The New Sudoku Players' Forum

[daj95376]

Let me rephrase. Mike Barker has classified the W-Wing as a Nice Loop. Is a grouped strong link acceptable for a W-Wing since it may not be a Nice Loop?

Code: Select all

 ..37.5..6.87..9.3.26.......8....7.......84.6767.31.8.......35...2..7..9.5...9....

 +-----------------------------------------------------------------------+
 |  9      1      3      |  7      24     5      |  24     8      6      |
 |  4      8      7      | *12     6      9      |  12     3      5      |
 |  2      6      5      |  148    3      18     |  1479   147    149    |
 |-----------------------+-----------------------+-----------------------|
 |  8      34     149    |  6      5      7      |  1349   124    12349  |
 |  13     5      2      |  9      8      4      |  13     6      7      |
 |  6      7      49     |  3      1      2      |  8      5      49     |
 |-----------------------+-----------------------+-----------------------|
 |  7      9      6      | *1248  *24     3      |  5     *12     128    |
 |  13     2      148    |  5      7      168    |  346    9      1348   |
 |  5      34     148    | *128    9      168    |  67     1247   238    |
 +-----------------------------------------------------------------------+

 ==>           r79c4 =2= r7c5
             /                 \
 1- r2c4 -2-                     -2- r7c8 -1  =>  [r7c4]<>1
             \                 /
               r9c4  =2= r7c45           <==


hobiwan will recognize this as #20 from Puzzle Set A.

[Edit: expanded everything.]

[ronk]

Is a grouped strong link acceptable for a W-Wing?

Code: Select all

 +-----------------------------------------------------------------------+
 |  9      1      3      |  7      24     5      |  24     8      6      |
 |  4      8      7      | *12     6      9      |  12     3      5      |
 |  2      6      5      |  148    3      18     |  1479   147    149    |
 |-----------------------+-----------------------+-----------------------|
 |  8      34     149    |  6      5      7      |  1349   124    12349  |
 |  13     5      2      |  9      8      4      |  13     6      7      |
 |  6      7      49     |  3      1      2      |  8      5      49     |
 |-----------------------+-----------------------+-----------------------|
 |  7      9      6      | *1248  *24     3      |  5     *12     128    |
 |  13     2      148    |  5      7      168    |  346    9      1348   |
 |  5      34     148    | *128    9      168    |  67     1247   238    |
 +-----------------------------------------------------------------------+

 1- r2c4 -2- r79c4 =2= r7c5 -2- r7c8 -1  =>  [r7c4]<>1


If it isn't, it should be IMO. Ditto for non-ER versions.

Code: Select all

top1465 #252
.2......6....41.....78....1......7....37.....6..412....1..74..5..8.5..7......39..

After SSTS
 1489 2    14   | 35   39   7    | 58    4589  6
 89   3    5    | 6    4    1    | 28    289   7
 49   6    7    | 8    2    59   | 345   3459  1
----------------+----------------+-----------------
 125  48   12   | 35   369  589  | 7     1246  249
 125  48   3    | 7    69   589  | 1246  1246  249
 6    7    9    | 4    1    2    | 35    35    8
----------------+----------------+-----------------
 3    1   *26   | 9    7    4    |*268  *268   5
*24   9    8    | 12   5    6    | 12-4  7     3
 7    5    26-4 | 12   8    3    | 9     1246 *24

[r8c7,r9c3] -4- r8c1 -2- r7c3 =2= r7c78 -2- r9c9 -4- [r8c7,r9c3] ==> r8c7,r9c3<>4

[daj95376]

I expanded/rephrased my initial post. It does not contradict anything ronk said.

[ronk]

Let me rephrase. Mike Barker has classified the W-Wing as a Nice Loop. Is a grouped strong link acceptable for a W-Wing since it may not be a Nice Loop?
[...]

Code: Select all

 ==>           r79c4 =2= r7c5
             /                 \
 1- r2c4 -2-                     -2- r7c8 -1  =>  [r7c4]<>1
             \                 /
               r9c4  =2= r7c45           <==


No question that it's a nice loop too. As to the candidate at the "hinge pin", I merely include it twice ...

r7c4 -1- r2c4 -2- r79c4 =2= r7c45 -2- r7c8 -1- r7c4 => [r7c4]<>1

... so that it reads "the same" right-to-left as left-to-right. Reading left-to-right for example, if r7c4<>2 is true on the left (of r79c4 =2= r7c45, then obviously r7c4=2 is false on the right.

However, if the loop were continuous (instead of a w-wing), all strong inferences would be converted to conjugate inferences, meaning a hinge pin would be an actual elimination.

[hobiwan]

If it isn't, it should be IMO. Ditto for non-ER versions.

What do you mean by "non-ER versions"?

[ronk]

If it isn't, it should be IMO. Ditto for non-ER versions.

What do you mean by "non-ER versions"?

Single-digit grouped strong links other than empty rectangles ... as in the example which followed my "ditto ... " statement.

[daj95376]

If it isn't, it should be IMO. Ditto for non-ER versions.

What do you mean by "non-ER versions"?

Single-digit grouped strong links other than empty rectangles ... as in the example which followed my "ditto ... " statement.

The grouped strong link in [b8] of my PM is associated with an Empty Rectangle pattern on '2' because [r89c56] don't contain '2'. All of the other cells in [b8] could contain '2' and a grouped strong link would still exist.

[udosuk]

I do think the Y-wing/W-wing is valid with a grouped strong link.

Meanwhile here is an ALS-xz yielding the same result:

Code: Select all

+-----------------------+-----------------------+-----------------------+
|  9      1      3      |  7     *24     5      |  24     8      6      |
|  4      8      7      | *12     6      9      |  12     3      5      |
|  2      6      5      |  148    3      18     |  1479   147    149    |
+-----------------------+-----------------------+-----------------------+
|  8      34     149    |  6      5      7      |  1349   124    12349  |
|  13     5      2      |  9      8      4      |  13     6      7      |
|  6      7      49     |  3      1      2      |  8      5      49     |
+-----------------------+-----------------------+-----------------------+
|  7      9      6      | -1248  *24     3      |  5     *12     128    |
|  13     2      148    |  5      7      168    |  346    9      1348   |
|  5      34     148    |  128    9      168    |  67     1247   238    |
+-----------------------+-----------------------+-----------------------+

ALS-xz:

ALS A: r1c5+r2c4={124}
ALS B: r7c58={124}
restricted common: x=4 (r17c5)
common: z=1 (r2c4+r7c8)

Therefore r7c4, seeing r2c4+r7c8, can't be 1.

[hobiwan]

Meanwhile here is an ALS-xz yielding the same result:...

There are lots of other possibilities for that elimination (your ALS-XZ for example is a W-Wing without grouped link, that can be seen as an XY-Chain), but I think that's not the point here.

Single-digit grouped strong links other than empty rectangles ... as in the example which followed my "ditto ... " statement.

The grouped strong link in [b8] of my PM is associated with an Empty Rectangle pattern on '2' because [r89c56] don't contain '2'. All of the other cells in [b8] could contain '2' and a grouped strong link would still exist.

Thanks, I see it now.

[udosuk]

Oh yes. Should have seen it as a normal Y-wing.

[daj95376]

It's not a Y-Wing

===== ===== ===== =====

How about a grouped and ungrouped W-Wing ... with the same starting cell ... that results in a Locked Candidate (2), Naked Triple, and Locked Candidate (1). Yes, we really need to update the definition of a W-Wing so that the grouped version is included.

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 +-----------------------------------------------------------------------+
 |  1      56     789    |  58     2      489    |  679    479    3      |
 |  678-9  4      278-9  |  1389  *39     1389   |  27-9   5      26     |
 | *39     235    259    |  6      45     7      |  1      8      249    |
 |-----------------------+-----------------------+-----------------------|
 |  479    127    3      |  12579  46     129    |  8      279    56     |
 |  5      27     2479   |  2379   8      46     |  679    2379   1      |
 |  789    1278   6      |  12379  57     1239   |  4      2379   579    |
 |-----------------------+-----------------------+-----------------------|
 |  3678   378    78     |  4     ~3679   5      |  239    1      279    |
 | +347    9      1      |  28    ~37     28     |  5      6      47     |
 |  2      3567   457    | +379    1      69     | *39     479    8      |
 +-----------------------------------------------------------------------+


Code: Select all

              r 8c5 =3= r8c1 -3- r3c1 -9  =>  [r2c13]<>9
            /
9- r2c5 -3-
            \
              r78c5 =3= r9c4 -3- r9c7 -9  =>  [r2c7 ]<>9


Code: Select all

 r2  b2  Locked Candidate 2              <> 9    [r1c6]
     b2  Naked  Triple                   <> 458  [r2c46]
 r1  b2  Locked Candidate 1              <> 8    [r1c3]


[daj95376]

Here is a Semi-Remote Naked Pair that cracks a puzzle, but it's not a W-Wing. I think I've seen an example of this within the last month or two. It had a different name, maybe. Does anyone remember it? (Just my luck it was buried in a break-down of an ALS that I performed.)

Code: Select all

 +-----------------------------------------------------+
 |  5    89   1    |  78-3 47  *38   |  2    6    49   |
 |  7    3    4    |  9    26   26   |  5    1    8    |
 |  6    2   +89   |  1    45  ~58   |  49   7    3    |
 |-----------------+-----------------+-----------------|
 |  34   159  2    |  6    89   7    |  149  38   45   |
 |  89   189  6    |  5    3    4    |  19   2    7    |
 |  34   59   7    |  2    89   1    |  6    38   459  |
 |-----------------+-----------------+-----------------|
 |  1    4   ~89   |  78   27   289  |  3    5    6    |
 | +89   6    5    | *38   1    9-3  |  7    4    2    |
 |  2    7    3    |  4    56   56   |  8    9    1    |
 +-----------------------------------------------------+


Code: Select all

3- r1c6 -8- r3c6 =8= r3c2 -8- r7c3 =8= r8c1 -8- r8c4 -3  =>  [r1c4],[r8c6]<>3


[ronk]

Here is a Semi-Remote Naked Pair that cracks a puzzle, but it's not a W-Wing.

I wasn't aware that re'born defined semi-remote pair any differently from a w-wing. AFAIK both are chains with exactly three strong inferences (in the AIC sense of strong inferences) -- two strong inferences due to identical bivalued cells and a third strong inference due to a conjugate link in one of the two digits.

Other than Adam Glesser's (aka re'born, aka rep'nA) proposal on Eureka!, where have you seen a definition that extends the length of the chain?

[daj95376]

I wasn't aware that re'born defined semi-remote naked pair any differently from a w-wing.

Count the number of cells in this post by re'born. It contains two grouped strong links -- one ER and one not.

http://forum.enjoysudoku.com/viewtopic.php?p=48056#p48056

[hobiwan]

Here is a Semi-Remote Naked Pair that cracks a puzzle, but it's not a W-Wing. I think I've seen an example of this within the last month or two. It had a different name, maybe. Does anyone remember it? (Just my luck it was buried in a break-down of an ALS that I performed.)

Code: Select all

 +-----------------------------------------------------+
 |  5    89   1    |  78-3 47  *38   |  2    6    49   |
 |  7    3    4    |  9    26   26   |  5    1    8    |
 |  6    2   +89   |  1    45  ~58   |  49   7    3    |
 |-----------------+-----------------+-----------------|
 |  34   159  2    |  6    89   7    |  149  38   45   |
 |  89   189  6    |  5    3    4    |  19   2    7    |
 |  34   59   7    |  2    89   1    |  6    38   459  |
 |-----------------+-----------------+-----------------|
 |  1    4   ~89   |  78   27   289  |  3    5    6    |
 | +89   6    5    | *38   1    9-3  |  7    4    2    |
 |  2    7    3    |  4    56   56   |  8    9    1    |
 +-----------------------------------------------------+


Code: Select all

3- r1c6 -8- r3c6 =8= r3c2 -8- r7c3 =8= r8c1 -8- r8c4 -3  =>  [r1c4],[r8c6]<>3


Do we really need a name for this? Why not stick with XY-Chain?