The New Sudoku Players' Forum

[rjamil]

Hi all,

I need to know in detail about XYZ-Wing Hybrid strategy.

Searched this forum and found nothing. However, the term found in Rule 19A: XYZ-Wing Hybrid discovered by Pritt Galford.

Maybe the term also known as different name but I am new to this. Please help to understand with examples.

R. Jamil

[eleven]

Code: Select all

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


Either r1c4=b or: r1c4=c and (r3c5=b and) r3c3=a => r1c1=b
So one of r1c1 and r1c4 must be b.

[rjamil]

Hi eleven,

Thanks for providing clear picture of XYZ-Wing Hybrid strategy.

However, need further clarification regarding proper definition.

What I understand from above scenario is as follows:
1) XYZ-Wing Hybrid strategy is based on four cells, i.e., one pivot cell and three pincer cells, that contain exactly three values (candidates) within a chute;
2) One pivot cell (or hinge or apex) contains all three values and three pincer cells contain two values each;
3) First pincer cell lying within pivot cell's line;
4) Second pincer cell having one common value with first pincer cell lying within pivot cell's box but does not lie within first pincer cell's line;
5) Third pincer cell having same values as first pincer cell (i.e., naked pair) lying within first pincer cell's box and second pincer cell's line;
6) Common pincers' value may be eliminated from cells lying within pivot cell and first pincer cell common line except cells from first pincer cell box.

... and therefore, the common candidate digit among Rule 19A XYZ-Wing's hinge and its pincer 1 and pincer 2 may be removed from any cells in the hinge's row except those in the hinge's box and in pincer 2's box.

Will some one please rephrase above scenario in simple understanding definition.

R. Jamil

[JasonLion]

Personally, I wouldn't call the "third pincer" a pincer. It works in a different way, linking the two pincers together. The original definition apparently did call it a pincer though, so we may be stuck with that naming.

You can generalize just a little from the definition, though I'm not sure everyone would still call the result an XYZ-Wing Hybrid. For the same logic to work, the second pincer doesn't need to be in the same box/block as the pivot, it just needs to share a house. Likewise the "third pincer" just needs to share a house with each of the other pincers, it doesn't need to share any specific kind of house.

More generally acceptably, you should probably call the shared row a line, as it could be either a row or a column. Otherwise you need language saying rows can be replaced by columns.

It would be better to rephrase your point 6. It is difficult to follow as written. The digit shared by the pivot and the first two pincers is eliminated either from all cells in the line shared by the pivot and the first pincer, that aren't otherwise part of the pattern;
OR from all cells in the line shared by the pivot and the first pincer that aren't otherwise part of the pattern and also aren't in the first pincers box/block. The difference depends on if you count the naked pair as part of the pattern, or make those eliminations separately. I consider the naked pair part of the pattern so I would include those eliminations, but not everyone would (eleven's exemplar doesn't).

The original definition seems to only allow you to remove b from cells in the line that are in third block/box (with neither the pivot or the first pincer). I'm not sure why it is written that way, as the additional eliminations all follow from the conditions present in their definition.

[rjamil]

Hi Jason,

How about third pincer cell called finned/hybrid cell?

Also, should I simplify pivot and first two pincers common value as just "first two pincer cells common value" in point 6?

Is XYZ-Wing Hybrid strategy detected after naked pair and simple XYZ-Wing strategies OR after naked pair and before simple XYZ-Wing moves?

I think that XYZ-Wing Hybrid strategy is completely different and does not overlap with simple XYZ-Wing strategy. Hence eliminations from pivot cell's box is unnecessary.

R. Jamil

[rjamil]

Hi eleven and Jason,

Let me conclude my understanding.

Code: Select all

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

1) XYZ-Wing Hybrid strategy is based on four cells, i.e., one pivot cell (or hinge or apex), two pincer cells (or wings) and one hybrid cell (or finned), that contain exactly three values (or candidates or digits) and align within a chute;
2) Pivot cell contains all three values; and pincer cells and hybrid cell contain two values each;
3) First pincer cell align with pivot cell's line;
4) Second pincer cell contains only one common value with first pincer cell and align with pivot cell's box but not first pincer cell's line;
5) Hybrid cell contains same values as first pincer cell (i.e., naked pair) and align with both first pincer cell's box and second pincer cell's line;
6) First and second pincers' common value may be eliminated from cells align with pivot cell and first pincer cell common line but not boxes.

R. Jamil
----------
A picture is worth a thousand words.

[JasonLion]

That does corresponds to the definition you referred to originally, and I like the wording. I would include at least eleven's additional eliminations, though then it would not exactly correspond to the original.

There is no well defined ordering of techniques. Basics are usually agreed to, but beyond that it is wide open. Personally, naked pairs come long before anything to do with XYZ-Wings, and I would put XYZ-Wing Hybrid after a regular XYZ-Wing. I suspect that most would agree with that ordering, even though we almost never agree when you include more techniques and try to order them.

[rjamil]

Hi Jason and eleven,

Thanks for clarifications. Actually, credit goes to original discoverer.

Coded for XYZ-Wing Hybrid and now under testing phase. Checked following puzzle:

Code: Select all

.3.....2.....4.9..7..6......8.3.2.........4.1.........4.9.6.......5...3.1........

After certain moves found XYZ-Wing Hybrid:

Code: Select all

         1        2        3        4        5        6        7        8        9
A        9        3       56       78      578        1       67        2        4
B        8        1       56        2        4       57        9       67        3
C        7        4        2        6        3        9        8        1        5
D       56        8        4        3        1        2      567        9       67
E        3        2        7       89      589      568        4      568        1
F       56        9        1        4      578     5678        3      568        2
G        4       57        9        1        6        3        2       57        8
H        2       67        8        5       79        4        1        3      679
I        1      567        3      789        2       78      567        4      679
8) Found XYZ-Wing Hybrid in Cells 78 61 6 16 Values 567 remove 7 from Cells 33 42 51
         1        2        3        4        5        6        7        8        9
A        9        3       56       78      578        1      +67        2        4
B        8        1       56        2        4       57        9      ^67        3
C        7        4        2        6        3        9        8        1        5
D       56        8        4        3        1        2      -56        9       67
E        3        2        7       89      589      568       -4      568        1
F       56        9        1        4      578     5678       -3      568        2
G        4       57        9        1        6        3        2      +57        8
H        2       67        8        5       79        4        1        3      679
I        1      567        3      789        2       78     *567        4      679

Note: Manually added notation for easy understanding as follows:
* before Pivot Cell
+ before Pincer Cells
^ before Hybrid Cell
- before elimination Cells

R. Jamil

[pjb]

Regarding this pattern:

Code: Select all

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


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:
(c)r1c4 = r3c5 - (c=a)r3c3 - (a=bc)r1c14 => -c r1c789
For me, if its a chain then its a chain (even XY wings!)

Cheers, Phil

[rjamil]

Hi Phil,

There are lot of strategies that are either completely or partially overlap each other.

Maybe adding eleven's suggested eliminations, i.e., -c r1c23, will help to consider separate strategy.

R. Jamil

[StrmCkr]

With four cells it's no longer a xyz wing- and falls under als-xz rules, als-xy rules

Or chain definitions.

[blue]

Edit: removed most of a long post ...

It looks like a special case of this pattern:

Code: Select all

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

ALS-XY-Wing:  (c=b)r1c4 - (b=a)r3c35 - (a=c)r1c14 => -cr1c2356789

If d=c then -cr1c56 is a naked pair elimination, and -cr1c23 is a standard XYZ-Wing elimination, leaving:

Code: Select all

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

(still) ALS-XY-Wing:  (c=b)r1c4 - (b=a)r3c35 - (a=c)r1c14 => -cr1c789

--

Here's something similar:

Code: Select all

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

ALS-XY-Wing:  (c=b)r3c3 - (b=a)<r3c5,r1c4> - (a=c)<r1c1,r3c3> => -cr1c23,-cr2c123,-cr3c12

If d=c then -cr3c12 is a naked pair elimination, and -cr1c23 is a standard XYZ-Wing elimination, leaving:

Code: Select all

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

(still) ALS-XY-Wing:  (c=b)r3c3 - (b=a)<r3c5,r1c4> - (a=c)<r1c1,r3c3> => -cr2c123

[eleven]

I did not want to argue with ALS's here, which are not even mentioned in this strange rules set.
If you think in ALS's, you probably would ask like Phil, why the xyz-pattern is named at all.
(bc)r1c14=ar1c1-(a=c)r3c3 => -cr1c23

Many people are trained to directly find xyz-wings (cause you need them in some harder newspaper puzzles).
So why not look for a pair then, which could allow more eliminations ?

[edit: corrected typo, thanks blue]

[StrmCkr]

Yeah, naming gets muddled at some point. techniques discovered earlier can be grouped under a single technique that covers it and more.. But that Is the nature of learning.

Xyz was named for the hinge having three digits on an xy wing.
But then again even xy wings fall under Als rules.

Thanks blue for reminding me it can also be an Al's xy

Or an aals-xz rule. (from an earlier post of mine on wxyz-wings that went into missing candidate cases), where it degenerates into subset xyz, xy wings)
But that's not a place for that here.

[blue]

I did not want to argue with ALS's here, ...

Fair points, and good points. Probably the right ones to make.

(bc)r1c14=ar1c1-(a=c)r3c3 => -cr1c23

Right ... or one of these:
ALX-XZ-Rule: (c=a)r1c14 - (a=c)r3c3 => -cr1c23
ALX-XZ-Rule: (c=b)r1c4 - (b=c)<r1c1,r3c3> => -cr1c23