The New Sudoku Players' Forum

[elisatems]

Hello, I'm new to this forum and this is my first post.

In the Fiendish daily puzzle of 2023-06-17, there is a true WXYZ-Wing that is fairly easy to find, but there are also at least three other patterns in the puzzle that the app's solver calls WXYZ-Wings that have 5 interacting candidates. Why does the app (I'm using Heart Sudoku on the Mac, if it matters) call these WXYZ-Wings? One seems to be a VWXYZ-Wing, the other two are equivalent alternate patterns that achieve the same result that I'd consider some kind of ALS-XZ.

I tried to attach some images but I cannot seem to upload any attachments, I get an error saying "Sorry, the board attachment quota has been reached." Does that quota reset periodically or is this condition permanent?

[elisatems]

Today's "Devious" puzzle has another example of a pattern I can't by any stretch think of as a WXYZ-Wing, even though it only involves 4 digits. I think it's an ALS-XZ where the two ALSs are

1) r5c1 and r46c3 (2568)
2) r4c6 (68)

X=8 (restricted common digit)
Z=6 (unrestricted common digit).

I still get "Sorry, the board attachment quota has been reached" when I try to upload an image, and I do not know how to generate the pretty-printed ascii puzzles that some people here post. Some guidance would be appreciated.

[elisatems]

Ok, I figured out how to post formatted ascii. The first example is the so-called WXYZ-Wing I mentioned earlier today, exported from Hodoku. The cells making up the pattern are: r46c3 r4c6 r5c1 (2568). My analysis:

ALS1 = r5c1 r46c3 (2568)
ALS2 = r4c6 (68)
X = 8
Z = 6

Result: r4c1 <> 6.

Enjoy Sudoku calls this a WXYZ-Wing, Is this correct? At least it involves only 4 digits, but the cells involved are spread all over a block, with another cell elsewhere in a row passing through the block, so it isn't what I would think of as a WXYZ-Wing. But at least the cells launch a pincer-like attack on the 6 in r4c1.

The second example involves 5 digits but Enjoy Sudoku calls this one a WXYZ-Wing as well. The cells making up the pattern are: r4c2 r4c8 r6c123. I analyze it as:

ALS1 = r4c2 r6c123 (13689)
ALS2 = r4c8 (39).
X=3
Z=9

Result: r4c3 <> 9 because if r4c2 <> 3, r6c123 reduces to a naked triple that includes 9 (though it does then reduce to a naked pair and a hidden single 9) and if r4c6 <> 3, it reduces to a naked single 9. This really doesn't seem like a "wing" to me, and anyway with 5 cells / digits, how can it be a WXYZ anything?

Code: Select all

| 8    6     1     | 37   37     9   | 2   4   5  |
| 4    5     7     | 6    2      1   | 3   9   8  |
| 3    29    29    | 4    58     58  | 7   6   1  |
:------------------+-----------------+------------:
| 126  1278  28    | 278  4      68  | 9   5   3  |
| 256  278   4     | 9    578    3   | 1   28  67 |
| 9    3     25    | 127  157    568 | 4   28  67 |
:------------------+-----------------+------------:
| 7    89    3589  | 38   3689   2   | 56  1   4  |
| 125  1289  23589 | 138  13689  4   | 56  7   29 |
| 12   4     6     | 5    19     7   | 8   3   29 |
'------------------'-----------------'------------'

Code: Select all

.----------------.-----------------.----------------.
| 9    5    1278 | 127   17   3    | 267  4    1678 |
| 126  167  127  | 4     8    9    | 237  5    137  |
| 4    178  3    | 1257  157  6    | 9    278  178  |
:----------------+-----------------+----------------:
| 7    36   59   | 56    2    8    | 1    39   4    |
| 135  2    4    | 157   9    157  | 8    6    37   |
| 168  168  189  | 167   3    4    | 27   279  5    |
:----------------+-----------------+----------------:
| 125  137  6    | 8     157  1257 | 4    37   9    |
| 125  9    1257 | 3     4    1257 | 567  78   678  |
| 358  4    578  | 9     6    57   | 357  1    2    |
'----------------'-----------------'----------------'

[jco]

I like this way of describing WXYZ-wing

If one can identify a group of four Cells containing various combinations of only the same four Candidates and if each of these four Candidates can see all the other Cells of the group where it is present, except for one of those Candidates, then this Candidate can not be the solution in any Cell outside of the group that can see all the Cells of the group where it is present.

(source: here)

VWXYZ can be described in analogous way. For the examples given:

Example 1

Code: Select all

.-------------------------------------------------.
| 8    6     1     | 37   37     9   | 2   4   5  |
| 4    5     7     | 6    2      1   | 3   9   8  |
| 3    29    29    | 4    58     58  | 7   6   1  |
|------------------+-----------------+------------|
| 12-6 1278 B28    | 278  4     A68  | 9   5   3  |
|C256  278   4     | 9    578    3   | 1   28  67 |
| 9    3    C25    | 127  157    568 | 4   28  67 |
|------------------+-----------------+------------|
| 7    89    3589  | 38   3689   2   | 56  1   4  |
| 125  1289  23589 | 138  13689  4   | 56  7   29 |
| 12   4     6     | 5    19     7   | 8   3   29 |
'------------------'-----------------'------------'

WXYZ(6825) r4c6,r4c3,(r5c1,r6c3) => -6 r4c1
(4 digits in 4 cells, except 6, all digits see other cells in the group containing that digit, and (6)r1c4 see both digits 6)
(pincers: r4c6 and (r5c1,r6c3), central part: r4c3)

Example 2

Code: Select all

.---------------------------------------------------.
| 9    5    1278 | 127   17   3    | 267  4    1678 |
| 126  167  127  | 4     8    9    | 237  5    137  |
| 4    178  3    | 1257  157  6    | 9    278  178  |
|----------------+-----------------+----------------|
| 7   B36   5-9  | 56    2    8    | 1   A39   4    |
| 135  2    4    | 157   9    157  | 8    6    37   |
|C168 C168 C189  | 167   3    4    | 27   27-9 5    |
|----------------+-----------------+----------------|
| 125  137  6    | 8     157  1257 | 4    37   9    |
| 125  9    1257 | 3     4    1257 | 567  78   678  |
| 358  4    578  | 9     6    57   | 357  1    2    |
'---------------------------------------------------'

VWXYZ (13689)r4c8, r4c2, r6c123 => -9 r4c3, r6c8
(5 digits in 5 cells, except 9, all digits see other cells in the group containing that digit, and (9)r4c3, r6c9 see both digits 9)
(pincers: r4c8 and r6c123; central part: r4c2)

[elisatems]

Interesting, that's a more general definition of WXYZ-Wing than I had seen before. "Each of these four Candidates can see all the other Cells of the group where it is present, except for one of those Candidates" could easily be restated in terms of restricted and unresticted common digits, i.e. the language of ALS-XZ and similar strategies based on ALSes. Now the example on the page you referenced is one that I would easily recognize as a WXYZ-Wing, but it could also be analyzed as an ALS-XZ with X = 4, Z = 9. This makes me wonder if maybe all WXYZ-Wings (and likely XYZ- and XY-Wings as well) can be analyzed in terms of ALSes.

But I still have to insist that Enjoy Sudoku shouldn't be calling these patterns with 5 digits and 5 cells WXYZ-Wings. VWXYZ-Wing would be more appropriate, using the more general definition you gave. If I ask the app for a hint and it tells me to look for a WXYZ-Wing, I should *at least* be confident that I need only look for a pattern with 4 digits / cells, just as if it says to look for an XYZ-Wing, I can comfortably restrict my search to a particular 3-cell pattern. WXYZ-Wings are harder to find anyway because the number of candidates in each cell is not fixed - why make it even harder by making the number of cells involved ambiguous?

[StrmCkr]

http://forum.enjoysudoku.com/wxyz-wings-t30012.htmlhttp://forum.enjoysudoku.com/bent-almost-restricted-n-aked-set-barn-t33464.html

Why cause they are badly programed, or never updated to new rules or ideas.

Yes
xy, xyz, wxyz wings are all als xz with 1,2rcc rules for eliminations triggers.

Xy can also be programed as als - xy rules.

[sudokuvalleyvenusrye]

Impressive!

[Hajime]

In the Puzzles topic this puzzle from SteveG48 also shows XYZ-wing or more .....
http://forum.enjoysudoku.com/7-26-2023-t41745.html

Code: Select all

 +-------------+------------+-------------+
 | 2  a59  1   | 6    7  59 | 48  48   3  |
 | 68 b589 46-5| 489 c58 3  | 1   7    2  |
 | 7   38  34  | 48   1  2  | 5   9    6  |
 +-------------+------------+-------------+
 | 1   4   7   | 2    3  8  | 6   5    9  |
 | 38  358 235 | 7    9  6  | 248 1248 18 |
 | 89  6   29  | 5    4  1  | 3   28   7  |
 +-------------+------------+-------------+
 | 5   2   8   | 1    6  7  | 9   3    4  |
 | 4   7   69  | 3    58 59 | 28  1268 18 |
 | 369 1   369 | 89   2  4  | 7   68   5  |
 +-------------+------------+-------------+

a and c are wings and b is the common hinge cell => r2c3<>5. XYZ-wing method.

OK, but now we add r2c1 (68) to the group as an extra hinge cell: WXYZ-wing of candidates 5689.
4 cells 4 candidates. This also works: r2c3<>5. WXYZ-wing method. A candidate eliminated !

But candidate 6 is the only possibility for the group in r2c1. A cell solved !
So r2c1=6. Is this logic valid?
(after solving the puzzle indeed r2c1=6)

[jco]

Hi Hajime,

Notice that including (68)r2c1 in that set does not guarantee that (6)r2c1 is true, since we could have
in the final configuration 3 digits in that 4 cells (as shown below).

Code: Select all

.-----------------------------------------------------------.
| 2    *5*    1     | 6     7     9     | 48    48    3     |
|*8*   *9*    6     | 4    *5*    3     | 1     7     2     |
| 7     3     4     | 8     1     2     | 5     9     6     |
|-------------------+-------------------+-------------------|


In the XYZ step (below), either (5)r2c5 is true, or (59) locked at r12c2, so -5 r2c3 (this digit can be eliminated).
This elimination allows a cascade of singles (some shown below, leading to +6r2c1).

Code: Select all

.-----------------------------------------------------------.
| 2    *59    1     | 6     7     59    | 48    48    3     |
| 8+6  *589   46-5  | 489  *58    3     | 1     7     2     |
| 7 ^   38    34 |  | 48    1     2     | 5     9     6     |
|----\-----------|--+-------------------+-------------------|
| 1  |  4     7  v  | 2     3     8     | 6     5     9     |
| 38 |  358  +5-23  | 7     9     6     | 248   1248  18    |
| 89 |  6     9+2 --| 5 --- 4 --- 1 --> | 3     2+8   7     |
|----|--------------+-------------------+---------|---------|
| 5  |  2     8     | 1     6     7     | 9     3 v   4     |
| 4  |  7     69    | 3     58    59    | 28    1268  18    |
| 39-6  1 <-- 369 --| 89 -- 2 --- 4  -- | 7     8+6   5     |
'-----------------------------------------------------------'

(-5)r2c3 -> +5 r5c3 -> +2 r6c3 -> +8 r6c8 -> +6 r9c8 -> -6 r9c9 -> +6 r2c1

So the placement of (6)r2c1 comes from a cascade of singles and
adding that cell (68)cell to that set doesn't guarantee (at that moment in the game)
that 6 must be true there
(the rule allows eliminations outside the set of cells, not placements in the set).

I hope this helps.

[StrmCkr]

Code: Select all

+-----------------+---------------+---------------+
| 2    (59)   1   | 6    7     59 | 48   48    3  |
| 68   (589)  46-5 | 489  (58)  3  | 1    7     2  |
| 7    38     34  | 48   1     2  | 5    9     6  |
+-----------------+---------------+---------------+
| 1    4      7   | 2    3     8  | 6    5     9  |
| 38   358    235 | 7    9     6  | 248  1248  18 |
| 89   6      29  | 5    4     1  | 3    28    7  |
+-----------------+---------------+---------------+
| 5    2      8   | 1    6     7  | 9    3     4  |
| 4    7      69  | 3    58    59 | 28   1268  18 |
| 369  1      369 | 89   2     4  | 7    68    5  |
+-----------------+---------------+---------------+

size three : b.a.r.n.s
xyz: wing

aka ALS - XZ

ALS A) r12c2 (589)
AlS b) r2c5 (58)
X: 8 {restricted common between two sets}
Z: 5 { non restricted common between both sets}
=> r2c3 <> 5 {peer cell of all the "5"s of both sets}

OK, but now we add r2c1 (68) to the group as an extra hinge cell: WXYZ-wing of candidates 5689.
4 cells 4 candidates. This also works: r2c3<>5. WXYZ-wing method. A candidate eliminated !

size 4: b.a.r.n.s
wxyz: wing

aka ALS - XZ

ALS A) r12c2,r2c1 (5689)
AlS b) r2c5 (58)
X: 8 {restricted common between two sets}
Z: 5 { non restricted common between both sets}
=> r2c3 <> 5 {peer cell of all the "5"s of both sets}

no difference.

you can even go bigger if u want:
aka ALS - XZ

ALS A) r123c2,r3c3, (34589)
AlS b) r2c5,r3c4 (458)
X: 4 {restricted common between two sets}
Z: 5 { non restricted common between both sets}
=> r2c3 <> 5 {peer cell of all the "5"s of both sets}