The New Sudoku Players' Forum

[rjamil]

H4-Wing uses two Strong Links where as H6-Wing uses only one Strong Link (out of two H4-Wing Strong Links) and both produce same eliminations?

R. Jamil

[SpAce]

H4-Wing uses two Strong Links where as H6-Wing uses only one Strong Link (out of two H4-Wing Strong Links) and both produce same eliminations?

No. They all use three strong links like all of these one-letter-wing types (otherwise they shouldn't be counted as wings at all). What makes them H4 is that one of the strong links is a is a bilocation digit, one is a bivalue cell, and one is an ALS. (That structure actually makes them a subtype of H3 in my classification, with one bivalue replaced by an ALS -- it's still V-V-L like H3, though what makes it different is the overlap of the first and last nodes and the elimination logic.) As far as I see, the same structure is true for H4, H5, and H6, so they're conceptually one and the same.

The simplest form is this:

H4-Wing: (x)A = (x)B - (x=y)C - (y=zx)DA => -x (seen by both A and D)

It can be generalized with a group link between the first two nodes, an ALS for the middle node, and a bigger ALS for the last node. It's still the same concept. Of course it might not be obvious if chaining is not your bread and butter.

If you disagree, please show me an example where this doesn't hold.

[rjamil]

Hi SpAce,

First of all, thanks for such a detail response.

Actually, what I am seeing Hybrid Wing types are by comparing with XYZ-Wing Hybrid types move.

Am not expert to claim any thing either correct or wrong.

I see some type of H-Wings are similar to as, once a useless/spent/flightless xy- or xyz-wing found, try to detect another strong/weak link to make it work (maybe I am looking in wrong direction).

R. Jamil

[SpAce]

Actually, what I and seeing Hybrid Wing types are by comparing with XYZ-Wing Hybrid types move.

Thanks for pointing out that similarity. In most cases those "Hybrid XYZ-Wings" seem to be H4-Wings.

(However, the "Hybrid" in the two names seem to mean two different things, and as you know, I never like overloaded terms. In H-Wings the "Hybrid" means that the chain contains both bivalue and bilocation strong links, which makes it very logical. There's no such logic for the Hybrid XYZ-Wing which would be better named as an Extended XYZ-Wing or something else.)

Let's look at eleven's diagram in that post, apparently depicting the original Hybrid XYZ-Wing (not verified because the link doesn't work):

Code: Select all

----------------------------------
 abc -b -b |  bc .  . | -b -b -b
  .  .  .  |  .  .  . |  .  .  .
  .  . ab  |  .  bc . |  .  .  .
----------------------------------


That's actually over-specified because there's no need for the r3c5 to be a bivalue cell (and it doesn't need the c there at all), as long as the b is strongly linked in box 2:

Code: Select all

--------------------------------------
 abc  -b  -b  |  bc  /   / | -b -b -b    ('/' -> no b in that cell
  .    .   .  |  /   /   / |  .  .  .    => bilocation strong link on b in box 2)
  .    .   ab |  /   b+  / |  .  .  .
--------------------------------------


Now we can easily see that it's an H4-Wing: (b)r1c4 = (b)r3c5 - (b=a)r3c3 - (a=bc)r1c14 => -b r1c23789, with the first link being a bilocation type. The first example can be written exactly the same way, ignoring the c in (bc)r3c5, so it's an H4-Wing as well.

The same is not true for blue's generalized examples, though:

Code: Select all

+-----------+------------+----------+
| abc -c -c |  bc -c  -c | -c -c -c |
|  .   .  . |  .   .   . |  .  .  . |
|  .   . ad |  .   bd  . |  .  .  . |   d=c is allowed
+-----------+------------+----------+

In that case the bivalue (bd)r3c5 is actually significant, and it can't be written as an H4-Wing. It's an overlapping ALS-XY-Wing.

The same here (blue's second example):

Code: Select all

+-----------+-----------+-------+
| abc -c -c |  ad  .  . | . . . |
| -c  -c -c |  .   .  . | . . . |
| -c  -c bc |  .   bd . | . . . | (d=c) is allowed
+-----------+-----------+-------+

That's not an H4-Wing either. (Again an overlapping ALS-XY-Wing.)

But this (blue's third example) is:

Code: Select all

+-----------+-----------+-------+
| abc  .  . |  ac  .  . | . . . |
| -c  -c -c |  .   .  . | . . . |
|  .   . bc |  .   bc . | . . . |
+-----------+-----------+-------+

...because it could be just as well this:

Code: Select all

+-------------+------------+-------+
| abc  .   .  |  ac  .   . | . . . |
| -c  -c  -c  |  .   .   . | . . . |
|  /   /   bc |  /   c+  / | / / / | ('/' -> no c in that cell
+-------------+------------+-------+  => bilocation strong link on c in row 3)


H4-Wing: (c)r3c3 = (c)r3c5 - (c=a)r1c4 - (a=bc)b1p19 => -c r2c123

(Edit: Actually, I think both of them should also get: -c r1c23.)

In other words, if one of the strong links is (or can be seen as) a bilocation (or grouped) type, this pattern is an H4-Wing. If all the strong links are bivalue or ALS types, it's not.

[rjamil]

Hi SpAce,

Thanks again for such an informative and descriptive reply.

And, yes, chaining is not my bread and butter. Actually, I am only looking and understand what is given in pattern forms atm.

Well, off topic, let me compare sudoku assumptive techniques with gambling, i.e., neither rocket science nor very complex mathematics involve, only luck (probability) works. (Throw a dice ten times. What is the probability of getting six all ten times?. Or, if nine times getting six, what is the probability if tenth time also six comes?) [If all ten times, six comes, then I will consider to replace the dice instead.] {Similarly, in monopoly game, if six comes by throwing a dice, another chance is given, if six comes second time then third chance is given. But, if third time, six comes, the turn is lapsed instead.}

Actually, your way of explaining XYZ-Wing Hybrid vs H4-Wing with exemplar forms simplify my concept and now I will definitely rethink about it that way. Also, will try to change my XYZ-Wing Hybrid routine to detect hybrid cell as bilocation digit instead of bivalue cell and see if it help to detect more cases.

By the way, I did not understand difference between H4-Wing and H6-Wing.

Similarly, I compiled H1-Wing as following exemplars:

Code: Select all

H1-Wing Type 1 (Row-Column wise):
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    /  +XZ   /  |  /   /   /  |  / +Z-Y /     /  +Z-X  /  |  /   /   /  |  / +YZ  /
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    .  XY    .  |  .   .   .  |  . XY   .     .  XY    .  |  .   .   .  |  . XY   .
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------  --------------+-------------+-----------

  --------------+-------------+-----------Bivalue r7c27
    .   /    .  |  .   .   .  |  .  /   . Strong Link Z @ r2c27
    / +Z-X   /  |  /   /   /  |  / +Z-Y / Strong Link X @ r27c2
    .   /    .  |  .   .   .  |  .  /   . Strong Link Y @ r27c7
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .  X-Y   .  |  .   .   .  |  . Y-X  .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------

However, there are lot of conversations involved to understand when Eureka notations and exemplar forms match. Like, for example, in Eureka, clues represent as X, Y, Z, etc., and cell as a, b, c, etc., whereas, in exemplar form, clues represent as A, B, C, etc., but no label given to cell.

Note: I see your reply, but, due editing, prefer to continue update the same post. (Sorry if it matters.)

R. Jamil

[SpAce]

Thanks again for such an informative and descriptive reply.

No problem. Glad if it helped!

And, yes, chaining is not my bread and butter. Actually, I am only looking and understand what is given in pattern forms atm.

I understand. Like I've said before, I would recommend studying chaining concepts too, because it makes it easier to see see the underlying differences and similarities in various patterns.

Actually, your way of explaining XYZ-Wing Hybrid vs H4-Wing with exemplar forms simplify my concept and now I will definitely rethink about it that way. Also, will try to change my XYZ-Wing Hybrid routine to detect hybrid cell as bilocation digit instead of bivalue cell and see if it help to detect more cases.

Logically it should find more cases that way. Please report if it actually does!

By the way, I did not understand difference between H4-Wing and H6-Wing.

Good for you because there isn't any (that would matter). It seems to me that StrmCkr's H4-Wing description is over-specified and should be replaced with the more generalized H6 description (*) (with some corrections). Also, the H5 should be a grouped subtype of H4 and not its own type (just like H1a, H2a, H3a). Furthermore, I think all of the H4, H5, and H6 descriptions/diagrams are flawed in various ways (mostly having unnecessary strong links), and should be replaced with one generalized and correctly described H4-Wing (with multiple examples of its various forms). The H1, H2, and H3 descriptions and their subtypes are correct (though H1 is not a real Hybrid Wing, having only bilocal strong links -- i.e. it should only be categorized as L3-Wing, as far as I'm concerned). Thus, the only H-Wing types I consider valid are: H2, H3, and H4 (and their subtypes).

(*) Based on that observation, you were actually correct when you wrote:

I strongly think that it's Dual H6-Wing (just like Dual Empty Rectangle).

But, like I said, there shouldn't even be an H6 (or H5) in the first place if H4 had a more generalized specification. That's why I prefer "Dual H4-Wing", because I'd like to get rid of H5 and H6.

[rjamil]

Hi SpAce,

(Edit: Actually, I think both of them should also get: -c r1c23.)

I don't agree with that, actually, Hybrid Wing move detection should be after basic XY- & XYZ-Wing move, therefore, -c r1c23 is unnecessary, as if hybrid cell make naked pair with either wing cell case, no need to be eliminate c from common cells of naked pair. (Also, as in the case of bilocation clue with either wing cell case.)

R. Jamil

[SpAce]

Similarly, I compiled H1-Wing as following exemplars:

First, I repeat myself but I don't think there should be any H1-Wing at all, because it's not logically a hybrid wing (using the logic of a "hybrid" having both bivalue and bilocal strong links -- it only has bilocal strong links which makes it an L3-Wing). Second, your first two examples are H2-Wings, not L3-Wings. The third example is a combination of one L3-Wing and two H2-Wings. All the eliminations in it are valid, but I don't think there's any wing type that would explain them all at once.

Code: Select all

H1-Wing Type 1 (Row-Column wise):
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    /  +XZ   /  |  /   /   /  |  / +Z-Y /     /  +Z-X  /  |  /   /   /  |  / +YZ  /
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
    .  XY    .  |  .   .   .  |  . XY   .     .  XY    .  |  .   .   .  |  . XY   .
    .   /    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------  --------------+-------------+-----------

H2-Wing: (Y=X)r8c8 - (X)r8c2 = (X-Z)r2c2 = (Z)r2c8 => -Y r2c8 (left)
H2-Wing: (X=Y)r8c2 - (Y)r8c8 = (Y-Z)r2c8 = (Z)r2c8 => -X r2c2 (right)

Code: Select all

  --------------+-------------+-----------Bivalue r7c27
    .   /    .  |  .   .   .  |  .  /   . Strong Link Z @ r2c27
    / +Z-X   /  |  /   /   /  |  / +Z-Y / Strong Link X @ r27c2
    .   /    .  |  .   .   .  |  .  /   . Strong Link Y @ r27c7
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .  X-Y   .  |  .   .   .  |  . Y-X  .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------

L3-Wing: (X)r8c2 = (X-Z)r2c2 = (Z-Y)r2c8 = (Y)r8c8 => -X r8c8, -Y r8c2
H2-Wing: (Y=X)r8c8 - (X)r8c2 = (X-Z)r2c2 = (Z)r2c8 => -Y r2c8
H2-Wing: (X=Y)r8c2 - (Y)r8c8 = (Y-Z)r2c8 = (Z)r2c8 => -X r2c2

[SpAce]

Hi SpAce,

(Edit: Actually, I think both of them should also get: -c r1c23.)

I don't agree with that, actually, Hybrid Wing move detection should be after basic XY- & XYZ-Wing move, therefore, -c r1c23 is unnecessary, as if hybrid cell make naked pair with either wing cell case, no need to be eliminate c from common cells of naked pair. (Also, as in the case of bilocation clue with either wing cell case.)

That's just an arbitrary rule. There's no need to abide by any hierarchy of moves so there's nothing wrong with using a more complicated move first. In fact, here it would be more efficient because we could get all the eliminations with just one move instead of two. Smart players use such shortcuts. Only typical software solvers are (by default) limited by fixed hierarchies, but it doesn't make sense for manual solving (at least for experienced players).

In any case, any such hierarchies shouldn't be a concern when describing the elimination potential of a single move. It is what it is, even if basics could take care of some of them.

[rjamil]

Hi SpAce,

There's no need to abide by any hierarchy of moves so there's nothing wrong with using a more complicated move first. In fact, here it would be more efficient because we could get all the eliminations with just one move instead of two. Smart players use such shortcuts. Only typical software solvers are (by default) limited by fixed hierarchies, but it doesn't make sense for manual solving (at least for experienced players).

In any case, any such hierarchies shouldn't be a concern when describing the elimination potential of a single move. It is what it is, even if basics could take care of some of them.

Well, no comments about that, it's a matter of individual taste. By the way JasonLion also preferred to include naked pair eliminations and basic XYZ-Wing eliminations with similar comments about ordering of moves in XYZ-Wing Hybrid move thread.

And, what about calling Dual H2-Wing move for L3-Wing move?

R. Jamil

[SpAce]

Well, no comments about that, it's a matter of individual taste.

It's certainly a matter of individual taste what kind of solving hierarchy you use when actually solving (it's part of the chosen strategy), but I don't think that's quite true when describing a move. I think every valid elimination produced by a particular pattern should be listed, without regard to any other patterns that might be contained. You should also include all valid eliminations when you code any pattern, unless you want to be forever bound to a particular solving hierarchy. Otherwise, if you reorder or turn off some techniques, you'll miss eliminations. I think it's a fundamental mistake if you build such interdependencies between your of techniques.

By the way JasonLion also preferred to include naked pair eliminations and basic XYZ-Wing eliminations with similar comments about ordering of moves in XYZ-Wing Hybrid move thread.

Yep. Personally I wouldn't include the naked pair eliminations because they're obvious anyway and not a core functionality of the pattern, but strictly speaking they should be there too. However, Jason's comments referred to the original version of the pattern which unnecessarily includes the naked pair. My generalized version doesn't, so it's not an issue anyway. I would definitely include the contained XYZ-Wing eliminations because it shouldn't be assumed that the user of the pattern chooses to use an XYZ-Wing first (or at all). As far as I'm concerned, every pattern should be described in isolation with no assumptions about a solving hierarchy (except maybe basics). It doesn't matter if it has overlapping eliminations with contained simpler techniques -- they're still valid eliminations of that pattern and should be listed.

And, what about calling Dual H2-Wing move for L3-Wing move?

I guess that interesting combo pattern might deserve its own name (or not), but I have no clue what it could be. Have you seen it before or did you imagine it yourself? Do you have any real examples of it? It's a pretty cool pattern! (Then again, in practice it's simplest to see it as any one of the contained Wings, because any single one of them would produce the same eliminations with ripple effects.)

[rjamil]

Hi SpAce,

I guess that interesting combo pattern might deserve its own name, but I have no clue what it could be. Have you seen it before or did you imagine it yourself? Do you have any real examples of it? It's a pretty cool pattern!

Code: Select all

  --------------+-------------+-----------Bivalues XY @ r7c27
    .   /    .  |  .   .   .  |  .  /   . Strong Link Z @ r2c27
    / +Z-X   /  |  /   /   /  |  / +Z-Y / Strong Link X @ r27c2
    .   /    .  |  .   .   .  |  .  /   . Strong Link Y @ r27c7
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------
    .   /    .  |  .   .   .  |  .  /   .
    .  X-Y   .  |  .   .   .  |  . Y-X  .
    .   /    .  |  .   .   .  |  .  /   .
  --------------+-------------+-----------

As far as above mentioned pattern is concern, just copy/paste below code in to HoDoKu and press "find all steps". There are four Discontinuous Nice Loop found. I combined all-in-one and got the same pattern:

Code: Select all

123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789
12456789  12456789  123456789 123456789 12456789  12456789  12456789  12456789  12456789
123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789
123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789
123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789
123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789
123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789
3456789   3456789   12        12        3456789   3456789   3456789   3456789   3456789
123456789 123456789 23456789  13456789  123456789 123456789 123456789 123456789 123456789

Actually, your way of explaining XYZ-Wing Hybrid vs H4-Wing with exemplar forms simplify my concept and now I will definitely rethink about it that way. Also, will try to change my XYZ-Wing Hybrid routine to detect hybrid cell as bilocation digit instead of bivalue cell and see if it help to detect more cases.

Logically it should find more cases that way. Please report if it actually does!

Yep. Personally I wouldn't include the naked pair eliminations because they're obvious anyway and not a core functionality of the pattern, but strictly speaking they should be there too. However, Jason's comments referred to the original version of the pattern which unnecessarily includes the naked pair. My generalized version doesn't, so it's not an issue anyway. I would definitely include the contained XYZ-Wing eliminations because it shouldn't be assumed that the user of the pattern chooses to use an XYZ-Wing first (or at all). As far as I'm concerned, every pattern should be described in isolation with no assumptions about a solving hierarchy (except maybe basics). It doesn't matter if it has overlapping eliminations with contained simpler techniques -- they're still valid eliminations of that pattern and should be listed.

Well, if searched H?-Wing before naked pair then it might be missing some cases (I think).

R. Jamil

[SpAce]

As far as above mentioned pattern is concern, just copy/paste below code in to HoDoKu and press "find all steps". There are four Discontinuous Nice Loop found. I combined all-in-one and got the same pattern:

Thanks, but I did that already before (no real need but I just wanted to see that Hodoku agreed with what I saw). Do you have any real examples of the pattern?

[rjamil]

Hi SpAce,

Just try the pattern in this thread op puzzle.

R. Jamil

[SpAce]

Just try the pattern in this thread op puzzle.

I don't see it. Simpler if you just show me what you mean.