The New Sudoku Players' Forum

by **StrmCkr** » Mon Feb 27, 2017 7:58 am

this thread is limited to only covering xy-wings using an incomplete Fish to determine extra eliminations via latent strong/weak link relation between the fish candidates and the selected wing cells.

the idea is not limited to the construct covered in this thread, and readily expands onto larger "wing classes" and bigger fish size links.

this thread is created based on the discussion found here

this exemplar list should be complete listing of all class types with sub-types present.

I do not endorse following the naming , types are classed to make sure i have all bases covered before i implement coding

T-Wing { transport wing should be sufficient}

I doubt this will attract much attention as it appears to be a kraken style deduction
Class A: xy-wing spanning Row + Col

Code: Select all: Type 1a) Col Type 1b) 1a Transposed Row -----------+-----------+---------- -----------+-----------+---------- . . Z | . . . | . . . . -Z . | . . . | . . . -Z XY Z | . . . | . XZ . . XY . | . . . | . YZ . . . Z | . . . | . . . Z Z Z | / / / | Z Z Z -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . Z | . . . | . . . . . . | . . . | . . . . YZ Z | . . . | . -z . . XZ . | . . . | . -z . . . Z | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 2a) Col Type 2b) 2a Transposed Row -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . -Z . | . . . | . . . -Z XY / | . . . | . XZ . . XY . | . . . | . YZ . . . Z | . . . | -Z -Z -Z / / Z | / / / | Z Z Z -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . Z | . . . | . . . . . -Z | . . . | . . . . YZ Z | . . . | . -z . . XZ -Z | . . . | . -z . . . Z | . . . | . . . . . -Z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 3a) Col Type 3b) 3a Transposed Row -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . . . | . . . | . . . . XY / | . . . | . XZ . . XY . | . . . | . YZ . . . / | . . . | . . . / / / | / Z / | Z Z Z -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . . . | . . . | . . . . . Z | . . . | . -Z . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . Z | . . . | . . . . . . | . . . | . . . . YZ Z | . . . | . -z . . XZ . | . -Z . | . -z . . . Z | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 4a) Col Type 4b) 4a Transposed Row -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . . . | . . . | . . . . XY Z | . . . | . XZ . . XY . | -Z -Z -Z | . YZ . . . / | . . . | . . . / Z / | Z Z Z | / / / -----------+-----------+---------- -----------+-----------+---------- . -Z Z | . . . | . . . . . . | . . . | . . . . -Z Z | . . . | . . . . . . | . . . | . . . . -Z Z | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . / | . . . | . . . . . . | . . . | . . . . YZ / | . . . | . -z . . XZ . | . . . | . -z . . . / | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 5a) Box Type 5b) 5a Transposed box -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . -Z . | Z Z Z | . . . -Z XY . | . . . | . XZ . . XY . | Z Z Z | . YZ . . . . | . . . | . . . . . . | / / / | . . . -----------+-----------+---------- -----------+-----------+---------- Z Z / | . . . | . . . . . . | . . . | . . . Z Z / | . . . | . . . . . . | . . . | . . . Z Z / | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . YZ . | . . . | . -z . . XZ . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- Equivalent to type 1a Equivalent to Type 1b

Code: Select all: Type 6a) Type 6b) 6a Transposed -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . XY . | . . . | . XZ . . XY . | . . . | . YZ . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | / Z Z . . . | . . . | . . . . . . | . . . | / Z Z . . . | . . . | . . . . . . | . . . | / Z Z -----------+-----------+---------- -----------+-----------+---------- . . . | / / / | . . . . . . | . . . | . . . . YZ . | Z Z Z | . -z . . XZ . | . . . | . -z -Z . . . | Z Z Z | . -Z . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 7a) Type 7b) 7a Transposed -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . XY . | -Z . . | . XZ . . XY . | . . . | . YZ . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | / Z / . . . | . . . | . . . . . . | . . . | / Z / . . . | . . . | . . . . -Z . | . . . | / Z Z -----------+-----------+---------- -----------+-----------+---------- . . . | / / / | . . . . . . | . . . | . . . . YZ . | Z Z Z | . -z . . XZ . | . . . | . -z -Z . . . | Z / / | . -Z . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 8a) ERI Type 8b) 8a Transposed ERI -----------+-----------+---------- -----------+-----------+---------- . . . | / Z / | . . . . . . | . . . | . . . . XY . | Z Z Z | . XZ . . XY . | . . . | . YZ . . . . | / Z / | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . / Z / | . . . | . . . . . . | . . . | . . . Z Z Z | . . . | . -Z . . . . | . . . | . . . / Z / | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . YZ . | . -Z . | . -z . . XZ . | . . . | . -Z . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 9a) REDUCED ERI Type 9b) 9a Transposed REDUCED ERI -----------+-----------+---------- -----------+-----------+---------- . -Z . | / Z / | . . . . . . | . . . | . . . . XY . | Z Z Z | . XZ . -Z XY . | . . . | . YZ . . . . | / / / | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . / Z / | . . . | . . . . . . | . . . | . . . Z Z / | . . . | . -Z . . . . | . . . | . . . / Z / | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . YZ . | . -Z . | . -z . . XZ . | . . . | . -Z . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- note: Combination OF 8A & 5b Combination OF 8b & 5a

Code: Select all: Type 10a) ERI Type 10b) 10a Transposed ERI -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . XY . | . -Z . | . XZ . . XY . | . . . | . YZ . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | / Z / . . . | . . . | . . . . -Z . | . . . | Z Z Z . . . | . . . | . . . . . . | . . . | / Z / -----------+-----------+---------- -----------+-----------+---------- . . . | / Z / | . . . . . . | . . . | . . . . YZ . | Z Z Z | . -z . . XZ . | . . . | . -z . . . . | / Z / | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 11a) reduced ERI Type 11b) 11a Transposed reduced ERI -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . XY . | . -Z . | . XZ . . XY . | . . . | . YZ . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | / Z / . . . | . . . | . . . . -Z . | . . . | / Z Z . . . | . . . | . . . . . . | . . . | / Z / -----------+-----------+---------- -----------+-----------+---------- . . . | / / / | . . . . . . | . . . | . . . . YZ . | Z Z Z | . -z . . XZ . | . . . | . -z -Z . . . | / Z / | . -Z . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 12a} ERI "Ring" Type 12b} ERI "Ring" 12a Transposed -----------+-----------+---------- -----------+-----------+---------- . -Y . | . . . | . -Z . . -X . | . . . | . -Z . -X XY -X | -X -X -X | -x XZ -x -Y XY -Y | -Y -Y -Y | -Y YZ -Y . -Y . | . . . | . -Z . . -X . | . . . | . -Z . -----------+-----------+---------- -----------+-----------+---------- . -Y . | . . . | . -Z . . -X . | . . . | . -Z . . -Y . | . . . | . -Z . . -X . | . . . | . -Z . . -Y . | . . . | . -Z . . -X . | . . . | . -Z . -----------+-----------+---------- -----------+-----------+---------- . -Y . | . . . | / Z / . -X . | . . . | / Z / -Z YZ -Z | -Z -Z -Z | Z * Z -Z XZ -Z | -Z -Z -Z | Z * Z . -Y . | . . . | / Z / . -X . | . . . | / Z / -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 13a} Col "Ring" Type 13b} Row "Ring" 13a Transposed -----------+-----------+---------- -----------+-----------+---------- . -Y . | . / . | . . . . -XZ . | . . . | . -Z . -XZ XY -XZ |-XZ Z-x -XZ|-XZ XZ -XZ -Y XY -Y | -Y -Y -Y | -Y YZ -Y . -Y . | . / . | . . . . -XZ . | . . . | . -Z . -----------+-----------+---------- -----------+-----------+---------- . -Y . | . / . | . . . . -XZ . | . . . | . -Z . . -Y . | . / . | . . . / z-X / | / / / | / z / . -Y . | . / . | . . . . -XZ . | . . . | . -Z . -----------+-----------+---------- -----------+-----------+---------- . -Y . | . / . | . . . . -XZ . | . . . | . -Z . -Z YZ -Z | - Z Z -Z | -Z -Z -Z . XZ . | . . . | . -Z . . -Y . | . / . | . . . . -XZ . | . . . | . -Z . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: type 14A ERI "Ring" Type 14b} ERI "Ring" 14a Transposed -----------+-----------+---------- -----------+-----------+---------- / Z-Y / | . . . | . . . / Z-X / | . . . | . . . Z-X XY Z-X |-XZ-XZ -XZ | -XZ XZ-XZ Z-Y XY Z-Y |-ZY -ZY -ZY| -ZY YZ -ZY / Z-Y / | . . . | . . . / Z-X / | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . -YZ . | . . . | . . . . -ZX . | . . . | . . . . -YZ . | . . . | . . . . -ZX . | . . . | . . . . -YZ . | . . . | . . . . -ZX . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . -YZ . | . . . | . . . . -ZX . | . . . | . . . . YZ . | . . . | . -z . . XZ . | . . . | . -z . . -YZ . | . . . | . . . . -ZX . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 15a) "ring" Type 15b) 15a Transposed -----------+-----------+---------- -----------+-----------+---------- . -Y . | . . . | . -Z . . -X . | . . . | Z -Z -Z -X XY -X | -X -X -X | -X XZ -X -Y XY -Y | -Y -Y -Y |Z-y YZ -Y . -Y . | . . . | . -Z . . -X . | . . . | Z -Z -Z -----------+-----------+---------- -----------+-----------+---------- . -Y . | . . . | . -Z . . -X . | . . . | / . . . -Y . | . . . | . -Z . . -X . | . . . | / . . . -Y . | . . . | . -Z . . -X . | . . . | / . . -----------+-----------+---------- -----------+-----------+---------- Z Z-y Z | / / / | / Z / . -X . | . . . | / . . -Z YZ -Z | . . . | . -z . -Z XZ -Z | -Z -Z -Z | Z -z -Z -Z -Y -Z | . . . | . -Z . . -X . | . . . | / . . -----------+-----------+---------- -----------+-----------+----------

Class B: Box + Row/col XY- wing

Code: Select all: Type 1a) Box Type 1b) type 1a Transposed Box -----------+-----------+---------- -----------+-----------+---------- -Z -Z -Z | Z Z Z | . . . -Z -z . | . . . | . . . -z xy -z | Z Z Z | . XZ . -Z XY . | . . . | . . . . . YZ | / / / | -z -z -z -Z -z YZ | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . Z Z / | . . . | . . . . . . | . . . | . . . Z Z / | . . . | . . . . . . | . . . | . . . Z Z / | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . -z | . . . | . . . . . . | . . . | . . . . XZ -z | . . . | . . . . . . | . . . | . . . . . -z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 2a) Box Type 2b) type 2a Transposed Box -----------+-----------+---------- -----------+-----------+---------- . . . | Z Z Z | -Z -Z -Z . -z . | . . . | . . . -z xy -z | / / / | . XZ . . XY . | . . . | . . . . . YZ | Z Z Z | -z -z -z . -z YZ | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . Z / Z | . . . | . . . . . . | . . . | . . . Z / Z | . . . | . . . . . . | . . . | . . . Z / Z | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . -Z . -z | . . . | . . . . . . | . . . | . . . -Z XZ -z | . . . | . . . . . . | . . . | . . . -Z . -z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 3a) Box Type 3b) type 3a Transposed Box -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | / / / . -z . | . . . | . . . -z xy -z | -Z -Z -Z | Z XZ Z . XY . | . . . | . . . . . YZ | . . . | Z Z Z . -z YZ | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . -Z . | . . . | . . . . . . | . . . | . . . . -Z . | . . . | . . . . . . | . . . | . . . . -Z . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . / Z Z | . . . | . . . . . . | . . . | . . . / XZ Z | . . . | . . . . . . | . . . | . . . / Z Z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 4a) row Type 4b) type 4a Transposed col -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | -Z -Z -Z . * . | . . . | . . . * xy * | / / / | Z XZ Z . XY . | . . . | . . . . . YZ | . . . | -z -z -z . * YZ | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . / . | . . . | . . . . . . | . . . | . . . . / . | . . . | . . . . . . | . . . | . . . . / . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . -Z Z -z | . . . | . . . . . . | . . . | . . . -Z XZ -z | . . . | . . . . . . | . . . | . . . -Z Z -z | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- note: equivalent to 2a equivalent to 2b

Code: Select all: Type 5a: "ring" Row Type 5b: "ring" Transposed Col -----------+-----------+---------- -----------+-----------+---------- Z-Y Z-y Z-y | / / / | Z Z Z Z-y -XYz -YZ | . . . | . . . -XYz XY -XYz| -X -X -X | -XZ XZ-XZ Z-y XY -YZ | . . . | . . . -YZ -YZ YZ| . . . |-z -z -z Z-y -XYz YZ | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . / -X . | . . . | . . . . . . | . . . | . . . / -X . | . . . | . . . . . . | . . . | . . . / -X . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . Z -Xz -z | . . . | . . . . . . | . . . | . . . Z XZ -z | . . . | . . . . . . | . . . | . . . Z -XZ -z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 6A: "ring" Box Type 6b: "ring" Transposed Box -----------+-----------+--------- -----------+-----------+---------- -Y -y -y | / / / | . . . -y -XYz -YZ | . . . | . . . -XYz XY -XYz| Z-X Z-X Z-X | -XZ XZ-XZ -y XY -YZ | . . . | . . . -YZ -YZ YZ| Z Z Z |-z -z -z -y -XYz YZ | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . / Z-X Z | . . . | . . . . . . | . . . | . . . / Z-X Z | . . . | . . . . . . | . . . | . . . / Z-X Z | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . -Xz -z | . . . | . . . . . . | . . . | . . . . XZ -z | . . . | . . . . . . | . . . | . . . . -XZ -z | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- Note: equivalent to 3a equivalent to 3b

Code: Select all: Type 7a: "ring" Type 7b: "ring" Transpose -----------+-----------+---------- -----------+-----------+---------- /-Y /-Y Z | / / / | / Z / /-Y -XYz -YZ| . . . | . . . -XYz XY -XYz| -X -X -X |-XZ XZ -XZ /-Y XY -YZ| . . . | . . . -YZ -YZ YZ| . . . | -z -z -z Z -XYz YZ | -z -z -z | -z -z -z -----------+-----------+---------- -----------+-----------+---------- . . -Z | . . . | . -Z . / -X . | . . . | . . . . . -Z | . . . | . -Z . / -X . | . . . | . . . . . -Z | . . . | . -Z . / -X . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . -Z | . . . | . -Z . / -XZ -z | . . . | . . . . . -Z | . . . | . -Z . Z XZ -z | -z -z -z | -z -z -z . . -Z | . . . | . -Z . / -XZ -z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: Type 8a: "ring" Type 8b: "ring" Transpose -----------+-----------+---------- -----------+-----------+---------- -Y -Y -Yz | . . . | . . . -Y -XYz -Y | . / . | . . . -XYz XY -XYz| -X -X -X |-XZ XZ -XZ -Y XY -Y | . / . | . . . -Y -Y YZ | . . . | -z -z -z -YZ -XYz YZ | -z z -z | -z -z -z -----------+-----------+---------- -----------+-----------+---------- . . -Z | . . . | . -Z . . -X . | . / . | . . . / / Z | / / / | / Z / . -X . | . / . | . . . . . -Z | . . . | . -Z . . -X . | . / . | . . . -----------+-----------+---------- -----------+-----------+---------- . . -Z | . . . | . -Z . . -XZ -z | . / . | . . . . . -Z | . . . | . -Z . . XZ -z | -z z -z | -z -z -z . . -Z | . . . | . -Z . . -XZ -z | . / . | . . . -----------+-----------+---------- -----------+-----------+----------

Updated:

A way to identify these: {this works for every N size "wing" }
build your wing identify the extra "z" candidate
pick a "Target" Sector that has no candidate "z" from the wing
choose a C sector that intersect the "target" sector
choose a D sector that intersect the "target" sector
Sector C & D intersection of "Target" contains all "z" candidates for "Target" sector
Sector C Contains "Z" candidates from "wing" found in C Sectors

all peer cells of "z" candidates in wing not used in C sector
and peer of Sectors D "z" candidates
cannot contain "z"

when sector D see all "Z" candidates from "wing" found in D Sectors
and D& C contain all "Z" candidates from the wing we have found a "ring" type

by **StrmCkr** » Sat Mar 25, 2017 8:08 pm

example grid:

Code: Select all: .-------------.-----------.------------. | 12 6 5 | 4 7 18 | 3 28 9 | | 23 239 7 | 89 5 6 | 1 28 4 | | 14 49 8 | 2 3 19 | 7 5 6 | :-------------+-----------+------------: | 9 1 2 | 6 8 4 | 5 3 7 | | 37 37 6 | 1 9 5 | 8 4 2 | | 8 5 4 | 7 2 3 | 6 9 1 | :-------------+-----------+------------: | 245 24 3 | 89 6 7 | 29 1 58 | | 6 8 9 | 5 1 2 | 4 7 3 | | 257 27 1 | 3 4 89 | 29 6 58 | '-------------'-----------'------------'

T - Xy wing :
Xy wing 249 @ R3C2,R7C27
Z = 9 @ R9C67
=>> R3C6 <> 9

T - Xy wing :
Xy wing 249 @ R3C2,R7C27
Z = 9 @ R7C4,R9C6
=>> R3C6 <> 9

T - Xy wing :
Xy wing 249 @ R3C2,R7C27
Z = 9 @ R7C4,R2C4
=>> R3C6 <> 9

T - Xy wing :
Xy wing 249 @ R3C2,R7C27
Z = 9 @ R2C24
=>> R7C4 <> 9

T - Xy wing :
Xy wing 249 @ R3C2,R7C27
Z = 9 @ R39C6
=>> R7C4,R9C7 <> 9

T - Xy wing :
Xy wing 249 @ R3C2,R7C27
Z = 9 @ R2C4,R3C6
=>> R7C4 <> 9

by **jco** » Mon Jul 27, 2020 8:36 pm

Hello StrmCkr,

While I was looking at these patterns, I noticed that for cases 3A and 3B of class B it seems that there are 3 more eliminations with three large Zs becoming -z.
Previously, there are two typos, with small Zs missing a minus sign, but in the transpose the minus sign was correctly there (in cases with lots of eliminations due to a continuous loop).
Anyway, I wrote this because I thought you would like to get rid of any typos.

Regards,
jco

[Added: found them: 12b of class A, r9c2 should be -x, and in 13a of class A, "z" should be "-z" in block 8 (r8c6)]

by **StrmCkr** » Wed Jul 29, 2020 5:58 am

[Added: found them: 12b of class A, r9c2 should be -x, and in 13a of class A, "z" should be "-z" in block 8 (r8c6)]

thanks for the finds on transcription errors they are now
fixed

While I was looking at these patterns, I noticed that for cases 3A and 3B of class B it seems that there are 3 more eliminations with three large Zs becoming -z.

that is correct it would contain a cannibalistic elimination which is hard to depict correctly with no confusion however it can be
viewed easier in this equivalent version

or adding a side note that the elimination for R3C789 as suggested is also directly derived from the contained xy-wing

Code: Select all: +-----------------+---------------+--------------+ | (3) (3) (3) | (3) (3) (3) | / / / | | -3 (12) -3 | -3 -3 -3 | . (23) . | | . . (13) | . . . | -3 -3 -3 | +-----------------+---------------+--------------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +-----------------+---------------+--------------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +-----------------+---------------+--------------+

strmckr

The New Sudoku Players' Forum

Fin Transport/ Irregular "xy-Wings" aka Kraken fish

Fin Transport/ Irregular "xy-Wings" aka Kraken fish

practical examples

Re: Fin Transport/ Irregular "xy-Wings" aka Kraken fish

Re: Fin Transport/ Irregular "xy-Wings" aka Kraken fish