| View previous topic :: View next topic |
| Author |
Message |
keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
|
 Posted: Tue May 15, 2018 3:32 am Post subject: Extending the Reach: Transporting Wing Pincers |
 |
|
Sudoku: Extending the Reach: Transporting Wing Pincers
A Wing With Transport
This is not new: I was looking for an article describing pincer transport, and could not find one that was not in the context of a particular example. So, here goes.
For years now, some of us (Marty, Keith, and Helmut, et al) have been using “useless” or “flightless” wings plus a link to make eliminations in more difficult puzzles. We have all remarked on how useful and powerful the technique might be.
In the following,
A-a, B-b, C-c are Single-Digit Strong Links (SDSLs).
a, b, c, ... are simply cell labels.
X is a cell where the candidate does occur.
/ is a cell where the candidate does not occur.
. is a cell that does not matter (some may need to be X)
* or # is a target cell where the candidate may be eliminated.
| Code: | +---------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+---------+---------+---------+
| . . . | XZ . Z*| . . . |
| . . . | . . Z*| . . . |
| . . . | . . Z*| . . . |
+---------+---------+---------+
| . . . | Z* . YZ| . . . |
| . . . | Z* . . | . . . |
| . . . | XY . . | . . . |
+---------+---------+---------+
Figure 1: An XY-wing |
XZ and YZ are pincers on Z. Standard stuff.
But now, suppose we add a strong link (SDSL) on Z:
| Code: | +---------+---------+---------+
| / . . | . . . | . . . |
| Za . . | # . . | . . . |
| / . . | . . . | . . . |
+---------+---------+---------+
| / . . | XZ . Z*| . . . |
| / . . | . . Z*| . . . |
| / . . | . . Z*| . . . |
+---------+---------+---------+
| ZA . . | Z* . YZ| . . . |
| / . . | Z* . . | . . . |
| / . . | XY . . | . . . |
+---------+---------+---------+
Figure 2: An XY-wing with transport by an SDSL |
The pincer on YZ is “transported” to Za, and there is a further elimination in R2C4 (in this illustration).
An Example
Here is a real example, courtesy of Helmut Saueregger.
| Code: | +-------+-------+-------+
| 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 |
+-------+-------+-------+
Figure 3: A real example |
After basics:
| Code: | +-------------------+-------------------+-------------------+
| 2 8 69h | 1 56H 59 | 34 34 7 |
| 39g 1 5 | 7 4 39G | 6 8 2 |
| 367 -3467 34-6# | 23ce 26f 8 | 9 1 5 |
+-------------------+-------------------+-------------------+
| 5 23467 346 | 36d 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# 35a 1 | 25b 7 4 | 28 6 9 |
+-------------------+-------------------+-------------------+
Figure 4: The example, after basics. |
There is a 2-35 XY-wing, making the elimination shown in R3C2. There is also a “useless” wing 23-6, def, in R3 and C4.
Note the SDSL on 3 in R2, Gg. It transports c to g, making the elimination of 3 in R9C1, #.
Also, the SDSL on 6 in R1, Hh, transporting f to h, making the elimination of 6 in R4C3, also marked #.
These transport eliminations (in particular the first), solve the puzzle.
Pincer transports like this are very easy to spot, if you remember to look for them. They are often very effective.
Helmut Saueregger (Nataraj) 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. He also uses this technique in grading the difficulty of his puzzles.
For the following, we will use XY-wings as the example. However, the same logic applies to W- and M-wings. In a sense, we have used the two-digit logic of the wing to establish a link in a single-digit chain.
You can, of course, use this technique to extend the pincers of Skyscrapers and Kites (Turbot Fish):
http://www.saueregger.at/?p=676
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.
http://www.saueregger.at/sudoku/HSH/HSH.htm
If this is new to you, start with Havard’s excellent explanation: http://forum.enjoysudoku.com/strong-links-for-beginners-t3326.html
For more on M- and W-wings see: http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=2143
Figuring the Logic
I do not carry images of pattern stencils and templates in my head. Rather, when figuring out these Single-Digit Strong Links (SDSLs), I work out the logic each time for each case.
The reason is that Wing pincers can have two cases:
1. One, or both are true, or;
2. One is true, one is false
You need to take care when building chains that include regular SDSLs and wing pincers.
Suppose you have a skyscraper:
| Code: | +---------+---------+---------+
| . . / | . . . | . / . |
| . . / | . . . | . / . |
| . . * | . . . | . Xb . |
+---------+---------+---------+
| . . / | . . . | . / . |
| . . Xa| . . . | . * . |
| . . / | . . . | . / . |
+---------+---------+---------+
| . . / | . . . | . / . |
| . . / | . . . | . / . |
| . . XA| . X . | . XB . |
+---------+---------+---------+
Figure 1: A Skyscraper: One or both pincers are true |
The logic is, one or both of A and B are false; one or both of a and b are true
But, suppose we have this:
| Code: | +---------+---------+---------+
| . . / | . . . | . / . |
| . . / | . . . | . / . |
| . . * | . . . | . Xb . |
+---------+---------+---------+
| . . / | . . . | . / . |
| . . Xa| . . . | . * . |
| . . / | . . . | . / . |
+---------+---------+---------+
| . . / | . . . | . / . |
| . . / | . . . | . / . |
| / / XA| / / / | / XB / |
+---------+---------+---------+
Figure 1: A Skyscraper: One pincer is true, the other is false |
Now, the logic is, one of A and B is true, the other is false; one of a and b is true, the other is false.
The eliminations are the same for both, but the logic when appending them to other links can be subtly different. So, we have:
XY-wing: One or both pincers are true
W-wing: One pincer is true, the other is false (This is incorrect, I am thinking ...)
M-wing: One pincer is true, the other is false
Turbot (skyscrapers and kites):
1. If the base is a strong link, one pincer is true, the other is false
2. If the base is a not strong link, one or both pincers are true
So, argue the logic for each case, and be careful.
Keith
Last edited by keith on Wed May 16, 2018 4:08 pm; edited 2 times in total |
|
| Back to top |
|
 |
strmckr
Joined: 18 Aug 2009
Posts: 64
|
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
Powered by phpBB © 2001, 2005 phpBB Group
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
