The New Sudoku Players' Forum

by **rjamil** » Thu Dec 08, 2016 4:08 pm

Hi all,

What I understand with another group of strategies (like X-Wings, Finned X-Wings and Sashimi Finned X-Wings) is as follows:

XYZ-Wings: 3 cells contain exactly 3 candidates/values/clues within box-line alignment.

XYZ-Wing Hybrid: 3 cells contain exactly 3 clues within box-line alignment and one hybrid/finned cell form pair clues with XYZ-Wings line cell's box.

R. Jamil
------------------
Am also not fluent in English.

by **rjamil** » Tue Jan 03, 2017 11:49 am

Hi blue,

blue wrote:
Code: Select all
+-----------+------------+----------+ | abc -c -c | bc -c -c | -c -c -c | | . . . | . . . | . . . | | . . ad | . bd . | . . . | d=c is allowed +-----------+------------+----------+ ALS-XY-Wing: (c=b)r1c4 - (b=a)r3c35 - (a=c)r1c14 => -cr1c2356789

How about also -d from rest of the unsolved cells in r3?

Code: Select all: +-----------+------------+----------+ | abc -c -c | bc -c -c | -c -c -c | | . . . | . . . | . . . | | -d -d ad | -d bd -d | -d -d -d | +-----------+------------+----------+

R. Jamil

Edited 20170105:
StrmCkr pointed me in pm that by excluding d from r3 unsolved cells may lead to zero state.

Permutation of all possible combinations are as follows:
acdb
bcab - zero state
bcad
bcdb - zero state
cbad

I think that it is some kind of W-Wing pattern.

by **rjamil** » Thu Jan 12, 2017 9:41 pm

Hi blue,

blue wrote:Here's something similar:

Code: Select all
+-----------+-----------+-------+ | abc -c -c | ad . . | . . . | | -c -c -c | . . . | . . . | | -c -c bc | . bd . | . . . | (d=c) is allowed +-----------+-----------+-------+ ALS-XY-Wing: (c=b)r3c3 - (b=a)<r3c5,r1c4> - (a=c)<r1c1,r3c3> => -cr1c23,-cr2c123,-cr3c12

If d=c then -cr3c12 is a naked pair elimination, and -cr1c23 is a standard XYZ-Wing elimination, leaving:

Code: Select all
+-----------+-----------+-------+ | abc . . | ac . . | . . . | | -c -c -c | . . . | . . . | | . . bc | . bc . | . . . | +-----------+-----------+-------+ (still) ALS-XY-Wing: (c=b)r3c3 - (b=a)<r3c5,r1c4> - (a=c)<r1c1,r3c3> => -cr2c123

I have completed the coding for XYZ-Wings Hybrid Type 2 as mentioned by you earlier.

Tested one of the Royal 17 Sudoku puzzle:

Code: Select all: ................12....345.....1.6..7..8.......53....4....9.......4.5....1.......6

Found both XYZ-Wings Hybrid patterns, i.e., Type 1 and Type 2.

However, coding is still under testing phase.

R. Jamil

by **blue** » Fri Jan 13, 2017 8:02 pm

rjamil wrote:I have completed the coding for XYZ-Wings Hybrid Type 2 as mentioned by you earlier.

Tested one of the Royal 17 Sudoku puzzle:
Code: Select all
................12....345.....1.6..7..8.......53....4....9.......4.5....1.......6

Found both XYZ-Wings Hybrid patterns, i.e., Type 1 and Type 2.

Very good !

It's interesting that when it found them, the normal XYZ wings parts, were already "spent" (to use your words).

PS: I'm sorry I missed your previous post.

by **StrmCkr** » Fri Jan 13, 2017 10:48 pm

Code: Select all: .---------------.---------------.-------------. | 5 8 2679 | 267 1 279 | 679 3 4 | | 3 4 679 | 5 79 8 | 679 1 2 | | 29 27 1 | 267 3 4 | 5 679 8 | :---------------+---------------+-------------: | 4 29 29 | 1 8 6 | 3 5 7 | | 7 1 8 | 3 4 5 | 26 26 9 | | 6 5 3 | 27 279 279 | 8 4 1 | :---------------+---------------+-------------: | 8 3 27 | 9 6 1 | 4 27 5 | | 29 6 4 | 8 5 27 | 1 279 3 | | 1 279 5 | 4 27 3 | 279 8 6 | '---------------'---------------'-------------'

nice example: for the hybrid

{this example also show cases that you can expand the bivalve chain to any theoretical length}

5 cells
(279) @ R7C38, R8C1,R9C25 ==> 2 <> R9C7

by **rjamil** » Mon Mar 27, 2017 4:42 pm

Hi all,

I am working on WXYZ-Wings Hybrid elimination patterns and found different types as follows:

A) For WXYZ-Wings Type 1 Row-Column wise, single elimination cell - No Hybrid elimination pattern found.

B) For WXYZ-Wings Type 2a Box-Line wise, five elimination cells - No Hybrid elimination pattern found.

C) For WXYZ-Wings Type 2b Box-Line wise, two elimination cells - No Hybrid elimination pattern found.

D) For WXYZ-Wings Type 3 Box-Line wise, two elimination cells - Following Hybrid elimination patterns found:

Code: Select all: --------------+-------------+----------- 01) . wz . | xyz . . | -Z -Z -Z -z wxyz -z | . xz yz | . . . . . . | . . . | . . . --------------+-------------+----------- 02) . wz . | wz . . | . . . -z wxyz -z | . xz yz | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 03) . xz yz | wz . . | -Z -Z -Z -z wxyz -z | . wz . | . . . . . . | . . . | . . . --------------+-------------+----------- 04) . xz yz | xyz . . | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 05) . wz . | xyz . . | -Z -Z -Z -z wxyz -z | . xy yz | . . . . . . | . . . | . . . --------------+-------------+----------- 06) . wz . | wz . . | . . . -z wxyz -z | . xy yz | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 07) . xy yz | wz . . | -Z -Z -Z -z wxyz -z | . wz . | . . . . . . | . . . | . . . --------------+-------------+----------- 08) . xy yz | xyz . . | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 09) . wz . | xyz . . | -Z -Z -Z -z wxyz -z | . xy xyz | . . . . . . | . . . | . . . --------------+-------------+----------- 10) . wz . | wz . . | . . . -z wxyz -z | . xy xyz | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 11) . xy xyz | wz . . | -Z -Z -Z -z wxyz -z | . wz . | . . . . . . | . . . | . . . --------------+-------------+----------- 12) . xy xyz | xyz . . | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 13) . wz . | xyz . . | -Z -Z -Z -z wxyz -z | . xz xyz | . . . . . . | . . . | . . . --------------+-------------+----------- 14) . wz . | wz . . | . . . -z wxyz -z | . xz xyz | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 15) . xz xyz | wz . . | -Z -Z -Z -z wxyz -z | . wz . | . . . . . . | . . . | . . . --------------+-------------+----------- 16) . xz xyz | xyz . . | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 17) . wz . | xyz . . | -Z -Z -Z -z wxyz -z | . xyz xyz | . . . . . . | . . . | . . . --------------+-------------+----------- 18) . wz . | wz . . | . . . -z wxyz -z | . xyz xyz | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- 19) . xyz xyz | wz . . | -Z -Z -Z -z wxyz -z | . wz . | . . . . . . | . . . | . . . --------------+-------------+----------- 20) . xyz xyz | xyz . . | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+-----------

Hope above will cover all the cases of WXYZ-Wings Hybrid elimination strategy.

R. Jamil

by **rjamil** » Wed Mar 29, 2017 2:48 pm

Hi all again,

Am not sure but doubt following are all the WXYZ-Wings Hybrid strategy patterns:

Code: Select all: WXYZ-Wings Hybrid Type 1a Box-Line wise:- three elimination cells --------------+-------------+----------- --------------+-------------+----------- 01) . wz . | xyZ . . | -Z -Z -Z 02) . xz yz | WZ . . | -Z -Z -Z -z wxyz -z | . xz yz | . . . -z wxyz -z | . wz . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 03) . wz . | XZ . . | -Z -Z -Z 04) . wz . | -Z -Z -Z | YZ . . -z wxyz -z | . xz . | . yz . -z wxyz -z | . xz . | . yz . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 05) . xz . | WZ . . | -Z -Z -Z 06) . xz . | . . . | . . . -z wxyz -z | . wz . | . . . -z wxyz -z | . wz . | . . . . yz . | . . . | . . . . yz . | WZ . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- 07) . wz . | xyZ . . | -Z -Z -Z 08) . xy yz | WZ . . | -Z -Z -Z -z wxyz -z | . xy yz | . . . -z wxyz -z | . wz . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 09) . wz . | -Z -Z -Z | YZ . . 10) . xy . | . . . | . . . -z wxyz -z | . xy . | . yz . -z wxyz -z | . wz . | . . . . . . | . . . | . . . . yz . | WZ . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- 11) . wz . | xyZ . . | -Z -Z -Z 12) . xy xyz | WZ . . | -Z -Z -Z -z wxyz -z | . xy xyz | . . . -z wxyz -z | . wz . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 13) . xy . | . . . | . . . -z wxyz -z | . wz . | . . . . xyz . | WZ . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- 14) . wz . | xyZ . . | -Z -Z -Z 15) . xz xyz | WZ . . | -Z -Z -Z -z wxyz -z | . xz xyz | . . . -z wxyz -z | . wz . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 16) . wz . | XZ . . | -Z -Z -Z -z wxyz -z | . xz . | . xyz . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 17) . xz . | WZ . . | -Z -Z -Z 18) . xz . | . . . | . . . -z wxyz -z | . wz . | . . . -z wxyz -z | . wz . | . . . . xyz . | . . . | . . . . xyz . | WZ . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- 19) . wz . | xyZ . . | -Z -Z -Z 20) . xyz xyz | WZ . . | -Z -Z -Z -z wxyz -z | . xyz xyz | . . . -z wxyz -z | . wz . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 21) . xyz . | WZ . . | -Z -Z -Z 22) . xyz . | . . . | . . . -z wxyz -z | . wz . | . . . -z wxyz -z | . wz . | . . . . xyz . | . . . | . . . . xyz . | WZ . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- WXYZ-Wings Hybrid Type 1b Box-Line wise:- three elimination cells --------------+-------------+----------- 01) . wz . | -Z -Z -Z | . xyZ xyz -z wxyz -z | . xy . | . xyz . . . . | . . . | . . . --------------+-------------+----------- 02) . wz . | -Z -Z -Z | . xyZ . -z wxyz -z | . xy . | . xyz xyz . . . | . . . | . . . --------------+-------------+----------- 03) . wz . | -Z -Z -Z | . xyZ . -z wxyz -z | . xy . | . xyz . . . . | . . . | xy . . --------------+-------------+----------- 04) . wz . | -Z -Z -Z | . xyZ xyz -z wxyz -z | . xz . | . xyz . . . . | . . . | . . . --------------+-------------+----------- 05) . wz . | -Z -Z -Z | . xyZ . -z wxyz -z | . xz . | . xyz xyz . . . | . . . | . . . --------------+-------------+----------- 06) . wz . | -Z -Z -Z | . xyZ . -z wxyz -z | . xz . | . xyz . . . . | . . . | xy . . --------------+-------------+----------- 07) . wz . | . xyZ xyz | -Z -Z -Z -z wxyz -z | . xyz . | . xyz . . . . | . . . | . . . --------------+-------------+----------- 08) . wz . | . xyZ . | -Z -Z -Z -z wxyz -z | . xyz xyz | . xyz . . . . | . . . | . . . --------------+-------------+----------- 09) . wz . | . xyZ . | -Z -Z -Z -z wxyz -z | . xyz . | . xyz . . . . | xy . . | . . . --------------+-------------+----------- 10) . wz . | -Z -Z -Z | . xyZ xyz -z wxyz -z | . xyz . | . xyz . . . . | . . . | . . . --------------+-------------+----------- 11) . wz . | -Z -Z -Z | . xyZ . -z wxyz -z | . xyz . | . xyz xyz . . . | . . . | . . . --------------+-------------+----------- 12) . wz . | -Z -Z -Z | . xyZ . -z wxyz -z | . xyz . | . xyz . . . . | . . . | xy . . --------------+-------------+----------- WXYZ-Wings Hybrid Type 2 Box-Line wise:- three elimination cells --------------+-------------+----------- --------------+-------------+----------- 01) . wz . | WZ . . | . . . 02) . xz yz | xyZ . . | . . . -z wxyz -z | . xz yz | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 03) . wz . | WZ . . | . . . 04) . wz . | . . . | WZ . . -z wxyz -z | . xz . | . yz . -z wxyz -z | . xz . | . yz . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 05) . wz . | WZ . . | . . . 06) . xy yz | xyZ . . | . . . -z wxyz -z | . xy yz | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 07) . wz . | . . . | WZ . . 08)-Z xy -Z | . . . | . . . -z wxyz -z | . xy . | . yz . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . . yz . | YZ . . | . . . --------------+-------------+----------- --------------+-------------+----------- 09) . wz . | WZ . . | . . . 10) . xy xyz | xyZ . . | . . . -z wxyz -z | . xy xyz | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 11) . wz . | . . . | WZ . . 12)-Z xy -Z | . . . | . . . -z wxyz -z | . xy . | . xyz . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . . xyz . | xyZ xyz . | . . . --------------+-------------+----------- --------------+-------------+----------- 13) . wz . | WZ . . | . . . 14) . xz xyz | xyZ . . | . . . -z wxyz -z | . xz xyz | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 15) . wz . | WZ . . | . . . 16) . wz . | . . . | WZ . . -z wxyz -z | . xz . | . xyz . -z wxyz -z | . xz . | . xyz . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 17) . wz . | WZ . . | . . . 18) . xyz xyz | xyZ . . | . . . -z wxyz -z | . xyz xyz | . . . -z wxyz -z | . wz . | . . . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- 19) . wz . | WZ . . | . . . 20) . wz . | . . . | WZ . . -z wxyz -z | . xyz . | . xyz . -z wxyz -z | . xyz . | . xyz . -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | . . . --------------+-------------+----------- --------------+-------------+-----------

R. Jamil

Edited as on 20170418.
Edited as on 20170428.

by **rjamil** » Tue May 21, 2019 3:25 pm

Hi all,

Just to update this thread in order to reflect all (corrected) exemplars as follows:

Code: Select all: XYZ-Hybrid (Row-Column wise) (2 exemplars, up to 7 exclusions): --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | . / . 02) . -Z . | . . . | . . . -Z xyz -Z | -Z -Z -Z | -Z xZ -Z . xyz . | . . . | . xz . . . . | . . . | . / . . -Z . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . / . . -Z . | . . . | . . . . . . | . . . | . / . . -Z . | . . . | . . . . . . | . . . | . / . . -Z . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . / . . -Z . | . . . | . . . . yz . | . . . | . +Z . / yZ / | / / / | / +Z / . . . | . . . | . / . . -Z . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Dual XYZ-Hybrid: (Row-Column wise) (1 exemplar, up to 14 exclusions): --------------+-------------+----------- 01) . -Z . | . . . | . / . -Z xyz -Z | -Z -Z -Z | -Z xZ -Z . -Z . | . . . | . / . --------------+-------------+----------- . -Z . | . . . | . / . . -Z . | . . . | . / . . -Z . | . . . | . / . --------------+-------------+----------- . -Z . | . . . | . / . / yZ / | / / / | / +Z / . -Z . | . . . | . / . --------------+-------------+----------- XYZ-Wing Hybrid (Box-Line wise) (3 exemplars, up to 3 exclusions): --------------+-------------+----------- 01)-z xyz -z | . xz . | . . . -Z -Z -Z | . . . | . . . / / yZ | +Z +Z +Z | / / / 01--------------+-------------+----------- (Theoretically): --------------+-------------+----------- --------------+-------------+----------- 02)-z xyz -z | / xZ / | -Z -Z -Z 03)-z xyz -z | . xZ . | -Z -Z -Z . . . | / / / | . . . . . . | . / . | . . . . . yz | +Z +Z +Z | . . . . . yz | . +Z . | . . . 01--------------+-------------+-----------01--------------+-------------+----------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . . --------------+-------------+----------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . . --------------+-------------+----------- Dual XYZ-Wing Hybrid (Box-Line wise Theoretically) (2 exemplars, up to 6 exclusions): --------------+-------------+----------- --------------+-------------+----------- 01)-z xyz -z | / xZ / | -Z -Z -Z 02)-z xyz -z | . xZ . | -Z -Z -Z -Z -Z -Z | / / / | . . . . . . | . / . | . . . / / yZ | +Z +Z +Z | / / / / / yZ | +Z +Z +Z | / / / --------------+-------------+-----------01--------------+-------------+----------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . . --------------+-------------+----------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . . --------------+-------------+-----------

Note: A theoretically derived exemplars never occurred in Ruud's 50k specialty puzzles.
After implementing above exemplars, total 9447 Ruud's 50k specialty puzzles solved without guess. (Remaining also solved but with trial and error!!!)
My program searches for each XY- & XYZ-Wing patterns after an Apex cell and 2 Wing cells found then do as, follows:
- if XY-Ring elimination(s) found then perform XY-Ring move; or
- if basic XY- / XYZ-Wing elimination(s) found then perform basic move; or
- if Transported XY- / XYZ-Wing elimination(s) found then perform transported move; or
- if Hybrid XY- / XYZ-Wing elimination(s) found then perform hybrid move; or
- Search next hierarchical order bunch of moves.

Added as on 20200124:
After implemented various aspects of XY- & XYZ-Wing Transport moves successfully, I now realized that [most/all of] the above mentioned XYZ-Wing Hybrid patterns (Box-Line wise) become redundant as they are already covered in to XYZ-Wing Transport (Box-Line wise) move. In order to speed things up in my program, I am now removing XYZ-Wing Hybrid and Dual XYZ-Wing Hybrid moves detection routine from my program by maintaining total puzzle solved without guess statistics. However, XYZ-Hybrid and Dual XYZ-Hybrid (Row-Column wise) moves are found unique and, therefore, remain intact.

R. Jamil

by **mark lar** » Wed May 29, 2019 7:35 am

The interesting thing about XYZ wings is that they are cell forcing chains. In Example 1, above, F9 is the "source" cell. You can draw links from it to the wing cells and then to F7 and then lastly, a weak link from F9 to F7 on 1. It forms a perfect cell forcing situation in which 3 chains, each of odd length and each ending on a weak link, all meet at the target cell, F7. And as in forcing chains, this forces the 1 to be eliminated in F7.
In WXYZ-Wing you explain it quite succinctly by saying "The easy principle is that each possible value of the hinge cell results in a Z value in one of the cells in the [WXYZ]-Wing pattern, thus leaving no room for a Z on any cell all [four] can 'see'."
I like the idea of "Bent Quads" for WXYZ-Wing, so I suppose XYZ-Wing could be considered a "Bent Triple"?!

by **SpAce** » Sun Jun 16, 2019 11:28 pm

mark lar wrote:The interesting thing about XYZ wings is that they are cell forcing chains.

The only interesting thing here is that the poster seems to be a spammer, having edited his first post to include a link to a porn site. Admins, can you check this?

by **Hajime** » Mon Jun 17, 2019 1:39 pm

Great PDF paper about XYZ Wings:
http://www.sudokuwiki.org/sudoku/Genera ... tegies.pdf

by **StrmCkr** » Mon Jun 17, 2019 7:40 pm

Yup, a paper on using advanced almost locked sets and extends it into more advanced set ups with more then 2 n-1 sets (als xz, xy) these can be extended further for n-K size with N common restrictions over n sets.

Als 2rc etc. (I'll post links to the stuff posted here on the forum if requested.

For a non informative example of how far they can extend SK loops are 4 sets of 4 digits with 2 restricted Commons per 2 sets In a loop

However this is thread about something else similarly related.

by **rjamil** » Tue Oct 22, 2019 8:28 pm

Hi experts,

I have got WayBack Archive image of original site that I have referred to in my opening post of this thread.

Now, look in to Ywing styles claiming, "You may not find another site describing tips on how to solve sudoku puzzles that pilots this specific strategy." Also got Steve K this thread explaining the same.

However, JSudoku site gives alias W-Wing alias Semi Remote Pair.

By looking "Y wing style example 1", is it also called XY-Wing Hybrid move?

If 23@g3 is apex; and, 12@a3 and 13@i1 are wings then, as per basic XY-Wing move, 1 may be excluded from hi3, abc1.
If either wings' unique value is present in abc1 (grouped cells) then a ring/loop is formed and several exclusions may be possible as illustrated in original site's above mentioned figure.

Am I interpreting right way in below mentioned exemplars form?

Code: Select all: XY-Wing Hybrid (Box-Line wise): --------------+-------------+----------- --------------+-------------+----------- -zXY xy -zXY | -X xz -X | -X -X -X -zXY xy -zXY | -XZ xz -XZ | -X -X -X -Y -Y -Y | . . . | . . . -Y -Y -Y | -Z -Z -Z | . . . -YZ -YZ yz |-z+x -z+x -z+x| -Z -Z -Z -Y -Y yz |-z+y -z+y -z+y| . . . --------------+-------------+----------- --------------+-------------+-----------

R. Jamil

by **SpAce** » Tue Oct 22, 2019 9:08 pm

rjamil wrote:By looking "Y wing style example 1", is it also called XY-Wing Hybrid move?

No. It's an L3-Wing. SteveK's "Y-Wing Styles" simply include the various one-letter-wings (Y,W,H,M,S,L) that have three strong links in different configurations. (Apparently the XYZ-Wing is also included, though its membership is based on a bit wider interpretation.) I guess those other wings besides the Y-Wing (i.e. XY-Wing) didn't have specific names back then, or SteveK wasn't aware of them, so he invented his own (somewhat confusing) collective name based on the only named pattern in the group. I think we should consider that name ("Y-Wing Styles") obsolete, while at the same time recognize SteveK's brilliance in seeing how all of those patterns fit into the same family. (I bet he was one of the first, if not the first to make that observation.)

Here's the pattern in question presented as a chain (first using SteveK's chess coordinates, and then the rYcX used here):

(1)a1 = (1-3)i1 = (3-2)g3 = (2)a3 => a3 <> 1, a1 <> 2

(1)r9c1 = (1-3)r9c9 = (3-2)r7c7 = (2)r7c1 => -1 r7c1, -2 r9c1

Clearly an L3-Wing. The other patterns on that same page are XYZ-Wing, Grouped M-Ring, and Grouped W-Wing.

However, JSudoku site gives alias W-Wing alias Semi Remote Pair.

Like I said, W-Wing is one example of SteveK's "Y-Wing Styles" patterns, not an alias for it. It just might be the most common one, or at least the easiest to spot. Looks like SteveK started calling it W-Wing himself here. ("Semi Remote Pair" is actually a very descriptive name for W-Wing, but no one (at least here) uses it, so you shouldn't either.) Also, Y-Wing is an alias for XY-Wing, not for W-Wing!! Thus this is completely false:

JSudoku wrote:A Y-Wing is a simple pattern formed by a strong link and two cells with two same candidates.

Should obviously be W-Wing. Looks like the JSudoku author had completely misunderstood SteveK's "Y-Wing Styles" idea and thought it only meant W-Wings.

Am I interpreting right way in below mentioned exemplars form?

Doesn't look like it at all, I'm afraid. It's not totally your fault, though. SteveK has some truly brilliant stuff in his blog, but a lot of it is hard to understand because of the peculiar naming, notation, and coordinate systems. That's why even common patterns can be somewhat hard to recognize. Even I still have to rewrite a lot of his stuff into a language that is easier to read for me, and I'm quite fluent in almost every sudoku notation there is.

That's why I kind of doubt it's the right place for you to dig into at the moment, to be honest. I'm repeating myself, once again, but you'd be better off learning the fundamentals of chaining first (SteveK does have good stuff on chaining too, being a fan of AICs, but it's just notated a bit differently). To really understand SteveK's stuff one should learn to read his matrices as well (that was the hardest part and the most recent acquisition for me, but well worth it). Otherwise you'll be likely to confuse yourself, like you just did.

PS. On the Finding Y Wing Styles page you'll find the general descriptions of each type in terms of strong link configurations and numbers of digits, which correspond directly with the one-letter-wings:

Code: Select all: 1. 3 strong cells, 3 total digits : Y-Wing / XYZ-Wing : VVV / V[V]V 2. 2 strong cells, 1 strength in location (house), 2 total digits : W-Wing : VLV 3. 2 strong cells, 1 strength in location, 3 total digits : H3-Wing : VVL 4. 1 strong cell, 2 strengths in location, 2 total digits : M-Wing / S-Wing : VLL / LVL 5. 1 strong cell, 2 strengths in location, 3 total digits : H2-Wing : VLL 6. 3 strengths in location, 1 digit : X-Chain (L1-Wing) : LLL 7. 3 strengths in location, 2 digits : L2-Wing : LLL 8. 3 strengths in location, 3 digits : L3-Wing : LLL

(Note that I've replaced "candidates" with "digits" and added the corresponding wing-names and strong-link configurations.)

Last but not least, one bit of wisdom from the same source:

SteveK wrote:I hate to name techniques, as they are all really just forbidding chains [i.e. AICs].

I couldn't agree more. There's no real need to know patterns and their names, except for easier communication.

by **rjamil** » Thu Oct 24, 2019 7:59 am

Hi SpAce,

SpAce wrote:
rjamil wrote:By looking "Y wing style example 1", is it also called XY-Wing Hybrid move?

No. It's an L3-Wing.

I think, I missed an asterisks and tild signs interpretation!!

If I am correct, then following are the exemplars of L3-Wings:

Code: Select all: *L3-Wing Type 1 (Rows-Columns wise) (2 exemplars, 1 exclusion): --------------+-------------+----------- --------------+-------------+----------- 01) . / . | . . . | . . . 02) . / . | . . . | . / . / +XY / | / / / | / +X-Z / / +XY / | / / / | / +XZ / . / . | . . . | . . . . / . | . . . | . / . 36--------------+-------------+-----------36--------------+-------------+----------- . / . | . . . | . . . . / . | . . . | . / . . / . | . . . | . . . . / . | . . . | . / . . / . | . . . | . . . . / . | . . . | . / . --------------+-------------+----------- --------------+-------------+----------- . / . | . . . | . . . . / . | . . . | . / . / +YZ / | / / / | / +Z / . +Y-Z . | . . . | . +Z . . / . | . . . | . . . . / . | . . . | . / . --------------+-------------+----------- --------------+-------------+----------- *Dual L3-Wing Type 1 (Rows-Columns wise) (1 exemplar, up to 2 exclusions): --------------+-------------+-----------Strong Link X @ r2c28 01) . / . | . . . | . / . Strong Link Y @ r28c2 / +XY / | / / / | / +X-Z / Strong Link Z @ r28c8 & r8c28 . / . | . . . | . / . 36--------------+-------------+----------- . / . | . . . | . / . . / . | . . . | . / . . / . | . . . | . / . --------------+-------------+----------- . / . | . . . | . / . / +Y-Z / | / / / | / +Z / . / . | . . . | . / . --------------+-------------+----------- *L3-Wing Type 2 (Boxes-Lines wise) (4 exemplars, 1 exclusion): --------------+-------------+----------- --------------+-------------+----------- 01) / +XY / | / / / | / +X-Z / 02) / +XY / | / / / | / +XZ / / / / | . . . | . . . / / / | . . . | / / / / / +YZ | / / / | +Z +Z +Z / / +Y-Z | . . . | +Z +Z +Z 36--------------+-------------+-----------36--------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 03) / +XY / | / / / | / +X-Z / 04) / +XY / | / / / | / +XZ / . / . | . . . | . . . / / / | . . . | . / . / +YZ / | / / / | +Z +Z +Z / / +Y-Z | . . . | . +Z . 12--------------+-------------+-----------12--------------+-------------+----------- . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . --------------+-------------+----------- --------------+-------------+----------- . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . --------------+-------------+----------- --------------+-------------+----------- *Dual L3-Wing Type 2 (Boxes-Lines wise) (4 exemplars, up to 2 exclusions): --------------+-------------+-----------Bivalues XY @ r3c37 01) / +XY / | / / / | / +X-Z / Strong Link Z @ r1c28 / / / | . . . | / / / Strong Link X @ b1p29 / / +Y-Z | / / / | +Z +Z +Z Strong Link Y @ b3p27 24--------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 02) / +XY / | / / / | / +X-Z / 03) / +XY / | / / / | / +X-Z / . / . | . . . | / / / / / / | . . . | . / . / +Y-Z / | / / / | +Z +Z +Z / / +Y-Z | / / / | +Z +Z +Z 12--------------+-------------+-----------12--------------+-------------+----------- . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . --------------+-------------+----------- --------------+-------------+----------- . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . . / . | . . . | . . . . . . | . . . | . / . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 04) / +XY / | / / / | / +X-Z / . / . | . . . | . / . / +Y-Z / | / / / | +Z +Z +Z 12--------------+-------------+----------- . / . | . . . | . / . . / . | . . . | . / . . / . | . . . | . / . --------------+-------------+----------- . / . | . . . | . / . . / . | . . . | . / . . / . | . . . | . / . --------------+-------------+-----------

My question is, if cells containing +XY, +XZ and +YZ values have no more than two values each, then no need to check bivalues and all the above mentioned L3-Wing patterns become XY-Wing Hybrid move's pattern?

Note: I see some clear mistakes in draft notes. Number before 1st and 2nd band separator calculates number of possible variations per pattern. Let first cell picked from unsolved cell list. Now calculation shows number of possible positions of rest of the cells.

R. Jamil

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