The New Sudoku Players' Forum

[ronk]

Deleted: seldom referenced and likely of little value

[ronk]

deleted

[StrmCkr]

restoring the original contents of this topic as it is needed and is refereed toand referenced to more then you may believe. {besides a lot of my hard work went into confirming these}

the original thread by Ronk has been lost and now is partially restored here

this the quoted from Ronk in the above link.

Here is what I believe to be a minimal set of fourteen m-wing and four m-ring exemplars. It is minimal in the sense that any valid m-wing (or m-ring) will match only one of the exemplars in this set. The lone exeption is shown in the Extensions section. For additional extensions, see StrmCkr's Addendum -- Useful Extensions to the Minimal Set{not restored} This thread was inspired by 999_Spring's and StrmCkr's postings {not restored} Thanks to both for the kickoff.

What I'm calling m-wing is generally known as "generalized" m-wing elsewhere. The original m-wing introduced by keith here is defined with five strong inferences, rather than the minimum three strong inferences required, as for an xy-wing and a w-wing. As the two extra strong inferences produce no extra eliminations AFAIK, it seems fair to say the original m-wing is "over-specified." Hence, the adjective "generalized" is dropped.

It is neither my expectation nor my intent that solvers use the "Type" numbers below. They are included merely to facilitate unambiguous discussion in this thread.

A general note about the exemplars: All cells required to be void (empty) of candidates 'a' and 'b' are not explicitly marked with '/'. However, there are only two grouped conjugate links and the unit (row, column, box) containing each should be clear. If not, I'm willing to consider changing the presentation.

MINIMAL EXEMPLAR SET:
M-WINGS:

Code: Select all


Type 1A:                             Type 1B:
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  ab .  | .  .  .  | . -b  .        .  ab .  | .  a  .  | . -b  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 /  a  /  | / ab+ /  | /  b  /        /  /  /  | / ab+ /  | /  b  /
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
1A: r2c8 -b- r2c2 -a- r5c2 =a= r5c5 =b= r5c8 -b- r2c8 --> r2c8<>b
1B: r2c8 -b- r2c2 -a- r2c5 =a= r5c5 =b= r5c8 -b- r2c8 --> r2c8<>b


Type 2A:                             Type 2B:
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  ab .  | .  . -b  | .  .  .        .  ab .  | .  a -b  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | /  /  b  | .  .  .        .  .  .  | /  /  b  | .  .  .
 /  a  /  | / ab+ b  | /  /  /        .  .  .  | / ab+ b  | .  .  .
 .  .  .  | /  /  b  | .  .  .        .  .  .  | /  /  b  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
2A: r2c6 -b- r2c2 -a- r5c2 =a= r5c5 =b= r456c6 -b- r2c6 --> r2c6<>b
2B: r2c6 -b- r2c2 -a- r2c5 =a= r5c5 =b= r456c6 -b- r2c6 --> r2c6<>b


Type 3A:                             Type 3B:
 .  .  .  | .  b  .  | .  .  .        .  .  .  | .  b  .  | .  .  .
 .  ab .  |-b  b -b  | .  .  .        .  ab .  |-b ab -b  | .  .  .
 .  .  .  | .  b  .  | .  .  .        .  .  .  | .  b  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 /  a  /  | / ab+ /  | /  /  /        .  .  .  | . ab+ .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
3A: r2c46 -b- r2c2 -a- r5c2 =a= r5c5 =b= r123c5 -b- r2c46 --> r2c46<>b
3B: r2c46 -b- r2c2 -a- r2c5 =a= r5c5 =b= r123c5 -b- r2c46 --> r2c46<>b


Type 4A:                             Type 4B:
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  ab .  |-b  / -b  | .  .  .        . ab  .  |-b  a -b  | .  .  .
-b -b -b  | .  b  .  | .  .  .       -b -b -b  | .  b  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 /  a  /  | / ab+ /  | /  /  /        .  .  .  | . ab+ .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
4A: r2c46 -b- r2c2 -a- r5c2 =a= r5c5 =b= r3c5 -b- r2c46 --> r2c46<>b,r3c123<>b
4B: r2c46 -b- r2c2 -a- r2c5 =a= r5c5 =b= r3c5 -b- r2c46 --> r2c46<>b,r3c123<>b


Type 5A:                             Type 5B:
 .  .  .  | .  /  .  | .  .  .        .  .  .  | /  /  /  | .  .  .
 .  ab .  | .  /  .  | .  .  .        .  ab .  | a  a  a  | .  .  .
 a  a  a  | / ab+ /  | /  /  /        .  .  .  | / ab+ /  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 . -b  .  | .  b  .  | .  .  .        . -b  .  | .  b  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
5A: r5c2 -b- r2c2 -a- r3c123 =a= r3c5 =b= r5c5 -b- r5c2 --> r5c2<>b
5B: r5c2 -b- r2c2 -a- r2c456 =a= r3c5 =b= r5c5 -b- r5c2 --> r5c2<>b


Type 6A:                             Type 6B:
-b -b -b  | b  b  b  | .  .  .       -b -b -b  | b  b  b  | .  .  .
 .  ab .  | /  /  /  | .  .  .        .  ab .  | a  a  a  | .  .  .
 a  a  a  | / ab+ /  | /  /  /        .  .  .  | / ab+ /  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  .  .  | .  .  .
6A: r1c123 -b- r2c2 -a- r3c123 =a= r3c5 =b= r1c456 -b- r1c123 --> r1c123<>b
6B: r1c123 -b- r2c2 -a- r2c456 =a= r3c5 =b= r1c456 -b- r1c123 --> r1c123<>b


Type 7A:                             Type 7B:
 .  .  .  | .  .  .  | .  .  .        .  .   . | /  /  /  | .  .  .
 .  ab .  | .  .  .  |-b -b -b        .  ab .  | a  a  a  |-b -b -b
 a  a  a  | / ab+ /  | b  b  b        /  /  /  | / ab+ /  | b  b  b
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  .  .  | .  .  .        .  .  .  | .  .  .  | .  .  .
7A: r2c789 -b- r2c2 -a- r3c123 =a= r3c5 =b= r3c789 -b- r2c789 --> r2c789<>b
7B: r2c789 -b- r2c2 -a- r2c456 =a= r3c5 =b= r3c789 -b- r2c789 --> r2c789<>b

M-RINGS:

Code: Select all


Type A:
 .  -a   .  | .  /  .  | .  .  .
-b  ab  -b  |-b  b -b  |-b -b -b
 .  -a   .  | .  /  .  | .  .  .
------------+----------+---------
 .  -a   .  | .  /  .  | .  .  .
 /   a   /  | / ab+ /  | /  /  /
 .  -a   .  | .  /  .  | .  .  .
------------+----------+---------
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
In addition, r5c5=ab
r2c2 -a- r5c2 =a= r5c5 =b= r2c5 -b- r2c2 - continuous loop


Type B:
-a -a  -a | /   /   / | .  .  .
-ab ab -ab| b   b   b |-b -b -b
 a  a   a | /  ab+  / | /  /  /
----------+-----------+---------
 .  .   . | .   .   . | .  .  .
In addition, r3c5=ab
r2c2 -a- r3c123 =a= r3c5 =b= r2c456 -b- r2c2 - continuous loop


Code: Select all

Type: B1 -- added by strmckr  {oct 19,2017}, 
-a  -a  -a  | /  /  /  | .  .  .
-ab ab  -ab | b  b  b  |-b -b -b
 /   a   /  | / ab+ /  | /  /  /
------------+----------+---------
 .  -a   .  | .  .  .  | .  .  .
 .  -a   .  | .  .  .  | .  .  .
 .  -a   .  | .  .  .  | .  .  .
------------+----------+---------
 .  -a   .  | .  .  .  | .  .  .
 .  -a   .  | .  .  .  | .  .  .
 .  -a   .  | .  .  .  | .  .  .
In addition, r3c5=ab
r2c2 -a- r3c2 =a= r3c5 =b= r2c456 -b- r2c2 - continuous loop


Type: AB -- added by strmckr {oct 19,2017}, patterned noted as a missing M-ring by Leren
example puzzle found by PJB

Code: Select all

Type: AB
-a  -a  -a  | .  /  .  | .  .  .
-ab ab  -ab | -b b  -b |-b -b -b
 /   a   /  | / ab+ /  | /  /  /
------------+----------+---------
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
------------+----------+---------
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
In addition, r3c5=ab
r2c2 -a- r3c2 =a= r3c5 =b= r2c5 -b- r2c2 - continuous loop


Code: Select all

 

Type C:
-ab -ab -ab | .  .  .  | .  .  .
-ab ab  -ab | .  .  .  | .  .  .
ab* ab* ab* | / ab+ /  | /  /  /
------------+----------+---------
 .   .   .  | .  .  .  | .  .  .
In addition, r3c5=ab
r2c2 -a- r3c123 =a= r3c5 =b= r3c123 -b- r2c2 - continuous loop


Type D:
 .   .   .  | /   /   / | .   .   .
-ab ab  -ab |ab* ab* ab*|-ab -ab -ab
 .   .   .  | /  ab+  / | .   .   .
------------+-----------+-----------
 .   .   .  | .   .   . | .   .   .
In addition, r3c5=ab
r2c2 -a- r2c456 =a= r3c5 =b= r2c456 -b- r2c2 - continuous loop

'ab' means a bivalued cell with candidates 'a' and 'b'
'ab+' means the cell must contain both 'a' and 'b' candidates, and possibly others
'ab*' means the cell may contain 'a' or 'b' or both, and very likely others
'-ab' means both 'a' and 'b' are eliminated

If the above is correct, any valid m-wing or m-ring will match only one of the above exemplars, with Type 2C (below) being the only known exception.

USEFUL EXTENSIONS to MINIMAL EXEMPLAR SET

Code: Select all


Type 2C: (Simultaneously a Type 2A and a transposed Type 2B)
 .  . . | .  .  . | . . .
 . ab . | .  . -b | . . .
 .  . . | .  .  . | . . .
--------+---------+-------
 .  . . | /  /  / | . . .
 /  a / | / ab+ / | / / /
 . -b . | /  /  b | . . .
--------+---------+-------
 .  . . | .  .  . | . . .
2: r2c6 -b- r2c2 -a- r5c2 =a= r5c5 =b= r6c6 -b- r2c6 --> r2c6<>b,r6c2<>b

added some newly noted exemplars: oct 19,2017

[daj95376]

StrmCkr requested that I post the puzzles that ronk found for his exemplars. I'm not sure if ronk ever posted the puzzles. He shared them with me for cross-checking of his results. The M-Wing/Ring appears after using only SSTS steps.

These puzzles fall under what ronk characterized as "Robust". Basics are all that's needed after the M-Wing/Ring.

Code: Select all

# m-wing1A:
9...5..3....1....8..6...4.2....7..2...42.68...9..3....8.3...2..7....9....4..8...6 # Ruud50k #17852
7.3..1..6.......3..9.6..2......7.8.1...3.2...5.8.9......1..4.2..7.......6..8..4.9 # Ruud50k #37876
..5..3.1...7.6....3.91.7..........25..8...9..74..........2.84.9....1.5...6.9..8.. # Ruud50k #39657

# m-wing1B:
......61......85..3..6...48...7.24.9..6...1..7.83.4...86...9..5..21......79...... # Ruud50k #19424
.....8.1...51..7.....92........6.....73...94....8..6.742...5....3..4.16...1....5. # Mike Barker

# m-wing2A:
..532.61...9.17.8.......4......8..5.9.......3.3..4......6.......1.45.3...83.627.. # Ruud50k #17199
9835...4....1.....2....3..8.....17..45.....92..62.....1..3....9.....4....4...5617 # Ruud50k #30439

# m-wing2B:
.....1..3....4..6..2.98..5....4.25....7...9....37.8....6..17.4..3..6....5..8..... # Ruud50k #20702
..2....35.1.....8....1.7.2.7....19......5......47....8.5.2.3....8.....4.92....8.. # Ruud50k #49585

# m-wing2C:
..6.5.......7...35....9..2..4.....875...8...127.....4..5..4....32...8.......1.9.. # Ruud50k #10270
...2......5.83.41.24...6..8..7..1...1.......6...4..3..3..1...87.91.62.3......4... # Ruud50k #41729

# m-wing3A:
..5.....4..36...1..1...26..8...1..5..7.....2..3..8...1..25...9..8...94..9.....7.. # Ruud50k #23559

# m-wing3B:
..4....1.7.15....8.8....9.....3.9...64.8.2.95...6.5.....8....6.3....45.9.2....1.. # Ruud50k #25209
.....1...6...98.1...54....34...7.........4..6..691..5..8...723..4......9..25..... # sudogen17 #136

# m-wing4A:
....9.1...6.3..74....4..2....4.5..1.6.......5.2..3.9....5..7....71..6.2...6.1.... # Ruud50k #21429
...67..242...........51.....4.....69..27.......8...31..5..3..4.4.....8.6...8.57.3 # sudogen4 #99874
....8..5.8.2.....3.3..6..42.46.1.............5.12.6...4........28.9..3.7........5 # sudogen4 #23891

# m-wing4B:
..4.1..5...1..53....73....2.8...9.2..95..7..3.......79...6.2...6....1.9.2.95...4. # Ruud50k #18611mrph

# m-wing5A:
.5...8..1..4.62.....8..1..2.9....6.5....3....8.2....9.5..6..1.....29.7..4..7...3. # Ruud50k #24894
.....254...94...2..4.81...6.5..7.9..2.......3..8.4..1.3...69.8..2...41...943..... # Ruud50k #34328
......6.9....7.5..6......1..7..412..9..2......4.9....8..3..4.....9.13.875.......3 # sudogen23 #949
9...8..6.87.4......52....1.2.9.7.........1..2..76.91.5.9..57.3..2...4.5....8..... # sudogen31 #2856

# m-wing5B:
..8.4.......9..45......5..7.2..19...97..8..41...47..8.3..6......85..3.......9.2.. # Ruud50k #19232

# m-wing6A:
.3.2...4...7.....8.2.64.....4.36....6...5...1....81.7.....17.8.9.....5...1...6.2. # Ruud50k #32681

# m-wing6B:

# m-wing7A:
...7.3...78.........3.18.6.............3.621..1.58...9.5....1.24........62..9.4.8 # Allan Barker

# m-wing7B:
.....8.9.1.....7.8..879..13.2......1.1..8..5.6......2.48..362..7.1.....4.3.4..... # Ruud50k #13610
.43...7......6....68..79...........8..1.8.3.....5..1.4.....1.6..5...2..39.7...8.. # Mike Barker

# m-ringA:
.4...5..9..8...3.......9.7.7..2...4.3..5.6..2.6...7..1.2.9.......7...5..4..8...3. # Ruud50k #27013
2....4.1......8.49..79...3.38.4....2....7....4....3.61.3...95..92.5......6.1....3 # Ruud50k #28880

# m-ringB:
..2397...18....2....9..8......26...8.6.....4.9...81......7..5....7....24...5198.. # Ruud50k #39874

# m-ringC:
6...5..9...7.....3.....847......4...7.2...5.1...9......593.....1.....6...8..1...7 # Ruud50k #29693
.....6.......385929.....7..5....4.8..6..8..3..7.6....9..2.....171346.......5..... # Ruud50k #22750
51.....2......1..8...6.73...4......7..9.6....6..4.....2..8..93.9.....5.4.8.....1. # sudogen17 #8686

# m-ringD:
.....21.....3...84....915...1...9..62.......35..8...9...394....48...7.....56..... # Ruud50k #6698
.......5..65.3.1...731....92...9.4.6.9..1..3..36.........2.19..........7...4.9..3 # sudogen1 #3959


These puzzles fall under what ronk characterized as "non-Robust". Concurrent M-Wings/Rings may be present ... and/or SSTS steps more complex than Basics may be needed to complete the puzzles.

Code: Select all

# m-wing2A
...2.5.6.4......1...6.9..35...7..5.2.........3.9..6...52..8.1...8......3.6.5.4... # Ruud50k #16508

# m-wing6A:
.3......272...9.1...9.5....5....6.....3.8.6.....7....8....4.5...4.8...736......9. # Ruud50k #12277
9...5.6.3.......4..4..6...21.2..9.....3...7.....3..1.54...8..7..3.......6.7.1...9 # Ruud50k #18408

# m-wing6B:
8..7....4.5....6............3.97...8....43..5....2.9....6......2...6...7.71..83.2 # top95 #70

# m-wing7A:
..3...9...26.....1....94.6.1..9.....5..4.7..8.....8..5.1.72....6.....72...8...1.. # Ruud50k #2670

# m-ringA:
6.8...94......48161.......5...5....2....9.6...8...27..95..671..86......9.238...6.

# m-ringB:
....71.......6..1.6..2..3...6.9..12..5.....4..98..4.6...5..2..7.8..9.......41.... # Ruud50k #16911

# m-ringD:
....36.....15...2.6.3...1...4.7....8.3.....9.1....2.6...9...8.6.7...85.....34.... # Ruud50k #12595


[Leren]

Code: Select all

daj95376 wrote: StrmCkr requested that I post the puzzles that ronk found for his exemplars.

I've tested all of these and they work pretty much as described except for #20702 which would be better placed in the non-robust section.

Also both Type 2C puzzles only make one elimination and could just as well be described as type 2A's. Can anyone provide an example of a puzzle
with a Type 2C M Wing that makes 2 eliminations, or is this just a theoretical construct for which no real life example has been found?

Leren

[daj95376]

I've tested all of these and they work pretty much as described except for #20702 which would be better placed in the non-robust section.

Also both Type 2C puzzles only make one elimination and could just as well be described as type 2A's. Can anyone provide an example of a puzzle
with a Type 2C M Wing that makes 2 eliminations, or is this just a theoretical construct for which no real life example has been found?

Here is my solver's solution. It qualifies as "Robust" using my earlier definition.

Code: Select all

Puzzle #8:   m-wing2B: Ruud50k #20702

.....1..3....4..6..2.98..5....4.25....7...9....37.8....6..17.4..3..6....5..8.....

 +-----------------------+
 | . . . | . . 1 | . . 3 |
 | . . . | . 4 . | . 6 . |
 | . 2 . | 9 8 . | . 5 . |
 |-------+-------+-------|
 | . . . | 4 . 2 | 5 . . |
 | . . 7 | . . . | 9 . . |
 | . . 3 | 7 . 8 | . . . |
 |-------+-------+-------|
 | . 6 . | . 1 7 | . 4 . |
 | . 3 . | . 6 . | . . . |
 | 5 . . | 8 . . | . . . |
 +-----------------------+

   c1b4  Locked Candidate 1              <> 2    r78c1
   c9b6  Locked Candidate 1              <> 4    r3c9

 r7  b7  Locked Candidate 2              <> 9    r8c13,r9c23

         Multiple Colors                 <> 7    r3c9   (part of SSTS)

   c1b4  Locked Candidate 2              <> 1    r4c23,r6c2
   c7b3  Locked Candidate 2              <> 7    r2c9

   c2    Hidden Pair                     =  17   r29c2

 +--------------------------------------------------------------+
 |  489   489   5     |  6     7     1     |  248   289   3     |
 |  3     17    189   |  2     4     5     |  78    6     89    |
 |  467   2     46    |  9     8     3     |  47    5     1     |
 |--------------------+--------------------+--------------------|
 |  1689  89    689   |  4     39    2     |  5     1378  78    |
 |  248   458   7     |  1     35    6     |  9     238   248   |
 |  1249  459   3     |  7     59    8     |  6     12    24    |
 |--------------------+--------------------+--------------------|
 |  89    6     289   |  3     1     7     |  28    4     5     |
 |  478   3     248   |  5     6     49    |  1     2789  2789  |
 |  5     17    14    |  8     2     49    |  3     79    6     |
 +--------------------------------------------------------------+
 # 64 eliminations remain

 M-Wing 2B (4=7)r3c7 - r3c1 = (7-4)r8c1 = (4)r89c3  =>  r3c3<>4

Solution:
495671283318245769726983451689432517247156938153798624962317845834569172571824396


Your comment on Type 2C vs Type 2A has led me to review my solver's classification on Type 2C. I'm still in the process, so I'll post my findings later. As for now, it's my conjecture that Type 2C indicates the potential for two eliminations because of the non-grouped strong link on "b" in the box containg "ab+". However, since there is only one elimination in these examples, the use of Type 2A is also acceptable.

I'll see if I can locate an example of Type 2C with two eliminations. I'm fairly sure that it's not just theoretical.

[daj95376]

On the issue of using Type 2C instead of Type 2A or Type 2B when there is one elimination for an M-Wing. My solver marks an M-Wing as Type 2C when the following constraints exist:

1) There is a non-grouped strong link between [ab+] and [b] in the same box.
2) The location of [b] is not in the same row or column as [ab+].

Here is an example of M-Wing Type 2C where two eliminations occur.

Code: Select all

Puzzle #315:   from top1465

8.2.....4.9......7..5..139..8..17......5.2..1.....8.36..71.....4...7....32...5...

 +-----------------------+
 | 8 . 2 | . . . | . . 4 |
 | . 9 . | . . . | . . 7 |
 | . . 5 | . . 1 | 3 9 . |
 |-------+-------+-------|
 | . 8 . | . 1 7 | . . . |
 | . . . | 5 . 2 | . . 1 |
 | . . . | . . 8 | . 3 6 |
 |-------+-------+-------|
 | . . 7 | 1 . . | . . . |
 | 4 . . | . 7 . | . . . |
 | 3 2 . | . . 5 | . . . |
 +-----------------------+

 r6  b5  Locked Pair                     <> 49   r4c4,r5c5,r6c1237

 r9  b9  Hidden Pair                     =  17   r9c78

 r7  b9  Locked Candidate 1              <> 4    r7c56
 r7  b7  Locked Candidate 1              <> 5    r7c789

         Multiple Colors                 <> 3    r1c4

 +-----------------------------------------------------------------------+
 |  8      367    2      |  679    3569   369    |  156    156    4      |
 |  1      9     r36     |  2368   2358-6 4      |  2568   2568   7      |
 |  67     4      5      |  2678   268    1      |  3      9      28     |
 |-----------------------+-----------------------+-----------------------|
 |  2569   8     s3469   | t36     1      7      |  2459   245    259    |
 |  679    367    439-6  |  5     u36     2      |  4789   478    1      |
 |  257    57     1      |  49     49     8      |  257    3      6      |
 |-----------------------+-----------------------+-----------------------|
 |  569    56     7      |  1      23689  369    |  24689  2468   2389   |
 |  4      1      689    |  23689  7      369    |  25689  2568   23589  |
 |  3      2      689    |  4689   4689   5      |  17     17     89     |
 +-----------------------------------------------------------------------+
 # 117 eliminations remain


 debug:  ux_0_l = 000002004001   unit  containing [ab]
 debug:  ux_0_r = 000002004001   unit  containing [ab]
 debug:  ux_1_l = 000010004010   units containing [a/aaa]
 debug:  ux_1_r = 000010010020   unit  containing [ab+]
 debug:  ux_2_l = 000010010020   unit  containing [ab+]
 debug:  ux_2_r = 000020020020   units containing [b/bbb]
 debug:  ux_wrk = 000000000000   units containing all elims
 debug:  ux_xyz = 000000000000   units containing [b/bbb] & all elims
 debug:  ux_xyz = 000000000000   units containing [ab]    & all elims

 format: crb_x_x  { "x"  -->>    count_bits( ux_2_l XOR ux_2_r ) == 4 }

 M-Wing 2C (6=3)r2c3 - r4c3 = (3-6)r4c4 = (6)r5c5  =>  r2c5,r5c3<>6


 *** also present ***


 debug:  ux_0_l = 000002004001   unit  containing [ab]
 debug:  ux_0_r = 000002004001   unit  containing [ab]
 debug:  ux_1_l = 000010004010   units containing [a/aaa]
 debug:  ux_1_r = 000010010020   unit  containing [ab+]
 debug:  ux_2_l = 000010010020   unit  containing [ab+]
 debug:  ux_2_r = 000010000010   units containing [b/bbb]
 debug:  ux_wrk = 000020004010   units containing all elims
 debug:  ux_xyz = 000000000010   units containing [b/bbb] & all elims
 debug:  ux_xyz = 000000004000   units containing [ab]    & all elims

 format: crR_b_c

 M-Wing 3B (6=3)r2c3 - r4c3 = (3-6)r4c4 = (6)r4c13  =>  r5c3<>6


 *** not solvable as non-Robust using ronk's constraints for his examples ***

Solution:
8.2.....419...4..7.45..139..8..17......5.2..1..1..8.36..71.....41..7....32...5...


[Leren]

Thanks very much for both those posts, Danny.

As for puzzle #20702 I can reproduce the solution path you described, the key issue being the <> 7 r3c9 elimination prior to the M Wing.

I also see the 2 elimination M Wing type 2C in Puzzle #315, so they do exist !

Intriguingly reached the following position a bit further on in that puzzle:

Code: Select all

*--------------------------------------------------------------*
| 8     7     2      | 9     3     6      | 15    15    4      |
| 1     9     3      | 28    5     4      | 268   268   7      |
| 6     4     5      | 7    b28    1      | 3     9    a28     |
|--------------------+--------------------+--------------------|
| 29    8     6      | 3     1     7      | 2459  245   259    |
| 79    3     4      | 5     6     2      | 789   78    1      |
| 27    5     1      | 4     9     8      | 27    3     6      |
|--------------------+--------------------+--------------------|
| 5     6     7      | 1    c28    39     | 2489  248   2389   |
| 4     1     89     |d28    7     39     | 25689 2568  359-28 |
| 3     2     89     | 6     4     5      | 17    17    89     |
*--------------------------------------------------------------*

M Wing Type 2C: (8=2) r3c9 - r3c5 = (2-8) r7c5 = r8c4 => - 8 r8c9, followed immediately by
M Wing Type 2C: (2=8) r3c9 - r3c5 = (8-2) r7c5 = r8c4 => - 2 r8c9

That's two M Wing Type 2C's that are identical except that the roles of a and b are reversed.

Could there be a case for an M Wing type 2D that may produce up to 4 eliminations, or is it just remote pairs by another name .... hmmmm

A while ago you posted the following definitions:

Code: Select all

 M-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      strong link   at weak inferences
gM-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      no constraint at weak inferences
                                             =>  elims for (X) in peers common to "a","d"

Is there a gM-Wing that isn't covered by M Wings Types 1-7 ?

Leren

[daj95376]

M Wing Type 2C: (8=2) r3c9 - r3c5 = (2-8) r7c5 = r8c4 => - 8 r8c9, followed immediately by
M Wing Type 2C: (2=8) r3c9 - r3c5 = (8-2) r7c5 = r8c4 => - 2 r8c9

That's two M Wing Type 2C's that are identical except that the roles of a and b are reversed.

Could there be a case for an M Wing type 2D that may produce up to 4 eliminations, or is it just remote pairs by another name .... hmmmm

You now know why my solver normally searches for Remote Pairs at the beginning of my chains() routine.

I have a special version of my solver that specifically finds MWSL-Wings/Rings. The M-Wing/Ring types are identified through analysis of their gM-Wing chains and a cross-reference table that assigns a Type to the pattern found. In my previous post, the "format:" line identifies the cross-reference table entry for the subsequent M-Wing/Ring.

A while ago you posted the following definitions:

Code: Select all

 M-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      strong link   at weak inferences
gM-Wing:  (X=Y)a - (Y)b ... = (Y-X)c = (X)d      no constraint at weak inferences
                                             =>  elims for (X) in peers common to "a","d"

Is there a gM-Wing that isn't covered by M Wings Types 1-7 ?

What I'm calling m-wing is generally known as "generalized" m-wing elsewhere. ... Hence, the adjective "generalized" is dropped.

All of ronk's M-Wing exemplars use my gM-Wing specification. Thus, all gM-Wings should be covered. Note: only gM-Wings/Rings using three strong inferences are given a Type specification. My solver identifies those of longer length as "M-Wing ??".

[Leren]

Thanks for all your help Danny and StrmCkr, I think I'm finally on top of M Wings.

Leren

[StrmCkr]

added 2 new exemplars classes

{I'm pretty sure these used to exists in the long lost compendium post, but not having that post anymore for if and or Else's added credit to the finders where it is due}

Good job Leren for noting its a M-Ring and phill for finding an example

Code: Select all

    Type: B1 -- added by strmckr  {oct 19,2017},  noticed its exclusion based on phill example
    -a  -a  -a  | /  /  /  | .  .  .
    -ab ab  -ab | b  b  b  |-b -b -b
     /   a   /  | / ab+ /  | /  /  /
    ------------+----------+---------
     .  -a   .  | .  .  .  | .  .  .
     .  -a   .  | .  .  .  | .  .  .
     .  -a   .  | .  .  .  | .  .  .
    ------------+----------+---------
     .  -a   .  | .  .  .  | .  .  .
     .  -a   .  | .  .  .  | .  .  .
     .  -a   .  | .  .  .  | .  .  .
    In addition, r3c5=ab
    r2c2 -a- r3c2 =a= r3c5 =b= r2c456 -b- r2c2 - continuous loop




Type: AB -- added by strmckr {oct 19,2017}, patterned noted as a missing M-ring by Leren
example puzzle found by PJB

Type: AB
-a  -a  -a  | .  /  .  | .  .  .
-ab ab  -ab | .  b  .  |-b -b -b
 /   a   /  | / ab+ /  | /  /  /
------------+----------+---------
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
------------+----------+---------
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
 .  -a   .  | .  /  .  | .  .  .
In addition, r3c5=ab
r2c2 -a- r3c2 =a= r3c5 =b= r2c5 -b- r2c2 - continuous loop

[Leren]

I'l just add the M Ring type AB example puzzle in the format previously posted

Code: Select all

# m-ringAB: .7..2..8.......1.2..36.....3....52...4..7..9..9...8..68..5.......9.....1.6..3.92. # ArkieTech # 18 Oct 2017

Leren

[rjamil]

Hi StrmCkr and experts,

I am analyzing the M-Wing and M-Ring moves recently (and slowly). Following two more exemplars are proposed/suggested as follows:

Code: Select all

Type 8A:                            Type 8B:
-b -b -b  | . +b  .  | .  .  .       -b -b -b  | / +b  /  | .  .  .
 . ab  .  | .  /  .  | .  .  .        . ab  .  |+a +a/ +a | .  .  .
+a +a +a  | / +ab /  | /  /  /        .  .  .  | / +ab /  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .

Where as:
In 8A: SL a Line wise and SL b Line wise; and
In 8B: SL a Box wise and SL b Line wise.

R. Jamil
Removed -b @ r2c46 as per below Leren suggested.

[Leren]

It looks to me like the removals of b in Box 2 of both types are unnecessary, because there are only 2 b's in Column 5, both in Box 2, and they would have been removed by a claiming intersection on b in Box 2.

Leren

[rjamil]

Hi Leren,

It looks to me like the removals of b in Box 2 of both types are unnecessary, because there are only 2 b's in Column 5, both in Box 2, and they would have been removed by a claiming intersection on b in Box 2.

Leren

Thanks for the clarification. You are right, -b @ r2c46 are redundant, similar to as M-Ring Type AB move.

R. Jamil