Two definitions of W-Wing, terminology question

Advanced methods and approaches for solving Sudoku puzzles

Re: Two definitions of W-Wing, terminology question

Postby ronk » Wed Aug 04, 2010 8:35 pm

ferb82 wrote:That's very strange with me? Is it a strategy?

Hi ferb82, welcome to the forum. If you're asking if the w-wing is a solving technique, the answer is "yes". You can see this technique used almost every day at dailysudoku.com. In addition to this thread, see W-Wing on sudopedia.org.
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W-Wings link two Type C

Postby rjamil » Fri Nov 24, 2017 7:06 pm

StrmCkr wrote:Grouped Type E:

you can link two type E's similar to that of
grouped empty rectangles.

and produce extended eliminations.

as in this example.

Code: Select all
 .  .  . |  /  a  / |  .  .  .
 . ab  . |  a  a  a |  .  -b .
 .  .  . |  /  a  / |  .  .  .
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
---------+----------+----------
 .  .  . |  /  a  / |  .  .  .
 .  -b . |  a  a  a |  .  ab .
 .  .  . |  /  a  / |  .  .  .

Is linking two type C similar to that grouped empty rectangle also work?
Code: Select all
 .  . -b |  .  .  . |  /  a  /
 . ab -b |  .  .  . |  a  a  a
 .  . -b |  .  .  . |  /  a  /
---------+----------+----------
 . -b  . |  .  .  . |  /  a  /
 . -b ab |  .  .  . |  a  a  a
 . -b  . |  .  .  . |  /  a  /
---------+----------+----------
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  .  .  . |  .  .  .
 Type C:

R. Jamil
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Re: Two definitions of W-Wing, terminology question

Postby rjamil » Tue Dec 12, 2017 6:05 am

Hi,

Wish to inform that I have completed coding for W-Wings strategy. (Hope that the W-Wings strategy did not fully cover by any other strategy.)

Following exemplars covered:
Code: Select all
W-Wings Type 1 (4 exemplars, up to 2 exclusions)
  --------------+-------------+-----------  --------------+-------------+-----------
01) .   .    .  |  .   .   .  |  .  .   . 02) .   .    .  |  .   .   .  |  .  .   .
    .  yz    .  |  .   .   .  |  . -Z   .     .  yz    .  |  .   .   .  |  . -Z   .
   +Y  +Y   +Y  |  /   /   /  |  / +Y   /     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     /  +Y    /  |  /   /   /  |  / +Y   /
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  . yz   .     .  -Z    .  |  .   .   .  |  . yz   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------

  --------------+-------------+-----------  --------------+-------------+-----------
03) .   .    .  |  .   .   .  |  / +Y   / 04) .   .    .  |  .   .   .  |  .  .   .
    .  yz    .  |  .   .   .  | +Y +Y-Z +Y    .  yz    .  |  .   .   .  |  . -Z   .
    .   .    .  |  .   .   .  |  / +Y   /     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     /  +Y    /  |  .   .   .  |  / +Y   /
    .   .    .  |  .   .   .  |  .  .   .    +Y  +Y   +Y  |  .   .   .  | +Y +Y  +Y
    .   .    .  |  .   .   .  |  .  .   .     /  +Y    /  |  .   .   .  |  / +Y   /
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .  -Z    .  |  .   .   .  |  . yz   .     .  -Z    .  |  .   .   .  |  . yz   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
W-Wings Type 2 (4 exemplars, up to 6 exclusions)
  --------------+-------------+-----------  --------------+-------------+-----------
01) .  yz    .  |  .   .   .  | -Z -Z  -Z 02) .  yz    .  | +Y  +Y  +Y  | -Z -Z  -Z
   +Y  +Y   +Y  |  /   /   /  | +Y +Y  +Y     .   .    .  |  /   /   /  |  .  .   .
   -Z  -Z   -Z  |  .   .   .  |  .  .  yz    -Z  -Z   -Z  | +Y  +Y  +Y  |  .  .  yz
  --------------+-------------+-----------  --------------+-------------+-----------

  --------------+-------------+-----------  --------------+-------------+-----------
03) .  yz    .  |  .   .   .  | -Z -Z  -Z 04) .  yz    .  |  .   .   .  | -Z -Z  -Z
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
   -Z  -Z   -Z  |  .   .   .  |  .  .  yz    -Z  -Z   -Z  |  .   .   .  |  .  .  yz
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
    .   .    .  |  .   .   .  |  .  .   .     .   .    .  |  .   .   .  |  .  .   .
  --------------+-------------+-----------  --------------+-------------+-----------
    .   .    .  |  .   .   .  |  .  .   .     /  +Y    /  |  .   .   .  |  /  /  +Y
    /  +Y    /  |  /   /   /  |  /  /  +Y    +Y  +Y   +Y  |  .   .   .  | +Y +Y  +Y
    .   .    .  |  .   .   .  |  .  .   .     /  +Y    /  |  .   .   .  |  /  /  +Y
  --------------+-------------+-----------  --------------+-------------+-----------

Since the W-Rings are the simultaneous combination of both the digit to form W-Wings, it is pending for development.

R. Jamil
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Re: Two definitions of W-Wing, terminology question

Postby StrmCkr » Tue Dec 12, 2017 6:15 am

Code: Select all
Is linking two type C similar to that grouped empty rectangle also work?

yes it also works, but should be noted as a W -wing {extension} as the chain length of strong links candidate can be any length.
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Re: Two definitions of W-Wing, terminology question

Postby StrmCkr » Tue Dec 12, 2017 7:04 am

this puzzles interesting as it show cases 2
"W-wing" examples not found in hodoku but found in xsudo

{it is also not found as any type of nice loop in hodoku as well. the skyscraper formed by the 9's is there}

also not covered by the w-wing definition page

Code: Select all
+-----------+----------------+---------------+
| 3   8   9 | 126  24    146 | 7     5  14   |
| 5   7   1 | 8    4(9)  3   | 2     6  4(9) |
| 6   4   2 | 15   579   179 | 19    3  8    |
+-----------+----------------+---------------+
| 24  13  8 | 7    6     5   | 14    9  123  |
| 9   35  7 | 4    1     2   | 6     8  35   |
| 24  15  6 | 9    3     8   | 145   7  125  |
+-----------+----------------+---------------+
| 8   6   3 | 125  25-9  19  | (59)  4  7    |
| 7   2   4 | 56   8     69  | 3     1  (59) |
| 1   9   5 | 3    47    47  | 8     2  6    |
+-----------+----------------+---------------+


Code: Select all
+-----------+-----------------+--------------+
| 3   8   9 | 126  24    146  | 7    5  14   |
| 5   7   1 | 8    (49)  3    | 2    6  (49) |
| 6   4   2 | 15   579   17-9 | 19   3  8    |
+-----------+-----------------+--------------+
| 24  13  8 | 7    6     5    | 14   9  123  |
| 9   35  7 | 4    1     2    | 6    8  35   |
| 24  15  6 | 9    3     8    | 145  7  125  |
+-----------+-----------------+--------------+
| 8   6   3 | 125  25-9  19   | 59   4  7    |
| 7   2   4 | 56   8     6(9) | 3    1  5(9) |
| 1   9   5 | 3    47    47   | 8    2  6    |
+-----------+-----------------+--------------+


interesting enough this would be a very good example of a subset using "fin transport" to extend eliminations
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Re: Two definitions of W-Wing, terminology question

Postby rjamil » Thu Dec 14, 2017 9:04 pm

Hi StrmCkr,

Code: Select all
389...75.5718.326.642....38..8765.9.9.741268...6938.7.863....47724.8.31.1953..826

I checked with my solver, with all strategies, without XY-Wings Type 1 Transport (32 developed patterns), and, without complete XY-Wings, XY-Wings Type 1 Transport and XYZ-Wings strategies. No W-Wings found and solved the puzzles each time without guess.

Also, it detected as Empty Rectangle after disabling WXYZ-Wings too, with one guess:
Code: Select all
389...75.5718.326.642....38..8765.9.9.741268...6938.7.863....47724.8.31.1953..826
 +---------+-------------+------------+
 | 3  8  9 | 126 24  146 | 7   5 14   |
 | 5  7  1 | 8   49  3   | 2   6 49   |
 | 6  4  2 | 15  579 179 | 19  3 8    |
 +---------+-------------+------------+
 | 24 13 8 | 7   6   5   | 14  9 1234 |
 | 9  35 7 | 4   1   2   | 6   8 35   |
 | 24 15 6 | 9   3   8   | 145 7 1245 |
 +---------+-------------+------------+
 | 8  6  3 | 125 259 19  | 59  4 7    |
 | 7  2  4 | 56  8   69  | 3   1 59   |
 | 1  9  5 | 3   47  47  | 8   2 6    |
 +---------+-------------+------------+
0) Found Box-Line Reduction Intersection Removal Cells 33 42 51 drop Clue 4 from Cells 34 35 43 44 52 53
 +---------+-------------+-----------+
 | 3  8  9 | 126 24  146 | 7   5 14  |
 | 5  7  1 | 8   49  3   | 2   6 49  |
 | 6  4  2 | 15  579 179 | 19  3 8   |
 +---------+-------------+-----------+
 | 24 13 8 | 7   6   5   | 14  9 123 |
 | 9  35 7 | 4   1   2   | 6   8 35  |
 | 24 15 6 | 9   3   8   | 145 7 125 |
 +---------+-------------+-----------+
 | 8  6  3 | 125 259 19  | 59  4 7   |
 | 7  2  4 | 56  8   69  | 3   1 59  |
 | 1  9  5 | 3   47  47  | 8   2 6   |
 +---------+-------------+-----------+
0) Found Empty Rectangle Intersection Cell 22 Strong Link Column between Cell 24 and Cell 60 drop Clue 9 from Cell 58
 +---------+-------------+-----------+
 | 3  8  9 | 126 24  146 | 7   5 14  |
 | 5  7  1 | 8   49  3   | 2   6 49  |
 | 6  4  2 | 15  579 179 | 19  3 8   |
 +---------+-------------+-----------+
 | 24 13 8 | 7   6   5   | 14  9 123 |
 | 9  35 7 | 4   1   2   | 6   8 35  |
 | 24 15 6 | 9   3   8   | 145 7 125 |
 +---------+-------------+-----------+
 | 8  6  3 | 125 25  19  | 59  4 7   |
 | 7  2  4 | 56  8   69  | 3   1 59  |
 | 1  9  5 | 3   47  47  | 8   2 6   |
 +---------+-------------+-----------+

I would love to see missing W-Wings patterns that found by Xsudo only.

R. Jamil
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Re: Two definitions of W-Wing, terminology question

Postby StrmCkr » Fri Dec 15, 2017 9:08 am

Code: Select all
No W-Wings found and solved the puzzles each time without guess.

correct, you wont find these neither did mine at first

as the formation of the Bivalves are them selves linked by the sector instead of connected at the end points of the bi-local single digit.

unfortunately these will more then likely always be subsumed by an easier "fish" pattern before you find them

these are the only 2 possible {not considering transformation}
Code: Select all
| . ab -A | .  .  . |  .  ab . |
| .  . -A | .  .  . |  .  .  . |
| .  . -A | .  .  . |  .  .  . |
--------------------------------
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
--------------------------------
| . -A  . | .  .  . |  .  .  . |
| /  /  A | /  /  / |  /  A  / |
| . -A  . | .  .  . |  .  .  . |


Code: Select all
| . ab  . | .  .  . |  .  ab . |
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
--------------------------------
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
--------------------------------
| . -A  . | .  .  . |  .  .  . |
| A  A  A | /  /  / |  /  A  / |
| . -A  . | .  .  . |  .  .  . |
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Re: Two definitions of W-Wing, terminology question

Postby rjamil » Fri Dec 15, 2017 11:55 am

Hi StrmCkr,

Are these really W-Wings?

What I learned about W-Wings formation is quoted from here as follows:
keith wrote:Suppose you have two cells, each with the same two candidates, that cannot "see" each other, so they are not a pair. And, suppose that each of these cells lines up with an end of a strong link in one of the candidates.

Where as, in your above mentioned exemplars, both bi-value cells are buddy each other.

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Re: Two definitions of W-Wing, terminology question

Postby StrmCkr » Fri Dec 15, 2017 1:00 pm

Keith's definition isn't the generalized version covered here, he also has stricter conditions on the strong linked digit can only be a strong link, thus grouped weaklinks didn't qualify either.

The definition covered here for it is 2 bivavle cells linked by a single digit through a strong link or grouped weak link.
which is what xsudoku rules are based off off.
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Re: Two definitions of W-Wing, terminology question

Postby rjamil » Fri Dec 15, 2017 2:26 pm

Hi StrmCkr,

Still something not fully covered as per W-Wings definition by missing 2 cases, and, that only found by xsudo.

Look in to this W-Wing definition:
It is required that A sees B, C sees D, and B and C has a strong link on the digit X. Then W can be eliminated from any cell that is seen by both A and D.

Now, if I say combined definition of W-Wing, it will be as follows:
"If two unsolved cells, A and B, not see each other; contain exactly same (identical) two candidates; and has either strong or weak link on one digit; then the other digit may be eliminated from cell(s) that see both A and B."

Again, may be I am wrong, but neither "see" rule nor "digit" rule satisfied by special 2 cases but still called W-Wings?
(Isn't called useless or spent naked pair transported by strong link on a digit?)

Added:
Code: Select all
| . ab -A | .  .  . |  .  ab . |
| .  . -A | .  .  . |  .  .  . |
| .  . -A | .  .  . |  .  .  . |
--------------------------------
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
--------------------------------
| . -A  . | .  .  . |  .  .  . |
| /  /  A | /  /  / |  /  A  / |
| . -A  . | .  .  . |  .  .  . |

I think, it is skyscraper. If r1c2 and r1c8 form naked pair, then it is also form strong link for digit a (and b too).
Similarly, r1c3 elimination is useless.

R. Jamil
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Re: Two definitions of W-Wing, terminology question

Postby StrmCkr » Fri Dec 15, 2017 9:04 pm

Code: Select all
If two unsolved cells not see each other
that's the part that's is not described in the linked definition as well:

what is described is that a & B both see different parts of the single strong/ grouped weak link --- which is how hodoku identifies them

also the link stipulates it is again exactly 4 cells. which would invalid most of the ones shown by ronk and my self in later posts.

instead of an even more generalized form: --- taken from xsudoku
2 bivalves sharing 1 strong/ weak grouped link

    A: bivalve cell with digits xy
    B: digit x is a weak link or Grouped weak link to A
    C: digit x is a strong link or strong grouped link to B
    D: bivalve cell with digits xy where d is a peer of A or digit x is a weak link C

    eliminate:
    if d is a weak link of c
    then
    peers of A & D <> digit y

    if D is peer of A
    then
    peers of d and peers of C <> digit y
    and peers of A & D <> x,y

Added:
(Isn't called useless or spent naked pair transported by strong link on a digit?)


Code: Select all
 
    | . ab -A | .  .  . |  .  ab . |
    | .  . -A | .  .  . |  .  .  . |
    | .  . -A | .  .  . |  .  .  . |
    --------------------------------
    | .  .  . | .  .  . |  .  .  . |
    | .  .  . | .  .  . |  .  .  . |
    | .  .  . | .  .  . |  .  .  . |
    --------------------------------
    | . -A  . | .  .  . |  .  .  . |
    | /  /  A | /  /  / |  /  A  / |
    | . -A  . | .  .  . |  .  .  . |

I think, it is skyscraper {shasimi - wing}. If r1c2 and r1c8 form naked pair, then it is also form strong link for digit a (and b too).
Similarly, r1c3 elimination is useless.

R. Jamil


pretty much the problem with a lot of named technique sets, they exhibit niche/specific cases that overlap one another.
this one is all 4 types. {skyscraper, shasmi-xwing, w-wing, fin transport on a pair}

i'll leave it for you to decide where and if you wish to include these 2 case as w-wings: i posted them as they did popup in xsudoku as w-wings
hopefully i explained how they could be classed as w-wings, by adding a 2nd elimination routine and dropped the elimination that d must see c
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Re: Two definitions of W-Wing, terminology question

Postby rjamil » Sat Dec 16, 2017 7:52 am

Hi StrmCkr,

Thanks for your patience and detail explanation.

Just one last question regarding this W-Wings pattern:
Code: Select all
| . ab  . | .  .  . |  .  ab . |
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
--------------------------------
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
| .  .  . | .  .  . |  .  .  . |
--------------------------------
| . -A  . | .  .  . |  .  .  . |
| A  A  A | /  /  / |  /  A  / |
| . -A  . | .  .  . |  .  .  . |

What are the other strategies that cover the above pattern apart from W-Wings?

FYI, I plan to cover such patterns in Skyscraper routine as they are more likely similar to it.

R. Jamil
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Re: Two definitions of W-Wing, terminology question

Postby StrmCkr » Sat Dec 16, 2017 8:01 am

As shown it's a finned x wing
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Re: Two definitions of W-Wing, terminology question

Postby rjamil » Sat Dec 16, 2017 8:23 am

Hi StrmCkr,

Many thanks for your quick and favourable response.

Skyscraper pattern belongs to Sashimi Mutant X-Wings (Turbot Fish) and it will be detected (or placed) before Wings family (once started developing).

I will also move 2-String Kite and Grouped 2-String Kite detection routine before Wings family as they also belongs to Sashimi Mutant X-Wings (Turbot Fish).

R. Jamil
rjamil
 
Posts: 150
Joined: 15 October 2014
Location: Karachi, Pakistan

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