## Line check for SudoCue Nightmare (Sun Dec 9, 2007)

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

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

Skyscrapers are sashimi X- wings, as its a combination of two minimal value sashimi Xwing.

It was named skyscraper as it looks like two tall buildings on a surface, and unified both sashimi x wings together for one elimination step instead of two.

You did hit the nail on the head for how x wings are named after the star wars craft

For the most part the "wing" was also kept for similar logic patterns that expanded extra body parts

Ie xy wing - > stuvwxyz wing

When the chain becomes continuous it swaps to ring instead of wing

Other stuff called wings as I listed befor in another post are from pincher attacks from end points

Harder to see but all are found and designed off the simpler logic from X- wings and xy wings

As far as I am aware there really is only three types of master systems and all others are subsets of these primaries and these and can be alternativly presented in equivalenlty in each other.

Disjointed distribution subsets: (subsets, subset counting, als, ahs. Alc... )
Graphical computing - - Alternating inference chains (nice loops) : all chain types
Cover sets (fish, rank logic, muti fish,)

The names are established as refrence points, as learned a name is easier to remeber how the thing functions
also logically the primary from which they derive came much much later and cover a very larger based to the point most people lose how they work.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

StrmCkr wrote:Skyscrapers are sashimi X- wings, as its a combination of two minimal value sashimi Xwing.

Yes, but I think it's a pretty complicated way of seeing it. Skyscraper is just a short X-Chain, and I'm pretty sure it's the simplest and most versatile perspective to see its elimination logic. Nothing wrong with seeing it from other perspectives too, of course. In fact, I think it's useful for deeper learning to understand the equivalences between different pattern names and families, e.g. Double Sashimi X-Wing == Skyscraper = Turbot Fish = X-Chain (length 4) = AIC (Hodoku Type 1). Similarly: Finned X-Wing == Grouped Skyscraper = Grouped X-Chain (length 4) = Grouped AIC (Hodoku Type 1). These kinds of discussions help me connect such dots, so thanks for that (not just you but Leren and others as well)!

It was named skyscraper as it looks like two tall buildings on a surface,

I see it as one building with a diagonal roof

and unified both sashimi x wings together for one elimination step instead of two.

It's just one step if you see it as a generic X-Chain, too. I never studied Skyscrapers, 2-String Kites, or other Turbot Fishes very hard because I'd rather be able to find any X-Chain/Cycle, including them, with a generic process. X-Chains are the simplest kind of chaining anyway, and pretty easy to find regardless of their shapes and lengths, so I don't quite get why so many pattern names are dedicated to their special cases. The most value I see in memorizing those patterns is for communicating on forums, and for simplifying the use of their almost-forms as nodes in non-trivial chains. Other than that, thinking in terms of generic X-Chains is much more versatile and just as easy, I think.

For the same reason I find it unnecessary to learn to spot finned and sashimi X-Wings as such (and normal X-Wings too, actually, except they're so easy to spot and probably the first advanced pattern anyone learns). They're all just short X-Chains. However, I still think it's useful to learn to see also the fish perspective of finned and sashimi (and normal) X-Wings, because it helps understanding the same concepts in bigger fishes that can't be seen as chains.

Pattern recognition can be useful, but concentrating on that too much seems like a waste of memory capacity to me, and it may even slow down learning of more generic concepts. For example, I recently talked to someone who was obviously good at spotting kites and scrapers but seemed to have trouble spotting longer and more complicated chains. I suspect it's the result of being too pattern-oriented and not seeing the big picture of chaining that well. I look for chains instead of patterns, so it doesn't really matter to me how long or what kind they turn out to be, or what their names are, as long as they get something useful done. AICs have the same connecting and elimination logic no matter what kind and how many nodes are between the two ends, so there's no real need to memorize all the different shapes and styles they can have -- just the few rules of building and applying them, which are quite logical (and thus easy to remember).

(Of course recognizing certain patterns may help to spot potential chains faster, but I think it's really helpful only after you understand chains generally. For example, this thread made me appreciate W-Wings more, thanks to Leren, because they're so easy to look for and apparently quite common.)

You did hit the nail on the head for how x wings are named after the star wars craft

Cool! Am I also right if I suspect the Y-Wing came after that and for the same reason (and was only later called XY-Wing)? That would explain why they're both called wings even though they're pretty different. (Why don't we have A-Wings and B-Wings to complete the Star Wars set, or do we?)

For the most part the "wing" was also kept for similar logic patterns that expanded extra body parts

That's where things took a wrong turn, as far as I'm concerned. I don't think the other wings (any I know at least) are logically similar to X-Wings at all. Even though X-Wing was (probably) the first "wing", it's now the weirdo in that group. You state the reason next:

When the chain becomes continuous it swaps to ring instead of wing

That's exactly why I don't think X-Wing is a wing. X-Ring would be more logical. That brings up yet another question: why do we have at least three different terms for the same shape: loop, cycle and ring? It's just another unnecessary complication unless they have distinct definitions. I don't know any difference between the first two (cycle==loop, right?), but is a ring always continuous (unlike loops/cycles that have several discontinuous variants)? If so, why don't we call all continuous loops/cycles rings?

Other stuff called wings as I listed befor in another post are from pincher attacks from end points

Yes, thanks for reminding me about that. I bookmarked your post back then, because a lot of it went over my head and I wanted to get back to it later. I might understand a bit more now. I'll take another look at those wing patterns, thanks.

As far as I am aware there really is only three types of master systems and all others are subsets of these primaries and these and can be alternativly presented in equivalenlty in each other.

This is exactly what I'm interested in. I like to learn the most generic forms and how things are related to each other both horizontally and vertically.

The names are established as refrence points, as learned a name is easier to remeber how the thing functions

Sure, if only the names were logical and consistent. When they're not, it complicates learning -- though it may also lead to deeper learning for those who bother to sort out the mess for themselves. Problem is, not everyone bothers and that can result in persistent misunderstandings.

also logically the primary from which they derive came much much later and cover a very larger based to the point most people lose how they work.

I understand. That's probably why the naming is a bit of a mess.
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### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

just one step if you see it as a generic X-Chain,
sure it can be, the chain would also include the starting and end points as the elimination cells {meaning it has a higher length} {at least that's my understanding of most of the code Ive seen for it}

bigger fishes that can't be seen as chains.

bigger fish can be seen and written as chains: several users are very good at converting and posting large fish logic into chain notation

so I don't quite get why so many pattern names are dedicated to their special cases.

most of the smaller stuff came long before some one connected the dots and created a single system that covers them all, and some times it was discovered that the shorter version eliminated the need to do most of the more complicated work of a bigger system that already existed.

ie:Turbots( x-cycles), single coloring, {these predate the stuff named and found by Harvard {empty rectangle, skyscraper, 2-string kite},

might be easier as a generalized forum, however these "simplest chaining system" covered every case from 1x1 fish up to 7x7+2 size fish and the incremental size expansion and involved a higher run time in code and a more complicated elimination rules, and often was depreciated as the complex systems work and out put was often simplified by the easier move set which depreciated x-cycles and single colours usage to the point of impractical coding.

being able to write smaller search codes implemented by hierarchy ordered based on a difficulty in learning / application speeds up solution solving time and mimics human solving approaches to a degree.

box-line reduction, x-wing,skyscrapers, finned/sashimi x-wings, 2-string kite, Empty Rectangle, -> 3x3 ->> 7x7+2 fish

(ps nxn+K Fish, nxn-fish to me is easier to code then a x-cycles and single colouring check out nxn+k fish )

I don't know any difference between the first two (cycle==loop, right?), but is a ring always continuous (unlike loops/cycles that have several discontinuous variants)? If so, why don't we call all continuous loops/cycles rings?

a cycle is a chain of N-length on a single digit usually labeled as "x" and not necessarily does the start and end point have to be peers

Nice Loop {named technique} - is a chain of N-length with n candidates where if the end points are peers of the starting point and can reduce the starting to a single via a shared candidate then it is a continuous nice loop other wise its discontinuous
{both types have different elimination rules}

Ring affirmation was suggested for specific wing cases which are found in {w-wing,m-wing, and a 4 cell xy-wing)
actually being used? i've never seen a reference asides from the exemplar cases listed.

is an x wing a ring ?
no, the end points do not see each other directly

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`on ---- off||off ---  On via consequence of first spot being true. `

2 views , to cover each corner and each has 1 pivot cell and 2 pincers. ( you have to Cross over ie "x" to get the other view: which is how i see it falling into the "wing" family and named)

I understand. That's probably why the naming is a bit of a mess.

naming a bit of a mess from the number of different stuff found by different people at different points of time, coupled with the fact many of them can have specific niche cases that overlap each other which is where the confusion lies:

coupled from the fact each primary can be converted directly into the other types: meaning everything has more then 1 point of view.
Last edited by StrmCkr on Sun Dec 17, 2017 12:05 am, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

StrmCkr wrote:
SpAce wrote:[Skyscraper is] just one step if you see it as a generic X-Chain,
sure it can be, the chain would also include the starting and end points as the elimination cells {meaning it has a higher length}

Why higher length? If I understand that correctly (possibly not), it means that it's seen as multiple discontinuous nice loops (length 5), which is inefficient. Why not see it as a simple chain (length 4) that starts and ends with a strong link on the same digit. Then all instances of that digit that share a house with both ends can be eliminated in a single step. That's how any chain (whose ends have a strong link on the same digit, i.e. Hodoku AIC Type 1) works, right? It's the classic pincer attack we've been talking about, so it could be classified as a wing too (as far as I understand). In fact, why don't we call all such chains wings? That'd be simple and logical.

{at least that's my understanding of most of the code Ive seen for it}

I'm only talking about manual (pencil and paper) human solving, as that's what I do (for now), but I assume the same principle would easily apply to coding as well. If you have a chain capable of multiple eliminations, it's inefficient to create a separate discontinuous loop for each elimination. For example, the SudokuWiki solver is pretty dumb in that regard -- in that only continuous loops and XY-Chains can provide multiple eliminations in a single step, but all other multiple-elimination-capable AICs (including X-Chains such as Skyscrapers) are seen as multiple discontinuous loops and multiple steps (except for some named patterns). Hodoku has no such deficiency, as far as I know, and it understands the general principle better: "Any AIC can be seen as a combination of one or more Discontinuous Nice Loops (HoDoKu will show an AIC only, if it provides more than one elimination; AICs with only one elimination are always shown as Discontinuous Nice Loops)."

bigger fish can be seen and written as chains: several users are very good at converting and posting large fish logic into chain notation

Can you link to any examples? I'd really like to see how it's done. For example, a swordfish with vertices spread into 9 boxes doesn't have any native strong links to work with. How do you convert that into a linear AIC (which I meant)? I can imagine it can be done with more complicated chains but not simple AICs.

(ps nxn+K Fish, nxn-fish to me is easier to code then a x-cycles and single colouring check out nxn+k fish )

Like I said, I'm only talking about manual solving here. While coding is interesting as well, what works there is hardly relevant to human solving.

SpAce wrote:I don't know any difference between the first two (cycle==loop, right?), but is a ring always continuous (unlike loops/cycles that have several discontinuous variants)? If so, why don't we call all continuous loops/cycles rings?

a cycle is a chain of N-length on a single digit usually labeled as "x" and not necessarily does the start and end point have to be peers

I know that. My point was that since there's apparently no other difference between cycles and loops, the term X-Cycle is redundant and confusing as we could just as easily talk about X-Loops (or just Cycles) without losing information. The X already tells us we're talking about single digit loops. The Cycle part is just confusing because it implies that it's somehow different from other loops which it isn't.

Nice Loop {named technique} - is a chain of N-length with n candidates where if the end points are peers of the starting point it is a continuous nice loop other wise its discontinuous {both types have different elimination rules}

Both? There are actually three different kinds of discontinuous nice loops. 1) Both ends have a strong link to the same digit and don't see each other (but the elimination cell sees both, i.e. the typical pincer attack or wing -- but seen as a discontinuous nice loop it can only attack one candidate at a time unlike an AIC or a wing), 2) Both ends have a strong link to the same digit and are in the same cell (eliminates all other candidates there; can be seen as a special case of the first, or just an AIC whose ends happen to be the same candidate), 3) Each end has a strong link to a different digit and they see each other (each can be eliminated from the opposite end -- but it requires two discontinuous nice loops (or just one AIC)). For some reason, case 3 is often forgotten even though it's probably the most common one.

All three of those can be seen as special cases of more generic AICs that can do multiple eliminations in a single step. That's why I no longer see much value in thinking in terms of discontinuous nice loops (which is a horrendously long name anyway, especially if you add the type distinction). As far as I'm concerned, only continuous nice loops should be called Nice Loops (and without the redundant "continuous"). Anything else is just one or the other kind of an AIC - either one with the same digit at both ends, or the other with different digits. That categorization is more efficient (shorter chains, possibly more eliminations) and easier to learn because of fewer rules: just (always continuous) Nice Loops and two kinds of AICs -- very simple.

To be continued...
Last edited by SpAce on Sat Dec 16, 2017 8:44 pm, edited 3 times in total.
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"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

StrmCkr wrote:Ring affirmation was suggested for specific wing cases which are found in {w-wing,m-wing, and a 4 cell xy-wing)
actually being used? i've never seen a reference asides from the exemplar cases listed.

Can you show and walk-through any examples that a human can understand? I still don't get what's the difference between a ring and a continuous loop.

SpAce wrote:
is an x wing a ring ?
no, the end points do not see each other directly

What do you consider the end points? If you see the X-Wing as a continuous X-Cycle, then it has two sets of strongly linked end points that do see each other directly:
Code: Select all
`A ==== B|      ||      |C ==== D`

That's a continuous X-Cycle: A=B-D=C-loop
It can be broken into two X-Chains:
1) A=B-D=C
2) B=A-C=D

In the first case the ends are A and C which see each other. In the second case the ends are B and D which also see each other. Both provide a separate pincer attack on their columns. So, two wings, not one. I don't know why I would see A and D or B and C (which don't see each other) as the end points of anything.

Code: Select all
`on ---- off||off ---  On via consequence of first spot being true. `

2 views , to cover each corner and each has 1 pivot cell and 2 pincers. ( you have to Cross over ie "x" to get the other view: which is how i see it falling into the "wing" family and named)

So, like I said before, I see here a double-wing (if it really must be included in the wing family). I don't think it can be seen as a normal wing without making the whole wing idea unnecessarily complicated. Wouldn't it be much simpler to see it either as a continuous X-Cycle or a 2-fish and leave the wing terminology out of it? Both ways will give us all of its eliminations in a single step. The other way is to see it as two X-Chains with two sets of pincers (i.e. a double-wing again), but that's two steps. I simply can't see it as a single wing. I think it's an extremely confusing abomination to try to force it into one, and this attempt looks more like POM to me than anything else. Otherwise we need a larger definition of a wing, but I don't think that would be helpful in practice. I'd personally prefer a simple definition that would cover all normal pincer attacks (Hodoku AIC Type 1) regardless of the chain length or node types, but that's it.
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"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 1572
Joined: 22 May 2017

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

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`.---------------------------------.---------------------------------.---------------------------------.| 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 |'---------------------------------'---------------------------------'---------------------------------'`

okay, ill make my point clearly:

That's a continuous X-Cycle: A=B-D=C-loop
It can be broken into two X-Chains:
1) A=B-D=C
2) B=A-C=D

A does not see C as a peer! [if it did and they shared a common candidate that reduce the other to a single then it is continuous]
B does not see D as a peer! [ if it did and they shared a common candidate that reduce the other to a single then it is continuous ]
they are Discontinuous

chains start with the Elimination cell and the chain construct proves it is invalid, meaning it has more cells and higher run time an x-wing
4 cells arent checked in an x-cycle and it is not a Continuous loop as the starting cell dose not see the last cell. it wont matter what corner you pick the last cell is always poler opposite of the starting cell.

load the example above into hudoku digit 2 forms an x-wing on cols

X-cycles as a turbot requires 2 moves to prove all the x-wing eliminations, these chains are bi directional as the end points{elimination cells} are also used in the chain!!

Turbot Fish: 2 r2c2 =2= r8c2 -2- r8c8 =2= r2c8 => r2c1345679<>2
Turbot Fish: 2 r8c8 =2= r2c8 -2- r2c2 =2= r8c2 => r8c1345679<>2

seen as an x-cycle requires 2 moves to prove all the x-wing eliminations, these chains are bi directional as the end points{elimination cells} are also used in the chain!!
X-Chain: 2 r2c2 =2= r8c2 -2- r8c8 =2= r2c8 => r2c1345679<>2
X-Chain: 2 r8c2 =2= r2c2 -2- r2c8 =2= r8c8 => r8c1345679<>2
it can also be an AIC requires 2 moves to prove all the x-wing eliminations, these chains are bi directional as the end points{elimination cells} are also used in the chain!!
AIC: 2 2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2 => r2c1345679<>2
AIC: 2 2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2 => r8c1345679<>2
Discontinuous Nice Loop is even worse as these can only remove 1 of the elimination cells at a time.

Discontinuous Nice Loop: 2 r2c1 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c1 => r2c1<>2
Discontinuous Nice Loop: 2 r2c3 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c3 => r2c3<>2
Discontinuous Nice Loop: 2 r2c4 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c4 => r2c4<>2
Discontinuous Nice Loop: 2 r2c5 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c5 => r2c5<>2
Discontinuous Nice Loop: 2 r2c6 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c6 => r2c6<>2
Discontinuous Nice Loop: 2 r2c7 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c7 => r2c7<>2
Discontinuous Nice Loop: 2 r2c9 -2- r2c2 =2= r8c2 -2- r8c8 =2= r2c8 -2- r2c9 => r2c9<>2
Discontinuous Nice Loop: 2 r8c1 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c1 => r8c1<>2
Discontinuous Nice Loop: 2 r8c3 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c3 => r8c3<>2
Discontinuous Nice Loop: 2 r8c4 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c4 => r8c4<>2
Discontinuous Nice Loop: 2 r8c5 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c5 => r8c5<>2
Discontinuous Nice Loop: 2 r8c6 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c6 => r8c6<>2
Discontinuous Nice Loop: 2 r8c7 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c7 => r8c7<>2
Discontinuous Nice Loop: 2 r8c9 -2- r8c2 =2= r2c2 -2- r2c8 =2= r8c8 -2- r8c9 => r8c9<>2

the only move set capable of removing all 14 elimination at once is the "x-wing" from the cover set algorithm used by the fish-finder or the pattern known as "x-wing"
X-Wing: 2 c28 r28 => r2c1345679,r8c1345679<>2

]I'm only talking about manual (pencil and paper) human solving, as that's what I do (for now), but I assume the same principle would easily apply to coding as well. If you have a chain capable of multiple eliminations, it's inefficient to create a separate discontinuous loop for each elimination. For example, the SudokuWiki solver is pretty dumb in that regard -- in that only continuous loops and XY-Chains can provide multiple eliminations in a single step, but all other multiple-elimination-capable AICs (including X-Chains such as Skyscrapers) are seen as multiple discontinuous loops and multiple steps (except for some named patterns). Hodoku has no such deficiency, as far as I know, and it understands the general principle better: "Any AIC can be seen as a combination of one or more Discontinuous Nice Loops (HoDoKu will show an AIC only, if it provides more than one elimination; AICs with only one elimination are always shown as Discontinuous Nice Loops)."

unfortunately it doesn't work that way, each technique set has a limitation on what it can eliminate and how it finds each: meaning it has multiple depth lengths and run times and cant actually find every elimination with out becoming even more complicated, which increases run time, even hodkou is programed to find every elimination within the scope of the name techniques abilities see above.

from a manual point of view: you might not see this side of it until you attempt to program it as described by the originator of the technique.

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this is a 4 cell xy-chain
visually as a manual solver i can see all the elimination it makes show cased easiest in ALS-xz double linked Rule
Almost Locked Set XZ-Rule: A=r15c2 {123}, B=r15c8 {234}, X=2,3 => r5c1345679<>3, r1c1345679<>2, r2346789c2<>1, r2346789c8<>4

however
Aic's & xy-chains need 4 to accomplish the same task {note: the xy-chain is exactly the same as the aic : xy-chains are Aic's and are constructed purely off bi-vavle cells.

AIC: 2 2- r1c2 -1- r5c2 -3- r5c8 -4- r1c8 -2 => r1c1345679<>2
AIC: 3 3- r5c2 -1- r1c2 -2- r1c8 -4- r5c8 -3 => r5c1345679<>3
AIC: 1 1- r1c2 -2- r1c8 -4- r5c8 -3- r5c2 -1 => r2346789c2<>1
AIC: 4 4- r1c8 -2- r1c2 -1- r5c2 -3- r5c8 -4 => r2346789c8<>4

im not even going to list discontinuous nice loops as there is 28 different ones for it.

AIc's with 1 elimination are possible

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`.---------------------------------.---------------------------------.---------------------------------.| 123456789  12         123456789 | 123456789  123456789  123456789 | 123456789  24         123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  12356789   123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  12356789   123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  12356789   123456789 || 123456789  13         123456789 | 123456789  123456789  123456789 | 123456789  34         123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  12356789   123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  12356789   123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  12356789   123456789 |'---------------------------------'---------------------------------'---------------------------------'`

AIC: 4 4- r1c8 -2- r1c2 -1- r5c2 -3- r5c8 -4 => r7c8<>4

{seems to be a labeling issue on hodoku as it misses it but still lists the xy-chain for it which is an aic }

Like I said, I'm only talking about manual solving here. While coding is interesting as well, what works there is hardly relevant to human solving.

you really should read up on obiwans approach to fish finding, it has huge implications as a manual solver and makes complicated fish actually easy.

these are named solving techniques.
Nice loops (discontinuous/continuous}
grouped nice loops (discontinuous/continuous}
A.I.C (alternative interface chain)
xy - chain
X-cycle

guess your biggest concern is why are the named techniques called "cycles,loops and chains". the difference is how they are coded! to function and what they can and cannot use to make the elimination.

for you its probably easier just to label everything "chain" and ignore the names, as that is what they all are and to install a single set of complex elimination rules. {manually}

instead of noting each of there limitations out lined below.

Nice loops (discontinuous/continuous}: strong -> weak link interfaces {bi locals only} on N+ digits
grouped nice loops (discontinuous/continuous} strong -> weak link interfaces {bi locals} & Grouped strong -> grouped weak interfaces on N+ digits
A.I.C (alternative interface chain) strong -> weak link interfaces & Grouped strong -> grouped weak interfaces where the weak interface is a digit change on a bivalve cell on N+ digits
xy - chain : strong-weak interface on bivalve cells only on N+ digits
X-cycle single digit: strong - weak-link interface and cannot use grouped nodes

for example x-cycles wont find the finned x-wing below.
Finned X-Wing: 2 c28 r25 fr1c2 fr3c2 => r2c13<>2
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`.---------------------------------.---------------------------------.---------------------------------.| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 || 123456789  13456789   123456789 | 123456789  123456789  123456789 | 123456789  13456789   123456789 |'---------------------------------'---------------------------------'---------------------------------'`

the other question was what is discontinuous and what is Continuous ie a real " loop or Ring"

discontinuous : start and end points are not peers of each other or start and end points are peers of each other and they do not share a common candidate that reduce the other to a single

continuous: start and end points are peers of each other and they do share a common candidate that reduce the other to a single then it is continuous {making the entire construct strong links}

here is a example of a continuous Nice loop
M-RINGS: wont matter which cell you start on the last cell resolved is always a peer of the first cell hence the name "ring" and it is a continuous nice loop"

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`    Type A:     .  -a   .  | .  /  .  | .  .  .    -b  ab  -b  |-b  b -b  |-b -b -b     .  -a   .  | .  /  .  | .  .  .    ------------+----------+---------     .  -a   .  | .  /  .  | .  .  .     /   a   /  | / ab+ /  | /  /  /     .  -a   .  | .  /  .  | .  .  .    ------------+----------+---------     .  -a   .  | .  /  .  | .  .  .     .  -a   .  | .  /  .  | .  .  .     .  -a   .  | .  /  .  | .  .  .    In addition, r5c5=ab    r2c2 -a- r5c2 =a= r5c5 =b= r2c5 -b- r2c2 - continuous loop`

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`.---------------------------------.---------------------------------.---------------------------------.| 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 || 123456789  12         123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 || 23456789   123456789  23456789  | 23456789   123456789  23456789  | 23456789   23456789   23456789  || 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  13456789   123456789 | 123456789  123456789  123456789 |'---------------------------------'---------------------------------'---------------------------------'`

Continuous Nice Loop: 1/2/3/4/5/6/7/8/9 2= r5c5 =1= r5c2 -1- r2c2 -2- r2c5 =2= r5c5 =1 => r1346789c2<>1, r2c1346789<>2, r5c5<>3, r5c5<>4, r5c5<>5, r5c5<>6, r5c5<>7, r5c5<>8, r5c5<>9

example of a {discontinuous Nice Loop}
M-wing
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`ype 1A:                             Type 1B: .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  . .  ab .  | .  .  .  | . -b  .        .  ab .  | .  a  .  | . -b  . .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .----------+----------+---------      ----------+----------+--------- .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  . /  a  /  | / ab+ /  | /  b  /        /  /  /  | / ab+ /  | /  b  / .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .----------+----------+---------      ----------+----------+--------- .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  . .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  . .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .1A: r2c8 -b- r2c2 -a- r5c2 =a= r5c5 =b= r5c8 -b- r2c8 --> r2c8<>b1B: r2c8 -b- r2c2 -a- r2c5 =a= r5c5 =b= r5c8 -b- r2c8 --> r2c8<>b`

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`.---------------------------------.---------------------------------.---------------------------------.| 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 || 123456789  12         123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 || 3456789    13456789   3456789   | 3456789    123456789  3456789   | 3456789    23456789   3456789   || 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  23456789   123456789 | 123456789  123456789  123456789 |'---------------------------------'---------------------------------'---------------------------------'`

Discontinuous Nice Loop: 2 r2c8 -2- r2c2 -1- r5c2 =1= r5c5 =2= r5c8 -2- r2c8 => r2c8<>2
Discontinuous Nice Loop: 2 r2c8 -2- r2c2 -1- r2c5 =1= r5c5 =2= r5c8 -2- r2c8 => r2c8<>2
Last edited by StrmCkr on Sun Dec 17, 2017 12:08 am, edited 5 times in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

http://forum.enjoysudoku.com/post37073.html#p37073
Here is an unfinned mutant jellyfish (4-fish) from #61 of the top1465.

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`  ...3.9.7.8..4.....1........2..5..6...3.....4.....1....5.....8......2.1.....7....9`

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`   46     2456   2456   | 3      8      9      | 245    7      1     8      2579   23579  | 4      567    1      | 2359   23569  2356     1      4579   34579  | 26     567    2567   | 3459   35689  34568    ----------------------+----------------------+---------------------     2      4789   4789   | 5      3479   3478   | 6      1      38     679    3      1      | 2689   679    2678   | 2579   4      258     4679   456789 456789 | 2689   1      234678 | 2379   2389   238    ----------------------+----------------------+---------------------     5      24679  24679  | 1      3469   346    | 8      236    23467     34679  46789  46789  | 689    2      34568  | 1      356    34567     346    1      2468   | 7      3456   34568  | 2345   2356   9`

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`   /  .  .  |  /  .  .  |  .  .  .     /  9  9  |  /  .  .  |  9  9  .     /  9  9  |  /  .  .  |  9  9  .    ----------+-----------+----------     / *9 *9  |  / *9  /  |  /  /  /    *9  .  .  | *9 -9  .  |  9  .  .    *9 -9 -9  | *9  .  .  |  9  9  .    ----------+-----------+----------     / *9 *9  |  / *9  /  |  /  /  /    *9 -9 -9  | *9  .  .  |  .  .  .     .  .  .  |  .  .  .  |  .  .  .     r47c14\b4578 nutant jellyfish    Key: * = base set candidate         / = required no candidate         - = exclusion`

The candidates of r47c14 are covered by b4578 for exclusions r5689c2356. Note there can be no candidates at the intersections of r47c14. The same exclusions are available via grouped single-digit coloring (empty rectangles).

r56c1=9=r4c23-r4c5=9=r56c4-9-r8c4=9=r7c5-9-r7c23=9=r8c1-9-r56c1= implying r5689c2356<>9

as requested from the fish page.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

StrmCkr, thanks for your thorough reply! I'll get back to that, although I must say that at first glance I vehemently disagree with some of it. In the mean time, I just updated my solution (not functionally) for the topic puzzle to represent my current preferences in chaining style. Any comments on that are welcome. The changes can be found in the first post (as well as the old steps) with a rationale for the changes. It has some relevance to this discussion as well. The updated steps also below:

Hidden Text: Show
1. AIC Type 2 (ALS, Grouped): (2=589)r4c156-(589=4)r4c8-r78c8=(4-7)r7c9=r9c7-r4c7=(7)r4c3 => -2 r4c3
2. X-Chain (2-String Kite): (8)r6c1=r3c1-r2c2=(8)r2c5 => -8 r6c5
3. AIC Type 2: (3)r3c5=(3-2)r7c5=(2-4)r7c2=(4-6)r6c2=(6-8)r6c1=(8)r3c1 => -8 r3c5
4. X-Chain (Grouped Skyscraper): (9)r3c8=r4c8-r4c6=(9)r13c6 => -9 r3c45
5. AIC Type 1: (9=8)r2c2-r2c5=(8-9)r3c6=(9)r3c8 => -9 r2c7
6. AIC Type 2: (9=8)r5c2-r2c2=r2c5-r3c6=(8-5)r4c6=r7c6-r9c5=r9c7-r5c7=(5)r5c3 => -9 r5c3
7. X-Chain (Empty Rectangle): (9)r5c7=r5c2-r2c2=(9)r1c3 => -9 r1c7; stte
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 1572
Joined: 22 May 2017

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

I vehemently disagree with some of it.
that's appropriate; there is a lot of stuff "named" on here that i don't like/agree with, {as per my understandings of its functionally}, but I do accept it and its author for their contributed works and lastly try to avoid further confusion by rewriting everything under one umbrella as that would also infuriate and depreciate the original persons work.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

StrmCkr, I must verify something before we continue. Are you really saying that X-Wing is NOT a continuous X-Cycle? That's just wrong. X-Cycles used to be called "fishy cycles" for a reason: a 2-2-2 Swordfish is also a continuous X-Cycle (length 6) just like an X-Wing is continuous X-Cycle (length 4). Continuous X-Cycles provide exactly the same eliminations as their fish counterparts, in one step.

I'm sure you know that Continuous Nice Loops (including X-Cycles which are a special case of Nice Loops) eliminate along ALL the weak links they have, so they don't have to be broken into multiple chains and steps (I just did it to make a point). Thus an X-Wing written as "A=B-D=C-loop" (or possibly more clearly expressed as: -A=B-D=C-A= which shows that A and C ARE peers) eliminates the candidates used in the weak links of the B-D and C-A lines from all the houses seen by both ends of those weak links. In the case of an X-Wing it means eliminations along BOTH rows (or columns), just like when seen as a fish. I'm sure you know all this, so can you please explain to me what you're really trying to say??? I'm completely puzzled if we have a disagreement on this.

I think you have a little bit different view from my current understanding of chains in general. The elimination cell(s) are not part of the AIC, as far as I'm concerned. The abomination that is called Discontinuous Nice Loops just make one think that way, but I now think it's fundamentally flawed and just complicates things. In my current view an AIC never starts or ends with a weak link. That reduces the number of different kinds of chains and loops to a minimum and simplifies things considerably.
-SpAce-: Show
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 1572
Joined: 22 May 2017

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

StrmCkr wrote:that's appropriate; there is a lot of stuff "named" on here that i don't like/agree with, {as per my understandings of its functionally}, but I do accept it and its author for their contributed works and lastly try to avoid further confusion by rewriting everything under one umbrella as that would also infuriate and depreciate the original persons work.

I understand that, and I respect the ingenuity and hard work of everyone who has contributed to the sudoku techniques. Make no mistake about that. That being said, I have no problem saying that some of it is a bit chaotic and unnecessarily complicated. It's part of the charm, all right, and navigating through the mess is a good deep learning experience. However, if it were a big software system for example, it would definitely benefit from some refactoring. Otherwise it just gets harder and harder for newbies to make sense of the complexity, even if old-timers have no problems.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 1572
Joined: 22 May 2017

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

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`That being said, I have no problem saying that some of it is a bit chaotic and unnecessarily complicated. It's part of the charm, all right, and navigating through the mess is a good deep learning experience. However, if it were a big software system for example, it would definitely benefit from some refactoring. Otherwise it just gets harder and harder for newbies to make sense of the complexity, even if old-timers have no problems.`
make no mistake, I do 100% agree with this

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`StrmCkr, I must verify something before we continue. Are you really saying that X-Wing is NOT a continuous X-Cycle? That's just wrong. X-Cycles used to be called "fishy cycles" for a reason: a 2-2-2 Swordfish is also a continuous X-Cycle (length 6) just like an X-Wing is continuous X-Cycle (length 4). Continuous X-Cycles provide exactly the same eliminations as their fish counterparts, in one step. `

i am
however i don't think i can show you the difference and what i am getting at so ill try one last time. if I can't then ill agree to call this debate moot, as its a difference of points of view

as they are found by the elimination cells connected to the a,b,c,d cells when building them meaning that the starting cells see both section of a&b cell and turn both cd as active, c & d are not visible to the elimination cell which is the starting point and they do no share a 2nd digit which turns the whole chain into strong links.

they are not direct peers, ie the 20 cells that are directly visible to it.
they are indirectly affected by it from construct.
{even if you are reducing it to 4 cells this still holds true, 1(start) cell sees 2 directly and indirectly implies the 4th (end point). }

they are built backwards or forwards {left to right or right to left }

Turbot Fish: 2 r2c2 =2= r8c2 -2- r8c8 =2= r2c8 => r2c1345679<>2
Turbot Fish: 2 r8c8 =2= r2c8 -2- r2c2 =2= r8c2 => r8c1345679<>2

X-Cycles provide exactly the same eliminations as their fish counterparts, in one step.
none of them are continuous, i have yet to see any solver list them as continuous to-date. as i outlined before the end point isn't a peer of the starting cell, nor do they share a 2nd digit that turns the set into all being "strong" links

That's just wrong.
not really that's the point of view of how a x-cycle is built and eliminations are inferred
starting from the elimination cells forward where the chain imply s a self contained contradiction, or in reverse direction the set implies the starting cells must be false.

and its very easy to reaffirm what i said by loading it into hodoku and cross checking {i copied and pasted all the chains directly from it}

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`A-- B|   |C -- D `

B = A - C = D - B = A
would be the expressed chain, which also shows it isn't a continuous loop of any kind as it only implies A = D or B = C
what can be interpreted is that any cell that sees A C may be eliminated and any cells the see B & D can be eliminated

In my current view an AIC never starts or ends with a weak link.
they can, but in all honesty I'm not going to debate that topic.

however i am keen on determining sources that quote 4,6 cell cycles as continuous and I'm guessing that's from scanraid
whom is using a definition I'm not familiar with.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

It's not my fault, nor does it prove anything, if Hodoku or other solvers fail to see basic logic. I know I'm right on this issue, and I'm astonished that we're even arguing about it. I know perfectly well that I'm a much less experienced and skilled solver than you in general, but there's one thing I think I understand pretty well and it's chains and loops. You gotta do better if you want to convince me that I have a fundamental misunderstanding of this magnitude with those.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 1572
Joined: 22 May 2017

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

If you really need a source that agrees with me, here's one:

https://www.paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm#othertechniques

Near the end there's a section "What about Nice Loops replacing other solving techniques?" and an X-Wing example [edit: changed the url to take there directly]. First it shows how multiple discontinuous nice loops can be used to provide the same eliminations, and then it says:

"Alternatively, the X-Wing can be described as a single continuous Nice Loop:

-[R2C3]=1=[R2C9]-1-[R5C9]=1=[R5C3]-1-[R2C3]=

The weak links [R5C3]-1-[R2C3] and [R2C9]-1-[R5C9] then eliminate candidate 1 from other squares in columns 3 and 9."

Do you still disagree?
Last edited by SpAce on Sun Dec 17, 2017 9:36 pm, edited 1 time in total.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 1572
Joined: 22 May 2017

### Re: Line check for SudoCue Nightmare (Sun Dec 9, 2007)

The only part I disagreed with is calling it continuous,

As it clashes with my perception and understanding of what makes it a full connected loop thus continuous, nothing further needs to be discussed on that as I cannot make my perception any clearer then I tried. I am also not here to change your mind either. Attempt to show case what I perceive as a continuous loop. And that's it.

Do I think you are wrong or misunderstanding something, nope At least for everything else except my point of view. I haven't seen anything from you that says other wise.

I agreed with the eliminations and sited how they work from my point of view and it is sound in mine and your point of view

I also quoted another site that also calls it continuous in quotes that agrees with you with same point of view, also i am probably the only one with an odd definition difference between the word and usage of continuous/ discontinuous
~this also highlights some of the flaws with multiple complex versions describing similar stuff that accomplishes the same end goal.

i will agree hodoku has flaws and bugs too. {it is a very solid solver in any regards}, some stuff needs updated to enhance it further and add the missing conditions on some techniques to expand their eliminations further.

to note, hodoku is 100% open source written in java, however the notes are written in German and needs translated plus it would take a while to sort out how it functions as a lot of stuff is nested within other search engines to speed up their findings.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 980
Joined: 05 September 2006

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