Do these WXYZ-Wing patterns have special name?

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Do these WXYZ-Wing patterns have special name?

Postby rjamil » Sat Mar 09, 2019 6:48 pm

Hi experts,

I am learning Sudoku techniques from puzzles topic of this forum. Currently I am focusing on WXYZ-Wing move and studying various patterns of the same, i.e., four cells contain four clues in total.

Recently, found XY-Ring move (that looks alike WXYZ-Wing move) and trying to figure out all its patterns for analyzing and coding purpose.

Here I am sharing another combination of patterns, which are also part of Almost Locked Set move patterns, as follows:
Code: Select all
Almost Locked Set Type 1a (Rows-Columns wise):
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .
   -Z  xyz  -Z  | -Z  -Z  -Z  | -Z yz  -Z
    .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .
    .  wx    .  |  .   .   .  |  . wy   .
    .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
Almost Locked Set Type 2a (Boxes-Lines wise):
  --------------+-------------+-----------  --------------+-------------+-----------
01)-Z  xyz  -Z  | yz  -YZ -YZ | -Z -Z  -Z 02)-Z  xyz  -Z  | wx   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .    -Z  -Z   -Z  |  .   .   .  |  .  .   .
    .   .   wx  |  .  wy   .  |  .  .   .    -YZ -YZ  yz  |  .  wy   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

  --------------+-------------+-----------
03)-Z  xyz  -Z  | wx   .   .  |  .  .   .
   -Z  -Z   -Z  |  .   .   .  |  .  .   .
   -YZ yz   -YZ |  .  wy   .  |  .  .   .
  --------------+-------------+-----------
    .  -Z    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
    .  -Z    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------

If the above mentioned patterns are correct (WXYZ-Wing move patterns?) then is/are there any special name(s) for them or are they simply called (extended) WXYZ-Wing move patterns?

R. Jamil

Edited to reflect additional -Y eliminations as per below given StrmCkr directions.
Edit as on 20190411 and relabeled WXYZ-Wing move to Almost Locked Set move.
Last edited by rjamil on Thu Apr 11, 2019 11:48 am, edited 2 times in total.
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Re: Do these WXYZ-Wing patterns have special name?

Postby StrmCkr » Sat Mar 09, 2019 7:58 pm

simply called (extended) WXYZ-Wing move patterns


these moves fall under the "theorized" patterns of the wxyz- thread i created specifically found here

these "4" eliminations are almost almost locked set conditions.
the "3" is the als-xz condition.
Code: Select all
+---------------+------------+--------------+
| .   .      .  | .   .   .  | .   .     .  |
| -4  (234)  -4 | -4  -4  -4 | -4  (34)  -4 |
| .   .      .  | .   .   .  | .   .     .  |
+---------------+------------+--------------+
| .   .      .  | .   .   .  | .   .     .  |
| .   .      .  | .   .   .  | .   .     .  |
| .   .      .  | .   .   .  | .   .     .  |
+---------------+------------+--------------+
| .   .      .  | .   .   .  | .   .     .  |
| .   (12)   .  | .   .   .  | .   (13)  .  |
| .   .      .  | .   .   .  | .   .     .  |
+---------------+------------+--------------+


Code: Select all
+-----------------+----------------+------------+
| .   .      .    | .     .     .  | .   .   .  |
| -4  (234)  -4   | (34)  -34   -34| -4  -4  -4 |
| .   .      (12) | .     (13)  .  | .   .   .  |
+-----------------+----------------+------------+
| .   .      .    | .     .     .  | .   .   .  |
| .   .      .    | .     .     .  | .   .   .  |
| .   .      .    | .     .     .  | .   .   .  |
+-----------------+----------------+------------+
| .   .      .    | .     .     .  | .   .   .  |
| .   .      .    | .     .     .  | .   .   .  |
| .   .      .    | .     .     .  | .   .   .  |
+-----------------+----------------+------------+


Code: Select all
+-----------------+---------------+---------+
| -4  -4     -4   | .     .     . | .  .  . |
| -4  (234)  -4   | (12)  .     . | .  .  . |
| -34  -34    (34) | .     (13)  . | .  .  . |
+-----------------+---------------+---------+
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
+-----------------+---------------+---------+
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
+-----------------+---------------+---------+

Code: Select all
 
+-----------------+---------------+---------+
| -4   -4     -4  | .     .     . | .  .  . |
| -4   (234)  -4  | (12)  .     . | .  .  . |
| -34  (34)   -34 | .     (13)  . | .  .  . |
+-----------------+---------------+---------+
| .    -4     .   | .     .     . | .  .  . |
| .    -4     .   | .     .     . | .  .  . |
| .    -4     .   | .     .     . | .  .  . |
+-----------------+---------------+---------+
| .    -4     .   | .     .     . | .  .  . |
| .    -4     .   | .     .     . | .  .  . |
| .    -4     .   | .     .     . | .  .  . |
+-----------------+---------------+---------+


edit: updated post
Udate corrected eliminations
Last edited by StrmCkr on Mon Mar 11, 2019 8:11 am, edited 2 times in total.
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Re: Do these WXYZ-Wing patterns have special name?

Postby rjamil » Sat Mar 09, 2019 8:07 pm

Hi StrmCkr,

Code: Select all
+-------------+---------------+---------+
| .  -4     . | .     .     . | .  .  . |
| .  (234)  . | (12)  .     . | .  .  . |
| .  (34)   . | .     (13)  . | .  .  . |
+-------------+---------------+---------+
| .  -4     . | .     .     . | .  .  . |
| .  -4     . | .     .     . | .  .  . |
| .  -4     . | .     .     . | .  .  . |
+-------------+---------------+---------+
| .  -4     . | .     .     . | .  .  . |
| .  -4     . | .     .     . | .  .  . |
| .  -4     . | .     .     . | .  .  . |
+-------------+---------------+---------+

My question is, why b1 other cells do not exclude -4 as well (as if r2c2 and r3c2 are not in same column case)?

R. Jamil
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sat Mar 09, 2019 8:50 pm

rjamil wrote:My question is, why b1 other cells do not exclude -4 as well (as if r2c2 and r3c2 are not in same column case)?

You're right; the b1 exclusions are valid as well.
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sat Mar 09, 2019 9:09 pm

StrmCkr wrote: these "z" eliminations are almost almost locked set conditions.

I would characterize them as overlapping ALS XY-Wings (but I'm not claiming it's the only way to see them). On the other hand, normal WXYZ-Wings are simply ALS XZ patterns. I think that's a significant difference, so personally I'd hesitate calling these patterns WXYZ-Wings, but I guess it all depends on how you define a WXYZ-Wing.
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Re: Do these WXYZ-Wing patterns have special name?

Postby rjamil » Sat Mar 09, 2019 9:43 pm

Hi SpAce,

Many thanks for the confirmation. Actually, I have derived such patterns from blue's post, that's why I thought they have some special name too (maybe WXYZ-Ring move patterns).

How to recognize these WXYZ-Wing move patterns are as follows:

Code: Select all
WXYZ-Wing (Rows-Columns wise):
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .
   -Z  xyz  -Z  | -Z  -Z  -Z  | -Z yz  -Z
    .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .
    .  wx    .  |  .   .   .  |  . wy   .
    .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------
a) Apex contains 3 clues;
b) 1st Wing within Apex Row but not Box and contains 2 clues;
c) Apex and 1st Wing contain 3 clues;
d) 2nd Wing within Apex Column but not Box and contains 2 clues;
e) Apex and 2nd Wing contain 4 clues;
f) 1st and 2nd Wings contain 4 clues;
g) 3rd Wing within 1st Wing Column and 2nd Wing Row and contains 2 clues;
h) 1st and 3rd Wings contain 3 clues;
i) 2nd and 3rd Wings contain 3 clues;
j) Apex and 3rd Wing contain 4 clues;
k) 1st Wing clue not in 3rd Wing may be excluded from Apex and 1st Wing Row other cells.
Note: Row can be replaced by Column (as suggested by JasonLion here).

Code: Select all
WXYZ-Wing (Boxes-Lines wise):
  --------------+-------------+-----------
01)-Z  xyz  -Z  | yz  -Z  -Z  | -Z -Z  -Z
    .   .    .  |  .   .   .  |  .  .   .
    .   .   wx  |  .  wy   .  |  .  .   .
  --------------+-------------+-----------
a) Apex contains 3 clues;
b) 1st Wing within Apex Line but not Box and contains 2 clues;
c) Apex and 1st Wing contain 3 clues;
d) 2nd Wing within Apex Box but not 1st Wing Line and contains 2 clues;
e) Apex and 2nd Wing contain 4 clues;
f) 1st and 2nd Wings contain 4 clues;
g) 3rd Wing within 1st Wing Box and 2nd Wing Line and contains 2 clues;
h) 1st and 3rd Wings contain 3 clues;
i) 2nd and 3rd Wings contain 3 clues;
j) Apex and 3rd Wing contain 4 clues;
k) 1st Wing clue not in 3rd Wing may be excluded from Apex and 1st Wing Line other cells.

  --------------+-------------+-----------  --------------+-------------+-----------
02)-Z  xyz  -Z  | wx   .   .  |  .  .   . 03)-Z  xyz  -Z  | wx   .   .  |  .  .   .
   -Z  -Z   -Z  |  .   .   .  |  .  .   .    -Z  -Z   -Z  |  .   .   .  |  .  .   .
   -Z  -Z   yz  |  .  wy   .  |  .  .   .    -Z  yz   -Z  |  .  wy   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
                                              .  -Z    .  |  .   .   .  |  .  .   .
                                              .  -Z    .  |  .   .   .  |  .  .   .
                                              .  -Z    .  |  .   .   .  |  .  .   .
                                            --------------+-------------+-----------
                                              .  -Z    .  |  .   .   .  |  .  .   .
                                              .  -Z    .  |  .   .   .  |  .  .   .
                                              .  -Z    .  |  .   .   .  |  .  .   .
                                            --------------+-------------+-----------
a) Apex contains 3 clues;
b) 1st Wing within Apex Line but not Box and contains 2 clues;
c) Apex and 1st Wing contain 4 clues;
d) 2nd Wing within Apex Box but not 1st Wing Line and contains 2 clues;
e) Apex and 2nd Wing contain 3 clues;
f) 1st and 2nd Wings contain 4 clues;
g) 3rd Wing within 1st Wing Box and 2nd Wing Line and contains 2 clues;
h) 1st and 3rd Wings contain 3 clues;
i) 2nd and 3rd Wings contain 3 clues;
j) Apex and 3rd Wing contain 4 clues;
k) 2nd Wing clue not in 3rd Wing may be excluded from Apex and 2nd Wing Box other cells.
l) If Apex and 2nd Wing within Line then 2nd Wing clue not in 3rd Wing may also be excluded from Apex and 2nd Wing Line but not Box.
Note: a Line could be either a Row or a Column.

Note: The above WXYZ-Wing (or WXYZ-Ring) move patterns recognition is similar to as XY-Ring move patterns, except Apex cell contains either two or three clues and number of exclusions.

R. Jamil
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sat Mar 09, 2019 10:26 pm

Hi rjamil,
rjamil wrote:Many thanks for the confirmation. Actually, I have derived such patterns from blue's post, that's why I thought they have some special name too (maybe WXYZ-Ring move patterns).

Definitely not any kind of rings, as rings are loops and these are not! Seems that blue said exactly what I said above: they're special cases (overlapping) of ALS-XY-Wings. Why not call them WXYZ-Hybrids if you're already calling those similar 3-digit patterns XYZ-Hybrids? These are very similar, except with four digits. Other than that, I have little to contribute. I'm mostly with Phil:

pjb wrote:Why should we have all this complicated argument about naming of patterns when all we have here is a simple chain with an ALS on the end ... For me, if its a chain then its a chain (even XY wings!)
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sat Mar 09, 2019 10:51 pm

rjamil wrote:Recently, found XY-Ring move (that looks alike WXYZ-Wing move) and trying to figure out all its patterns for analyzing and coding purpose.

As I stated in that post, the XY-Ring could conceivably be called WXYZ-Ring, because it can be considered a looping WXYZ-Wing. For me a defining feature of any (VW)XYZ-Wing is that it can be described as an ALS-XZ, which is true for the XY-Ring. It just happens to be a doubly-linked ALS-XZ, which means a loop, which in wing-terminology is called a ring. That's why I thought WXYZ-Ring would have been a logical name, but since the pattern already has a name, there's no need to confuse things.

On the other hand, these extended patterns are neither ALS-XZ nor loops, so they're very different beasts. Definitely not rings, but any other characterizations are debatable I guess.
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Re: Do these WXYZ-Wing patterns have special name?

Postby StrmCkr » Sun Mar 10, 2019 10:09 am

My question is, why b1 other cells do not exclude -4 as well (as if r2c2 and r3c2 are not in same column case)?
i was still editing the puzzles when i had to go to work, post is updated above.

so they're very different beasts
exactly, they are Almost almost Locked sets as i mentioned before and was pointed out by ronk and blue way back in my wxyz-thread
were i first purposed the existence of such beasties

the first one i found is this one..
Code: Select all
Almost Locked Set XY-Wing: A=r3c27 {234}, B=r23c2 {124}, C=r2c7 {13}, X,Y=1,3, Z=2,4 => r3c13<>2, r3c13<>4
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     (124)  .   | .  .  . | (13)  .      . |
| (24)  -24    -24 | .  .  . | .     (234)  . |
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
+------------------+---------+----------------+


my temp glitchy code from long ago came up with this

Code: Select all
 might actually break the mold.
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     (123)  .  | .  .  . | (14)  -2  -2 |
| (34)  -2     -2 | .  .  . | (24)  .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+


it was suggested i develop them in their own niche thread under a AALS-xz rule context i was going to do so however
my general consensus was considering so few examples found and or produced most of those happened to be already covered under the als-xy rule thus I relegated the effect to "already covered".

these ones might put me back on the fence to code and test them out, but i doubt it once i do some digging ill know for sure.

there is advanced rules
http://forum.enjoysudoku.com/almost-locked-rules-for-now-t2510.html for more complicated als formations.
probably covered under one of them... but i wouldn't know for sure as i don't have them all coded to test out. {have to do some digging}

the als stuff i do have coded didn't hit the eliminations Edit: same fix below resolved the no finding issue in my als-xy code.

edit found it:

Code: Select all
.---------------------------------.---------------------------------.---------------------------------.
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  234        123456789 | 12         123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  34         123456789 | 123456789  13         123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
'---------------------------------'---------------------------------'---------------------------------'

Almost Locked Set XY-Wing: A=r3c25 {134}, B=r23c2 {234}, C=r2c4 {12}, X,Y=1,2, Z=3,4 => r3c13<>3, r1c123,r2c13,r3c13,r456789c2<>4
{had to turn on allow "overlap" in hodoku and in my code}
Last edited by StrmCkr on Sun Mar 10, 2019 9:05 pm, edited 2 times in total.
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sun Mar 10, 2019 2:05 pm

StrmCkr wrote:
so they're very different beasts
exactly, they are Almost almost Locked sets as i mentioned before and was pointed out by ronk and blue way back in my wxyz-thread

I think you're talking about a different thing. I don't see anything AALS in the earlier examples above. Like I (and blue, and your own copy of Hodoku) have said: they're overlapping ALS-XY-Wings. Nothing more complicated than that.

Your example here is something else:

Code: Select all
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     (123)  .  | .  .  . | (14)  -2  -2 |
| (34)  -2     -2 | .  .  . | (24)  .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
| .     .      .  | .  .  . | .     .   .  |
+-----------------+---------+--------------+

I don't think that can be described as any normal ALS move at all. As a chain it requires branching (unlike ALS-XZ or -XY moves, overlapping or not). That's why I don't think that example should be put in the same basket as the earlier examples. You need a third category for these because they're clearly more complex specimens.

it was suggested i develop them in their own niche thread under a AALS-xz rule context

I guess the above example might belong there. It does have visible AALS nodes, but the earlier examples did not. Then again, I wouldn't know how you'd describe it as an AALS move either. I just see it as a split-node AIC:

Code: Select all
(2=4)r3c7 - (4=13)r2c7,r3c1 - (1|3=2)r2c2 => -2 r2c89,r3c23

or a Kraken Cell:

Code: Select all
(1)r2c2 - (1=42)r23c7
||
(2)r2c2
||
(3)r2c2 - (3=42)r3c17

Maybe the Kraken gives a hint to how it could be seen as an AALS move:

Code: Select all
AALS A: (123)r2c2
 ALS B: (124)r23c7
 ALS C: (234)r3c17

X=1, Y=3, Z=2

But I'm just guessing. If I try to write it as truths and links, I get something like this:

Code: Select all
Siamese Alien 4-Fish (Mixed Rank 2|1; link triplet @4r3c7)

{2N27 3N17} \ {1r2 2r2b3|2r3b1 3b1 4r3c7} => -2 r2c89,r3c23

but that's even more guesswork because I've never used XSudo.

there is advanced rules
http://forum.enjoysudoku.com/almost-locked-rules-for-now-t2510.html for more complicated als formations.
probably covered under one of them... but i wouldn't know for sure as i don't have them all coded to test out. {have to do some digging}

If anything, I guess it must be under the "2 ALS 2 restricted common" umbrella (or "n ALS n"). I can't think in those terms very well, so like I said, I'm just guessing.

edit found it:
...
Almost Locked Set XY-Wing: A=r3c25 {134}, B=r23c2 {234}, C=r2c4 {12}, X,Y=1,2, Z=3,4 => r3c13<>3, r1c123,r2c13,r3c13,r456789c2<>4
{had to turn on allow "overlap" in hodoku and in my code}

Yeah, but that's one of the earlier types, and Hodoku just agrees with what I said about them: overlapping ALS-XY-Wing. It's not an example of the more complex kind you just presented (which is not an ALS-XY-Wing, overlapping or not).

This overlapping ALS-XY-Wing I see as a simple AIC:

Code: Select all
(4=3)r3c2 - (3=12)b2p84 - (2=34)r23c2 => -4 c2,b1; (-3 r3c13)

(the 3-eliminations are because of the embedded shorter chain which is an ALS-XZ)

or as truths and links (smaller rank than the other):

Code: Select all
Siamese Alien 4-Fish (Mixed Rank 1|0; link triplet @3r3c2)

{2N24 3N25} \ {1b2 2r2 3r3b1 4c2|4b1} => -4 c2,b1; -3 r3c13

(Btw, since you have XSudo, can you tell me if my manual translations are even close to correct? I'm not at all sure about that triplet logic, which I tried the first time here.)
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Re: Do these WXYZ-Wing patterns have special name?

Postby StrmCkr » Sun Mar 10, 2019 9:12 pm

I don't think that can be described as any normal ALS move at all. As a chain it requires branching (unlike ALS-XZ or -XY moves, overlapping or not). That's why I don't think that example should be put in the same basket as the earlier examples. You need a third category for these because they're clearly more complex specimens.


think your right, i know my first oddity translated into an als-xy move easily.. {see updated post for that example}

the 2nd one below it diffidently wont fit it was found by a really off the way test engine i was attempting to code for finding als but it was way to glitchy to be useful.. it did however find this oddity.
Some do, some teach, the rest look it up.
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Re: Do these WXYZ-Wing patterns have special name?

Postby eleven » Sun Mar 10, 2019 9:15 pm

StrmCkr wrote:
Code: Select all
+-----------------+---------------+---------+
| -4  -4     -4   | .     .     . | .  .  . |
| -34 (234)  -34  | (12)  .     . | .  .  . |
| -4  -4     (34) | .     (13)  . | .  .  . |
+-----------------+---------------+---------+
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
+-----------------+---------------+---------+
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
+-----------------+---------------+---------+


Somewhere else i already mentioned my way to handle such patters:
4 digits 4 cells, either all digits are in the 4 cells or (at least) one is twice, i.e. in 2 different units. Here only 3 can be twice (in r2c2 and r3c5), forcing a 4 in r3c3.
So in both cases the 4 is restricted to r2c2 and r3c3.

But i can't see, why the 3 could be eliminated in r2c13 here.
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sun Mar 10, 2019 9:52 pm

eleven wrote:Somewhere else i already mentioned my way to handle such patters:
4 digits 4 cells, either all digits are in the 4 cells or (at least) one is twice, i.e. in 2 different units. Here only 3 can be twice (in r2c2 and r3c5), forcing a 4 in r3c3.
So in both cases the 4 is restricted to r2c2 and r3c3.

That works. Sounds somewhat similar to subset counting. (I just see it as a chain, as usual.)

But i can't see, why the 3 could be eliminated in r2c13 here.

I think it should be -3 r3c12 (via an embedded ALS-XZ):

Code: Select all
+-----------------+---------------+---------+
| -4  -4     -4   | .     .     . | .  .  . |
| -4  (234)  -4   | (12)  .     . | .  .  . |
| -34 -34    (34) | .     (13)  . | .  .  . |
+-----------------+---------------+---------+
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
+-----------------+---------------+---------+
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
| .   .      .    | .     .     . | .  .  . |
+-----------------+---------------+---------+

Overlapping ALS-XY-Wing with embedded ALS-XZ:

(4=3)r3c3 - (@3=12)b2p84 - (2=34)b1p59 => -4 b1; -3 r3c12
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Re: Do these WXYZ-Wing patterns have special name?

Postby SpAce » Sun Mar 10, 2019 10:13 pm

StrmCkr wrote:think your right, i know my first oddity translated into an als-xy move easily.. {see updated post for that example}
...
[the updated post:

the first one i found is this one..
Code: Select all
Almost Locked Set XY-Wing: A=r3c27 {234}, B=r23c2 {124}, C=r2c7 {13}, X,Y=1,3, Z=2,4 => r3c13<>2, r3c13<>4
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     (124)  .   | .  .  . | (13)  .      . |
| (24)  -24    -24 | .  .  . | .     (234)  . |
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
+------------------+---------+----------------+
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
| .     .      .   | .  .  . | .     .      . |
+------------------+---------+----------------+
]

Yes, I agree with this one. It's like the others except for the one weirdo. I also see it as:

Overlapping ALS-XY-Wing:

(24=3)r3c18 - (3=1)r2c7 - (1=24)b1p57 => -24 r3c23

the 2nd one below it diffidently wont fit it was found by a really off the way test engine i was attempting to code for finding als but it was way to glitchy to be useful.. it did however find this oddity.

Well, I think it's an interesting case! A lucky glitch in a way.
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Re: Do these WXYZ-Wing patterns have special name?

Postby eleven » Sun Mar 10, 2019 10:41 pm

SpAce wrote:I think it should be -3 r3c12 (via an embedded ALS-XZ):

Right, in both cases the 3 must be in r2c2 or r3c35.

[Added:]
SpAce wrote:That works. Sounds somewhat similar to subset counting. (I just see it as a chain, as usual.)

No, i read that thread now, but i can't see a common point.
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