Hi Alfredo!
atrotta wrote:Hi SpAce, here I am again. In the last period I went in particular through the threads "Nishio vs AICs. When is it considered cheating?" and "Solving without pencilmarks". Now the questions arise: using techniques like 3D coloring or GEM, where the player maps the grid highlighting any possible elimination and goes back (if he wants) to draw the chain, could lead to solve almost any puzzle. If forcing chains are added, probably even "almost" can be eliminated to the previous sentence. Even if the player is left the decision on the seed nodes to start with, where experience could help, even a poorly skilled one, can eventually solve even very difficult puzzles (maybe with the exception of using groups or ALS as nodes, that I guess requires a deeper knowledge).
I think you might be a bit optimistic about the omnipotence of GEM and related techniques
While they do help tremendously at lower levels, I've found that their limits are quickly reached when trying to solve puzzles beyond SE 9.0 (which I haven't much done, though). They still help, but you have to be much more creative about finding sources of derived strong links or using larger strong inference sets (which GEM doesn't really support), as the native bivalue and bilocation types and even useful ALSs are scarce. Hodoku is really good at finding most forcing chains and nets if they're to be found, but even its repertoire dries up at around SE 9.6 (as reported by 200e200w in this thread) -- and the techniques it uses at those levels are hardly human-friendly. To solve harder puzzles logically you have to be creative and/or knowledgeable about techniques like Exocets and Multi-Sector Locked Sets. As far as I understand, some puzzles still resist any humanly applicable techniques (except guessing, but that's not a very interesting option -- except maybe for speed solving).
I am at a turning point. Is it worth spending a lot of time looking for patterns like XYWZ-wings, Sue de Coq or ALS-XZ, or proceed with a trial and error approach looking for AICs or even XY-chains, when such powerful techniques like 3D coloring or GEM exist?
The answer to your question depends on one's personal goals, and it probably changes along with one's development as well. I personally think the best investment early on is to learn the fundamentals of chaining (and networking) logic well, in which techniques like GEM help. It's more important than memorizing a bunch of ready-made patterns which are based on those fundamentals anyway. Once you have those fundamentals, then it gets much easier and interesting to learn various patterns too, because they actually make sense and it's not just memorizing (which I hate). Being able to recognize and name certain recurring patterns, and understanding their relationships with each other, is both satisfying and also efficient, plus it makes it easier to communicate with others. So I'd say it's worth it. The fundamentals are more important, but studying both feeds each other and helps over-all learning.
On the other hand, the thread "Solving without pencilmarks" and the fact that in sudoku championships candidates are not prefilled, led me to start practicing with no candidate filling or with candidates filled by me, feeling like solving a puzzle in this way is the only "true" way as only relying on my own skills.
Solving harder puzzles without pencil marks is a skill I envy and respect. In my pencil&paper solving I always start puzzles without pencil marks, but I don't usually get very far beyond the basics (if even that), so I can't really give any advice on that part. I'm sure it's a skill that can be improved (and I have), but I don't really enjoy straining my working memory (and yes, I know RW says that it's not about good memory but I don't quite believe that). That's why I've developed various memory aids so I can concentrate on the logic, which I find more enjoyable. My goal is not the ultimate speed or efficiency, so my methods may not be suitable for someone aiming for championships. They're very reliable, though.
Could you give me your point of view and possibly some hints on techniques (the way it is more profitable indicating candidates) to be used when solving without auto-filled pencilmarks (obviously I do not mean filling all candidates manually)
Well, my first piece of advice would be: don't use numbers. Writing those takes a lot of time, and it's mostly useless information taking up space that could be used more efficiently. Use the 3x3 space of the cells to map which candidates are possible or not, using some kind of quick-to-draw markers. For the simplest and quickest mark-up you can use just dots (either to mark possible or impossible values depending on the system -- I dot impossibles). You can also use more elaborate markers to indicate relationships between candidates, for which you wouldn't have space if you wrote actual numbers. It may take a while to learn to read the dot-patterns automatically, but it's worth learning.
Another generic tip: don't erase anything (unless you make an actual mistake, of course). It's a waste of time as well, probably ends up messy, and also loses information. Just highlight the true candidates somehow instead of forcing them into big numbers, and dot, blacken or cross out the false ones. I only use big numbers until I start using pencil marks, which also shows afterwards how far I got without pm. The end result is surprisingly clean and easy to read once you get used to it, and it also stores a lot of information about the solving process which would be gone if you erased and replaced it with big numbers. Partial blackening can also be used to implement multi-phase eliminations and placements, which I use to ensure that my mark-up stays up-to-date when anything changes. Without something like that, maintaining the candidate lists (and any external helpers) could be a nightmare, but my system does that practically just as reliably as software (though not quite as quickly).
Secondly, I almost never fill in just some pencil marks, though it might be quicker in some cases. If I use pm at all, which is practically always with anything beyond basic+ puzzles, I do it very methodically when I start the process. Before adding pm I've already exhausted most if not all basic techniques and some easy non-basics like obvious URs and X-Wings (and maybe Skyscrapers and Kites), so there's probably very little I could find with a partial mark-up (which is much more error-prone as well). I do my mark-up in layers, though, which means I don't have to do the whole thing if a lower layer is enough. Also, if an obvious opening presents itself I may take it even while marking up a layer (because it might solve the puzzle or at least simplify the remaining mark-up), but then I just have to be a bit more careful and remember what I was doing when interrupted.
The (almost) lowest layer of my mark-up is a mechanical dotting of impossible values (using the 3x3 space in the cells), which is very easy and quite quick because I just look at the givens and the solved cells (in the first round) -- zero thinking required, which makes it extremely reliable. (See * for an alternative way.) I always dot the boxes first, then the rows, and lastly the columns, just to keep the process standard and to not miss anything. On the second round I dot the victims of any pointing pairs/triples and other easy patterns (like hidden pairs etc) I'd identified in the no-pm stage (I use a very light-weight mark-up to remember those patterns, which would be the actual lowest layer). At this stage the non-dotted spaces in the cells represent the possible values, and I use those to look for naked patterns (especially triples and quads) I might have missed in the no-pm stage (without pm it's easier to find hidden sets than naked sets, which is reversed when pm are added). Of course any missed naked singles and pairs are found as well, but I do my best to locate those before dotting. If it's a harder basic or basic+ puzzle, I can probably complete it with just this mark-up.
If it's something harder, I add another layer for visualizing candidate relationships. Those I draw in the empty spaces representing candidates, and for the detail level I have two options depending on the expected difficulty. If it's an easier non-basic puzzle, I go with the quicker route that only marks conjugate pairings within boxes, rows and columns. That's enough for finding any basic AICs (and also guarantees that any hidden singles/pairs, claimings etc possibly missed earlier are found -- but I do hit myself if I've missed those!). For harder puzzles I use my complete mark-up that also marks group relationships, which makes finding more complicated chains easier. It's quite laborious so I only use it for puzzles that I expect to take several hours, or perhaps days, to solve (unfortunately it's also somewhat incompatible with the lighter system so I have to decide beforehand which one to use).
That being said, I admit that I'm nowadays using Hodoku more than my own system mainly for its quickness (after learning to use its coloring facilities) -- but I do miss the better visualization of chains in my paper solving. With Hodoku I have to use coloring much more to find chains which would have been obvious on paper. Life is full of trade-offs. I still use paper if I want the full satisfaction of solving, or if it's a hard enough puzzle that would really benefit from my system. Perhaps I'll go hybrid at some point or maybe even code my system as a patch for Hodoku or something. I guess at some point I'll need to install XSudo because it seems very valuable for understanding harder patterns and puzzles.
(*) Another possibility for the lowest mark-up would be to dot possible values, which may be quicker on easier puzzles but it's also more error-prone and leaves less room for elaborate relationship markers. An example of such a system with basic conjugate markers can be found
here. My dot patterns are obviously the exact opposites of those.
[Added: If you're confident about your abilities, you could mark just certain candidates or impossibilities instead of the whole grid. For example, you could apply a cheating version of RW's no-pm techniques by dotting pattern- or chain-based eliminations that he says he memorizes. Then you'd just have to read the other impossibilities from the givens and the solved cells. I choose to mark the whole grid because I think it's less of a burden than mentally mapping the possibilities/impossibilities all the time.]
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