need help with this puzzle, and technique in general

Post the puzzle or solving technique that's causing you trouble and someone will help

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

Postby 200e200w » Sat Feb 03, 2018 10:10 am

Hi, SpAce!
Is there good (or any) documentation available for the techniques SE uses? Some of the names it uses aren't quite standard, so it would be helpful to know their correspondence with more familiar names.

I wrote a compendium of some solving techniques used by SE. They are Unique Loops, BUG type 2, 3 and 4, and all techniques from Bidirectional X-Cycle and up to the highest currently known level of Nested Forcing Chains, with their usual ratings. It is posted here as an attachment. You should be able to open it with any textual editor.

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SE Techniques.txt
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Re: need help with this puzzle, and technique in general

Postby SpAce » Sat Feb 03, 2018 10:04 pm

Thanks a lot, 200e200w! I appreciate it. That provides a much better picture of what's going on.
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Re: need help with this puzzle, and technique in general

Postby 200e200w » Sat Feb 03, 2018 10:11 pm

Note that there is a small typo in Aligned Triplet Exclusion description, should be:
Hidden Text: Show
Aligned Triplet Exclusion - like Aligned Pair Exclusion (which is not listed there because it is used in Andrew's solver), but eliminates candidates from three cells, instead of two. Rated 7.5.


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

Postby SpAce » Sat Feb 03, 2018 11:04 pm

200e200w wrote:Note that there is a small typo in Aligned Triplet Exclusion description, should be:
Hidden Text: Show
Aligned Triplet Exclusion - like Aligned Pair Exclusion (which is not listed there because it is used in Andrew's solver), but eliminates candidates from three cells, instead of two. Rated 7.5.

About that... I've been wondering if any human players actually use either? APE is one of the techniques I always switch off if I run the SudokuWiki solver, because I'd never look for (nor probably spot) those things myself. It seems pretty T&E and quite tedious at that to me, except maybe in some very obvious situations. Perhaps there are some heuristics that help to spot them easily as patterns but I haven't noticed (nor really tried either).
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Re: need help with this puzzle, and technique in general

Postby StrmCkr » Sun Feb 04, 2018 1:58 am

most of the ape,apt, death blossom, and sue de coq types are easier to spot and use when they are considered as subset exclusion rules
doubly linked als-xz rules, als-xy rules, als-chain rules

for the most part ape, apt, are used on that website and not much on the forums and are basically obsolete as a more powerful technique was developed off them with less 'counting" so to speak {almost locked set types}

for a point of interest these also all fall under disjointed Distributed subset technique which also covers all the above stuff as well, but harder to use.
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Re: need help with this puzzle, and technique in general

Postby SpAce » Sun Feb 04, 2018 3:14 am

StrmCkr, thanks for confirming my suspicions!
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Re: need help with this puzzle, and technique in general

Postby SpAce » Sun Feb 04, 2018 7:18 am

As an exercise relating to recent discussions in another thread, I tried to turn 200e200w's krakens into AIC-like nets. No, I'm not suggesting they're an improvement in any way :) Let's see...

200e200w wrote:Kraken Finned X-Wing.
Finned X-Wing: 8 r78/c18 fr7c5,r8c2
(8)r7c1 - (8=56)r34c1 - (5=136)r124c5 - 3r2c4
(8-3)r7c5 = r7c4 - r2c4
(8)r8c1 - (8=56)r34c1 - (5=136)r124c5 - 3r2c4
(8)r8c2 - (8=56)r58c8 - 5r5c2 = r4c12 - (5=136)r124c5 - 3r2c4
=> -3 r2c4[/code]

My version:

Code: Select all
.------------------------.----------------------.---------------------.
|   3       5689   1689  |  2     g16     4     | 15689  7      5689  |
|   4569    7      1469  | x6-3   g1(3)6  8     | 1569   2      569   |
|  D68      2      168   |  7      9      5     | 168    4      3     |
:------------------------+----------------------+---------------------:
|F'D568   F'3568   368   |  4     g56     1     | 2      9      7     |
|   2     E'569    69    |  8      7      3     | 4    D'56     1     |
|   1       4      7     |  569    2      69    | 568    3      568   |
:------------------------+----------------------+---------------------:
|  C679*8   1      2     |a(3)569 b356#8  679   | 569    56*8   4     |
|  C679*8 C'69#8   5     |  1      4      679   | 3    D'6*8    2     |
|   4689    3689   34689 |  569    568    2     | 7      1      569   |
'------------------------'----------------------'---------------------'

(3)r7c4 = (3-8)r7c5 = [Finned X-Wing 8 r78/c18 fr8c2]: [(8) r78c1|r8c2] - [r34c1,r58c8] = [(6,5)r34c1 | [(5,6)r58c8-(5)r5c2=r4c12]] - (5=6,1,3)r412c5

=> (3r7c4 | 3r2c5) => -3 r2c4

Yes, I also think it's ugly as hell :D The other one:

Code: Select all
Kraken Finned Franken X-Wing.
Finned Franken X-Wing: 9 r69/c4b7 fr6c6,r9c9
(9-6)r6c6 = r6c79 - (6=5)r5c8 - r5c2
(9-4)r9c1 = (4-5)r2c1 = r4c1 - r5c2
(9)r9c2 - r789c1 = (9-5)r2c1 = r4c1 - r5c2
(9)r9c3 - r5c3 = (9-5)r5c2
(9)r9c9 - (9=5)r2c9 - r2c1 = r4c1 - r5c2
=> -5 r5c2

My version (I used the same chain for the c2 and c3 branches to keep things a bit simpler):

Code: Select all
.---------------------------.---------------------.---------------------.
|    3       5689    689    | 2      1      4     | 5689   7      5689  |
|   f459     7       149    | 6      3      8     | 159    2   E''59    |
|    68      2       168    | 7      9      5     | 168    4      3     |
:---------------------------+---------------------+---------------------:
|  g(5)68    3568    368    | 4      56     1     | 2      9      7     |
|    2      x6-5     69     | 8      7      3     | 4    a(5)6    1     |
|    1       4       7      | 5*9    2     c6#9   |b568    3     b568   |
:---------------------------+---------------------+---------------------:
|  E'6789    1       2      | 3      568    679   | 569    568    4     |
|  E'6789    689     5      | 1      4      679   | 3      68     2     |
|E'ED468*9 D'368*9 D'3468*9 | 5*9    568    2     | 7      1   D''56#9  |
'---------------------------'---------------------'---------------------'

(5=6)r5c8 - r6c79 = (6-9)r6c6 = [Finned Franken X-Wing 9 r69/c4b7 fr9c9]: [(9) r9c1|r9c23|r9c9] - [(4)r9c1,(9)r789c1,r2c9] = [(4|9)r2c1 | (5)r2c9] - (5)r2c1 = (5) r4c1

=> -5 r5c2

Yes, it's ugly too, but is that actually a valid AIC (split-nodes only)? Then again, I think it's much simpler if we forget the fishy stuff and just use the row:

(5=6)r5c8 - r6c79 = (6-9)r6c6 = r6c4 - r9c4 = [r9c1|r9c23|r9c9] - [(4)r9c1,(9)r789c1,r2c9] = [(4|9)r2c1 | (5)r2c9] - (5)r2c1 = (5)r4c1

That's not so bad, is it?
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        *        |=()=|    /  _  \    |=()=|               *
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Re: need help with this puzzle, and technique in general

Postby atrotta » Sun Aug 19, 2018 6:30 am

SpAce wrote:My current manual solving skill and tool sets support finding chains pretty well


HI Space, can you give some hint on how you are able to spot AICs so easily? I'm astonished that you do that in paper also.
Please advice
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Re: need help with this puzzle, and technique in general

Postby SpAce » Mon Aug 20, 2018 7:23 am

atrotta wrote:HI Space, can you give some hint on how you are able to spot AICs so easily? I'm astonished that you do that in paper also. Please advice

Well, about a year and half ago I would have been astonished too! :D That's when I started studying non-basic techniques (of which X-Wing was the only thing I'd ever used before). When I first looked at some of the more complicated chains found by the SudokuWiki solver (the only solver I knew at the time) back then, I was pretty certain it wasn't humanly possible to find them manually, at least for me. I was obviously wrong, and it didn't even take very long to start spotting them, which surprised myself too. It has taken quite a bit of studying, practicing, and developing spotting aids, though, and it's a work in progress. I can share the process which I've gone through and has helped me, but I can't know what works for others.

First, I might recommend learning coloring if you haven't already. That's how I started, and it helped me find chaining eliminations before I even understood how chains really worked. In a quick succession I studied Simple Coloring, 3D-Medusa, Multi-Coloring, Weak Colors, and X-Colors (none of which I actually used) until I found David Bird's GEM which was exactly what I was looking for. It's the most powerful humanly applicable coloring technique I know. It's especially powerful for a pencil-and-paper solver, even though David doesn't present it as such. In fact, I think his spreadsheet-based way of presenting it has probably been an epic marketing blunder, because it makes it seem more complicated than it is. I'm probably one of the very few people who actually uses GEM besides David himself, and it's because I'd had similar (but not as fully developed) ideas which made me see its value immediately despite the not-so-attractive interface. Once I created a human-friendly way to apply it on paper, it's been an invaluable tool. At first it worked as training wheels for chaining stuff, but I still use it as a backup in tough spots or when I want to find effective eliminations faster. It's also possible to use with a software solver that has candidate coloring, like Hodoku, but it's a bit painful as it requires so many color mappings.

There's one caveat about using coloring methods, and especially GEM. They're easy to use without thinking (and I admit to having used GEM without thinking early on, because it allowed me to solve puzzles I couldn't have dreamed of solving otherwise at that time). However, to actually learn something, you should always build a chain (or a net) for each elimination you find. You can do that mentally, but even better, I highly recommend learning the Eureka notation and writing down all the chains you find (if you don't already). I'm pretty sure that actually helps understanding chains better and thus spotting them also. When I started using GEM, I couldn't explain many of the eliminations it found, so it seemed a bit like magic. Some of those eliminations were actually based on nets, which is another thing to be aware of as GEM makes using them easy as well (a matter of personal preference if such eliminations are accepted or not -- I think nets are fine and fun as long as the player understands and can explain them).

Another problem with coloring methods is that they work a bit backwards by finding eliminations first, after which the player should construct chains (or nets) to prove them. What about finding chains and their eliminations directly? That's a bit tougher but also more rewarding. It's especially tough with a standard pencil mark grid without any visual clues about the strong links. For that reason I've created my own candidate mark-up system which shows all bilocation strong-links, including group links. I recommend something like that to any serious p&p solver. It makes visualizing AICs a lot easier, and it also helps applying GEM if need be. Early on I experimented a bit with external B/B plots, but quickly figured they just produced useless spaghetti. With harder puzzles I might draw a couple of helper plots, though: one for single digits (easier to see X-Chains and fishes) and sometimes one for bivalue cells (mostly useless). If none of those help enough (or fast enough), then I resort to using GEM. If that doesn't help either, then it's probably an SE 9+ puzzle for which my tools aren't sharp enough.

One last generic piece of advice is to deepen your understanding of chains by simply looking at them and studying them a lot, which makes it easier to see them as well. For example, I've learned a lot from the solutions in the Puzzles section of this forum. Studying chains found by software solvers, such as Hodoku, helps too. It might be a good exercise to try to see (and write!) some variants of those chains yourself. Eventually, especially with good visual aids for the strong links, it's possible to start seeing at least simpler chains or chain fragments as patterns on the grid. It's also important to recognize the different AIC types and their differing elimination possibilities to know what to look for. There are four main types, as far as I know:

AIC Type 1: End nodes have the same digit and don't see each other: eliminate any candidate of that digit weakly linked to both ends.
AIC Type 2: End nodes have different digits and see each other (but aren't in the same cell): each end eliminates its own digit from the opposite end node.
AIC-Loop: End nodes are weakly linked to each other. Every weak link eliminates in its scope.
AIC-Loop with ALS nodes: In addition to the previous, ALS bystanders get locked and also eliminate in their scopes.

I don't know if this helped at all as it's all pretty generic, but I'm happy to answer any specific questions. Like I said, it's a work in progress for me too, and communicating helps to organize one's thoughts and sometimes figure out new ideas. 

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

Postby atrotta » Mon Aug 20, 2018 7:57 am

Wow!!! There is a lot of hard (but fun) work waiting for me.
Thank you very much for such an extensive reply and for sharing your knowledge with me.
I am very confident I'll make another step forward (and maybe 2 or 3) in the magic world of sudoku.
I am sure I will profit of your availability for future needs... ;)
Bye
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Re: need help with this puzzle, and technique in general

Postby atrotta » Sun Aug 26, 2018 2:46 pm

Another quick questions: can GEM be used also to draw conclusions derived by forcing chains?
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Re: need help with this puzzle, and technique in general

Postby SpAce » Sun Aug 26, 2018 5:08 pm

atrotta wrote:Another quick questions: can GEM be used also to draw conclusions derived by forcing chains?

An excellent question! If by "forcing chain" you mean what we call "krakens" here, the answer is: not directly. GEM only supports binary starting points, and the strong inference sets in krakens (usually) have three or more members which means as many chains (and thus would require that many coloring groups). I haven't figured out a way to build a manually working GEM extension for that, but I guess it could be done with software.

However, GEM can find the same eliminations indirectly if one or the other starting parity produces a contradiction (equivalent to Nishio). If, for example, one parity empties a 3+ member cell, you know that parity is wrong (and all of its par-candidates can be eliminated). Hodoku would call that a "forcing chain contradiction" (or a "forcing net contradiction" if the original branches also branch). If you want to express that as a kraken (which Hodoku calls "forcing chain/net verity"), it takes a bit more effort as you need to reverse-engineer it by using the contradiction cell and all of its candidates as the starting hub and finding chains that eliminate the original par-candidate (or any of them) that produced the contradiction. The same is true if the contradiction removes all instances of a digit from a house (then the starting hub of the kraken is all of those digit instances).

Here's what I wrote about these some time ago, though not from the point of view of GEM:
http://forum.enjoysudoku.com/forcing-chains-nishios-krakens-aics-dnls-t34574.html
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: need help with this puzzle, and technique in general

Postby atrotta » Wed Aug 29, 2018 6:03 pm

Actually, by forcing chain I mean the techniques indicated in sudokuwiki

http://www.sudokuwiki.org/Strategy_Families

under Forcing Chains subgroup.

I gave a look to the post you reference in your last reply but I still must learn about kraken fishes (... and I also found out for the very first time about the existence of "nested" AICs!!! :shock: )

As with AICs, my big problem is how to spot the starting point for forcing chains. I guess it is not a trial and error with any possible verity or contradiction, therefore I wondered if GEM can help me like it did with AICs (and I have to admit it was really enlightening!!!; now I am probably the third one using GEM apart from you and David ;) ), or if there is any other tip or trick that can help me.
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Re: need help with this puzzle, and technique in general

Postby SpAce » Wed Aug 29, 2018 8:02 pm

atrotta wrote:Actually, by forcing chain I mean the techniques indicated in sudokuwiki ... under Forcing Chains subgroup.

Most of them are what we call Krakens here. In sudoku, there are often many names for the same things. SudokuWiki lists four kinds of forcing chains: Nishio Forcing Chains (not kraken), Digit Forcing Chains (kraken), Cell Forcing Chains (kraken), and Unit Forcing Chains (kraken). The first two of them are actually useless, and in general, SudokuWiki isn't the best source for understanding chaining (at least as an only source). As I wrote in that linked piece:

SpAce wrote:Let's look at some SudokuWiki examples. Its Triple/Quad Cell Forcing Chains and Unit Forcing Chains are what we call Krakens, and they're also the only relevant forcing chains on that site. Its Nishios, Digit Forcing Chains, and Dual Cell/Unit Forcing Chains are unnecessary, except conceptually, as they can all be turned into simple AICs. (It's a good exercise for beginners, by the way, to go over those examples and do just that.)

In other words, the SudokuWiki Nishios and Digit Forcing Chains are completely useless, as they can (and should) always be replaced with basic AICs (which SudokuWiki doesn't really have, except as XY-Chains and ALS XZ moves, even though it inaccurately calls its nice loops AICs). That leaves the Cell/Unit Forcing Chains the only relevant types, and even they are only useful if the starting hub has at least three members (otherwise they also can be replaced with simple AICs). They are also what we call Krakens, and what Hodoku calls Forcing Chain Verities.

I gave a look to the post you reference in your last reply but I still must learn about kraken fishes

I see you have the same confusion I had when I first heard "kraken" being used as a synonym for any (verity type) forcing chains. Previously I'd also seen that term related to fishes only. I guess the term originated with finned fishes whose fins were used as starting points for forcing chains, but since then it's been used (at least on this forum) for any kind of verity producing forcing chains. In addition to fish fins (+the fish itself), the starting hub can be any strong-inference-set (SIS), such as all instances of a digit in a house ("Unit Forcing Chains") or all candidates in a cell ("Cell Forcing Chain") or all extra candidates of a deadly pattern (Oddagons, BUGs, URs, etc) -- what's common to all of them is that (at least) one starting point must be true, so if you can prove the same elimination (or placement) with all of them, it must be true. All of those different kinds are called Krakens here, even though most of them have nothing to do with fishes. I'm first to admit that it's a bit confusing.

(... and I also found out for the very first time about the existence of "nested" AICs!!! :shock: )

Don't worry about that too much. I just wanted to show a way to write krakens as AICs, but I don't recommend it. It's usually much more readable to present them as krakens, starting with the SIS hub.

As with AICs, my big problem is how to spot the starting point for forcing chains. I guess it is not a trial and error with any possible verity or contradiction, therefore I wondered if GEM can help me like it did with AICs

It can, but like I said, not directly (except for dual forcing chains, but they're better expressed as AICs anyway). For example, if one parity of your GEM coloring empties a cell of all candidates or a house of one type of digit, you have a contradiction and know that that parity is false. How to express it as a solution step?

You have two options. One is to build a Nishio forcing chain/net starting with one of the false par-candidates which produces the the contradiction and proves the starting candidate false. That's usually considered ugly. The other option is to start with the emptied cell and work backwards by building a Cell Forcing Chain (i.e. a Kraken Cell) that eliminates a par candidate. Similarly, if one parity empties a house (row, col, box) of all candidates of a certain digit, you can build a Unit Forcing Chain (another kind of kraken; Kraken Row/Col/Box) with those candidates. GEM only finds forcing chain contradictions (aka Nishios) directly, and you must reverse-engineer them into Krakens (forum term) aka Forcing Chain Verities (Hodoku term) aka Cell/Unit Forcing Chains (SudokuWiki term) if you want to express them as such (which is generally preferred to showing contradictions directly).

Note: it's generally a good idea to first and foremost try to find a simple AIC solution (also for those contradictions) instead of a forcing chain (much less a forcing net). Real forcing chains are only required for pretty difficult puzzles (SE 8+) and forcing nets are even more of a last resort thing (SE 9+), but of course you're free to use whatever methods you find and like with any puzzle. (My SE minimums are just estimates anyway.)

(and I have to admit it was really enlightening!!!; now I am probably the third one using GEM apart from you and David ;) ), or if there is any other tip or trick that can help me.

Cool! If you have any specific GEM -related questions, feel free to ask. I'll be happy to answer if David won't. Lately I've been using it more and more with the Hodoku coloring system, and it actually works pretty well, even though I'm still more comfortable with pencil and paper.
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        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   
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Re: need help with this puzzle, and technique in general

Postby StrmCkr » Wed Aug 29, 2018 11:33 pm

Above 9.5 it's using dynamic subnets and forcing subnets.

It's missing all almost locked sets, and a host of other techniques developed well past when se was released... So it rates alot of puzzles more difficult then they should be.

But it is all we have for rating atm.
Some do, some teach, the rest look it up.
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