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
- 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. - If this is new to you, start with Havard’s excellent explanation: http://forum.enjoysudoku.com/strong-links-for-beginners-t3326.html
- See also http://hodoku.sourceforge.net/en/tech_sdp.php for more on Skyscrapers, Kites, and Turbots.
- 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 - 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.