April 22, 2017

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April 22, 2017

Postby ArkieTech » Fri Apr 21, 2017 11:18 pm

Code: Select all
 *-----------*
 |.4.|...|8.2|
 |2..|..5|..1|
 |...|.48|...|
 |---+---+---|
 |.1.|..3|7..|
 |...|564|...|
 |.52|8..|.6.|
 |---+---+---|
 |...|.7.|...|
 |8..|3..|..9|
 |9.1|...|.4.|
 *-----------*


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dan
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Re: April 22, 2017

Postby SteveG48 » Fri Apr 21, 2017 11:37 pm

Code: Select all
 *-----------------------------------------------------------*
 | 357   4     3579  | 1     39    6     | 8    a359-7 2     |
 | 2     68    68    | 7     39    5     | 4     39    1     |
 | 1     39    3579  | 2     4     8     | 356  a3579  567   |
 *-------------------+-------------------+-------------------|
 | 46    1     68    | 9     2     3     | 7    b58   c458   |
 | 37    389   379   | 5     6     4     | 12    12    38    |
 | 34    5     2     | 8     1     7     | 9     6     34    |
 *-------------------+-------------------+-------------------|
 | 356   236   35    | 4     7     9     | 1236  1238  68    |
 | 8     267   4     | 3     5     1     | 26    2-7   9     |
 | 9     37    1     | 6     8     2     | 35    4    d57    |
 *-----------------------------------------------------------*


W-wing:

(7=359)r13c8 - 5r4c8 = r4c9 - (5=7)r9c9 => -7 r3c9,r8c8 ; stte

Or:
Code: Select all
 *------------------------------------------------------------*
 | 357   4     3579  | 1     39    6     |  8     3579  2     |
 | 2     68    68    | 7     39    5     |  4     39    1     |
 | 1     39    3579  | 2     4     8     |  35-6  3579  567   |
 *-------------------+-------------------+--------------------|
 | 46    1     68    | 9     2     3     |  7     58    458   |
 | 37    389   379   | 5     6     4     | a12    12    38    |
 | 34    5     2     | 8     1     7     |  9     6     34    |
 *-------------------+-------------------+--------------------|
 | 356   236   35    | 4     7     9     | a1236  1238  8-6   |
 | 8     267   4     | 3     5     1     |ab26   b27    9     |
 | 9     37    1     | 6     8     2     | a35    4    b57    |
 *------------------------------------------------------------*


(6=1235)r5789c7 - (5=267)b9p459 => -6 r7c9,r3c7 ; stte
Steve
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Re: April 22, 2017

Postby Leren » Sat Apr 22, 2017 12:50 am

Code: Select all
*--------------------------------------------------------------*
| 357   4     3579   | 1     39    6      | 8     3579  2      |
| 2     68    68     | 7     39    5      | 4     39    1      |
| 1     39    3579   | 2     4     8      |c356   3579 d56-7   |
|--------------------+--------------------+--------------------|
| 46    1     68     | 9     2     3      | 7     58    458    |
| 37    389   379    | 5     6     4      | 12    12    38     |
| 34    5     2      | 8     1     7      | 9     6     34     |
|--------------------+--------------------+--------------------|
| 356   236   35     | 4     7     9      | 1236  1238  68     |
| 8     267   4      | 3     5     1      | 26    27    9      |
| 9     37    1      | 6     8     2      |b35    4    a57     |
*--------------------------------------------------------------*

H2 Wing: (7=5) r9c9 - r9c7 = (5-6) r3c7 = (6) r3c9 => - 7 r3c9; stte

Leren
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Re: April 22, 2017

Postby pjb » Sat Apr 22, 2017 3:15 am

Code: Select all
 357     4       3579   | 1      39     6      | 8      3579   2     
 2       68      68     | 7      39     5      | 4      39     1     
 1       39      3579   | 2      4      8      |b35-6   3579  a567   
------------------------+----------------------+---------------------
 46      1       68     | 9      2      3      | 7      58     458   
 37      389     379    | 5      6      4      | 12     12     38     
 34      5       2      | 8      1      7      | 9      6      34     
------------------------+----------------------+---------------------
 356     236     35     | 4      7      9      | 1236   1238   8-6     
 8       267     4      | 3      5      1      |f26    e27     9     
 9       37      1      | 6      8      2      |c35     4     d57

(6)r3c9 = (6-5)r3c7 = r9c7 - (5=7)r9c9 - (7=2)r8c8 - (2=6)r8c7 => -6 r3c7, r7c9; stte

Phil
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Re: April 22, 2017

Postby Ngisa » Sat Apr 22, 2017 8:07 am

Code: Select all
+--------------+--------+---------------+
| 357 4   3579 | 1 39 6 | 8    a3579 2   |
| 2   68  68   | 7 39 5 | 4    39   1   |
| 1   39  3579 | 2 4  8 | e356  a3579 f56-7 |
+--------------+--------+---------------+
| 46  1   68   | 9 2  3 | 7    58   458 |
| 37  389 379  | 5 6  4 | 12   12   38  |
| 34  5   2    | 8 1  7 | 9    6    34  |
+--------------+--------+---------------+
| 356 236 35   | 4 7  9 | 1236 1238 68  |
| 8   267 4    | 3 5  1 | 26   b27   9   |
| 9   37  1    | 6 8  2 | d35   4    c57  |
+--------------+--------+---------------+

(7)r13c8 = r8c8 - (7=5)r9c9 - r9c7 = (5-6)r3c7 = (6)r3c9 => - 7 r3c9; stte

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Re: April 22, 2017

Postby Cenoman » Sat Apr 22, 2017 12:41 pm

Code: Select all
 +---------------------+-----------------+----------------------+
 |  357   4     3579   |  1    39   6    |  8      3579   2     |
 |  2     68    68     |  7    39   5    |  4      39     1     |
 |  1     39    3579   |  2    4    8    |  356    3579  g56-7  |
 +---------------------+-----------------+----------------------+
 |  46    1     68     |  9    2    3    |  7      58     458   |
 |  37    389   379    |  5    6    4    | d12    e12     38    |
 |  34    5     2      |  8    1    7    |  9      6      34    |
 +---------------------+-----------------+----------------------+
 |  356   236   35     |  4    7    9    |  1236  f1238  f68    |
 |  8     267   4      |  3    5    1    | c26*   b27*    9     |
 |  9     37    1      |  6    8    2    |  35     4     a57    |
 +---------------------+-----------------+----------------------+

UR(12)r57c78 using externals (2r8c7==2r8c8)
(7)r9c9 = (7-2)r8c8 == (2)r8c7 - r5c7 = (2-1)r5c8 = (18-6)r7c89 = (6)r3c9 => -7 r3c9; stte

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Re: April 22, 2017

Postby Sudtyro2 » Sat Apr 22, 2017 7:14 pm

Code: Select all
 *----------------------------------------------------*
 | 357   4     3579  | 1   39* 6  | 8    a3579*  2    |
 | 2     68    68    | 7   39* 5  | 4     39*    1    |
 | 1     39    3579  | 2   4   8  | 36-5  3579  b567  |
 |-------------------+------------+-------------------|
 | 46    1     68    | 9   2   3  | 7     58     458  |
 | 37    389   379   | 5   6   4  | 12    12     38   |
 | 34    5     2     | 8   1   7  | 9     6      34   |
 |-------------------+------------+-------------------|
 | 356   236   35    | 4   7   9  | 1236  1238   68   |
 | 8     267   4     | 3   5   1  | 26    27     9    |
 | 9     37    1     | 6   8   2  |d35    4     c57   |
 *----------------------------------------------------*
Another ADP(39)r12c58, using [internals].
[5=7]r1c8 - r3c9 = (7-5)r9c9 = 5r9c7 => -5r3c7; stte

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Re: April 22, 2017

Postby eleven » Sat Apr 22, 2017 8:27 pm

Code: Select all
 *------------------------------------------------*
 |  357  4    3579  | 1 39  6 |  8     3579  2    |
 |  2    68   68    | 7 39  5 |  4     39    1    |
 |  1    39   3579  | 2 4   8 |  356   3579  567  |
 |------------------+---------+-------------------|
 |  46   1    68    | 9 2   3 |  7     58    458  |
 |  37   389  379   | 5 6   4 | b12    12    38   |
 |  34   5    2     | 8 1   7 |  9     6     34   |
 |------------------+---------+-------------------|
 | a356  236 a35    | 4 7   9 | b1236  1238  8-6  |
 |  8    267  4     | 3 5   1 | b26    27    9    |
 |  9    37   1     | 6 8   2 |  35    4     57   |
 *------------------------------------------------*

(6=3)r7c13-(3=6)r578c7 => -6r7c9, stte
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Re: April 22, 2017

Postby Sudtyro2 » Sun Apr 23, 2017 4:12 pm

Cenoman wrote:
Code: Select all
 +---------------------+-----------------+----------------------+
 |  357   4     3579   |  1    39   6    |  8      3579   2     |
 |  2     68    68     |  7    39   5    |  4      39     1     |
 |  1     39    3579   |  2    4    8    |  356    3579  g56-7  |
 +---------------------+-----------------+----------------------+
 |  46    1     68     |  9    2    3    |  7      58     458   |
 |  37    389   379    |  5    6    4    | d12    e12     38    |
 |  34    5     2      |  8    1    7    |  9      6      34    |
 +---------------------+-----------------+----------------------+
 |  356   236   35     |  4    7    9    |  1236  f1238  f68    |
 |  8     267   4      |  3    5    1    | c26*   b27*    9     |
 |  9     37    1      |  6    8    2    |  35     4     a57    |
 +---------------------+-----------------+----------------------+

UR(12)r57c78 using externals (2r8c7==2r8c8)
(7)r9c9 = (7-2)r8c8 == (2)r8c7 - r5c7 = (2-1)r5c8 = (18-6)r7c89 = (6)r3c9 => -7 r3c9; stte

Hi Cenoman,
I have one question about your UR externals chain regarding the node(f) notation marked above in red...
Is this an abbreviated version of something like (1-8)r7c8 = (8-6)r7c9? I assume it is, but have not seen that notation used before. Curiously, what did come to mind was that this node is also an example of Myth's Weak ALS discussed here. As I understand it, this Weak ALS is a complement to the regular ALS(12356)r7c1237 or ALS(123567)b9p14579, either of which could be used (with additional nodes in the chain) to reach (6)r3c9. However, the Weak ALS has the property that its non-locked digits (1236) all exclude (are weakly linked to) each other. Hence, one could maybe write the node(f) as simply as (1-6)r7c89. Does this sound reasonably correct or perhaps just "weak" in some regard? :)

SteveC
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Re: April 22, 2017

Postby Cenoman » Sun Apr 23, 2017 9:49 pm

Hi SteveC,

I am happy that you read so deeply my path. Thank you!
You have caught exactly what is at stake in my node(f).
Let's assume that in one unit, you have an ALS of n cells, containing n+1 digits, and a complement of p unsolved cells, p>1 (p=1 is a trivial case). The n+p unsolved cells in the unit contain exactly n+p digits. Therefore the p cells contain n+p-(n+1) = p-1 digits that are not in the ALS, and are thus locked in the p duale cells. If p=2, 1 digit is locked i.e. a bivalue, if p=3, 2 digits are locked, ...

I didn't know Myth's post you have referenced. My own reference would rather be champagne's Full Tagging http://forum.enjoysudoku.com/full-tagging-t5624.html that has been written also in French. Anyhow, the result is the theorem that you have expressed:
non-locked digits ... all exclude (are weakly linked to) each other.

Your concern is how to notate such weak links, and maybe how to name them.
Myth's post is rather old. I am not in favour of the label "weak ALS" that I find confusing with the regular ALS, and personnally I use the label AHS (Almost Hidden Set), since the choice of one digit joined to the p-1 locked digits form a hidden set in the p duale cells.
In the example above, you are right: (18-6)r7c89 is an abbreviation for (1-8)r7c8 = (8-6)r7c9, but be aware that the developed version is not so easy to write when p=3 or more
I have already stated my position about omitting bystanders in ALS's and AHS's in short discussions following December 1 and December 5 puzzles (http://forum.enjoysudoku.com/december-1-2016-t33425.html#p253742 and http://forum.enjoysudoku.com/december-5-2016-t33433.html#p253824)
You have been involved in these discussions. I summerize my position:
When using AHS's locked digits must always be included in the notation for sake of legibility.
You have seen that now, my practise is to omit bystanders in ALS's, and to include locked digits in AHS's (unconsistant with my previous posts...)
You propose
one could maybe notate the node(f) as simply as (1-6)r7c89. Does this sound reasonably correct or perhaps just "weak" in some regard?

To me such a notation is fully correct. It is exactly the symetric convention to writing ALS's with omitted bystanders. The notation is unambiguous since weak links between different digits in a common set of cells can result only of this technique.
The only drawback I see is legibility: the reader has to spot the locked digits by himself; this not always easy in AHS's of 3 or 4 cells. Writing or omitting the locked digits depends how concise you want to be.

Note: an AHS link can always be translated into an ALS link (and reciprocal). For the above puzzle:
Code: Select all
 +---------------------+-----------------+----------------------+
 |  357   4     3579   |  1    39   6    |  8      3579   2     |
 |  2     68    68     |  7    39   5    |  4      39     1     |
 |  1     39    3579   |  2    4    8    |  356    3579  g56-7  |
 +---------------------+-----------------+----------------------+
 |  46    1     68     |  9    2    3    |  7      58     458   |
 |  37    389   379    |  5    6    4    | d12     12     38    |
 |  34    5     2      |  8    1    7    |  9      6      34    |
 +---------------------+-----------------+----------------------+
 | e356  e236  e35     |  4    7    9    | e1236   1238  f68    |
 |  8     267   4      |  3    5    1    | c26*   b27*    9     |
 |  9     37    1      |  6    8    2    |  35     4     a57    |
 +---------------------+-----------------+----------------------+

UR(12)r57c78 using externals (2r8c7==2r8c8)
(7)r9c9 = (7-2)r8c8 == (2)r8c7 - r5c7 = (2-1)r5c8 = (1-6)r7c89 = (6)r3c9 => -7 r3c9; stte
versus
(7)r9c9 = (7-2)r8c8 == (2)r8c7 - (2=1)r5c7 - (1=6)r7c1237 - r7c9 = (6)r3c9 => -7 r3c9; stte
I have given my preference to the AHS version because of the 4 cell-ALS vs 2 cell-AHS (easier to spot).

Cenoman
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