on paper, I still have a strong reluctance to add in that candidate with eight positions in a box. But that reluctance is foolish, if I’ve done the preceding study well. It simply slows me down, because once I have a full candidate list, more possibilities arise and become easier. Not only intermediate patterns like fish, wings, and kites, but also chaining. When I’m chaining — with coloring — I don’t want to be worrying about whether or not there is some extra candidate not noted.

        So, then, coloring. Coloring is marking candidates distinctively, according to some scheme or process. I color in ink by circling or “triangling” the dots. It works with small candidate numbers on printed puzzles in positional notation, because the numbers are nice and spread out. In Hodoku, I literally color candidates (and color the seed cell for Bivalue Simultaneous Nishio so that it can be found. On paper, I developed SBN with ink, but sometimes I needed to make additional colorings, and it got complicated, so I now color on paper in pencil over inked candidates. Mutual eliminations and resolutions are marked in ink, but the coloring can be erased if it gets in the way, leaving the candidates untouched.

        What I do is simple, easily taught, and cracks all difficult sudoku except the “unsolvables,” which may require recursive techniques. (I’ve solved unsolvables, average time to solution seems to be about four hours, with up to another four hours to prove uniqueness.)

        I do not think of the coloring I do from a bivalue or bilocation seed as “true and false.” They are simply networks, and cooperate in finding solutions. Thus the method is not “trial and error,” because there is no error, there is only what one finds when exploring the chains. I pay no attention, per se, to “strong” or “weak” links, just what a propose resolution requires, and, as it is an exclusive pair, how they interact to require results (either elimination or resolution, I’m happy to see either, they accumulate.) The big discovery that I’ve not seen documented anywhere else is that with ordinary puzzles, with many possible bifurcation seeds, *most seeds generate results.*

      • Sudent says:

        Thanks for explaining your basic process and SMB. Sysudoku bypass is similarly parsimonious, marking only clues and subset candidates. Box strong links, your box pairs, are added in box marking, and line slinks and remaining candidates, a third process, line marking. Subsets and box/lines are added all along.
        Yes, dot marking hides the redundancy, and it may enhance the visionary benefit of phone positioning. I promote PowerPoint grids along with pencil marks and slink marking.
        You rightfully distinguish your coloring from Medusa coloring. My dashed and solid curves do your coloring, but are not practical for representing possible paths, only the final ones. You must agree that the final product is more visually accessible. I do manually peck in the curves. It’s not as hard as it looks, and the documentary power is astounding. Look at your bales of paper.
        As to SMB, it’s a trial method that may lead to a logical conclusion. Sets of candidates are constructed one of which must be true. The constructions may reach a logical conclusion that one of the sets is indeed true. I use Medusa coloring in the same way, not by directly confirming that one color is false or true, but by expanding the coloring until one color contradicts itself logically. But usually, I can report which of the other methods human solvers know by name helped me make the placements. I promote looking for them before coloring.
        You might enjoy the SMB parallels with my AIC building: Starting with cell with a slink candidate, follow all AIC until one returns to a different candidate in the cell. The “boomerang” is an eliminating or confirming almost nice loop, or a nice loop.. In my rating a puzzle goes from advanced to extreme when I have to resort to AIC building, because of the multitude of slinks and AIC from each that I may need to explore.

  1. abdlomax says:

    I have commented on the above appreciated comment here. https://www.reddit.com/r/Sudoku_meta/comments/fsd2u4/conversation_with_john_welch/ Comments here or there are welcome. Thanks.

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