The New Sudoku Players' Forum

[ArkieTech]

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 *-----------*
 |85.|..9|...|
 |...|..5|.7.|
 |...|.6.|.9.|
 |---+---+---|
 |5..|.4.|.29|
 |72.|198|.54|
 |48.|.5.|..7|
 |---+---+---|
 |.1.|.8.|...|
 |.4.|7..|...|
 |...|9..|.83|
 *-----------*


Play/Print this puzzle online

[SteveG48]

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.-----------------.-----------------.-------------------.
|  8     5   2346 | 234   7    9    | 12346  1346  126  |
|  123-6 9   2346 | 2348 b123  5    | 2346   7     268  |
| d123   37  2347 | 2348  6   c123  | 2345   9     258  |
:-----------------+-----------------+-------------------:
|  5     36  1    | 36    4    7    | 8      2     9    |
|  7     2   36   | 1     9    8    | 36     5     4    |
|  4     8   9    | 236   5    23   | 136    136   7    |
:-----------------+-----------------+-------------------:
| d2369  1   237-6| 5     8    2346 | 24679  46    26   |
| d2369  4   8    | 7     123  1236 | 12569  16    1256 |
|ad26    7-6 5    | 9    a12   1246 | 12467  8     3    |
'-----------------'-----------------'-------------------'


(6=12)r9c15 - 1r2c5 = r3c6 - (1=2369)r3789c1 => -6 r2c1,b7p58 ; stte

[Ngisa]

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+--------------------+---------------------+-----------------------+
|  8       5    2346 | 234     7      9    | 12346    1346    126  |
| c1236    9    2346 | 2348   b123    5    | 2346     7       268  |
|  123     37   2347 | 2348    6      123  | 2345     9       258  |
+--------------------+---------------------+-----------------------+
|  5       36   1    | 36      4      7    | 8        2       9    |
|  7       2    36   | 1       9      8    | 36       5       4    |
|  4       8    9    | 236     5      236  | 136      136     7    |
+--------------------+---------------------+-----------------------+
| d2369    1    237-6| 5       8      2346 | 24679    46      26   |
| d2369    4    8    | 7       123    1236 | 12569    16      1256 |
|da26      7-6  5    | 9      a12     1246 | 12467    8       3    |
+--------------------+---------------------+-----------------------+


Almost like Steve
(6=21)r9c15 - (1)r2c5 = (1-6)r2c1 = r789c1 => - 6r7c3,r9c2; stte

Clement

[StrmCkr]

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+-------------------+-------------------+-------------------+
| 8        5   2346 | 234   7      9    | 12346  1346  126  |
| 23-6(1)  9   2346 | 2348  23(1)  5    | 2346   7     268  |
| 123      37  2347 | 2348  6      123  | 2345   9     258  |
+-------------------+-------------------+-------------------+
| 5        36  1    | 36    4      7    | 8      2     9    |
| 7        2   36   | 1     9      8    | 36     5     4    |
| 4        8   9    | 236   5      23   | 136    136   7    |
+-------------------+-------------------+-------------------+
| 2369     1   2367 | 5     8      2346 | 24679  46    26   |
| 2369     4   8    | 7     123    1236 | 12569  16    1256 |
| (26)     67  5    | 9     (12)   1246 | 12467  8     3    |
+-------------------+-------------------+-------------------+

H1 - wing : 6 r2c1 -6- r9c1 -2- r9c5 -1- r2c5 =1= r2c1 => r2c1<>6 {name defined by xsudoku}

correctly its a Hybrid type 3 wing as per definitions outlined in my thread as mentioned further down...


1 locked candidate and singles to the end.

{or add the extra cells like the two did above and have the "extra" eliminations to make it all singles to the end.

edit lots identifying the "hybrid name class it falls into"

[SpAce]

H1 - wing : 6 r2c1 -6- r9c1 -2- r9c5 -1- r2c5 =1= r2c1 => r2c1<>6

Hi StrmCkr! I agree that it's an H-Wing all right, but what definition of H1 are you using? Personally I could live without the type numbers anyway, but if they're used, I think your chain is a better match for your H3 definition here:

"StrmCkr]

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H1-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>X
H2-Wing:  (X=Y)a - (Y)b = (Y-Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X
H3-Wing:  (X=Y)a - (Y=Z)b - (Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X
H4-Wing:  (X)a = (X)b - (X=Y)c - (Y=ZX)dx     no known restrictions on "a" and "dx" cell locations

It's just not very clear from the way you wrote it, but it's easier to see if written as an AIC:

(6=2)r9c1 - (2=1)r9c5 - r2c5 = (1)r2c1 => -6 r2c1

I see it as an H-Wing because it has 1) three strong links (makes it a wing), which include 2) both bivalue and bilocal strong links (makes it a hybrid, which excludes XY-Wings and L-Wings), and 3) it's not an M-Wing, S-Wing, or W-Wing (so it must be an H-Wing). The exact type doesn't matter to me, but H1 it is not -- at least according to your definition above.

Then again, I don't think that H1 definition matches the general logic of H-Wings at all anyway, so it shouldn't even be listed as such -- it's clearly an L-Wing (L3 to be exact, since it has three digits), and L-Wings do not overlap with H-Wings by any logic. I know you claim otherwise here, but I can't see the logic.

L-Wings and XY-Wings are the only pure-bred types because they have just one type of strong links (either bilocal => L-Wing; or bivalue => XY-Wing). On the other hand, M-Wings, S-Wings, and W-Wings have both bilocal and bivalue strong links, so they're hybrids just like H-Wings. L-Wings and XY-Wings are the only ones that are not, so I don't see how any L-Wings could logically overlap with any H-Wings.

[StrmCkr]

Xsudo listed as a hybrid type 1 wing using what ever definition it uses, (older then the standardized version I posted and was given from other users) I left it as that, did not cross refrence to my own solver for a name. As I found it by hand.

Yes, L3 wings overlap with hybrid wings type 1

According to what source do you have that makes a distinction between the following and how they are classed:
use bi-local links
uses bivalve cells and links.
When a strong bi-local link lands on a bivavle the two are equivalent and can be classed under both distinctions.

If you look at the two code representation of h1. And l3 wing They are identical {see below, and further down-post}

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H1-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>X
L3-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>X

The difference apparently to your comment is ones supposed to use bi locals only however I've never seen that distinction made by anyone as the code representation was generic for truth streams regardless of form.
And that's how they are logically equivalent.

updated for clarity - phone posting is not conclusive.

[SpAce]

Xsudo listed as a hybrid type 1 wing using what ever deffintion it uses, (older then the standardized version I posted and was given from other users)

In that case it looks like XSudo is at least correct in recognizing it as a hybrid wing. On the other hand, your definition of H1-Wing is not a hybrid at all, so it should not be listed as such. I'm suspecting it's taken from a different naming standard that is not related to the other wings at all. You should pick one or the other, but they can't be logically combined. I'd recommend picking the one that has some logic built into it, so it doesn't require rote memorization. It's the only option for me anyway, because I refuse to learn or use anything that has no logic (or worse, has bad logic).

Yes, L wings over lap with hybrid wings type 1

No, they don't. Or more accurately, in your naming system they actually do but shouldn't -- your "H1" is really L3 and should be removed from the H-Wing category for good. The same pattern should not be in two logically non-overlapping categories, and there's no reason for it here at all (because it's clearly only an L-Wing). Your choice of naming (or promoting someone else's naming) it H1 just causes confusion because it totally breaks any naming logic in the single-letter wing family.

It's one of the reasons why those names are hard to learn in the first place, because it seems there's no logic at all -- but there is (at least some), if confusing mix-ups like that are removed. I only recently figured that out, which is why I've avoided those names thus far (even though I've been using those patterns all a long as generic chains). If there truly were no logic, those names would be unlearnable for me, but I think I've finally understood their relationships. Based on that newly found enlightenment, your H1 is clearly a misfit.

According to?
Both use strong/weak links and one of them uses cells and links.

When a strong link lands on a bivavle the two are equivalent.

If you look at the two code repsentations of h1. And l wing They are identical

Same occured with l3 & h3 wings. Plus others that overlapped.
And that's how they are logically equivalent.

I'm sorry to say, but none of that makes any sense. For an analogy, X-Wing and Naked Pair are logically equivalent if you look at them in 3D, and they can be coded similarly, but that doesn't make them the same sudoku pattern at all from a manual solver's point of view (unless multiple spaces are used simultaneously, but few are willing to do that). Coding arguments are irrelevant when we discuss names made for human consumption.

If we stick to the rc-space and manual solving, as we should here, then there's a very simple and easily identifiable logic differentiating L-Wings (local) and H-Wings (hybrid), and according to that they have zero overlap (except that both have exactly three strong links, but that's true about all these single-letter wings). That logic can be deduced from their names as well as from this simple list posted apparently by Dan (arkietech), and also from other similar sources.

The difference apprently is ones supposed to use bilocals only however I've never seen that distinction made by anyone

I have -- for example in the link above:

Simply stated a wing is a chain of 3. There are three strong links, at the beginning in the middle and at the end. Thay have names according to the pattern of whether the strong link is internal (a bivalue cell) or cell to cell (local).

It's also the only distinction that makes sense. L-Wing is the only type that uses only bilocal strong links (or grouped or AHS links in generalized cases). XY-Wing is the only type that uses only bivalue strong links (or ALS/ANS links in generalized cases). Anything else is a hybrid of some kind.

as the code representation was generic for truth streams regardless of form.

Like I said, coding arguments are irrelevant when we talk about patterns meant to be recognized by humans. In code you can easily look at the grid from different points of view (spaces), which can make many otherwise different-looking things logically equivalent and easily generalized, but that's not true in manual solving. (I actually use my 3D notation partly to reduce that gap, but you've seen how popular that is). Besides, even space-transformations wouldn't make L-Wing and H-Wing equivalent.

Here's how I look at this:

The single-letter wings are generally defined as having three strong links. Strong links (in this context) can be either Local or Value types, which is a generalization of bilocal and bivalue allowing Grouped or AHS (both local) and ALS/ANS (value) links to be treated similarly. In simple chains without such complications they just mean bilocal and bivalue strong links. We have eight possible combinations of such links:

000: V-V-V
001: V-V-L
010: V-L-V
011: V-L-L
100: L-V-V (*)
101: L-V-L
110: L-L-V (*)
111: L-L-L

Two of them (marked with *) are just mirrors, so we're left with six distinct combinations. Obviously only the first (V-V-V) and the last (L-L-L), more commonly known as XY-Wings and L-Wings (i.e. Local Wings), are purely of one type (and the exact opposites of each other). Thus they can have zero overlap with anything else. The other four are all hybrids of different V-L combinations, and cover the spectrum of W-Wings, S-Wings, M-Wings, and H-Wings. I would categorize them like this:

1. Pure-breds:
   
   
   1. V-V-V : XY-Wing (could logically be called V-Wing in this family, but obviously isn't)
   2. L-L-L : L-Wing (Local Wing); optional type-numbering is used to indicate the number of different digits in the pattern:
      
      1. (L1-Wing): 1 digit; logically this would be an X-Chain of length 6, but obviously no one calls it L1-Wing)
      2. L2-Wing: 2 digits
      3. L3-Wing: 3 digits
2. Hybrids:
   
   
   1. Symmetrical:
      
      1. V-L-V : W-Wing (named after the inventor)
      2. L-V-L : S-Wing (Split-Wing)
   2. Asymmetrical:
      
      1. V-L-L : name depends on the exact configuration of the digits (unfortunately):
         
         1. M-Wing (named after the inventor): two digits; same digit at both chain ends
         2. H-Wing (Hybrid Wing): all that aren't M-Wings; e.g. type H2 in your list
      2. V-V-L : H-Wing (Hybrid Wing); e.g. type H3 in your list

Once you understand that hierarchy, it gets really easy to name any chain with three strong links -- it's one of those wings (or rings, if looped), and more complex cases can be attached with a "Grouped" or "AHS" (applies to L-links) or "ALS"/"ANS" (applies to V-links) designation or both/all. There's no need to memorize all the zillion patterns and their type numberings because there's a relatively simple rule that governs the whole family.

My biggest problem with it is the V-L-L case with both M-Wings and H-Wings. I think they should just be M-Wings, and we'd have a cleaner hierarchy. As it is, the type numbering for H-Wings should mainly differentiate the V-L-L and V-V-L types. In your system they're H2 and H3, respectively, and to me they're the only useful type designations in that list (H1 is simply wrong, and it seems that H4+ are just ALS complications of H2 and H3, which makes the type numbering way too complex for human use).

[StrmCkr]

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I'm sorry to say, but none of that makes any sense.

edited for clarity, and added the following to hope it make sense

on the daily sudoku the L3 wing was simply used as the Local wing. ie L-wing and the 3 was dropped completely.

on this form the H1- wing was devised and the sub types independently from the other forum.

Hybrid Wings are defined as 3 digits with 3 strong link over 4 cells. the types found are the ways we identified to place 3 digits into 4 cells that could be used to form eliminations
{the h1 case was created under those contexts and thus overlapped with the L3 wing definitions}

if the L3 wing was actually further expanded into a more generalized form it would have also included the h2,h3 wings etc, but the daily Sudoku forum often stuck to using bi-local and bivalve chains.
{which is why we have a (g)M-wing and a M-wing difference, when the two forums shared ideas}

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    L3-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>X

    H1-Wing:  same as L3-Wing
    H2-Wing:  (X=Y)a - (Y)b = (Y-Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X
    H3-Wing:  (X=Y)a - (Y=Z)b - (Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X

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L2-Wing, M-Wing, S-Wing, and W-Wing use two candidate values:

     M-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      strong link   at weak inferences
    gM-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      no constraint at weak inferences
                                                 =>  elims for (X) in peers common to "a","d"
     M-Ring:                                     =>  continuous loop if "a","d" in same unit

     W-Wing:  (X=Y)a - (Y)b     = (Y)c - (Y=X)d      strong link   at weak inferences
    eW-Wing:  (X=Y)a - (Y)b ... = (Y)c - (Y=X)d      no constraint at weak inferences
                                                 =>  elims for (X) in peers common to "a","d"

    iW-Wing:  (X)s = (X-Y)a = (Y)b - (Y)c = (Y-X)d = (X)t   Inverted W-Wing (courtesy of Norm)

     S-Wing:  (X)a = (X)b - (X=Y)c - (Y)d = (Y)e     "a" and "e" in same unit; a<>Y, e<>X
                                                     but not in the same cell -- else M-Ring

    L2-Wing:  (X)a = (X)b - (X)c = (X-Y)d = (Y)e     "a" and "e" in same unit; a<>Y, e<>X

as emailed to me by others from multiple different Sudoku forms.

there is zero rules or limitations on what they are using as either bi locals or bivalves for the link type used in the above depiction. names classed purely from link interaction, and cell count and the arrangements that created eliminations.
so there is overlap

if i'm reading your long post correctly it seems to me to be the same argument you are purposing is what caused us to have a (g)M-wing and a M- wing
as the original M-wing exclusively used bivalve cells and bi-local. { the generalized form instead can use grouped links }

think your chain is a better match for your H3 definition here:

yes the chain matches H3 type, i will agree on that.
why xsudoku called it a type 1 is a mystery

your naming schematic is interesting

but how does it differentiate when bivalves overlap with bilocal links. { ie either or could take presidency}

Hybrid Wings are defined as 3 digits with 3 strong link over 4 cells. the types found are the ways we identified to place 3 digits into 4 cells that could be used to form eliminations
{the h1 case was created under those contexts and thus overlapped with the L3 wing definitions}

if the L3 wing was actually further expanded into a more generalized form it would have also included the h2,h3 wings etc, but the daily Sudoku forum often stuck to using bi-local and bivalve chains.
{which is why we have a (g)M-wing and a M-wing difference, when the two forums shared ideas}

stuff like this overlap was one of the leading conditions that the member RonK was against naming every type of chain based on its arrangement potential as it could lead potentially to more confusion and endless names that had some similarities in context and a lot of overlap which is why i stopped exploring past invertedW-Wings and expanding any of the linking links like the eW-wing.

[SpAce]

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I'm sorry to say, but none of that makes any sense.

edited for clarity, and added the following to hope it make sense

I'm afraid there's no such hope, sorry

on the daily sudoku the L3 wing was simply used as the Local wing. ie L-wing and the 3 was dropped completely.

As far as I'm concerned, dropping the type designator is perfectly fine -- as long as the mere L-Wing is understood as the parent type that covers both L2 and L3 (and even L1, though it's never used for obvious reasons). Reserving the generic L-Wing to be equivalent to just L3 makes no sense.

on this forum the H1- wing was devised and the sub types independently from the other forum.

By whom? Do you have any links to the history of the H1-Wing? Besides your stuff, all I've seen about hybrid wings on this forum is this, and that's an example of your H2-Wing H3-Wing which is a true Hybrid Wing by all definitions. [Edit: It's of course an H3-Wing. I don't know how I first looked at it. There's also more stuff in that post that I'd missed, but more about that in a separate post.]

Hybrid Wings are defined as 3 digits with 3 strong link over 4 cells. the types found are the ways we identified to place 3 digits into 4 cells that could be used to form eliminations

By whom? Links? Again, I haven't seen that definition used by anyone but you. To me it makes no sense because I don't see what connects it to the name "Hybrid". A named definition should have a logical connection to what it describes, but what exactly is "hybrid" in yours? The other one defines "hybrid" as having both bilocal and bivalue strong links in the same three-strong-link chain, which makes it very intuitive. I don't see anything resembling "hybrid" in yours. Also, your cell count definition excludes any grouped/AHS/ALS extensions, which is not a limitation in the other one (those extensions can be used with any of the V-L configurations).

{the h1 case was created under those contexts and thus overlapped with the L3 wing definitions}

Sure, under that definition they do overlap. The problem is then with the definition that causes the overlap. If you really want to have a category for patterns with "3 digits with 3 strong link over 4 cells", they should be called something other than "Hybrid Wings", imho. Otherwise you're creating an overloaded definition for hybrid wings (with nothing intuitively "hybrid" about it) and you know how much I hate that. The other definition for hybrid wings is more intuitive and much more in line with the other single-letter wing types, causes no overlap issues, needs less subtyping, and also allows mentioned extensions -- so I think it wins hands down.

if the L3 wing was actually further expanded into a more generalized form it would have also included the h2,h3 wings etc, but the daily Sudoku forum often stuck to using bi-local and bivalve chains.

What would the generalized form be that would do such a trick? The only logical way to generalize any L-Wing is to use grouped or AHS links (because it has no bivalue strong links), but it doesn't change the logic or make it a hybrid by my definition (because it still wouldn't have any (bi)value strong links). Any generalization that switches the link types between (bi)local and (bi)value makes no sense, because then all names and definitions lose meaning. L=Local <=> covers only (bi)local strong links. There's no logical way to generalize it to include (bi)value links as well.

{which is why we have a (g)M-wing and a M-wing difference, when the two forums shared ideas}

The original M-Wing was just poorly defined. There's no need for the distinction at all because the (g)M-Wing is the only one that should have ever existed. Cells that contain weak links can obviously have any number of candidates, so the original definition with a bivalue requirement for the weak link cell made no sense. To me M-Wing is simply the one that used to be called (g)M-Wing, and that's that.

(If I could, I'd actually include your H2 under M-Wing too, because they're both V-L-L configurations. Logically they would be M2 and M3 subtypes, using the digit count for subtyping as with L-Wings (the difference being that there couldn't be any M1 even theoretically). That way H-Wings would only cover V-V-L (now H3) and every link configuration would have its own letter without any overlap.)

Code: Select all

    L3-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>X

    H1-Wing:  same as L3-Wing
    H2-Wing:  (X=Y)a - (Y)b = (Y-Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X
    H3-Wing:  (X=Y)a - (Y=Z)b - (Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X

Code: Select all

L2-Wing, M-Wing, S-Wing, and W-Wing use two candidate values:

     M-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      strong link   at weak inferences
    gM-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      no constraint at weak inferences
                                                 =>  elims for (X) in peers common to "a","d"
     M-Ring:                                     =>  continuous loop if "a","d" in same unit

     W-Wing:  (X=Y)a - (Y)b     = (Y)c - (Y=X)d      strong link   at weak inferences
    eW-Wing:  (X=Y)a - (Y)b ... = (Y)c - (Y=X)d      no constraint at weak inferences
                                                 =>  elims for (X) in peers common to "a","d"

    iW-Wing:  (X)s = (X-Y)a = (Y)b - (Y)c = (Y-X)d = (X)t   Inverted W-Wing (courtesy of Norm)

     S-Wing:  (X)a = (X)b - (X=Y)c - (Y)d = (Y)e     "a" and "e" in same unit; a<>Y, e<>X
                                                     but not in the same cell -- else M-Ring

    L2-Wing:  (X)a = (X)b - (X)c = (X-Y)d = (Y)e     "a" and "e" in same unit; a<>Y, e<>X

as emailed to me by others from multiple different Sudoku forms.

there is zero rules or limitations on what they are using as either bi locals or bivalves for the link type used in the above depiction.

Maybe not explicitly, but they're easily deduced from the chains. It's also mentioned in Dan's post, so I certainly didn't invent it.

names classed purely from link interaction, and cell count and the arrangements that created eliminations.
so there is overlap

I don't see any overlap in the wings/chains you listed -- except with your H1/L3. If Dan's definitions are used, there's no overlap at all. So, it's an easy choice for me which definition I prefer. I'd just drop H1 and be done with it. (Besides, cell counts and digit counts create poor definitions because they're impossible to generalize, unlike those based on link configurations.)

if i'm reading your long post correctly it seems to me to be the same argument you are purposing is what caused us to have a (g)M-wing and a M- wing
as the original M-wing exclusively used bivalve cells and bi-local. { the generalized form instead can use grouped links }

No. You must have misunderstood both what I said and the original M-Wing/(g)M-Wing controversy. As far as I know, it had nothing to do with grouped links (which would be a true generalization). The original M-Wing definition was just over-specified to use a bivalue cell for a weak link. There was for no reason for that, of course, except maybe to make the pattern more recognizable (but leaving out lots of valid cases).

yes the chain matches H3 type, i will agree on that.
why xsudoku called it a type 1 is a mystery

I don't know, but I'm betting it's probably using the same definition of H-Wing as myself (i.e. only including your H2 and H3, but calling them H1 and H2 in the reverse order). I'm just guessing because I don't have XSudo and can't check that, but I don't think Allan Barker would have accepted your H-Wing definition. It should actually tell you something that you didn't even remember your own definition since you named your chain as H1 without any bells ringing. If your definitions were clear and simple enough, you should have seen the conflict between the two yourself.

your naming schematic is interesting but how does it differentiate when bivalves overlap with bilocal links. { ie either or could take presidency}

It doesn't because it's unnecessary. It's all about the links actually used in the chain, and they can only be in one of the six possible configurations which don't overlap. If the same cells and candidates allow multiple configurations (which I haven't seen, but am not claiming to be impossible at this point), then all suitable names would be valid. Can you show an an example of a configuration which could fall into multiple categories at the same time? (Even if it's possible, it doesn't break the naming system.)

Generally speaking, a bivalue cell can be used as both a strong link and a weak link, but in a particular chain it's only used for one or the other role, so there's no ambiguity. If a cell is used for a strong link, then it must be bivalue, but if it's used for a weak link, then it can have any number of candidates -- being bivalue makes no difference at all if it's used for a weak link. I think some misunderstanding about that simple truth was what caused the original M-Wing controversy.

stuff like this overlap was one of the leading conditions that the member RonK was against naming every type of chain based on its arrangement potential as it could lead potentially to more confusion and endless names that had some similarities in context and a lot of overlap which is why i stopped exploring past invertedW-Wings and expanding any of the linking links like the eW-wing.

I mostly agree with ronk. If one understands the basics of chaining, there's no real need to memorize a bunch of named chain patterns. For the shortest of chains it's useful and fun to have names, but any expanded forms can quickly get out of hand unless it's obvious how they're built on the simpler stuff and there's a logic to their naming.

For me the cutoff for a simple pattern worthy of naming is at three strong links, but I accept some easy extensions things like iW and eW (though I don't count them as "wings" because they have more than three strong links). Grouped, AHS and ALS/ANS extensions are also perfectly acceptable to me because they're easy to add to the name and don't change the linking logic -- but they only make sense if only the link types/counts are used to specify the main pattern. If cell counts are part of the definition (as in yours), then those extensions are obviously impossible and you're stuck with creating separate types for them, which unnecessarily complicates things.

[Edit: corrected H2 -> H3 (udosuk's chain)]

[SpAce]

As a demonstration of the power of my naming system, here's what it would call Steve's and Clement's chains above. Since they both have three strong links, they can be classified as wings:

(6=12)r9c15 - 1r2c5 = r3c6 - (1=2369)r3789c1 => -6 r2c1,b7p58; stte

That's a V-L-V configuration with both Vs containing ALS nodes. Thus:

ALS-W-Wing.

(6=21)r9c15 - (1)r2c5 = (1-6)r2c1 = r789c1 => - 6r7c3,r9c2; stte

That's a V-L-L configuration with the same digit at both ends, with the V containing an ALS node and the latter L a group node. Thus:

Grouped ALS-M-Wing.

Simple, huh? It's the exact same logic that was apparently used to name ALS-XY-Wings (which are V-V-V configurations with any V containing an ALS). No need for complicated type numbers even for these extended cases.

Another demonstration from March 12 ("Day of the Wings") puzzles:

(3=7)r4c1 - (734=9)r5c169 - r4c7 = (9)r4c2 => -3 r4c2; ste

That's a V-V-L configuration with one V containing an ALS. Thus:

ALS-H3-Wing

(9=34)r5c96 - (4=59)r61c5 - (9)r[1=4]c2 => -9 r4c7,r5c3; stte

That's also a V-V-L configuration with both Vs containing ALSs. Thus also:

ALS-H3-Wing

Note that a simple H3-Wing could not have the same digit at both ends, but with ALS nodes it's possible (like in my chain). Since my classification is based on the link configuration, they're still both H3-Wings. That's one reason why using cell/digit counts or end digits as the main classification works poorly as it destroys any extensibility. They're better for subtyping if need be.

(Btw, by "ALS" I mean anything larger than a bivalue cell. Of course I know that bivalue cells are also ALSs (almost naked singles), but you get the point. Similarly bilocation links are in fact AHSs (almost hidden singles). Those facts are what make the ALS/AHS extensions work exactly the same way as the simple cases -- because the are the same.)

[StrmCkr]

an Interesting way of doing that.

I don't technically use cell counts persay I use it more as a node which could be grouped etc.
As long as the links match and the node count matches then I'll tag a class name with numbers indicating which pattern it links to with in that name branch if i have time to look it up.

in this example i simply went with what allan had listed as the type with out cross checking its accuracy.
does it mean i lack the compunction to recognize the class type better, no i lack time atm.

Do i use or really bother to look up sub-type digits- for the most part no, they are their mostly to test if my coding engine finds them all correctly. { ie M ring/wing has 13 sub-types, and 1 case that happens to be in minimal and overlaps 2 }

Allan barker for the most part used my naming schematics from all the topics I developed/assisted with At the time he made his solver. {xsudoku} { 2010/2011 }

how allan implemented or detects the 3 H types he has in his solver code i cannot answer, no do i have any Idea why the numbers don't match the three types outlined by udosuk,springs etc

Hwings and its three types: listed by udosuk{ in the link you proved and it outlined 4 types {1 being a ring class ie m-Ring} and later by pointed out by springs in the exact same order i have my 1,2,3 listed.
which predates any use of the L3- Wing

http://forum.enjoysudoku.com/combinations-of-3-or-4-strong-and-weak-inferences-t30109.html#p203604
this is technically a 2nd rehash the original post which was deleted by springs and had more development of the types by him from pooling together many different posts and ideas with cross referencing links.

as for the development http://forum.enjoysudoku.com/post269036.html#p269036

udoksu he comes up with the pattern designs on page 2, which include the 3 main ones that you{strmckr} and i call types 1,2,3, as well as the m-ring (3 strong + 3 weak continuous loop pattern) which arguably shouldn't be there. there may have been other posts on the topic but presumably they got lost in the big forum crash of 2009 so couldn't find them

for some fun a wing type I've never actually seen used.

Code: Select all

 Strong Ring
+--------------------+--------------------+---------+
| .  .             . | .  .             . | .  .  . |
| .  -2456789(13)  . | .  -3456789(12)  . | .  .  . |
| .  .             . | .  .             . | .  .  . |
+--------------------+--------------------+---------+
| .  -1256789(34)  . | .  -1356789(24)  . | .  .  . |
| .  .             . | .  .             . | .  .  . |
| .  .             . | .  .             . | .  .  . |
+--------------------+--------------------+---------+
| .  .             . | .  .             . | .  .  . |
| .  .             . | .  .             . | .  .  . |
| .  .             . | .  .             . | .  .  . |
+--------------------+--------------------+---------+

each digit is a bi-local to 1 row and 1 col.
=> the 4 cells are locked to only contains the 4 digits in their respective position.

Edit renamed to ring

[SpAce]

I'll get back to the rest later, but now about this:

for some fun a wing type I've never actually seen used.

Code: Select all

 Strong Wing 
+--------------------+--------------------+---------+
| .  .             . | .  .             . | .  .  . |
| .  -2456789(13)  . | .  -3456789(12)  . | .  .  . |
| .  .             . | .  .             . | .  .  . |
+--------------------+--------------------+---------+
| .  -1256789(34)  . | .  -1356789(24)  . | .  .  . |
| .  .             . | .  .             . | .  .  . |
| .  .             . | .  .             . | .  .  . |
+--------------------+--------------------+---------+


each digit is a bi-local to 1 row and 1 col.
=> the 4 cells are locked to only contains the 4 digits in their respective position.

That's a nice pattern, but also another obvious misnomer in so many ways. First, "Strong" means nothing. Second, it's a loop, so it should be called "ring" and not "wing", if anything. (It's the same with X-Wing, but let's not get back into that historical debate.) Third, it has four strong links, which makes it a questionable ring candidate too. Fourth, its inverse is called XY-Ring, so logically this should be L(4)-Ring (or Inverse XY-Ring).

Added: [

Btw, looks like I'm not the only one who's noticed the wing/ring discrepancy (link):

When w<>z, it's aStrong Ring, a different bird.

It also appears that here the pattern has been (more) logically named Strong Ring:

Code: Select all

*---------1---------*
| . . | . . . | . . |
| . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . |
2 . . | . . . | . . 3
| . . | . . . | . . |
|-----+-------+-----|
| . . | . . . | . . |
| . . | . . . | . . |
*---------4---------*
2. Strong Ring

]

Anyway, XY-Ring is a misnomer too, because it implies a looping version of XY-Wing, which it is not (obviously, because it would be an impossible pattern in vanilla sudoku). The same of course applies to its inverse (because with normal wing conventions of three strong links there's no L-Ring possibility). So, there's no obviously great name for this pretty pattern, unless we relax the conventions and the requirement for exactly matching wings and rings of the same name.

Still a cool pattern, so thanks for bringing it up!

Btw, in today's puzzle I found a nice special case of H3-Wing. What's your type number for that?

[SpAce]

StrmCkr, thanks for the references! They cleared up some possible misunderstandings about the history on my part. Didn't change my opinion, though, but that's unlikely anyway.

an Interesting way of doing that.

I don't know about that, but for me it's the only way to make some sense out of the naming mess.

I don't technically use cell counts persay I use it more as a node which could be grouped etc.

Then you should say so in your definition instead of talking about cells.

in this example i simply went with what allan had listed as the type with out cross checking its accuracy.
does it mean i lack the compunction to recognize the class type better, no i lack time atm.

I wasn't implying anything about your skills, only the complexity of the name/type system you use. We all make mistakes -- including myself, for example when I incorrectly labeled udosuk's example H2-Wing (it's of course H3-Wing; now corrected).

Do i use or really bother to look up sub-type digits- for the most part no, they are their mostly to test if my coding engine finds them all correctly. { ie M ring/wing has 13 sub-types, and 1 case that happens to be in minimal and overlaps 2 }

I understand why those listed subtypes might be useful for coding purposes. For human solving, not so much. For that the naming system must be simple enough so that the names can be derived for each possible pattern with a few simple rules instead of using a look-up table every time. My preferred wing-naming system requires knowing just the six link configurations and their matching letters, plus the extension rules, which is still a lot but manageable compared to the tons of numbered types lacking any apparent logic.

Allan barker for the most part used my naming schematics from all the topics I developed/assisted with At the time he made his solver. {xsudoku} { 2010/2011 }

Ok. I didn't know that, but that doesn't surprise me. You've obviously done a lot of awesome pioneering work. Please don't ever get me wrong if I criticize some details -- it doesn't mean I wouldn't respect your and all the other pioneers' accomplishments. Some things just can be improved over time, that's all.

how allan implemented or detects the 3 H types he has in his solver code i cannot answer, no do i have any Idea why the numbers don't match the three types outlined by udosuk,springs etc

Does his solver have L-Wings? If so, I could imagine he'd seen the same thing I did and moved the H1 there. Then again, that doesn't explain why he still has three H-Wings as you say (what is the third if your H1 is not there?). Hard to speculate without seeing the program.

Hwings and its three types: listed by udosuk{ in the link you proved and it outlined 4 types

You mean here. You're right, it does list 4 types, including the L3/H1, though I can't see your H2 there (but it might be because I can't figure out the last diagram). I have to admit that I probably didn't get that far in that post because it's kind of tiresome to read those old notations. So, it seems that I've missed some important details. My mistake, sorry about that. Of course it doesn't change my opinion about the naming, but it proves that you didn't invent it.

You still haven't answered my question, though: what exactly makes udosuk's types (especially the L3/H1 variant) and your definition "hybrid" in your opinion? I guess there must be a reason because you've accepted and promoted that classification.

Let's look at udosuk's four types and my interpretations of them:

Hybrid-Wing with 3 weak links + 1 strong link (as cited by me on p.1)

Code: Select all

xy -  ?
|    ||
|     x
|    ||
yz -  can't be z

(z=y) - (y=x) - x = x : V-V-L : H3-Wing

[Hybrid-Wing with 1 weak link + 3 strong links (as cited by Luke on p.1)

Code: Select all

?  =x=  ?
||     ||
y       w
||     ||
?  ---  can't be y

y = (y-x) = (x-w) = w : L-L-L : L3-Wing (your H1)

My question still stands: what makes this "hybrid"?

Hybrid-Wing with 2 weak links + 2 strong links

Code: Select all

xy ---  ?
|      ||
|       x
|      ||
?  =y=  must be x or y

y = y - (y=x) - x = x - loop : L-V-L-loop : S-Ring | M-Ring

S-Ring/M-Ring is a hybrid type -- just a special case -- so this is actually fine. Both names are fine also, although M-Ring must be more common. (I've never actually seen anyone use S-Ring, but that's how I saw it, and it's just as logical a name.)

Hybrid-Wing with 2 weak links + 2 strong links

Code: Select all

?  =x= vz
||      |
y       |
||      |
vw ---  can't be v

I can't make any sense out of that. What is it? (The missing H2, perhaps? But how?)

As a general note, his strong/weak link counts make no sense, as aran pointed out. Also the name Strong Wing is poor, but that was already covered. All in all, I don't think this is a great naming reference for all times, though I'm definitely not disrespecting it as a starting point.

{1 being a ring class ie m-Ring}

Funny thing... I saw it clearly as an S-Ring! But you're right, it's also an M-Ring. So, we found an example of a pattern that can be validly named in two different ways even in my preferred system. That's a different kind of overlap, though, and one that I don't see as a problem at all. On the other hand, the L3/H1 overlap is caused by two different definitions of H-Wings, which is a problem. Yours/udosuk's/999_Spring's definition may be older, but it doesn't play well with the other single-letter wing types. I prefer a unified system that covers all wings with consistent name-derivation rules.

and later by pointed out by springs in the exact same order i have my 1,2,3 listed.
which predates any use of the L3- Wing

Ok. I can't dispute the timeline, so let's assume it is so. In that case I must tune my argument a bit. If it is the case that L3 was in fact first counted as a hybrid wing, then why was the idea of L-Wings born at all? Because it makes more sense! It's rarely the case that the first ideas are the best regarding all details, even though they're important as stepping stones. Obviously someone figured out a better way to classify the wing types, and that was reflected in Dan's post (2012) that I linked.

I don't think there's any reason to keep using bad ideas just because they came first (unless they're so widely used that it's impossible to change them). At least to me it's clear Dan's classification (or whoever originally developed it) has been much better thought through, because it allows the names to be derived according to simple rules instead of memorization. Things like that take time to figure out, so I'm not blaming udosuk for not creating a perfect system from scratch.

udoksu he comes up with the pattern designs on page 2, which include the 3 main ones that you{strmckr} and i call types 1,2,3, as well as the m-ring (3 strong + 3 weak continuous loop pattern) which arguably shouldn't be there. there may have been other posts on the topic but presumably they got lost in the big forum crash of 2009 so couldn't find them

Ok. I didn't find the (H-Wing) type 2 in udosuk's post, though. Was it supposed to be the diagram that I couldn't interpret?

Btw, about the famous "purple cow" pattern, I completely agree with you of course:

moreover your depiction would drop it directly over the l2-wing i documented and coded

Yes, it's clearly L2-Wing. 999_Springs' diagrams (2010) actually covered all three L-Wing types, including L1-Wing and L1-Ring -- more commonly known as X-Chain and X-Loop. (Obviously he didn't use any of those names, though.)

[StrmCkr]

I've never actually seen anyone use S-Ring,

cause they cant exist as an Split wing, the very definition of the technique didn't allow the end points to be overlapped or looped. { other wise they were not discontinuous }

plus all of them where already labeled under M-wing/ring

Code: Select all

You still haven't answered my question, though: what exactly makes udosuk's types (especially the L3/H1 variant) and your definition "hybrid" in your opinion? I guess there must be a reason because you've accepted and promoted that classification.

nothing to my knowledge keyed it to being a "hybrid" in the literate sense, the only key features was 3- strong links over 4 cells {nodes} as its lose configuration definition,
all configurations of that type of requirement was dropped under the hybrid name and that's pretty much it: at least to my understanding.

if there was a more literal reason behind it i didn't see it in the early posts either.

xsudoku Hybrid Type 1:

Code: Select all

+-------------+------------+---------+
| .  .      . | .  .     . | .  .  . |
| .  (1)    . | .  (12)  . | .  .  . |
| .  .      . | .  .     . | .  .  . |
+-------------+------------+---------+
| .  .      . | .  .     . | .  .  . |
| .  -3(1)  . | .  (23)  . | .  .  . |
| .  .      . | .  .     . | .  .  . |
+-------------+------------+---------+
| .  .      . | .  .     . | .  .  . |
| .  .      . | .  .     . | .  .  . |
| .  .      . | .  .     . | .  .  . |
+-------------+------------+---------+

xsudoku hybrid Wing type 2

Code: Select all

+--------------+------------+---------+
| .  .       . | .  .     . | .  .  . |
| .  (12)    . | .  (1)   . | .  .  . |
| .  .       . | .  .     . | .  .  . |
+--------------+------------+---------+
| .  .       . | .  .     . | .  .  . |
| .   -3(2)  . | .  (13)  . | .  .  . |
| .  .       . | .  .     . | .  .  . |
+--------------+------------+---------+
| .  .       . | .  .     . | .  .  . |
| .  .       . | .  .     . | .  .  . |
| .  .       . | .  .     . | .  .  . |
+--------------+------------+---------+


xsudoku Hybrid wing Type 3

Code: Select all

+-------------+-------------+---------+
| .  .      . | .  .      . | .  .  . |
| .  (13)   . | .  (12)   . | .  .  . |
| .  .      . | .  .      . | .  .  . |
+-------------+-------------+---------+
| .  -2(3)  . | .  -3(2)  . | .  .  . |
| .  .      . | .  .      . | .  .  . |
| .  .      . | .  .      . | .  .  . |
+-------------+-------------+---------+
| .  .      . | .  .      . | .  .  . |
| .  .      . | .  .      . | .  .  . |
| .  .      . | .  .      . | .  .  . |
+-------------+-------------+---------+

types 1 & 3 are swapped in xsudoku.


oh i found more random stuff on the strong "wing"

[SpAce]

I've never actually seen anyone use S-Ring,

cause they cant exist as an Split wing, the very definition of the technique didn't allow the end points to be overlapped or looped. { other wise they were not discontinuous }

That makes no sense. An S-Wing is discontinuous of course (just like M-Wing), but if we connect the ends it becomes continuous and is then logically called S-Ring -- just like any other wing that has a looping possibility. Why would it be different? Since the ends have different digits they can only be linked in a cell, and then it's indistinguishable from an M-Ring. How can you not see that?

It appears that the M-Wing and the S-Wing are in fact the only three-link wings that can have useful ring forms. They just turn out to be the same pattern. It's pretty easy to see why.

1. At least four cells are needed to have a loop in vanilla sudoku, which rules out XY-Wing directly (only 3 cells).
2. If the end digits of the wing chain are the same, then four cells is enough for a loop too (because the end points can have a "local" weak link). That group includes M-Wing, W-Wing, and L1-Wing. However, if the end cells of a W-Wing see each other it's a naked pair; thus a degenerate case. L1-Ring (6 cells) is a useful pattern, but more commonly known as X-Loop, so that can be counted out too. That leaves just M-Ring.
3. If the end digits are different, then the wing form must take at least 5 cells, because one cell is lost when a loop is formed. That rules out L3 and H2/H3-Wings (4 cells) directly. L2 (5 cells) works in theory, but is degenerate (X-Wing), and so is an unnamed useless type of H-Wing of the form (x=y) - y = y - y = y. The only thing left is S-Wing (5 cells), which works (but its ring form is the same as M-Ring).

Code: Select all

VVV : XY-Wing : 3 cells, same -> no ring
VVL : H3-Wing : 4 cells, diff -> no ring
VLV : W-Wing  : 4 cells, same -> * ring (degenerate: naked pair)
VLL : M-Wing  : 4 cells, same -> * RING *
      H2-Wing : 4 cells, diff -> no ring
      H!-Wing : 5 cells, diff -> * ring (degenerate: Turbot Fish)
LVL : S-Wing  : 5 cells, diff -> * RING * (but same as M-Ring)
LLL : L1      : 6 cells, same -> * ring (better name: X-Loop)
      L2      : 5 cells, diff -> * ring (degenerate: X-Wing)
      L3      : 4 cells, diff -> no ring

So, we effectively have only one ring type for the three-link wings. It can, however, be validly called either M-Ring or S-Ring, but I realize that M-Ring probably causes less confusion.

plus all of them where already labeled under M-wing/ring

That's a more valid reason, but only because of conventions. It doesn't invalidate the option of seeing it as an S-Ring too (and calling it that). We have many patterns that have lots of valid names because they can be seen from multiple points of view. It's actually positive overlapping, because the more ways of seeing the same thing, the more chances of spotting something useful.

Since S-Wing is a symmetric pattern and M-Wing is not, I bet spotting an S-Ring is actually easier than spotting the same as an M-Ring. Just like I actually did, which kind of proves my point. To be honest, I didn't even realize it was also an M-Ring until you said so (though I should have). So, if you insist that it can't be seen or called an S-Ring, you're actually removing a valid way to spot the pattern. What's the point in that?

You still haven't answered my question, though: what exactly makes udosuk's types (especially the L3/H1 variant) and your definition "hybrid" in your opinion? I guess there must be a reason because you've accepted and promoted that classification.

nothing to my knowledge keyed it to being a "hybrid" in the literate sense, the only key features was 3- strong links over 4 cells {nodes} as its lose configuration definition,
all configurations of that type of requirement was dropped under the hybrid name and that's pretty much it: at least to my understanding.

if there was a more literal reason behind it i didn't see it in the early posts either.

Thank you. So we can safely conclude that there was no deeper thought put into that name. That's what I thought. On the other hand, the other "hybrid" definition actually means something, which is one more reason to prefer it.

types 1 & 3 are swapped in xsudoku.

Yes, it seems so. Thanks for digging that up. So, unfortunately XSudo is using the flawed H-Wing definition. No one's perfect, not even Allan. Then again, he probably didn't put much thought into naming, and just used whatever names were already available. Apparently L-Wings weren't a thing yet at that point.

oh i found more random stuff on the strong "wing"

Yes, you did, thanks for that. Did you notice that it doesn't describe a loop and uses only three strong links (unlike the pattern you showed earlier)? So, I have much less of a problem accepting it as a "wing". It's also described as the inverse of XY-Wing, and I think there's a name for that... what was it again? Oh yes, L-Wing!

As I already explained here, Strong Wing is actually a dual L3-Wing. As I said earlier (and others had pointed out before me), your example was a loop and had four links -- thus not a Strong Wing. I might accept "Strong Ring", but I don't like that either, because the pattern requires a fourth link unlike the wing version (but so does XY-Ring).