Sudoku: Using Wing Pincers as a Link in a Skyscraper or Kite

For years now, some of us (Marty, Keith, and Helmut, et al) have been using “useless” or “flightless” wings as a link to make eliminations in more difficult puzzles.  We have all remarked on how useful and powerful the technique might be.

More recently, Helmut Saueregger (Nataraj) engaged me in a new discussion on this, and he has extended his Helmut’s Sudoku Helper (HSH) to find these things.  HSH is here:

http://www.saueregger.at/sudoku/HSH/HSH.htm (Note 1)

You should be looking at HSH V4.1 or greater.

For the following, we will use XY-wings as the example.  However, the same logic applies to W- and M-wings.

There are two requirements:

1. You know how to find Kites and Skyscrapers, which are collectively known as Turbot Fish (Note 2).

2. You know how to find an XY-wing.

(We also imply that you use pencil and paper to solve Sudoku for personal enjoyment. If you see Sudoku solving as a contest in computer software, please do not read further.)

The simple point here is that the pincers of a Wing can be one link of the two links that make up a Turbot pattern.

Here is an example (from Helmut):

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

After basics:

+-------------------+-------------------+-------------------+
| 2     8     69    | 1     56    59    | 34    34    7     |
| 39    1     5     | 7     4     39    | 6     8     2     |
| 367   3467  346   | 23    26    8     | 9     1     5     |
+-------------------+-------------------+-------------------+
| 5     23467 346   | 36    9     137   | 123   237   8     |
| 379   37    8     | 4     15    2     | 15    379   6     |
| 1     2367  369   | 356   8     357   | 235   2379  4     |
+-------------------+-------------------+-------------------+
| 68    56    7     | 9     125   15    | 248   24    3     |
| 4     9     2     | 8     3     6     | 7     5     1     |
| 38    35    1     | 25    7     4     | 28    6     9     |
+-------------------+-------------------+-------------------+

There is an XY-wing 2-35 in R9C4.  After that:

+-------------------+-------------------+-------------------+
| 2     8     69    | 1     56    59    | 34    34    7     |
| 39#   1     5     | 7     4     39#   | 6     8     2     |
| 367   467   346   | 23@   26    8     | 9     1     5     |
+-------------------+-------------------+-------------------+
| 5     23467 346   | 36    9     137   | 123   237   8     |
| 379   37    8     | 4     15    2     | 15    379   6     |
| 1     2367  369   | 356   8     357   | 235   2379  4     |
+-------------------+-------------------+-------------------+
| 68    56    7     | 9     125   15    | 248   24    3     |
| 4     9     2     | 8     3     6     | 7     5     1     |
|-38    35@   1     | 25    7     4     | 28    6     9     |
+-------------------+-------------------+-------------------+

It seems you now have to join the chain gang (Note 3). But, let’s look closer:
@@ are the Wing pincers.  One or both is 3.
## is a strong link on 3.  Together @@ and ## make a sort of Kite.
R9C1 is not 3, puzzle solved!
Note that there is also a flightless XY-wing 23-6 in R3C4 that takes out 6 in R4C3:

+-------------------+-------------------+-------------------+
| 2     8     69#   | 1     56#   59    | 34    34    7     |
| 39    1     5     | 7     4     39    | 6     8     2     |
| 367   467   346   | 23    26@   8     | 9     1     5     |
+-------------------+-------------------+-------------------+
| 5     23467 34-6  | 36@   9     137   | 123   237   8     |
| 379   37    8     | 4     15    2     | 15    379   6     |
| 1     2367  369   | 356   8     357   | 235   2379  4     |
+-------------------+-------------------+-------------------+
| 68    56    7     | 9     125   15    | 248   24    3     |
| 4     9     2     | 8     3     6     | 7     5     1     |
| 38    35    1     | 25    7     4     | 28    6     9     |
+-------------------+-------------------+-------------------+

How difficult is this?  I think it is quite easy.
Personally, after doing the basics, I check for strong links to find single-digit eliminations (usually Turbots, which are Skyscrapers and Kites). That is explained here:
http://forum.enjoysudoku.com/post247168.html#p247168
As a side benefit, this Turbot search is a check that you have done the basics correctly.
After that, I look for XY-, W- and M-wings (note 4). Even if these wings do not make eliminations by themselves (they are “flightless”), I now have all the information to find the “Turbot Wings” described here (Note 5).
So, I think this is not a very “advanced” technique. Actually, I think it simplifies the issue, by taking links found by multi-digit techniques back into the single-digit world.

Keith

  1. Notes:
    Helmut’s Sudoku Helper (HSH) is an interesting tool that allows you to explore paths through puzzles. It is not a Sudoku solver per se.
  2. If this is new to you, start with Havard’s excellent explanation: http://forum.enjoysudoku.com/strong-links-for-beginners-t3326.html
  3. See also http://hodoku.sourceforge.net/en/tech_sdp.php for more on Skyscrapers, Kites, and Turbots.
  4. https://www.youtube.com/watch?v=zBn5aIfZElE
    For more on M- and W-wings see: http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
  5. Names are an aid to communication, and I think the name “Turbot Wing” is appropriately descriptive of a Turbot where one of the two links comes from a Wing.

 

Dieser Eintrag wurde veröffentlicht in Sudoku von Keith Meintjes. Permanenter Link des Eintrags.
Keith Meintjes

Über Keith Meintjes

Keith Meintjes is a retired automotive engineer who lives in Michigan, USA. He says, "I suppose I am a teacher at heart. I like to write things down to explain them to other people." Keith has written many articles on ways to solve Sudoku that are particularly useful to those who use pencil and paper (rather than software.)

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