## VWXYZ-Wing?

Post the puzzle or solving technique that's causing you trouble and someone will help

### Re: VWXYZ-Wing?

Cenoman wrote:One could write also this Sue de Coq: (79)r8c5 -79- (456789)r123c5,r2c4 -48- (48)r2c6

That surely works too, but shouldn't the core be completely on a mini-line if one wishes to call it Sue de Coq?

pjb wrote:Interestingly, the double ALS at r2c6, r1358c5, X=4, Z=8: [ (4=8)r2c6 - (8=4)r1358c5 - loop ] is similarly devastating

Not similarly. It's actually a bit more devastating as it gives 10 direct eliminations (-4 b2p4579, -8 b2p59, -5 r24c5, -9 r47c5)! It's also the simplest and the most powerful Sue de Coq here, I think. Nice find!

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`.---------------.-------------------------.---------------.| 58  4589  458 | 3      a4589    1       | 2     6  7    || 7   1458  2   | 56-4    6-458  b48      | 3     9  148  || 3   1489  6   | 279-4  a4789    279-48  | 18    5  148  |:---------------+-------------------------+---------------:| 58  458   7   | 1       348-59  3489    | 569   2  3569 || 1   2     3   | 579    c579     6       | 4     8  59   || 9   6     458 | 45      2       348     | 15    7  135  |:---------------+-------------------------+---------------:| 4   7     58  | 269     36-9    239     | 5689  1  5689 || 6   3     1   | 8      c79      5       | 79    4  2    || 2   58    9   | 467     1       47      | 5678  3  568  |'---------------'-------------------------'---------------'(a, b, c: the Sue de Coq parts).`

eleven wrote:Some time ago i called this a vwxyz-wing.

A very nice move, but I have a hard time seeing the vwxyz-wing there! The wxyz-wing and the xyz-wing are both obvious, but I don't see how linking them together makes a vwxyz-wing. Can you explain?
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: VWXYZ-Wing?

As long as the als a - als b cells are in the same band/stack and intersection contains all the restricted digits then it falls within a barn constructions by my definitions which is an over simplified als xz system
And can go from size 1-8 cells with 9 digits on both a and b als. (as Long as the total cell count = the total digit count) {then i use a hybrid als-xz rule coupled with subset counting to make eliminations}
there by a
RSTUVWXYZ - WING IS plausible.

ps: These also includes double linked rule on my barns page

i posted this over on Andrews stewards page to hopefully get him to update his als-xz engine as a test case...

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`.---------------.------------.-----------------.| 5    478  1   | 2   6   3  | 789    78    49 || 34   6    247 | 1   8   9  | 237    5     34 || 9    238  28  | 7   5   4  | 2368   2368  1  |:---------------+------------+-----------------:| 2    9    3   | 6   4   8  | 5      1     7  || 48   478  478 | 59  19  15 | 236    236   36 || 1    5    6   | 3   2   7  | 4      9     8  |:---------------+------------+-----------------:| 7    38   5   | 4   19  6  | 1389   38    2  || 36   1    9   | 8   7   2  | 36     4     5  || 468  248  248 | 59  3   15 | 16789  678   69 |'---------------'------------'-----------------'`

case study puzzle for technique testing.

als-xz double linked rule can and does apply to some formations of

wxyz-wings:

Almost Locked Set XZ-Rule {double link rule}: A=r1c8 {78}, B=r79c8,r8c7 {3678}, X=7,8 => r3c8<>8, r7c7<>3, r9c79<>6

double linked rule is pretty simple:
For each digit in A and not in B are restricted to A cells. all peers of these cells may be eliminated for said digit.
For each digit in B and not in A are restricted to B cells all peers of these cells may be eliminated for said digit.
For each digit in A & B are restricted to A & B cells, all peers of these cells may be eliminated for said digit.

I created B.A.R.N.(s) merely because John refused to accept that. early xy, xyz, Wxyz wings{predominantly this issue}, sue du coq, ape, ate, all fall under Als rules developed later on and there by its extensions should and can apply extending the reach of those Technique where applicable.{in some cases simplified or obsoleted the technique completely}

Which is what I did by early on forWxyz wing extensions from the old forum be for the crash.
it originally covered all permutations of this technique, and later compressed the list down to 4 basic formations. With some context on extending it beyond 4 cells and 4 digits, and some notes on sub-classes for an almost almost locked version that mimicked als-Xy rule as a potential almost almost locked Set xz rule.

{which is what lead to me and john headbutting over the named technique shouldn't be extended etc when he discovered my suggestion over 3 years after the fact and I already had the work in place and finally convinced Andrew to updated his solver to reflect the idea and improved its effectiveness of this extremely rare function by over ~1500% putting the technique back into his solver! instead of scrapped}

John still refuses to accept my wxyz-wing extensions as Wxyz wings even after a two year debate... so I took his self dubbed idea in my name and came up with a "barns" definition which for what ever reason he now also Defers it to some one Else's definition again leading to more arguments. (never ending battle as he won't join this site for rational discussion and instead refers to his own lingo on the blog...= Much confusion when trying to point stuff out.)

interesting to see an Al's xy double linked rule I've been working on that idea with my new code engine. I'll have to check that out as well..
( a loop rule for start and end als using same set is also applicable in these cases)

Subset counting covers alot of stuff, and has extension as well: Disjointed Distributed Subset and obiwans Almost Disjointed distributed subset

i do have dds and adds coded into my solver and my barn code is technically based on subset-counting and als-xz rules for eliminations

as far as i'm aware: mike baker, myth jellies,danny, obi and pascal and possibly Ronk & Ruud had the only fully implemented subset functions.. {none of these guys have been on in 3-6+ years} {since the programmers forum became obsolete,and ours was kindly relocated here in.}
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

### Re: VWXYZ-Wing?

StrmCkr, would you agree that my example is both a VWXYZ-Wing and a Barn?

I'm a bit confused about the Barn definitions, however. I think you and John Welch still use different ones. To me his idea of Barn is strictly limited to the cases where exactly one digit (Z) is non-restricted and is the only source of eliminations (just like how Andrew describes his WXYZ-version, attributed to you). Also, I think he only considers cases where there's exactly N digits and N cells. If I haven't misunderstood something, your idea of Barn covers much more, such as the fully restricted cases and when the number of digits and cells differ (Type 4). Those extensions actually make the acronym illogical: fully restricted cases aren't almost restricted, and Type 4 isn't an N-set at all, right? That makes me think you shouldn't have accepted John's name for your idea because it's clearly larger than what he had in mind when he proposed the name.

Another source of confusion is in how you compare Barn to ALS techniques. For example:

StrmCkr wrote:As long as the als a - als b cells are in the same band/stack and intersection contains all the restricted digits then it falls within a barn constructions by my definitions which is an over simplified als xz system

I don't think the bolded part describes it accurately. Not everything that falls under your Barn examples is an ALS XZ type. I'm not an expert on ALS techniques, but to me your Type 3 and Type 4 examples look like ALS XY Wings with overlapping. My example above is ALS ++ AALS. Wouldn't you agree that they're more complex situations than ALS XZs?

i do have dds and adds coded into my solver and my barn code is technically based on subset-counting and als-xz rules for eliminations

Can you describe the exact relationship of Barn with DDS and ADDS? It seems to me that there's a lot of overlap.
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: VWXYZ-Wing?

Type 3 eliminations are derived by the same, Methods of subset counting (almost almost locked set)
In essence it checks the cell counts when the restricted Commons are place.

Type 4 was an accident discovery, when I set my barn code to fin a n set within n cells, it didn't consider all n digits actually occurred. So technically it is n cells with n digits (just all the cells happen to be lacking the same digit)
Hence the n=n-m

The relation ship between als_xz and barns is clear in type 1 and 2, and the potential eliminations from type 3 and 4 eliminations are applicable to als-xz extension eliminations rules which involve subset counting.

however it is easier to view them as an Al's-xy rule for simplicity instead of writing a huge list of detection rules to identify potential eliminations from these extra cases.

Now you see the whole joke part of Barn and why I came up with it, and then had some fun with the concept actually Making it do more potent stuff then normally als-xz basic rules could do by exploring internal subset arrangements.

N CELLS holding N DIGITS With x restricted Commons where by the cells are linked and almost locked

Is pretty much my only deffintion, (type 4 appears to violate that concept when u look at the fact only 3 digits are used)

DD's, adds, subsetcounting find eliminations by identifying restrictions with in the selected sets of cells and digits.

Als rules use the restrictions to join two sets together and note the common digit between the sets used as the eliminations
And for simplicity dose t fully explore all subsets with in th selected cells,
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

### Re: VWXYZ-Wing?

StrmCkr wrote:i posted this over on Andrews stewards page to hopefully get him to update his als-xz engine as a test case...

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`.---------------.------------.-----------------.| 5    478  1   | 2   6   3  | 789    78    49 || 34   6    247 | 1   8   9  | 237    5     34 || 9    238  28  | 7   5   4  | 2368   2368  1  |:---------------+------------+-----------------:| 2    9    3   | 6   4   8  | 5      1     7  || 48   478  478 | 59  19  15 | 236    236   36 || 1    5    6   | 3   2   7  | 4      9     8  |:---------------+------------+-----------------:| 7    38   5   | 4   19  6  | 1389   38    2  || 36   1    9   | 8   7   2  | 36     4     5  || 468  248  248 | 59  3   15 | 16789  678   69 |'---------------'------------'-----------------'`

Almost Locked Set XZ-Rule {double link rule}: A=r1c8 {78}, B=r79c8,r8c7 {3678}, X=7,8 => r3c8<>8, r7c7<>3, r9c79<>6

As far as I see, Andrew's ALS XZ and Sue de Coq implementations already do exactly that (the 3r7c7 gets eliminated by the naked pair first, though). His WXYZ-Wing implementation does not see that, but I'm not really sure it should either. I have a bit of mixed feelings about calling fully restricted n-sets (rank-0 logic) wings (or barns, for that matter). Somehow I think it's more natural to see wings as those that have a single non-restricted Z-candidate with rank-1 logic. That would also be the most logical definition of BARN if you consider the meaning of the original acronym. Any extensions to that principle -- especially fully restricted ones -- would be better off with other names, as far as I'm concerned.
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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Joined: 22 May 2017

### Re: VWXYZ-Wing?

SpAce wrote:
eleven wrote:Some time ago i called this a vwxyz-wing.

A very nice move, but I have a hard time seeing the vwxyz-wing there! The wxyz-wing and the xyz-wing are both obvious, but I don't see how linking them together makes a vwxyz-wing. Can you explain?

No.
You are right, this combination of 2 wings with 5 candidates does not make a vwxyz-wing.
I don't care much about technique names and definitions (just about logical correctness), but i really should, when i use a name. Sorry for wasting your time.
eleven

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Joined: 10 February 2008

### Re: VWXYZ-Wing?

eleven wrote:You are right, this combination of 2 wings with 4 candidates does not make a vwxyz-wing.
I don't care much about technique names and definitions (just about logical correctness), but i really should, when i use them.

Don't sweat it. I really enjoy seeing your brilliant moves, no matter what you call them. This one was especially interesting. Thanks for the clarification anyway!
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: VWXYZ-Wing?

StrmCkr wrote:as far as i'm aware: mike baker, myth jellies,danny, obi and pascal and possibly Ronk & Ruud had the only fully implemented subset functions.. {none of these guys have been on in 3-6+ years} {since the programmers forum became obsolete,and ours was kindly relocated here in.}

From working with sudoku variants it is clear that DDS is a generalised form of locked set (generalised naked subset) and therefore it can also -following the same principles- show a generalised form of ALS AALS ... ALS XZ rule ALS XY rules and even dual links. Programming this now with faster computer should be possible!!!

In a 9x9 vanilla sudoku we may have up to 9 different candidates in 9 different cells snaking around the grid to form this generalised locked set. What is scary though that if you find a 9 cell locked set then you may potentially have a generalised hidden set within it

tarek

tarek

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### Re: VWXYZ-Wing?

eleven wrote:
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` *--------------------------------------------------------------------* |  7       1      3     |  5     9     8      |  6      4     2      | |  8       9      2     |  6     4     1      |  5      3     7      | | b46      46     5     |  2     37    37     |  1      9     8      | |-----------------------+---------------------+----------------------| | a469     3     a69    |  1     2     679    |  479    8     5      | |  24569   4568   1     |  39    378   3679   |  3479   27    369    | | a2-69    7     a689   |  4    b38    5      | b39     12    1369   | |-----------------------+---------------------+----------------------| |  39      56     4     |  7     156   2      |  8      15    39     | |  1359    58     7     |  389   15    39     |  2      6     4      | |  13569   2      689   |  389   156   4      |  379    157   139    | *--------------------------------------------------------------------*`

(2=48)r46c13-(4|8=69)r3c1,r6c57 => -69r6c1, stte

I just used this as an exercise for subset counting. For the six cells [r34c1, r4c3, r6c357] we have five digits [34689] with counts [11212]. That adds up to 7, or +1 (7-6). Candidates that -- if true -- would make the sum negative are (69)r6c1 and (6)r5c1, thus they can be eliminated. That's one more candidate (6r5c1) than what eleven's cool move gets. Can someone see a normal move that could kill them all at once?
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: VWXYZ-Wing?

Agreeded Tarek, which is why I also developed almost hidden xz, xy function and run a dual search for size 1-4 on als-xz, and a size 1-4 in hidden now instead of a max size range on als-xz to find all.

Works pretty effective once I figured out they are complimentary.

Deffintly can do the same, for DD's and adds..
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

### Re: VWXYZ-Wing?

The double linked Wxyz example can also be viewed as 2 separate Wxyz wings if you really wanted to be technical as the x and z simply swap spots. Plus the normal. Rotation of other shared z digits for eliminations.

So I consider your argument against rank zero barns as moot, as double linked is a Compressed view of 2 identical sets and cells functions And adding in the after effects of a locked set step {box line reductions} which would come after it.

As to keeping the barn as more kin to its name of almost is still an almost locked by the same convention above. Type 3 and type 4 are there for those that want to explore full potential of subset counting and extended view them as you wish.

Those are the ones that are oddities that worked under my code to find tyoe 1 and 2 barns.

Last edited by StrmCkr on Mon Aug 13, 2018 5:33 am, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

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Joined: 05 September 2006

### Re: VWXYZ-Wing?

StrmCkr wrote:The double linked Wxyz example can also be viewed as 2 separate Wxyz wings if you really wanted to be technical as the x and z simply swap spots. Plus the normal. Rotation of other shared z digits for eliminations.

So I consider your argument against rank zero barns as moot, as double linked is a Compressed view of 2 identical sets and cells functions

If it were just that, I'd have less of a problem.

And adding in the after effects of a locked set step which would come after it.

That's what makes it very different. If we consider the simplest wings -- XY-Wings and XYZ-Wings -- there's no possibility of such a step. Adding more cells and digits to the pattern makes it possible, but should such a pattern belong to the same family then? I don't know and I'm too tired to think this through now. I have another related question, though.

How do subset counting and Barn handle this:

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`.--------------------.--------------.----------------------.| 234579  2579  234  | 134  8    49 |  14569  5679  124579 || 23459   259   1    | 7    349  6  |  8      59    2459   || 4789    6     48   | 5    149  2  |  149    3     1479   |:--------------------+--------------+----------------------:| 269     4     7    | 26   269  58 |  3      1     58     || 1       29    23   | 234  7    58 |  459    589   6      || 36      8     5    | 136  136  49 |  7      2     49     |:--------------------+--------------+----------------------:| 2578    3    a268  | 9   a26   1  |ab56     4    b578    || 457     157   9    | 8    46   3  |  2     b567   17-5   || 248     12    2468 | 246  5    7  |  169    689   3      |'--------------------'--------------'----------------------'(5=268)r7c357 - (8=675)b9p135 => -5 r8c9`

What we have is an overlapping ALS XZ: a=(2568)r7c357, b=(5678)b9p135, x=8, z=5). Subset counting gives: [25678] -> [11211] (+1). Our elimination does not make that sum negative (only zero). How does subset counting work with overlapping ALS moves?
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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### Re: VWXYZ-Wing?

SpAce wrote:Can someone see a normal move that could kill them all at once?

Do you suggest that eleven's move is not a normal one ? I'm kidding...

Yes I see a "normal" move that could kill also 6r5c1. Once again a poor ALS-XY chain...

(46=9)r34c1 - (9=6)r4c3 - (6=389)r6c357 => -69 r6c1, -6r5c1

To make it simple:
- subchain (46=9)r34c1 - (9=6)r4c3 => -6 r6c1, -6r5c1
- subchain (9=6)r4c3 - (6=389)r6c357 => -9 r6c1

Otherwise, consider the whole chain and make use the specific rule when the target is in sight of a restricted common.
Cenoman
Cenoman

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### Re: VWXYZ-Wing?

Cenoman wrote:Do you suggest that eleven's move is not a normal one ? I'm kidding...

Well, it's not really "normal" because it's brilliant It's a perfectly valid AIC, though, so nothing abnormal in that sense. (It was just the subset counting move I didn't consider "normal".)

Yes I see a "normal" move that could kill also 6r5c1. Once again a poor ALS-XY chain...

(46=9)r34c1 - (9=6)r4c3 - (6=389)r6c357 => -69 r6c1, -6r5c1

Hmm. This one I wouldn't consider a normal move, however It's two moves combined into a single chain which wouldn't eliminate anything if viewed as a normal AIC (only the end nodes can eliminate, unless it's a loop). Unless AIC rules are changed to allow such subchains (with supporting mark-up that would make them obvious), I would prefer the simpler option with two moves:

To make it simple:
- subchain (46=9)r34c1 - (9=6)r4c3 => -6 r6c1, -6r5c1
- subchain (9=6)r4c3 - (6=389)r6c357 => -9 r6c1

I think it's much clearer that way. However, if the shared section were longer than one node, then I'd see more value in the combined chain (if proper mark-up were added to make it clear how it's to be interpreted). In principle I don't have anything against extending the AIC spec to allow certain optimizations -- as long as it's kept readable. As you know, I've broken the rules myself by adding more heads to AIC Type 2s and dubbing them AIC-Hydras:

http://forum.enjoysudoku.com/where-to-find-extreme-puzzles-t34018-30.html#p265068
http://forum.enjoysudoku.com/one-or-two-aic-moves-t34563.html
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`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

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Joined: 22 May 2017

### Re: VWXYZ-Wing?

If we consider the simplest wings -- XY-Wings and XYZ-Wings -- there's no possibility of such a step.

actually there is double linked xy,xyz -wings that when viewed as "normal " moves include a subset move of box line reduction

im sure most of them would fall out side the box for most peoples thinking on what is a xy-wing or xyz-wing

like this fun example which is by definitions an als-xz move or a classic "xy-wing" without extended double link rules.
Code: Select all
`.---------------------------------.---------------------------------.---------------------------------.| 13         12         123456789 | 123456789  123456789  123456789 | 123456789  23         123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |:---------------------------------+---------------------------------+---------------------------------:| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 || 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |'---------------------------------'---------------------------------'---------------------------------'`

Almost Locked Set XZ-Rule: A=r1c1 {13}, B=r1c28 {123}, X=1,3 => r1c345679<>3, r1c345679,r2c123,r3c123<>1, r1c345679<>2

you could see it as this
Almost Locked Set XZ-Rule: A=r1c18 {123}, B=r1c28 {123}, X=1, Z=2,3 => r1c345679<>2, r1c345679<>3
and follow it with a box line reduction for digit 1.

or see it as three traditional style xy-wings
XY-Wing: 2/3/1 in r1c128 => r1c345679,r2c123,r3c123<>1
XY-Wing: 1/3/2 in r1c128 => r1c345679<>2
XY-Wing: 1/2/3 in r1c128 => r1c345679<>3

or more traditionally as a naked triple and still have to apply a box line reduction afterwards if the program blindly apply a same sector removal instead of a peers removal for all included digits as individuals
Naked Triple: 1,2,3 in r1c128 => r1c345679<>1, r1c345679<>2, r1c345679<>3 {as seen in hodoku which does a sector removal instead of digit sum => peers}
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1165
Joined: 05 September 2006

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