The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|9.1|.8.|
 |4.9|5..|...|
 |...|.8.|.5.|
 |---+---+---|
 |2..|198|.36|
 |..6|7.5|2..|
 |53.|264|..8|
 |---+---+---|
 |.4.|.5.|...|
 |...|..7|3.5|
 |.2.|3.9|...|
 *-----------*


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[pjb]

Code: Select all

d367    5     d237    | 9     d247    1      | 467    8     d237   
 4      8      9      | 5      27     236    | 167    1267   1237   
 1367  c16     237    | 6-4    8      236    | 4679   5      2379   
---------------------+----------------------+---------------------
 2      7      4      | 1      9      8      | 5      3      6     
 8      9      6      | 7      3      5      | 2      14     14     
 5      3      1      | 2      6      4      | 79     79     8     
---------------------+----------------------+---------------------
 13679  4      37     | 8      5      26     | 1679   12679  1279   
 169   b16     8      |a46     12-4   7      | 3      12469  5     
 167    2      5      | 3      14     9      | 8      1467   147 

(4=6) r8c4 - (6=1) r8c2 - (1=6) r3c2 - (6=3724) r1c1359 => r3c4,r8c5 <> 4; stte

Phil

[Leren]

Code: Select all

*--------------------------------------------------------------*
|a367   5     237    | 9     247   1      |b467   8     237    |
| 4     8     9      | 5     27    236    | 167   1267  1237   |
| 137-6 1-6   237    |d46    8     236    |c4679  5     2379   |
|--------------------+--------------------+--------------------|
| 2     7     4      | 1     9     8      | 5     3     6      |
| 8     9     6      | 7     3     5      | 2     14    14     |
| 5     3     1      | 2     6     4      | 79    79    8      |
|--------------------+--------------------+--------------------|
| 13679 4     37     | 8     5     26     | 1679  12679 1279   |
| 169   16    8      | 46    124   7      | 3     12469 5      |
| 167   2     5      | 3     14    9      | 8     1467  147    |
*--------------------------------------------------------------*

h-wing: -6 r1c1 = (6-4) r1c7 = r3c7 - (4=6) r3c4 => -6 r3c12; stte

Leren

[7b53]

A 3 cells chain...
(6)r1c7=(4)r1c5=(6)r3c4 => no solution. r1c7<>6.

[Marty R.]

Code: Select all

+--------------+------------+-----------------+
| 367   5  237 | 9  247 1   | 467  8     237  |
| 4     8  9   | 5  27  236 | 167  1267  1237 |
| 1367  16 237 | 46 8   236 | 4679 5     2379 |
+--------------+------------+-----------------+
| 2     7  4   | 1  9   8   | 5    3     6    |
| 8     9  6   | 7  3   5   | 2    14    14   |
| 5     3  1   | 2  6   4   | 79   79    8    |
+--------------+------------+-----------------+
| 13679 4  37  | 8  5   26  | 1679 12679 1279 |
| 169   16 8   | 46 124 7   | 3    12469 5    |
| 167   2  5   | 3  14  9   | 8    1467  147  |
+--------------+------------+-----------------+


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Unnamed chain

4r3c7=(4-6)r1c7=r1c1-r3c2=r8c2-(6=4)r8c4=>r3c4<>4

[Marty R.]

Code: Select all

*--------------------------------------------------------------*
|a367   5     237    | 9     247   1      |b467   8     237    |
| 4     8     9      | 5     27    236    | 167   1267  1237   |
| 137-6 1-6   237    |d46    8     236    |c4679  5     2379   |
|--------------------+--------------------+--------------------|
| 2     7     4      | 1     9     8      | 5     3     6      |
| 8     9     6      | 7     3     5      | 2     14    14     |
| 5     3     1      | 2     6     4      | 79    79    8      |
|--------------------+--------------------+--------------------|
| 13679 4     37     | 8     5     26     | 1679  12679 1279   |
| 169   16    8      | 46    124   7      | 3     12469 5      |
| 167   2     5      | 3     14    9      | 8     1467  147    |
*--------------------------------------------------------------*

h-wing: -6 r1c1 = (6-4) r1c7 = r3c7 - (4=6) r3c4 => -6 r3c12; stte

Leren

Leren,

Below are the definitions off an H-Wing that I was told. Are there additional definitions?

Hybrid wing H-WING (x=y)-y=(y-z)=z x can be eliminated from the ending cell.

Hybrid wing H-WING (x=y)-(y=z)-z=z x can be eliminated from the ending cell.

[Leren]

Leren,

Below are the definitions off an H-Wing that I was told. Are there additional definitions?

Hybrid wing H-WING (x=y)-y=(y-z)=z x can be eliminated from the ending cell.

Hybrid wing H-WING (x=y)-(y=z)-z=z x can be eliminated from the ending cell.

My understanding of h-wings is that they are 3 Strong link AIC's with 1 or 2 local Strong links and
2 or 1 non-local (bi-value cell) Strong links. Your definitions satisfy this as AIC Type 2's but they should say that
(1) the first and last cells should see each other and (2) they can be read from right to left as well as from left to right, so
z can be eliminated from the start cell and x and be eliminated from the end cell (where they exist in those cells).

If z = x then these constructions still work, but as IAC Type 1's. The first and last cells don't necessarily have to see each other
and you can eliminate z(=x) from all cells that can see the first and last cells. If you set z=x and read your first case from
right to left you have the move I used in this puzzle. Maybe you could make a distinction between h2 wings (z=x) and h3 wings (z<>x) if
you feel that's important.

Leren

[Marty R.]

Maybe you could make a distinction between h2 wings (z=x) and h3 wings (z<>x) if
you feel that's important.

I don't know enough to make a distinction. I was just comparing it to the definitions I had and noticed a difference.

Thanks for the information.

[daj95376]

H-Wings and L3-Wing use three candidate values:

Code: Select all

L3-Wing:  (X)a = (X   -  Y)b = (Y-Z)c = (Z)d     "a" and "d" in same unit; a<>Z, d<>X

H1-Wing:  same as L3-Wing
H2-Wing:  (X=Y)a - (Y)b = (Y-Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X
H3-Wing:  (X=Y)a - (Y=Z)b - (Z)c = (Z)d          "a" and "d" in same unit; a<>Z, d<>X


L2-Wing, M-Wing, S-Wing, and W-Wing use two candidate values:

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"
 M-Ring:                                     =>  continuous loop if "a","d" in same unit

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

iW-Wing:  (X)s = (X-Y)a = (Y)b - (Y)c = (Y-X)d = (X)t   Inverted W-Wing (courtesy of Norm)

 S-Wing:  (X)a = (X)b - (X=Y)c - (Y)d = (Y)e     "a" and "e" in same unit; a<>Y, e<>X
                                                 but not in the same cell -- else M-Ring

L2-Wing:  (X)a = (X)b - (X)c = (X-Y)d = (Y)e     "a" and "e" in same unit; a<>Y, e<>X


Leren's chain, read from r-to-l, is an M-Wing:

Code: Select all

 M-Wing 7A (6=4)r3c4 - r1c5 = (4-6)r1c7 = (6)r1c1  =>  r3c12<>6
 M-Wing 7B (6=4)r3c4 - r3c7 = (4-6)r1c7 = (6)r1c1  =>  r3c12<>6   *** Leren's chain