## What is this technique called?

Advanced methods and approaches for solving Sudoku puzzles

### What is this technique called?

Code: Select all
`..5.374...........8.3..52.6....5....5..8..7.26.2...8.17.6.43.2.......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?
udosuk

Posts: 2698
Joined: 17 July 2005

### Re: What is this technique called?

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
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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"?
udosuk

Posts: 2698
Joined: 17 July 2005

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.
udosuk

Posts: 2698
Joined: 17 July 2005

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)...
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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.

Luke
2015 Supporter

Posts: 435
Joined: 06 August 2006
Location: Southern Northern California

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.
Hidden Text: Show
Once upon a time I was a teenager who was active on here 2007-2011
999_Springs

Posts: 367
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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?
udosuk

Posts: 2698
Joined: 17 July 2005