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by **ArkieTech** » Thu May 16, 2013 12:33 am

Code: Select all: *-----------* |1..|...|..8| |.9.|.2.|.4.| |...|185|...| |---+---+---| |..1|592|8..| |5.8|3.7|6.9| |..9|816|2..| |---+---+---| |...|254|...| |.8.|.7.|.6.| |9..|...|..7| *-----------*

Play/Print this puzzle online

by **StrmCkr** » Thu May 16, 2013 2:37 am

Code: Select all: .-------------------.---------.---------------. | 1 357 2357 | 4 6 9 | 357 235 8 | | 8 9 56 | 7 2 3 | 15 4 156 | | 23467 3467 3467 | 1 8 5 | 37 9 236 | :-------------------+---------+---------------: | 3467 3467 1 | 5 9 2 | 8 37 34 | | 5 2 8 | 3 4 7 | 6 1 9 | | 347 347 9 | 8 1 6 | 2 357 345 | :-------------------+---------+---------------: | 367 1367 367 | 2 5 4 | 9 8 13 | | 234 8 345 | 9 7 1 | 345 6 235 | | 9 145 245 | 6 3 8 | 145 25 7 | '-------------------'---------'---------------'

m-wing type 4a: 5 5- r1c2 =5= r9c2 =1= r9c7 -1- r2c7 -5 => r1c78,r2c3<>5 stte;

by **pjb** » Thu May 16, 2013 2:53 am

Code: Select all: 1 b357 2357 | 4 6 9 | 357 235 8 8 9 a56 | 7 2 3 |e15 4 156 23467 3467 23467 | 1 8 5 | 37 9 236 ---------------------+----------------------+--------------------- 3467 3467 1 | 5 9 2 | 8 37 34 5 2 8 | 3 4 7 | 6 1 9 347 347 9 | 8 1 6 | 2 357 345 ---------------------+----------------------+--------------------- 367 1367 367 | 2 5 4 | 9 8 13 234 8 2345 | 9 7 1 | 345 6 235 9 c145 245 | 6 3 8 |d145 25 7

Discontinuous loop: (6=5) r2c3 - r1c2 = (5-1) r9c2 = r9c7 - (1=5) r2c7 - (5=6) r2c3, => -5 r2c3; stte

Phil

by **Leren** » Thu May 16, 2013 3:54 am

Code: Select all: *--------------------------------------------------------------* | 1 d357 2357 | 4 6 9 | 357 235 8 | | 8 9 6-5 | 7 2 3 |a15 4 156 | | 23467 3467 23467 | 1 8 5 | 37 9 236 | |--------------------+--------------------+--------------------| | 3467 3467 1 | 5 9 2 | 8 37 34 | | 5 2 8 | 3 4 7 | 6 1 9 | | 347 347 9 | 8 1 6 | 2 357 345 | |--------------------+--------------------+--------------------| | 367 1367 367 | 2 5 4 | 9 8 13 | | 234 8 d2345 | 9 7 1 | 345 6 235 | | 9 c145 d245 | 6 3 8 |b145 25 7 | *--------------------------------------------------------------*

M-Wing Type 2a (5=1) r2c7 - r9c7 = (1-5) r9c2 = r89c3 => -5 r2c3; stte, or

Leren

PS Amended typo Type 1a changed to 1b

PPS Removed types 3a and 1b - see discussions below.

Leren

by **daj95376** » Thu May 16, 2013 7:16 am

Leren wrote:
Code: Select all
*--------------------------------------------------------------* | 1 d357 2357 | 4 6 9 | 357 235 8 | | 8 9 6-5 | 7 2 3 |a15 4 156 | | 23467 3467 23467 | 1 8 5 | 37 9 236 | |--------------------+--------------------+--------------------| | 3467 3467 1 | 5 9 2 | 8 37 34 | | 5 2 8 | 3 4 7 | 6 1 9 | | 347 347 9 | 8 1 6 | 2 357 345 | |--------------------+--------------------+--------------------| | 367 1367 367 | 2 5 4 | 9 8 13 | | 234 8 d2345 | 9 7 1 | 345 6 235 | | 9 c145 d245 | 6 3 8 |b145 25 7 | *--------------------------------------------------------------*

M-Wing Type 2a (5=1) r2c7 - r9c7 = (1-5) r9c2 = r89c3 => -5 r2c3; stte, or

M-Wing Type 3a (5=1) r2c7 - r9c7 = (1-5) r9c2 = r1{23}c2 => -5 r2c3; stte, or

M-Wing Type 1a (5=1) r2c7 - r9c7 = (1-5) r9c2 = r1c2 => -5 r2c3, r1c78; stte

Leren,

Here's ronk's pattern for an M-Wing Type 1A and Type 4A:

Type 1A: (b=a)r2c2 - (a)r5c2 = (a-b)r5c5 = (b)r5c8 => r2c8<>b

Code: Select all: . . . | . . . | . . . . ab . | . . . | . -b . . . . | . . . | . . . ----------+----------+--------- . . . | . . . | . . . / a / | / ab+ / | / b / . . . | . . . | . . . ----------+----------+--------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .

Type 4A: (b=a)r2c2 - (a)r5c2 = (a-b)r5c5 = (b)r3c5 => r2c46,r3c123<>b

Code: Select all: . . . | . / . | . . . . ab . |-b / -b | . . . -b -b -b | . b . | . . . ----------+----------+--------- . . . | . / . | . . . / a / | / ab+ / | / / / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . .

I'm pretty sure that your "M-Wing Type 1a" is an "M-Wing Type 4A".

In addition, the "M-Wing Type 3A" is just an "M-Wing Type 4A" using a grouped strong link on "b". Your SL isn't grouped.

Type 3A: (b=a)r2c2 - (a)r5c2 = (a-b)r5c5 = (b)r123c5 => r2c46<>b

Code: Select all: . . . | . b . | . . . . ab . |-b b -b | . . . . . . | . b . | . . . ----------+----------+--------- . . . | . / . | . . . / a / | / ab+ / | / / / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . .

Regards, Danny

by **Leren** » Thu May 16, 2013 12:31 pm

daj95376 wrote: Here's ronk's pattern for an M-Wing Type 1A and Type 4A

My apologies, I should have said type 1B not 1A and I've amended my post. I've also put the 1B and 4A diagrams together for easy comparison.

Code: Select all: Type 1B: . . . | . / . | . . . . ab . | . a . | . -b . . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . / / / | / ab+ / | / b / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . . Type 4A: . . . | . / . | . . . . ab . |-b / -b | . . . -b -b -b | . b . | . . . ----------+----------+--------- . . . | . / . | . . . / a / | / ab+ / | / / / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . .

I've interpreted the 1B diagram to mean that the second b in Row 5 can be in any Stack. I can see that there is overlap with Type 4A (transposed) if it is in
Stack 1 but not if it's in Stack 2. Am I correct in declaring an M Wing to be type 1B whatever the position of the second b in Row 5 ?

Leren

by **daj95376** » Thu May 16, 2013 3:01 pm

Leren wrote:I've interpreted the 1B diagram to mean that the second b in Row 5 can be in any Stack. I can see that there is overlap with Type 4A (transposed) if it is in
Stack 1 but not if it's in Stack 2. Am I correct in declaring an M Wing to be type 1B whatever the position of the second b in Row 5 ?

No, direction is integral in ronk's examples. Here is the transpose of Type 1B in comparison to Type 4A:

Code: Select all: Type 1B transpose: final "b" not in chute with initial "ab" . . . | . / . | . . . . ab . | . / . | . . . . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . / a / | / ab+ / | / / / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . -b . | . b . | . . . . . . | . / . | . . . Type 4A: final "b" in chute with initial "ab" . . . | . / . | . . . . ab . |-b / -b | . . . -b -b -b | . b . | . . . ----------+----------+--------- . . . | . / . | . . . / a / | / ab+ / | / / / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . .

by **StrmCkr** » Fri May 17, 2013 12:42 am

Here's ronk's pattern

collaborated work by ronk and my self

not sure why and when ronk decided to remove his post on the topic:

heres a copied version of it that i kept on a different site.
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=4255

{seeing how my link keeps breaking i'll just re post it back on this here under the old thread

http://forum.enjoysudoku.com/m-wings-m-rings-exemplars-examples-t30030.html

when we built the post we kept it uniform as:

ab cell seeing its links for A + B as located on the following:
Row {uses same row}
Col {uses same Col}
Row+Row
Row+Col
Row+Box
Col +Box
Box+Box
and grouped links as variations to each type
we also excluded transpositions after confirming them.

by **Leren** » Fri May 17, 2013 1:53 am

daj95376 wrote: Here is the transpose of Type 1B in comparison to Type 4A:

Code: Select all: Type 1B transpose: final "b" not in chute with initial "ab" . . . | . / . | . . . . ab . | . / . | . . . . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . / a / | / ab+ / | / / / . . . | . / . | . . . ----------+----------+--------- . . . | . / . | . . . . -b . | . b . | . . . . . . | . / . | . . .

Here's my current understanding of this M wing labelling issue:

Obviously the various M Wing diagrams can be rotated, reflected or transposed without changing the type. To facilitate the following discussion
I'll refer to the last M Wing Type 1B diagram that Danny posted. This is transposed from its presentation in the ronk/StrmCkr classic post on the subject.

What was clear from the diagram is that there must be exactly 2 b's in column 5, but it wasn't clear to me whether the final b had to be in rows 789 with the other positions
being covered by other types. I now believe this to be true. Specifically if the final b is in each row of column 5 then the following M Wing/M Ring types would apply:

r1c5 - M Wing Type 4A
r2c5 - M Ring Type A
r3c5 - M Wing Type 4A
r4c5 - M Wing Type 2B (transposed from its usual presentation)
r5c5 - N/A - location of ab+ cell
r5c5 - M Wing Type 2B (transposed from its usual presentation)
r7c5 - M Wing Type 1B (transposed from its usual presentation)
r8c5 - M Wing Type 1B (transposed from its usual presentation)
r9c5 - M Wing Type 1B (transposed from its usual presentation)

The original post on the subject was recently removed from this site but it can be found at the following link

https://www.speedsudoku.com/forum/viewtopic.php?f=58&t=695

Leren

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