## What is XYZ-Wing Hybrid strategy?

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

### Re: What is XYZ-Wing Hybrid strategy?

Your examples are correct, but they're so theoretical that I'm not sure I see their point in this context.

Moslty the point was to show the diffrence of digit linking vrs spacial linking. And that reductions are applicable to more then just er patterms and often ignored for simpler approaches like the blr they harbour.

As tarric mentioned mini row minincols show no diffrence between 1 or 3 digits as its reduces to one.
my theoretical examples threw a wrench in my early codes for a skyscraper as it was built using mini rows.. I had to re conceptualize the eliminations because of it.

my 2 string kite code was also built using eri cells searching outwards Not identifing the hinge as on or off borked that idea quickly becaus both r/c could be true and no longer acted as link between row or col. once i fixed that the code worked.

I had examples for complex fish using eris where some of them onky functioned when 1 ore more of them had empty eri cells.
Brdiging muti ers to 2 string kites. (but keep the center cells on the 2 strings as active and not knowing they are 2 string kites is basically what they resembled..

Yes it is easier to build 2 string kites out side box first.

The real point is to note that eris are link node.
Used for er pattern regardless of eri on/off(basic) they function as a move center node.
but when used as links knowing the status of the center cell allows it to be more then one type of link strong or weak.

Ps tarric
Andrews solver is bredth first and cant do depth it also cant find shortest path for solutioms because of bredth.

Mines can exhaust singular or all techniques at any instance of solving steps. (makes it very slow)
Also allows for finding shorest path out of a group of solutions as well(manually for now) . It can also list how many moves there are and how many are dead end with no eliminations.(currently disabled in release version)
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

### Re: What is XYZ-Wing Hybrid strategy?

Hi SpAce,

SpAce wrote:
In that case, let's wait for an expert/senior opinion.

And now this again:

If I missed any conclusion, presented by seniors/experts before, then accept my apology.

So you still don't count me as a "senior/expert". That's an understandable position, considering my short time around, but it also represents a certain lack of judgment. Length of experience is not always an accurate way to estimate someone's skills and depth of understanding. The quality of one's arguments should be. Besides, my shorter experience makes me probably better at seeing problems that old-time veterans have become blind to.

Believe me, I will definitely change my wordings at once after finalized. Meanwhile, please accept the same for the time being.

R. Jamil
rjamil

Posts: 596
Joined: 15 October 2014
Location: Karachi, Pakistan

### Re: What is XYZ-Wing Hybrid strategy?

Hi tarek,

tarek wrote:On a different matter here is an example with 2 different types of strong link groupings in a box:
Code: Select all
`+-------------------+-------------------+-------------------+| 6     9     5     | 237   1     278   | 2347  23478 2378  || 137   8     137   | 4    %237   9     | 6    %237   5     || 37    2     4     | 5     378   6     | 9     378   1     |+-------------------+-------------------+-------------------+| 13579 3456  1379  | 69   ^24578 ^24578| 2347  23478 23789 || 8     46    2     | 69    47    3     | 5     1     79    || 3579  345   379   | 1    ^24578 ^24578| 2347  6     23789 |+-------------------+-------------------+-------------------+| 2345  7     8     | 23    9     245   | 1    *235   6     || 2359  35    39    | 237   6     1     | 8    *2357  4     || 2345  1     6     | 8     23457 457-2 |*237   9    *237   |+-------------------+-------------------+-------------------+3 grouped strong links % ^ * r9c6<>2Finned Franken Swordfish r2b59/c58b8 Fins r57c6, r9c79`

My solver detect in two separate steps as follows:
Code: Select all
` +-------------------+----------------------+-------------------------+ | 6      9     5    | [2]37  (1)     [2]78 | [2]347  (23478)  [2]378 | | 137    8     137  | 4      [2]37   9     | 6       [2]37    5      | | 37     2     4    | 5      378     6     | 9       378      1      | +-------------------+----------------------+-------------------------+ | 13579  3456  1379 | 69     24578   24578 | 2347    23478    23789  | | 8      46    2    | 69     47      3     | 5       1        79     | | 3579   345   379  | 1      24578   24578 | 2347    6        23789  | +-------------------+----------------------+-------------------------+ | 2345   7     8    | 23     9       245   | 1       [2]35    6      | | 2359   35    39   | 237    6       1     | 8       [2]357   4      | | 2345   1     6    | 8      3457-2  2457  | [2]37   (9)      [2]37  | +-------------------+----------------------+-------------------------+ERI 2 @ b2r1c5 Column 8 between ERI 2 @ b3r1c8 and ERI 2 @ b9r9c8 => -2 @ r9c5 +-------------------+---------------------+-------------------------+ | 6      9     5    | 2[3]7  (1)    278   | 2[3]47  (2347)8  2[3]78 | | 137    8     137  | 4      2[3]7  9     | 6       2[3]7    5      | | 37     2     4    | 5      [3]78  6     | 9       [3]78    1      | +-------------------+---------------------+-------------------------+ | 13579  3456  1379 | 69     24578  24578 | 2347    23478    23789  | | 8      46    2    | 69     47     3     | 5       1        79     | | 3579   345   379  | 1      24578  24578 | 2347    6        23789  | +-------------------+---------------------+-------------------------+ | 2345   7     8    | 23     9      245   | 1       2[3]5    6      | | 2359   35    39   | 237    6      1     | 8       2[3]57   4      | | 2345   1     6    | 8      457-3  2457  | 2[3]7   (9)      2[3]7  | +-------------------+---------------------+-------------------------+ERI 3 @ b2r1c5 Column 8 between ERI 3 @ b3r1c8 and ERI 3 @ b9r9c8 => -3 @ r9c5`

[Added as on 20191104] Following moves also detected by my solver along with above mentioned moves:
=> Empty Rectangle: ERI 7 @ b2r1c5 SL Row 5 between Cell 7 @ r5c5 and Cell 7 @ r5c9 => -7 @ r1c9
=> 3-Empty Rectangles: ERI 7 @ b2r1c5 Column 8 between ERI 7 @ b3r1c8 and ERI 7 @ b9r9c8 => -7 @ r9c5
=> 3-Empty Rectangles: ERI 3 @ b3r1c8 Row 9 between ERI 3 @ b9r9c8 and ERI 3 @ b8r9c4 => -3 @ r1c4
=> Empty Rectangle: ERI 7 @ b3r1c8 SL Row 8 between Cell 7 @ r8c8 and Cell 7 @ r8c4 => -7 @ r1c4
=> Empty Rectangle: ERI 7 @ b3r1c8 SL Column 4 between Cell 7 @ r1c4 and Cell 7 @ r8c4 => -7 @ r8c8
=> Empty Rectangle: ERI 7 @ b3r1c8 Row 9 between ERI 7 @ b9r9c8 and ERI 7 @ b8r9c4 => -7 @ r1c4
=> Empty Rectangle: ERI 7 @ b3r1c8 SL Column 4 between Cell 7 @ r1c4 and Cell 7 @ r8c4 => -7 @ r8c8
=> Empty Rectangle: ERI 7 @ b3r1c8 SL Row 8 between Cell 7 @ r8c8 and Cell 7 @ r8c4 => -7 @ r1c4
=> 3-Empty Rectangles: ERI 3 @ b8r9c4 Column 8 between ERI 3 @ b9r9c8 and ERI 3 @ b3r1c8 => -3 @ r1c4
=> 3-Empty Rectangles: ERI 7 @ b8r9c4 Column 8 between ERI 7 @ b9r9c8 and ERI 7 @ b3r1c8 => -7 @ r1c4
=> 3-Empty Rectangles: ERI 2 @ b9r9c8 Row 1 between ERI 2 @ b3r1c8 and ERI 2 @ b2r1c5 => -2 @ r9c5
=> Empty Rectangle: ERI 2 @ b9r9c8 SL Row 2 between Cell 2 @ r2c8 and Cell 2 @ r2c5 => -2 @ r9c5
=> 3-Empty Rectangles: ERI 3 @ b9r9c8 Row 1 between ERI 3 @ b3r1c8 and ERI 3 @ b2r1c5 => -3 @ r9c5
=> 3-Empty Rectangles: ERI 7 @ b9r9c8 Row 1 between ERI 7 @ b3r1c8 and ERI 7 @ b2r1c5 => -7 @ r9c5

(Need to check and omit duplicate moves detections for ER patterns.)

Please note that, I have also solved your pencilmark grid previously but forgot to mentioned for which accept my apology.

R. Jamil
Last edited by rjamil on Mon Nov 04, 2019 3:54 pm, edited 1 time in total.
rjamil

Posts: 596
Joined: 15 October 2014
Location: Karachi, Pakistan

### Re: Empty mini-Area EmA

I'm hoping that this would be the last of the terminology sessions.

I came to the conclusion that the term Empty rectangle must only be used to describe a Single grouped strong link in a box where the inference of the strong link is derived from a mini-column and mini-row within that box.

We shouldn't therefore use "Empty rectangle" to describe a pattern of 2 strong links (one in a line and the other a grouped strong link in box). The term should be used to simplify the description of that Grouped strong link when used within a pattern (e.g. W-wing using an empty rectangle) (e.g. 2 strong links pattern using an empty rectangle)

the following is an attempt to categorize these Grouped strong links in location with a view to simplify description and reduce current confusion about terminology:

Code: Select all
`Empty mini-Area (EmA):======================1. Empty mini-Rectangle (EmR):------------------------------+---------+| .  X (X)|| X  /  / ||(X) /  / |+---------+Commonly referred to as Empty Rectangle(ER)2. Empty mini-Line (EmL):-------------------------These have 4 varietiesa. in a Line (rows)+-------+------+-------+|X(X) . |X . . | / / / ||. .  . |. . . | . . . ||. .  . |. . . | . . . |+-------+------+-------+b. in a Line (columns)+-------+| X . . ||(X). . || . . . |+-------+| X . . || . . . || . . . |+-------+| / . . || / . . || / . . |+-------+c. in a box (mini-rows)+--------+| X(X)(X)|| X(X) . || / /  / |+--------+d. in a box (mini-columns)+-------+| X  X /||(X)(X)/||(X) . /|+-------+`

The exemplars above are what defines each category when all parenthesized candidates are present (regardless on how the dotted cells are filled). Any reduction in the number of candidates within parenthesis with how the dotted cells are filled can lead to equivalence between some of these categories and may lead to a simple strong link in location (conjugate pair) when reduced to 2 candidate exemplar.

[Edit: corrected an error in exemplar]
[Edit2: Adjusted the wording of last paragraph]
[Edit3: Adjusted EmL 3 4 exemplar due to equivalence in some cases]
Last edited by tarek on Sun Nov 03, 2019 3:47 pm, edited 2 times in total.

tarek

Posts: 3745
Joined: 05 January 2006

### Re: What is XYZ-Wing Hybrid strategy?

SpAce,
I haven't gone as far as looking to the weak links yet

StrmCkr,
Thanks … yes I agree but he decided to show all available Empty rectangles at once in his solver.

rjamil,
Thanks for the clarification. I'm also aware of that stupid typo I still make with the "/" on this keyboard I'm using

tarek

Posts: 3745
Joined: 05 January 2006

### Re: What is XYZ-Wing Hybrid strategy?

here you go, all the "empty" mini line formations
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

### Re: What is XYZ-Wing Hybrid strategy?

here you go, all the "empty" mini line formations

Thanks,
Have you described or came across what I described above as EmL types c or d where the inference of a strong link is derived from 2 parallel mini lines in a box?

Code: Select all
`+----------------------+----------------------+----------------------+| 5689   59     569    | 1      2      3      |*589    7      4      || 1789   4      12379  | 89     5      789    |*12389  6     *389    || 15789  123579 1359   | 46     789    46     |*13589  12    *3589   |+----------------------+----------------------+----------------------+| 2      159    1589   | 356    389    1568-9 | 4      389    7      || 3      6      17     |^89     4      17     |^89     5      2      || 4      579    5789   | 2      3789   578-9  | 6      389    1      |+----------------------+----------------------+----------------------+| 15679  123579 135679 | 345    389    4589   | 17     12     3569   || 17     8      127    | 35     6     %59     | 127    4     %359    || 569    359    4      | 7      1      2      | 3589   89     35689  |+----------------------+----------------------+----------------------+3-Turbot Crane (using 1 grouped strong link)9:* ^ % r46c6<>9b3 has an EmL type c/db1r58\c79b5 fin r8c6 r46c6<>9+-------------------+-------------------+-------------------+| 268   7     249   | 1248  28    5     | 369   36    139   || 3     5     29    | 127   79    26    | 4     68    189   || 689   469   1     | 489   3     46    | 2     7     5     |+-------------------+-------------------+-------------------+| 7     1     359   | 23458 28   %234   |*39   *2348  6     || 269   269-3 8     | 234   1     7     | 5    *234  *239   || 4     23    235   | 2358  6     9     | 7     1     28    |+-------------------+-------------------+-------------------+| 259   8     7     | 239   4     1     | 36    2356  23    || 259  ^239   6     | 237   79    8     | 1     235   4     || 1    ^234  ^234   | 6     5    %23    | 8     9     7     |+-------------------+-------------------+-------------------+3-Turbot Crane (using 2 grouped strong links)3:* ^ % r5c2<>3b5 has an EmL type c/dc6b67\r49b4 fins r5c89, r8c2`

There are often Grouped Strong links in a line (Type a/b) that complement them unless the value is uncovered and placed in the complimentary line.

tarek

tarek

Posts: 3745
Joined: 05 January 2006

### Re: What is XYZ-Wing Hybrid strategy?

one reason why you may use these EmL c/d when there is actually a complementary EmL a/b is to avoid base sector intersection (i.e. creating an endofin). Despite the logic still holding, it may further complicate what should be an easier to spot technique. I have decided in the Sukaku explainer to prevent base sector overlap and this will deliver more EmL type c/d or miss some pattern eliminations. These would hopefully get picked up with the generalised technique solver or a complex fish catcher.

Tarek

tarek

Posts: 3745
Joined: 05 January 2006

### Re: What is XYZ-Wing Hybrid strategy?

Yes i have actually alot since i program using mini sectors for rows, cols and again for row/col defined by box.
Which is 4x3x27 mini sectors
comes up with equivalent moves for m, s, l, w, h, wings when i implmented the box version.
a few confirmed versions are found in the m wing thread
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

### Re: What is XYZ-Wing Hybrid strategy?

StrmCkr wrote:Yes i have actually alot since i program using mini sectors for rows, cols and again for row/col defined by box.
Which is 4x3x27 mini sectors

Thanks

tarek

Posts: 3745
Joined: 05 January 2006

### Re: What is XYZ-Wing Hybrid strategy?

In Sukaku explainer the finalized L1 pattern names will be (X is the number of strong links):
X Skyscrapers: Parallel strong links in lines
X-String Kite: Mixed Line type Strong links (No boxes)
X Turbot Blocks: Only boxes strong links (No lines). "Block" is the word used by SE to describe "Box"
X-Turbot Crane: Box and Line mixture
Added in parenthesis would be the number of Grouped strong links if used

I hope that this is fair and would put an end to some the confusion about technique names. In the technique explanation I do mention that it is part of x-chains which is then part of AIC and mentioned that the popular name of "empty rectangle" is used to describe a type of grouped strong link in a box (EmR)

I did mention that I'll avoid (at this time) Strong link intersections in Sukaku Explainer to avoid the "endofin" just because to my eyes it complicates an otherwise a "simpler to spot technique"

tarek

Posts: 3745
Joined: 05 January 2006

### Re: What is XYZ-Wing Hybrid strategy?

Based on empirical tests, Types D1 and D2 below are equivalent:
Code: Select all
` -b  .  a |  .  .  . |  .  .  .       -b  .  . |  .  .  . |  .  .  .-b ab  a |  .  .  . |  .  .  .       -b ab  . |  .  .  . |  .  .  .-b  .  a |  .  .  . |  .  .  .       -b  .  . |  .  .  . |  .  .  .---------+----------+----------      ---------+----------+---------- . -b  a |  .  .  . |  .  .  .        . -b  . |  .  .  . |  .  .  .ab -b  a |  .  .  . |  .  .  .       ab -b  . |  .  .  . |  .  .  . . -b  a |  .  .  . |  .  .  .        . -b  . |  .  .  . |  .  .  .---------+----------+----------      ---------+----------+---------- .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  . .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  . .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  . Type D1:                             Type D2:`

Found the thread with a clearer example. {w-wings}

Here is a technique set ive never seen used as its an inverted als works off the empty line intersections
http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html

in simplicity terms it is a hidden als
Last edited by StrmCkr on Fri Nov 08, 2019 8:10 am, edited 2 times in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

### Re: What is XYZ-Wing Hybrid strategy?

StrmCkr wrote:Based on empirical tests, Types D1 and D2 below are equivalent:

They're Grouped W-Wings:

(b=a)r2c2 - r123c3 = r456c3 - (a=b)r5c1 => -b r123c1,r456c2

(b=a)r2c2 - r789c2 = r789c1 - (a=b)r5c1 => -b r123c1,r456c2

Found the thread with a clearer example.

...of a completely different pattern! A much more interesting one, though, so thanks for that.

Here is a technique set ive never seen used as its an inverted als works off the empty line intersections
http://sudopedia.enjoysudoku.com/Almost_Locked_Candidates.html

The first example is a Grouped M2-Ring, just reusing some cells:

(x=y)r2c1 - r1c123 = (y-x)r1c4 = (x)r1c123 - loop => -xy b1p56789, -(~(xy)) r1c4

The same eliminations are available through a Sue de Coq / Doubly-Linked ALS-XZ. The above loop seems kind of like its hidden counterpart. I'm actually betting that a similar pattern always exists when a Sue de Coq is around. (Or rather, I'm sure of it.)

I don't know what to call the second example (a complex M2-Ring?), but it's a similar loop anyway:

(x=yz)r2c12 - (y|z)r1c123 = (yz-x)r1c45 = (x)r1c123 - loop => -xyz b1p6789, -(~(xyz)) r1c45

Again, a Sue de Coq with the same eliminations is available.

In both cases the cells r1c4 or r1c45 are not restricted to XY or XYZ values, unlike what the description seems to imply, but any other digits are eliminated from them afterwards. It's the same misconception as with the original M-Wing (until it was generalized). Only one bivalue/ALS node is needed for the pattern to work, as the other two strong links use location.

SpAce

Posts: 2559
Joined: 22 May 2017

### Re: What is XYZ-Wing Hybrid strategy?

The above loop seems kind of like its hidden counterpart
exactly what they are. the often forgotten and unused hidden als

unlike what the description seems to imply, but any other digits are eliminated from them afterwards. It's the same misconception as with the original M-Wing (until it was generalized).
good catch, also noted here

....its something that should have been developed further to find .... edit removed...

Code: Select all
`    -bce abce  a |  .  .  . |  .  .  .       -bce abce  . |  .  .  . |  .  .  .    -bce abce  a |  .  .  . |  .  .  .       -bce abce  . |  .  .  . |  .  .  .    -bce abce  a |  .  .  . |  .  .  .       -bce abce  . |  .  .  . |  .  .  .    ---------+----------+----------      ---------+----------+----------    abce -bce  a |  .  .  . |  .  .  .       abce -bce  . |  .  .  . |  .  .  .    abce -bce  a |  .  .  . |  .  .  .       abce -bce  . |  .  .  . |  .  .  .    abce -bce  a |  .  .  . |  .  .  .       abce -bce  . |  .  .  . |  .  .  .    ---------+----------+----------      ---------+----------+----------     .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .     .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .     .  .  / |  .  .  . |  .  .  .        a  a  / |  .  .  . |  .  .  .     Type D1:                             Type D2:`

now these are interesting. als a linked to als b using a single candidate which is the restricted common.
this is also something not done anywhere.
Code: Select all
`+----------------+------------------------+---------+| .  (1234)  .   | .       .       .      | .  .  . || .  (1234)  (1) | .       .       .      | .  .  . || .  (1234)  .   | .       .       .      | .  .  . |+----------------+------------------------+---------+| .  .       .   | .       .       .      | .  .  . || .  -234    (1) | (1234)  (1234)  (1234) | .  .  . || .  .       .   | .       .       .      | .  .  . |+----------------+------------------------+---------+| .  .       .   | .       .       .      | .  .  . || .  .       .   | .       .       .      | .  .  . || .  .       .   | .       .       .      | .  .  . |+----------------+------------------------+---------+`
Last edited by StrmCkr on Fri Nov 08, 2019 10:54 am, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

### Re: What is XYZ-Wing Hybrid strategy?

StrmCkr wrote: exactly what they are. the often forgotten and unused hidden als
...
good catch, also noted here

Ok, thanks for the confirmation! So nothing new under the sun, as I expected.

still its something that should have been developed further to find stuff like these...

I don't see any relation to the previous hidden pattern, because the link types don't match and there's no looping or reuse of cells. As before, these are just complex W-Wings using the VLV link-pattern where the V is an ALS (instead of a bivalue cell) and L is a grouped strong link (instead of a simple bilocation link). Much simpler than the previous pattern, I think. I might call them Grouped ALS-W-Wings:

(bce=a)r456c1 - r456c3 = r123c3 - (a=bce)r123c2 => -bce r123c1,r456c2

(bce=a)r456c1 - r789c1 = r789c2 - (a=bce)r123c2 => -bce r123c1,r456c2

now these are interesting. als a linked to als b using a single candidate which is the restricted common.
this is also something not done anywhere.

Oh, I'm sure it's done. It's just another example of an ALS-W-Wing, only simpler than the previous ones because the bilocation strong link is not grouped:

(234=1)r123c2 - r2c3 = r5c3 - (1=234)r5c456 => -234 r5c2

Anyone who understands chains and ALSs is certainly capable of spotting and using any of these. Such multi-elimination end points are just rare catches, so they're not often seen. Still I'm quite sure I've used something like this several times.

SpAce

Posts: 2559
Joined: 22 May 2017

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