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au tough June 23, 2012
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arkietech



Joined: 31 Jul 2008
Posts: 1708
Location: Northwest Arkansas USA

PostPosted: Tue Jun 26, 2012 7:20 am    Post subject: au tough June 23, 2012 Reply with quote

Code:

 *-----------*
 |..4|...|.67|
 |..1|3..|...|
 |7..|..8|5..|
 |---+---+---|
 |...|.4.|..6|
 |...|2.1|...|
 |1..|.3.|...|
 |---+---+---|
 |..9|1..|..2|
 |...|..5|3..|
 |85.|...|4..|
 *-----------*
 

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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Tue Jun 26, 2012 8:51 am    Post subject: Reply with quote

While looking for M-wings:
Code:
+-------------------+-------------------+-------------------+
| 2359  2389  4     | 59    1259  29    | 1289  6     7     |
| 2569  2689  1     | 3     25679 24679 | 289   2489  489   |
| 7     269  A26    | 469   1269  8     | 5     12349 1349  |
+-------------------+-------------------+-------------------+
| 239   2379  23578 | 5789  4     79    | 12789 12389 6     |
| 3469  34679 35678 | 2     5679  1     | 789   3489  34589 |
| 1     24679 25678 | 56789 3     679   | 2789  2489  4589  |
+-------------------+-------------------+-------------------+
| 34    347   9     | 1     8     347   | 6     5     2     |
|B246   1     267   | 4679  2679  5     | 3     789   89    |
| 8     5     2367  | 679   2679  23679 | 4     179   19    |
+-------------------+-------------------+-------------------+

If A is 2, B is 2.
If A is 6, B is 6.
B <>4. Done.

Keith
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arkietech



Joined: 31 Jul 2008
Posts: 1708
Location: Northwest Arkansas USA

PostPosted: Tue Jun 26, 2012 1:49 pm    Post subject: Reply with quote

keith wrote:
If A is 2, B is 2.
If A is 6, B is 6.
B <>4. Done.

Code:
 *--------------------------------------------------------------------*
 | 2359   2389   4      | 59     1259   29     | 1289   6      7      |
 | 2569   2689   1      | 3      25679  24679  | 289    2489   489    |
 | 7      269   b26     | 469    1269   8      | 5      12349  1349   |
 |----------------------+----------------------+----------------------|
 | 239    2379   3578-2 | 5789   4      79     | 12789  12389  6      |
 | 3469   34679  3578-6 | 2      5679   1      | 789    3489   34589  |
 | 1      24679  578-26 | 56789  3      679    | 2789   2489   4589   |
 |----------------------+----------------------+----------------------|
 |c34    c347    9      | 1      8      347    | 6      5      2      |
 | 26-4   1     a267    | 4679   2679   5      | 3      789    89     |
 | 8      5     a2367   | 679    2679   23679  | 4      179    19     |
 *--------------------------------------------------------------------*
Sue de Cog
{2367}r89c3, {26}r3c3,  {347}r7c12 => -26r456c3, -4r8c1
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Tue Jun 26, 2012 1:53 pm    Post subject: Reply with quote

I used a favorite technique, an anp(34), that involved similar cells as Keith's solution.

anp(34=7)r7c12-(726=3)r389c3-(3=4)r7c1; r7c6,r8c1<>4

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5119
Location: Rochester, NY, USA

PostPosted: Tue Jun 26, 2012 5:25 pm    Post subject: Reply with quote

keith wrote:
While looking for M-wings:
Code:
+-------------------+-------------------+-------------------+
| 2359  2389  4     | 59    1259  29    | 1289  6     7     |
| 2569  2689  1     | 3     25679 24679 | 289   2489  489   |
| 7     269  A26    | 469   1269  8     | 5     12349 1349  |
+-------------------+-------------------+-------------------+
| 239   2379  23578 | 5789  4     79    | 12789 12389 6     |
| 3469  34679 35678 | 2     5679  1     | 789   3489  34589 |
| 1     24679 25678 | 56789 3     679   | 2789  2489  4589  |
+-------------------+-------------------+-------------------+
| 34    347   9     | 1     8     347   | 6     5     2     |
|B246   1     267   | 4679  2679  5     | 3     789   89    |
| 8     5     2367  | 679   2679  23679 | 4     179   19    |
+-------------------+-------------------+-------------------+

If A is 2, B is 2.
If A is 6, B is 6.
B <>4. Done.

Keith


I was also looking at the potential of the 26 M-Wing and noted that whatever r3c3 was, r8c1 had the same value. But the thought that r8c1 had to be<>4 never occurred to me. Embarassed Mad
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Wed Jun 27, 2012 3:37 am    Post subject: Reply with quote

Marty R. wrote:
keith wrote:
While looking for M-wings:
Code:
+-------------------+-------------------+-------------------+
| 2359  2389  4     | 59    1259  29    | 1289  6     7     |
| 2569  2689  1     | 3     25679 24679 | 289   2489  489   |
| 7     269  A26    | 469   1269  8     | 5     12349 1349  |
+-------------------+-------------------+-------------------+
| 239   2379  23578 | 5789  4     79    | 12789 12389 6     |
| 3469  34679 35678 | 2     5679  1     | 789   3489  34589 |
| 1     24679 25678 | 56789 3     679   | 2789  2489  4589  |
+-------------------+-------------------+-------------------+
| 34    347   9     | 1     8     347   | 6     5     2     |
|B246   1     267   | 4679  2679  5     | 3     789   89    |
| 8     5     2367  | 679   2679  23679 | 4     179   19    |
+-------------------+-------------------+-------------------+

If A is 2, B is 2.
If A is 6, B is 6.
B <>4. Done.

Keith


I was also looking at the potential of the 26 M-Wing and noted that whatever r3c3 was, r8c1 had the same value. But the thought that r8c1 had to be<>4 never occurred to me. Embarassed Mad

That's the beauty of it. The human insights, in spite of all the software and automatons out there.

Keith
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Thu Jun 28, 2012 6:55 am    Post subject: Reply with quote

arkietech wrote:
keith wrote:
If A is 2, B is 2.
If A is 6, B is 6.
B <>4. Done.

Code:
 *--------------------------------------------------------------------*
 | 2359   2389   4      | 59     1259   29     | 1289   6      7      |
 | 2569   2689   1      | 3      25679  24679  | 289    2489   489    |
 | 7      269   b26     | 469    1269   8      | 5      12349  1349   |
 |----------------------+----------------------+----------------------|
 | 239    2379   3578-2 | 5789   4      79     | 12789  12389  6      |
 | 3469   34679  3578-6 | 2      5679   1      | 789    3489   34589  |
 | 1      24679  578-26 | 56789  3      679    | 2789   2489   4589   |
 |----------------------+----------------------+----------------------|
 |c34    c347    9      | 1      8      347    | 6      5      2      |
 | 26-4   1     a267    | 4679   2679   5      | 3      789    89     |
 | 8      5     a2367   | 679    2679   23679  | 4      179    19     |
 *--------------------------------------------------------------------*
Sue de Cog
{2367}r89c3, {26}r3c3,  {347}r7c12 => -26r456c3, -4r8c1

Just for interest, the SdC misses r7c6<>4, as opposed to the doubly-linked ALS-xz perspective of the same pattern.

...or maybe that's just a HoDoKu glitch.
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arkietech



Joined: 31 Jul 2008
Posts: 1708
Location: Northwest Arkansas USA

PostPosted: Thu Jun 28, 2012 7:24 am    Post subject: Reply with quote

Luke451 wrote:
Just for interest, the SdC misses r7c6<>4, as opposed to the doubly-linked ALS-xz perspective of the same pattern.

...or maybe that's just a HoDoKu glitch.


Thanks,

Got to start looking "outside the box" Very Happy

In this case the box/line of the SdC.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Thu Jun 28, 2012 11:36 am    Post subject: Reply with quote

Luke451 wrote:
keith wrote:
Sue de Cog
{2367}r89c3, {26}r3c3, {347}r7c12 => -26r456c3, -4r8c1

Just for interest, the SdC misses r7c6<>4, as opposed to the doubly-linked ALS-xz perspective of the same pattern.

...or maybe that's just a HoDoKu glitch.

Including r7c6<>4 would overlay a locked candidates move on the SDC, so I think HoDoKu has it right.
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Thu Jun 28, 2012 12:40 pm    Post subject: Reply with quote

Ronk wrote:

Including r7c6<>4 would overlay a locked candidates move on the SDC, so I think HoDoKu has it right.


Not only a somewhat convoluted definition but somewhat convoluted elimination rules as well...

And to point out that were Hoduko or any such program to see SDC as a particular instance of DL-ALS, then the additional elimination to which Luke points would be natural.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Thu Jun 28, 2012 1:54 pm    Post subject: Reply with quote

aran wrote:
Ronk wrote:

Including r7c6<>4 would overlay a locked candidates move on the SDC, so I think HoDoKu has it right.
Not only a somewhat convoluted definition but somewhat convoluted elimination rules as well...

And to point out that were Hoduko or any such program to see SDC as a particular instance of DL-ALS, then the additional elimination to which Luke points would be natural.

Sigh! No matter the name, a 0-rank pattern is a 0-rank pattern.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Thu Jun 28, 2012 3:41 pm    Post subject: Reply with quote

Code:
 *--------------------------------------------------------------------*
 | 359   2389    4      | 59     1259   29     | 1289   6      7      |
 | 2569   2689   1      | 3      25679  24679  | 289    2489   489    |
 | 7      269   *26     | 469    1269   8      | 5      12349  1349   |
 |----------------------+----------------------+----------------------|
 | 239    2379   23578  | 5789   4      79     | 12789  12389  6      |
 | 3469   34679  35678  | 2      5679   1      | 789    3489   34589  |
 | 1      24679  25678  | 56789  3      679    | 2789   2489   4589   |
 |----------------------+----------------------+----------------------|
 |*34    *347    9      | 1      8      347    | 6      5      2      |
 | 246    1     *267    | 4679   2679   5      | 3      789    89     |
 | 8      5     *2367   | 679    2679   23679  | 4      179    19     |
 *--------------------------------------------------------------------*

Is r7c6<>4 a legitimate elimination?

If so, I don't understand why the Sue de Coq approach misses an elimination that the doubly-linked ALS makes.

I only consulted HoDoKu after seeing the SdC elims posted by arkietech were not what I expected.

I realize this isn't a really good example, as r8c1<>4 also takes care of (4)r7c6 in the wash. Still, if one approach finds additional eliminations over the other, why even use the other?
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Thu Jun 28, 2012 4:57 pm    Post subject: Reply with quote

Luke451 wrote:
Is r7c6<>4 a legitimate elimination?

If so, I don't understand why the Sue de Coq approach misses an elimination that the doubly-linked ALS makes.

The eliminations should be the same. They should also be the same as for the partially and fully complementary patterns using SIS 26b7. R7c6<>4 is left out as a direct elimination here too. I'm not saying a player should ignore a follow-on locked candidate move, just recognize that it is one, at least once in a while. Smile

_____ ___

Luke451 wrote:
I realize this isn't a really good example, as r8c1<>4 also takes care of (4)r7c6 in the wash. Still, if one approach finds additional eliminations over the other, why even use the other?

Such a "wash" would always be the case in a practical example.

[edits: 1) added images; 2) narrow the 2nd image]


Last edited by ronk on Thu Jun 28, 2012 8:03 pm; edited 2 times in total
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DonM



Joined: 15 Sep 2009
Posts: 51

PostPosted: Thu Jun 28, 2012 5:12 pm    Post subject: Reply with quote

(Revised over original post)

The original SDC pattern examples, including my own (http://forum.enjoysudoku.com/sue-de-coq-revisited-again-asi-1-t6410.html) were such that the digits in the 'outlying cells' (in this case,(26)r3c3 and (347)r7c12) were also present in the 'core' aals or aaals (in this case, (2367)r89c3). However, more recently, examples of 'extended' SDCs such as the one above have been described where the 4s in r89c3, not present in the 'core', allow the usual eliminations of a SDC, but also add eliminations of all 4s within the same box as r7c12.

As far as the issue of r7c6<>4 goes. Theoretically, based on the issue that a SDC is simply an expression of a DL-ALS, r7c6 should be <>4, but in practice it can cause confusion for the manual pattern solver since the eliminations from the other digits in r7c12 apply only to the same box.

'IMO' applies to all of the following:
Patterns such as SDC were meant to aid the manual pattern solver to find eliminations. It was never originally described as an alternate way to find DL-ALS patterns. While I find Aran's premise that, approached a certain way, DL-ALS patterns should be just as easy as corresponding SDCs interesting, on further thought and review, I disagree. The written rules for finding an SDC may seem obscure, but when you see practical examples, the pattern is relatively easy and straightforward for pattern solvers such as myself. The DL-ALS, not so much.

So, I have no problem with an 'extended' SDC not allowing for an elimination such as r7c6<>4. If a manual solver is skilled enough to add it then good for him/her. As to the question why use one pattern over the other if one of them potentially provides more eliminations: If the one that provides more eliminations is far less likely to be found by manual solvers than the other, then it's advantage is more theoretical than practical. Besides, the situation in question in this SDC is relatively rare.

(Btw: You can also have an 'extended' SDC where digits (commensurate with a valid 'extended' SDC) in the outlying row or column (as the case may be) outlying cells are not in the 'core' aals and aaals. All same-value digits in that row or column (outside of the 'core') can be eliminated.)


Last edited by DonM on Thu Jun 28, 2012 7:53 pm; edited 5 times in total
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Jun 28, 2012 6:31 pm    Post subject: Reply with quote

keith wrote:
While looking for M-wings:

Since no one else mentioned it, your cells also correspond to ...

Code:
 +-----------------------------------------------------------------------+
 |  2359   2389   4      |  59     1259   29     |  1289   6      7      |
 |  2569   2689   1      |  3      25679  24679  |  289    2489   489    |
 |  7      269    26     |  469    1269   8      |  5      12349  1349   |
 |-----------------------+-----------------------+-----------------------|
 |  239    2379   23578  |  5789   4      79     |  12789  12389  6      |
 |  3469   34679  35678  |  2      5679   1      |  789    3489   34589  |
 |  1      24679  25678  |  56789  3      679    |  2789   2489   4589   |
 |-----------------------+-----------------------+-----------------------|
 |  34     347    9      |  1      8      347    |  6      5      2      |
 |  246    1      267    |  4679   2679   5      |  3      789    89     |
 |  8      5      2367   |  679    2679   23679  |  4      179    19     |
 +-----------------------------------------------------------------------+
 # 150 eliminations remain

 M-Ring  D (2=6)r3c3 - r89c3 = (6-2)r8c1 = (2)r89c3 - loop  =>  r456c3<>26; r8c1<>4

 S-Wing    (2)r8c1 = r89c3 - (2=6)r3c3 - r89c3 = (6)r8c1    =>  r456c3<>26; r8c1<>4
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 28, 2012 7:58 pm    Post subject: Reply with quote

daj95376 wrote:
keith wrote:
While looking for M-wings:

Since no one else mentioned it, your cells also correspond to ...

Code:
 +-----------------------------------------------------------------------+
 |  2359   2389   4      |  59     1259   29     |  1289   6      7      |
 |  2569   2689   1      |  3      25679  24679  |  289    2489   489    |
 |  7      269    26     |  469    1269   8      |  5      12349  1349   |
 |-----------------------+-----------------------+-----------------------|
 |  239    2379   23578  |  5789   4      79     |  12789  12389  6      |
 |  3469   34679  35678  |  2      5679   1      |  789    3489   34589  |
 |  1      24679  25678  |  56789  3      679    |  2789   2489   4589   |
 |-----------------------+-----------------------+-----------------------|
 |  34     347    9      |  1      8      347    |  6      5      2      |
 |  246    1      267    |  4679   2679   5      |  3      789    89     |
 |  8      5      2367   |  679    2679   23679  |  4      179    19     |
 +-----------------------------------------------------------------------+
 # 150 eliminations remain

 M-Ring  D (2=6)r3c3 - r89c3 = (6-2)r8c1 = (2)r89c3 - loop  =>  r456c3<>26; r8c1<4>  r456c3<>26; r8c1<>4

Danny,

I am not sure whether this serves to complify or to simplicate the discussion. Razz

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Thu Jun 28, 2012 10:20 pm    Post subject: Reply with quote

keith wrote:
I am not sure whether this serves to complify or to simplicate the discussion.

Sorry. Since you went to the trouble of mentioning that you were originally looking for an M-Wing, I thought you might not have noticed that your cells formed an M-Ring.

Regards, Danny
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keith



Joined: 19 Sep 2005
Posts: 3150
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 28, 2012 11:13 pm    Post subject: Reply with quote

daj95376 wrote:
keith wrote:
I am not sure whether this serves to complify or to simplicate the discussion.

Sorry. Since you went to the trouble of mentioning that you were originally looking for an M-Wing, I thought you might not have noticed that your cells formed an M-Ring.

Regards, Danny

Danny,

My observation was a bit of serendipity. I did not look further for an official pattern. You should not apologize!

If anything, I can be accused of using the 26 in R3C3 as a guess.

But, it is nice when one finds such a concise solution.

Keith
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Fri Jun 29, 2012 9:43 am    Post subject: Reply with quote

ronk wrote:

I'm not saying a player should ignore a follow-on locked candidate move, just recognize that it is one, at least once in a while.

The simplicity of DL-ALS - apart even from the definition - lies in the elimination rule :
any candidate which reduces EITHER ALS to a locked set is false.
There is no hierarchy among those candidates.
In the example 4r8c1 and 4r7c6 SEPARATELY, INDEPENDENTLY and...admirably...qualify as eliminations.
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ronk



Joined: 07 May 2006
Posts: 397

PostPosted: Fri Jun 29, 2012 12:00 pm    Post subject: Reply with quote

aran wrote:
ronk wrote:

I'm not saying a player should ignore a follow-on locked candidate move, just recognize that it is one, at least once in a while.

There is no hierarchy among those candidates.
In the example 4r8c1 and 4r7c6 SEPARATELY, INDEPENDENTLY and...admirably...qualify as eliminations.

Perhaps too subtle for someone who has argued that an almost-naked-pair is a hidden-pair but, in my book, "SEPARATELY, INDEPENDENTLY" indicates follow-on action of some sort. For this single ALS, e.g., there are two scans for eliminations, once in a box and once in a line. One scan follows the other.
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