What is this technique called?

Advanced methods and approaches for solving Sudoku puzzles

What is this technique called?

Postby udosuk » Wed May 28, 2008 3:18 am

Code: Select all
..5.374..
.........
8.3..52.6
....5....
5..8..7.2
6.2...8.1
7.6.43.2.
......3..
..8.62..5

+----------------------+----------------------+----------------------+
| 12     126    5      | 16     3      7      | 4      8      9      |
| 49    *14679  149    |*146    2      8      | 5      137    37     |
| 8     *147    3      |*149    19     5      | 2      17     6      |
+----------------------+----------------------+----------------------+
| 1349   8      7      | 2      5      149    | 6      349    34     |
| 5      1349   149    | 8      19     6      | 7      349    2      |
| 6      49     2      | 3      7      49     | 8      5      1      |
+----------------------+----------------------+----------------------+
| 7      159    6      | 159    4      3      | 19     2      8      |
| 1249   12459  149    | 1579   8      19     | 3      6      47     |
| 1349   1349   8      | 179    6      2      | 19     47     5      |
+----------------------+----------------------+----------------------+

6 @ r2 locked @ r2c24
7 @ c2 locked @ r23c2
4 @ r3 locked @ r3c24
4 @ c4 locked @ r23c4

Therefore r2c4 & r3c2 can't be 4 => r3c4=4

What is this technique called?:?:
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Re: What is this technique called?

Postby ronk » Wed May 28, 2008 3:51 am

udosuk wrote:6 @ r2 locked @ r2c24
7 @ c2 locked @ r23c2
4 @ r3 locked @ r3c24
4 @ c4 locked @ r23c4

Therefore r2c4 & r3c2 can't be 4 => r3c4=4

What is this technique called?:?:

According to Jeff's Forcing chains: Terminology and Definition thread, it's a strong wing, a discontinuous strong cycle or discontinuous strong inference loop.

r3c4 =4= r3c2 =7= r2c2 =6= r2c4 =4= r3c4, ==> r3c4=4
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Postby udosuk » Wed May 28, 2008 5:25 am

Thanks Ron.:) First time to hear this term, and the existence of that thread. (Guess I'm not a big fan of forcing chains.)

I like the name "strong wing". Wonder if there is a "weak wing"?:)
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Postby ronk » Wed May 28, 2008 11:36 am

udosuk wrote:First time to hear this term, and [...] I like the name "strong wing".

I don't recall seeing the term used either.

I don't think I like the term, primarily because "strong" is too general, too common. IOW, search utilities are unlikely to yield useful results.
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Postby udosuk » Thu May 29, 2008 7:46 am

According to google "strong wing" is linked to a Chinese company name, also a term for kiting/paragliding.:)

Anyway from the players' perspective we often like moves with catchy names, so that they're easy to remember. I guess "strong link" is in a sense as general/common as "strong wing", if not more.
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Postby 999_Springs » Thu May 29, 2008 8:36 pm

Compare:
Code: Select all
xy-wing:

... |... |...
..12|..13|...
... |... |...
----+----+---
... |... |...
..23|..34|...
... |... |...
----+----+---
... |... |...
... |... |...
... |... |...
r5c6<>3

with:
Code: Select all
strong wing:

... |... |...
..*-1--* |...
..| |..| |...
--2-+--3-+---
..| |..| |...
..*-3--* |...
... |... |...
----+----+---
... |... |...
... |... |...
... |... |...
r5c6=3


You have an example of the second pattern. The pattern seems to be related to the XY-wing but involving strong links, so the term "strong wing" might seem appropriate (and your "weak wing" might just be an XY-wing)...
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Postby ronk » Thu May 29, 2008 9:18 pm

999_Springs wrote:The pattern seems to be related to the XY-wing but involving strong links, so the term "strong wing" might seem appropriate (and your "weak wing" might just be an XY-wing)...

Agreed, clearly the "strong" of "strong wing" comes from "pure strong inference loop." Agree on your "weak wing" POV too.
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Postby Luke » Fri May 30, 2008 7:26 am

I thought this was referred to as an alternating inference chain. If the chain begins and ends on a strong link, that cell must contain the candidate. If it begins and ends on a weak link, it cannot contain the candidate.

I'd like to think of it as the profitable by-product of a unique rectangle search. From the "UR Meets X-wing" thread:
While searching for unique rectangles I’m finding that it’s worthwhile to pay attention to strong links even if there’s no AUR to be found. There often is an elimination within the rectangle by other means.

With a rectangle like this with so many strong links, something always has to give. If two strong links meets in one cell as the 4's do in r3c4, that's the best place to start. If either 1 or 9 is in this cell, then both 6 and 7 would have to be in r2c2.
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Postby 999_Springs » Fri May 30, 2008 8:45 pm

udosuk wrote:According to google "strong wing" is linked to a Chinese company name, also a term for kiting/paragliding.

Yahoo does rather better: on its FIFTY-SIXTH [oops-edit: FIFTY-FIFTH]page of results I found this.
Last edited by 999_Springs on Sat May 31, 2008 3:24 pm, edited 1 time in total.
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Postby udosuk » Sat May 31, 2008 4:13 am

Thanks for the good effort, 999_Springs.:)

It's surprising the Strong Wing never gets popular for players and solving software like XY-Wing does. Perhaps all strong-link-based moves are harder to spot than weak-link-based ones?

Also very interesting about the AIR (Almost Impossible Rectangle). Wonder anyone has found any real life example?
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