need help with this puzzle, and technique in general

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Re: need help with this puzzle, and technique in general

Postby atrotta » Sun Sep 16, 2018 5:30 pm

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 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?
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.
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 :lol:)?
Thanks a lot
Alfredo
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Re: need help with this puzzle, and technique in general

Postby SpAce » Tue Sep 18, 2018 2:52 am

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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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: need help with this puzzle, and technique in general

Postby atrotta » Sun Sep 23, 2018 5:26 pm

Hi SpAce, just some clarifications:

SpAce wrote:Partial blackening can also be used to implement multi-phase eliminations and placements

What do you mean exactly with partial blackening?

Could you please clarify better your dotting system? My first impression is that marking the impossibles in each cell could be messier than marking the possibles, but maybe I did not fully understand. Could you send me some examples with the different layers filled (of course if your system is not copywrited ;))?

SpAce wrote: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)

I use Hodoku too. I find its coloring very useful to map GEM and forcing chains. For GEM I use a different pair of colors to mark par, super and sub grades (a color of the pair for each parity. For forcing chains, just two colors, one for the true option and one for the false. Could you explain how you use it, just for the sake of comparison?

Thanks again for your very useful replies. You are acting more and more like a mentor for me. A big responsibility for you... :)
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Re: need help with this puzzle, and technique in general

Postby SpAce » Tue Sep 25, 2018 5:06 pm

atrotta wrote:What do you mean exactly with partial blackening?

That applies to the eliminations of the second layer of my markup when I've filled the non-dotted spaces with actual candidate markers (little circles with the relationship markers drawn inside of them). While the first stage eliminations are marked with dots (or little crosses which I use for non-obvious eliminations to remind me why they're there), the second stage eliminations are marked by blackening the candidate circles to keep the survivors clearly visible (since I don't erase). If I did a full blackening immediately when I've identified an elimination, how would I make sure that I remember to check any resulting hidden singles or patterns as well as to update all the relationship markers for the survivors? Some patterns can cause lots of immediate eliminations, and all of those need to be processed. It's easy to miss something, so I developed a cure to avoid it.

What I actually do is that I start by blackening only part of each eliminated circle, and I complete it only when I've fully processed its effects. I do it one quarter at a time to mark different stages of the the processing (like rows and columns). That's how I know exactly what's been done and what not, and I can even leave the puzzle at any stage and continue the next day without missing a beat. In fact, I think partial blackening has been one of my best inventions for paper solving with candidates. Before that I already had a similar system for processing the effects of placements, but that's simpler anyway.

Could you please clarify better your dotting system? My first impression is that marking the impossibles in each cell could be messier than marking the possibles, but maybe I did not fully understand.

I don't think it's messy at all, but I'm partial of course. I'll produce a picture later, so you can judge yourself. In any case I think it pays off, because it's so much easier than filling in possibles directly, as it can be done completely mechanically (which makes it very easy to teach to a complete newbie too). It's also very reliable and fast because you're using the same pattern for each cell in a box, row or column. If you're filling possibles directly, you have to do it one cell at a time and be much more careful. If you miss adding a valid possibility, you're potentially screwed. The only way to screw up the impossibility dotting is to accidentally dot possible candidates, but it doesn't happen as easily.

Could you send me some examples with the different layers filled (of course if your system is not copywrited

I've been planning to do a proper presentation of the whole thing at some point. Now that someone's expressed actual interest, I might do it more quickly :) There seem to be few paper solvers nowadays, so it hasn't been a top priority.

I use Hodoku too. I find its coloring very useful to map GEM and forcing chains. For GEM I use a different pair of colors to mark par, super and sub grades (a color of the pair for each parity. For forcing chains, just two colors, one for the true option and one for the false. Could you explain how you use it, just for the sake of comparison?

Very similarly, I bet. For GEM I use four color pairs (the hue representing the marker type, and the shade representing the parity) + one color for identified eliminations and another for identified placements. Because the dark and light shades differentiate the two parities, I see it as a battle between the Dark Side and the Light Side (I root for the dark side of course) :)

I use a bluish hue for par candidates, greenish for super candidates, reddish for sub candidates, yellowish for super-group candidates, dark gray for eliminations, and cyan for placements. Of those the placement marker is quite optional and I rarely use it, but everything else I use heavily, including the super-group markers which are actually more useful than David's description lets on (on the other hand, I haven't found any use for the par-group markers, but I understand that they're in the spec for completeness). In fact, I use the super-group markers in a bit expanded way to mark not only single digit groups (as in David's specs) but multi-digit subsets as well (which I think is often more useful).

Below is an example using the puzzle from this thread. When I actually solved it, I didn't do nearly as complete a coloring, but I'm just demonstrating what it could have looked like for a particular seed:

gem1b.png
gem1b.png (109.8 KiB) Viewed 67 times

The four bluish 5s and the single 3 form the initial par cluster, and everything else stems from that. The dark gray candidates are found eliminations (they see par/super candidates of both parities; i.e. color trap), and it's pretty easy to see the corresponding chains because no branching has been done so far. Because of those eliminations there's also a known placement: 9r6c8, but I haven't marked it as such, because as a single move it would require a branching chain, and I defer those until all non-branching options have been covered. Besides, it wouldn't solve the puzzle so it's worthless when looking for a single-step solution (which was the goal here). There are also a couple of places where I could add super-markers (r79c8) or super-group markers (r12c9) and continue coloring, but I've put that off for the same branching reason. There's also a notable example of how super-group markers revealed a hidden pair for the light parity in r13c3 (an added benefit David's spec doesn't mention).



What does the coloring reveal, besides the direct elimination possibilities? Well, it seems that the dark parity has emptied box 8 of all 1s, which is a clear contradiction. So we know that the dark parity can't be true (damn!), and we could safely eliminate its par-candidates 5r3c7 and 3r9c7, which would solve the puzzle.

However, we still need to figure out how to express the move as an AIC, or a Kraken, or a Net, or using some mighty pattern. Contradictions can be handled in many ways, because we can push the contradiction point around. In this case we have a couple of obvious possibilities. One, we could play it directly as a Kraken Box using the 1s. Two, we could use either 1r6c4 or 1r8c7 to push the contradiction to empty the other cell and play it as a Kraken Cell (see Cenoman's solution using Kraken Cell (139)r6c4). Three, if we push the contradiction to cell r8c7, we could use the revealed naked pair (34)r48c7 or the hidden triple (179)r135 to yield a linear AIC, which is what I did in my solution.

Here's what it would look like if the branching-based supers (and the one placement) were used as well:

gem2c.png
gem2c.png (98.4 KiB) Viewed 59 times

Thanks again for your very useful replies. You are acting more and more like a mentor for me. A big responsibility for you...

You're welcome! And thanks for the compliment, I guess :) I'm glad if my thoughts have been helpful. However, don't take anything I say as the only truth. I'm still a relative newbie myself, and you'll probably see me change my mind on several issues while I learn more. Then again, I'd also say that don't take anyone's (even the most accomplished veterans') opinions as the only truth. Learn from many sources, experiment, think for yourself, and you might come up with better ideas! In fact, I already have a feeling that you're that kind of a person anyway.
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
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Re: need help with this puzzle, and technique in general

Postby SpAce » Wed Sep 26, 2018 3:42 pm

atrotta wrote:Could you please clarify better your dotting system? My first impression is that marking the impossibles in each cell could be messier than marking the possibles, but maybe I did not fully understand. Could you send me some examples with the different layers filled (of course if your system is not copywrited ;))?

Below you find an example with layers 0 and 1. It was a puzzle I should have solved easily without pm, but was lazy or blind or something. Nevertheless, dotting made it trivial, and there was no need for further layers. Too bad I don't have an image of the initial dotting stage, as I wasn't planning to use this as a demo, but hope it will do. It's pretty authentic as it has even a little mistake as good demos should.

.9.3.1..5..8..91......7..4.8..9..276....1....972..5..4.1..9......72..5..6..1.7.8.

ex1c.JPG
ex1c.JPG (57.27 KiB) Viewed 52 times

The key basic pattern I'd missed without pm was the hidden pair (89)r35c9. Usually I find those but this time I didn't until I added the dots. You can see the corresponding eliminations as the two little crosses (23) in r3c9. Like I said, I mark pattern-based eliminations like that to remember their cause. Anyway, that hidden pair solved the puzzle up to this point. The little circles with upright crosses are solved cells. In non-solved cells, dots and little crosses represent eliminations and empty spaces are still valid candidates. Thus, it's equivalent to this candidate grid:

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.-----------.-------------.------------.
| 7  9   46 | 3   468  1  | 68   2  5  |
| 5  46  8  | 46  2    9  | 1    3  7  |
| 1  2   3  | 5   7    68 | 689  4  89 |
:-----------+-------------+------------:
| 8  5   1  | 9   34   34 | 2    7  6  |
| 3  46  46 | 7   1    2  | 89   5  89 |
| 9  7   2  | 68  68   5  | 3    1  4  |
:-----------+-------------+------------:
| 2  1   5  | 48  9    48 | 7    6  3  |
| 4  8   7  | 2   36   36 | 5    9  1  |
| 6  3   9  | 1   5    7  | 4    8  2  |
'-----------'-------------'------------'

The UR Type 1 (89)r35c79 is trivial to see either way, don't you think? Other easy possibilities are BUG+2 or W-Wing, but the UR is the most obvious one (at least to me). In fact, if I'd originally seen the hidden pair in the no-pm stage as I should have, I would have seen the UR too and never needed dotting at all -- but then we wouldn't have this demo.
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: need help with this puzzle, and technique in general

Postby SpAce » Wed Sep 26, 2018 4:23 pm

Here's what a puzzle solved with my full system looks like afterwards:

ex3c.JPG
ex3c.JPG (57.83 KiB) Viewed 48 times

It might not be pretty, but it tells a more interesting story about the solving process than a typical solution grid (which tells exactly nothing). For example, it's possible to see that I'd missed the naked single 9r7c9 during the no-pm stage. That's unsurprising, because I don't usually spend time looking for those if I know that I'll be dotting anyway (which reveals them automatically).
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   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
SpAce
 
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