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Sudopedia--wings

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Thu Nov 22, 2012 10:04 pm    Post subject: Sudopedia--wings Reply with quote

Keith, is there anything on some of the wings that are strange to me, such as H, L and S?
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keith



Joined: 19 Sep 2005
Posts: 3162
Location: near Detroit, Michigan, USA

PostPosted: Fri Nov 23, 2012 2:38 am    Post subject: Reply with quote

Marty,

No. Here is the index to wings:

Quote:
Wings

XY-Wing

Three cells with pivot cell XY and two pincer cells XZ and YZ.
XYZ-Wing
Three cells with pivot cell XYZ and two pincer cells XZ and YZ.
WXYZ-Wing
Four cells with pivot cell WXYZ and three pincer cells WZ, XZ and YZ.
W-Wing
Four cells in a chain: a cell WX, a cell with X as a candidate, another cell with X as a candidate, another cell WX, such that the two cells containing X as a candidate have a strong link.


Not even an M-wing.

Keith
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arkietech



Joined: 31 Jul 2008
Posts: 1712
Location: Northwest Arkansas USA

PostPosted: Fri Nov 23, 2012 12:09 pm    Post subject: Reply with quote

Simply stated a wing is a chain of 3. There are three strong links, at the beginning in the middle and at the end. Thay have names according to the pattern of whether the strong link is internal (a bivalue cell) or cell to cell (local).

XY-WING (x=y)-(y=z)-(z=x) any x that can see both ends can be eliminated.

ALS XY-WING is an xy-wing where one or more of the bivalue cells is replaced with a almost locked set (als)

W-WING (x=y)-y=y-(y=x) any x that can see both ends can be eliminated.

M-WING (x=y)-y=(y-x)=x any x that can see both ends can be eliminated.

Split wing S-WING x=y-(y=x)-x=y y may be eliminated from the beginning cell and x can be eliminated from the ending cell.

Local wing L-WING x=(x-z)=(z-y)=y y may be eliminated from the beginning cell and x can be eliminated from the ending cell.

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.

XYZ-WING (x=y)-(y=xz)-(z=x) any x that can see both ends can be eliminated.

Exceptions:

X-WING is a fish pattern involving 2 rows and 2 columns.

WXYZ-WING two als's wxyz and wz one in a line the other in a box with the w's seeing each other. All other z's in both box and line that see all z's in als's can be removed.

it is the same as an ALS XZ rule with W as the restricted common

Code:

.-----------.----------.----------.
| *  *  WXYZ| .  XZ .  | YZ .  .  |
| .  WZ .   | .  .  .  | .  .  .  |
| .  .  .   | .  .  .  | .  .  .  |
:-----------+----------+----------:

.-----------.----------.----------.
| *  *  WXYZ| .  .  .  | WZ .  .  |
| XZ .  .   | .  .  .  | .  .  .  |
| .  YZ .   | .  .  .  | .  .  .  |
:-----------+----------+----------:
 



There probably are exceptions, editing and additions needed to this definition and list. They are welcome.

already editing Very Happy


Last edited by arkietech on Tue Nov 27, 2012 1:00 pm; edited 4 times in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Fri Nov 23, 2012 8:06 pm    Post subject: Reply with quote

Code:
  *--------------------------------------------------*
 | 1    28   6    | 9    7    4    | 3    28   5    |
 | 258  7    23   | 35   1    6    | 9    4    28   |
 | 45   34   9    | 35   8    2    | 1    6    7    |
 |----------------+----------------+----------------|
 | 3    5    12   | 4    9    7    | 28   128  6    |
 | 24   124  8    | 6    3    5    | 7    129  129  |
 | 9    6    7    | 1    2    8    | 5    3    4    |
 |----------------+----------------+----------------|
 | 28   238  5    | 7    4    13   | 6    129  129  |
 | 7    9    34   | 2    6    13   | 48   5    18   |
 | 6    12   124  | 8    5    9    | 24   7    3    |
 *--------------------------------------------------*


My solution was (2)r4c7 = (4)r9c7 = (1)r9c3 = r4c3 => r4c3<2>

followed by a Kite in 2s r2c39,r9c3,r7c9 => r7c12,r9c7 <2>

Love that H Wing.

The above is the Fiendish from Nov. 18 and one guy's solution.

Is that first move really an H-Wing? I can't see how it fits your pattern of:

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

If he's eliminating a 2, that suggests that 2=x. That should mean that 8=y, but I don't see an 8 in the rest of the notation. Confused
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arkietech



Joined: 31 Jul 2008
Posts: 1712
Location: Northwest Arkansas USA

PostPosted: Fri Nov 23, 2012 8:56 pm    Post subject: Reply with quote

I don't see an H-wing here:

Code:
 *--------------------------------------------------*
 | 1    28   6    | 9    7    4    | 3    28   5    |
 | 258  7    23   | 35   1    6    | 9    4    28   |
 | 45   34   9    | 35   8    2    | 1    6    7    |
 |----------------+----------------+----------------|
 | 3    5    12   | 4    9    7    | 28   128  6    |
 | 24   124  8    | 6    3    5    | 7    129  129  |
 | 9    6    7    | 1    2    8    | 5    3    4    |
 |----------------+----------------+----------------|
 | 28   238  5    | 7    4    13   | 6    129  129  |
 | 7    9    34   | 2    6    13   | 48   5    18   |
 | 6    12   124  | 8    5    9    | 24   7    3    |
 *--------------------------------------------------*

(2)r4c7 = (4)r9c7 = (1)r9c3 = r4c3 => r4c3<2>


This is short-cut notation that shows no weak links. I can't see how it works.


Maybe someone else can explain this notation. Confused
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Sat Nov 24, 2012 12:48 am    Post subject: Reply with quote

Dan, you'll rue the day you posted those explanations. But if I don't ask these questions I have -0- chance of learning.

Quote:
Local wing L-WING x=(y-z)=(z-x)=y y may be eliminated from the beginning cell and x can be eliminated from the ending cell.


The first inference shows three different numbers, xyz.

That's not the case below, where there is a 1 on each side of the = sign

Code:
 *-----------------------------------------------------------*
 | 2     5     3     | 8     7     4     | 19    19    6     |
 | 689   689   689   | 1     2     3     | 5     4     7     |
 | 7     1     4     | 6     5     9     | 2     38    38    |
 |-------------------+-------------------+-------------------|
 | 3     4689  1     | 2     469   5     | 49    7     48    |
 | 469   7     5     | 349   8    d6-1   | 1349  2    a134   |
 | 489   2     89    | 349   149   7     | 6     1389  5     |
 |-------------------+-------------------+-------------------|
 | 49    349   7     | 5     1469 c126   | 8     13   b1234  |
 | 1     469   269   | 49    3     8     | 7     5     24    |
 | 5     348   28    | 7     14    12    | 134   6     9     |
 *-----------------------------------------------------------*
L-wing
1r5c9=(1-2)r7c9=(2-6)r7c6=6r5c6 => -1r5c6; stte
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arkietech



Joined: 31 Jul 2008
Posts: 1712
Location: Northwest Arkansas USA

PostPosted: Sat Nov 24, 2012 1:59 am    Post subject: Reply with quote

1r5c9=(1-2)r7c9=(2-6)r7c6=6r5c6 => -1r5c6; stte

x=(y-z)=(z-x)=y

should be

x=(x-z)=(z-y)=y

my boo boo I will correct it Thanks.

x=1
z=2
y=6

hope this helps
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Sat Nov 24, 2012 2:09 am    Post subject: Reply with quote

arkietech wrote:
Code:
 *--------------------------------------------------*
 | 1    28   6    | 9    7    4    | 3    28   5    |
 | 258  7    23   | 35   1    6    | 9    4    28   |
 | 45   34   9    | 35   8    2    | 1    6    7    |
 |----------------+----------------+----------------| D
 | 3    5    12   | 4    9    7    | 28   128  6    |
 | 24   124  8    | 6    3    5    | 7    129  129  |
 | 9    6    7    | 1    2    8    | 5    3    4    |
 |----------------+----------------+----------------|
 | 28   238  5    | 7    4    13   | 6    129  129  |
 | 7    9    34   | 2    6    13   | 48   5    18   |
 | 6    12   124  | 8    5    9    | 24   7    3    |
 *--------------------------------------------------*

(2)r4c7 = (4)r9c7 = (1)r9c3 = r4c3 => r4c3<2>
This is short-cut notation that shows no weak links. I can't see how it works. Maybe someone else can explain this notation.

Ill-advised shorthand for: (2)r4c7 = (2-4)r9c7 = (4-1)r9c3 = (1)r4c3 => r4c3<>2
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arkietech



Joined: 31 Jul 2008
Posts: 1712
Location: Northwest Arkansas USA

PostPosted: Sat Nov 24, 2012 2:26 am    Post subject: Reply with quote

ronk wrote:
Ill-advised shorthand for: (2)r4c7 = (2-4)r9c7 = (4-1)r9c3 = (1)r4c3 => r4c3<>2


Thanks ronk, .... nice example of an L-wing..
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Sun Nov 25, 2012 4:21 pm    Post subject: Reply with quote

L-Wing.

Quote:
x=(x-z)=(z-y)=y


Code:

+-----------+----------+-----------+
| .  .   .  | .  .  .  | .   .   . |
| .  .   .  | .  .  .  | .   .   . |
| .  .   .  | .  .  .  | .   .   . |
+-----------+----------+-----------+
| .  .   .  | .  .  .  | .   .   . |
| .  .   .  | .  .  .  | .   .   . |
| .  .   .  | .  .  .  | .   .   . |
+-----------+----------+-----------+
| 4  3   9  | 2  7  6  | 5   1   8 |
| 25 8   57 | 3  1  59 | 4   279 6 |
| 6  257 1  | 58 89 4  | 279 279 3 |
+-----------+----------+-----------+

Play this puzzle online at the Daily Sudoku site

Might this be one? (Be funny if it is, since this is the first puzzle where I looked for one).

5r9c4=(5-9)r8c6=(9-2)r8c8=2r8c1=>r8c1<>5
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arkietech



Joined: 31 Jul 2008
Posts: 1712
Location: Northwest Arkansas USA

PostPosted: Sun Nov 25, 2012 8:42 pm    Post subject: Reply with quote

Marty R. wrote:
Might this be one?


5r9c4=(5-9)r8c6=(9-2)r8c8=2r8c1=>r8c1<>5

5r9c4 does not "see" r8c1

5r8c2=(5-9)als:r9c4|r8c6=(9-2)r8c8=2r8c1 => -5r8c1

ALS L-wing? Confused
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Marty R.



Joined: 12 Feb 2006
Posts: 5148
Location: Rochester, NY, USA

PostPosted: Sun Nov 25, 2012 10:17 pm    Post subject: Reply with quote

I thought that was too easy. Thanks, back to the drawing board. Sad
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