April 5, 2017

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April 5, 2017

Postby ArkieTech » Tue Apr 04, 2017 10:05 pm

Code: Select all
 *-----------*
 |...|.4.|65.|
 |...|59.|8..|
 |94.|.7.|..2|
 |---+---+---|
 |..4|...|..5|
 |...|...|...|
 |8.1|...|97.|
 |---+---+---|
 |.62|.1.|...|
 |...|3..|..1|
 |.8.|.24|.3.|
 *-----------*


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dan
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Re: April 5, 2017

Postby Leren » Tue Apr 04, 2017 10:51 pm

Code: Select all
*-----------------------------------------------------------------------*
| 27     1237   8       | 12     4      123     | 6      5      9       |
| 26     123    36      | 5      9      123     | 8      4      7       |
| 9      4      5       | 68     7      68      | 3      1      2       |
|-----------------------+-----------------------+-----------------------|
| 267   b2379   4       | 1279 fa38     1279    | 12    e68-2   5       |
| 5      279-3 c36      | 12479  38     1279    | 124   d268    348     |
| 8      2-3    1       | 246    5      26      | 9      7      34      |
|-----------------------+-----------------------+-----------------------|
| 3      6      2       | 789    1      5       | 47     89     48      |
| 4      5      79      | 3      6      789     | 27     289    1       |
| 1      8      79      | 79     2      4       | 5      3      6       |
*-----------------------------------------------------------------------*

(3) r4c5 = r4c2 - (3=6) r5c3 - r5c8 = (6-8) r4c8 = (8) r4c5 loop => - 2 r4c8, -3 r56c2; stte

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Re: April 5, 2017

Postby SteveG48 » Wed Apr 05, 2017 12:08 am

Code: Select all
 *--------------------------------------------------------------------*
 | 27     1237   8      | 12     4      123    | 6      5      9      |
 | 26     123    36     | 5      9      123    | 8      4      7      |
 | 9      4      5      | 68     7     f68     | 3      1      2      |
 *----------------------+----------------------+----------------------|
 | 267    2379   4      | 1279   38     1279   | 12     268    5      |
 | 5      2379   6-3    | 12479 a38     1279   | 124    268   b348    |
 | 8     g23     1      | 246    5     f26     | 9      7      34     |
 *----------------------+----------------------+----------------------|
 | 3      6      2      | 789    1      5      | 47     89    c48     |
 | 4      5      79     | 3      6     e789    | 27    d289    1      |
 | 1      8      79     | 79     2      4      | 5      3      6      |
 *--------------------------------------------------------------------*


(3=8)r5c5 - r5c9 = r7c9 - r8c8 = r8c6 - (8=26)r36c6 - (2=3)r6c2 => -3 r5c3 ; stte

Or:
Code: Select all
 *--------------------------------------------------------------------*
 | 27     1237   8      |a12     4      123    | 6      5      9      |
 | 26     123    36     | 5      9      123    | 8      4      7      |
 | 9      4      5      | 68     7      68     | 3      1      2      |
 *----------------------+----------------------+----------------------|
 | 267    2379   4      |a1279   38     1279   | 12     268    5      |
 | 5      2379   36     |a12479  38     1279   | 124    268    38-4   |
 | 8      23     1      | 246    5      26     | 9      7      34     |
 *----------------------+----------------------+----------------------|
 | 3      6      2      |a789    1      5      | 47     89    b48     |
 | 4      5      79     | 3      6      789    | 27     289    1      |
 | 1      8      79     |a79     2      4      | 5      3      6      |
 *--------------------------------------------------------------------*


(4=12789)r14579 - (8=4)r7c9 => -4 r5c9 ; lclste
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Re: April 5, 2017

Postby Ngisa » Wed Apr 05, 2017 9:03 am

Code: Select all
+-------------+---------------+-------------+
| 27  1237 8  | 12    4  123  | 6   5   9   |
| 26  123  36 | 5     9  123  | 8   4   7   |
| 9   4    5  | 68    7  68   | 3   1   2   |
+-------------+---------------+-------------+
| 267 a2379 4  | 1279  b38 1279 | 12  c268 5   |
| 5   279-3 e36 | 12479 38 1279 | 124 d268 348 |
| 8   2-3   1  | 246   5  26   | 9   7   34  |
+-------------+---------------+-------------+
| 3   6    2  | 789   1  5    | 47  89  48  |
| 4   5    79 | 3     6  789  | 27  289 1   5 |
| 1   8    79 | 79    2  4    | 5   3   6   |
+-------------+---------------+-------------+

Almost like Leren

(3)r4c2 = (3-8)r4c5 = (8-6)r4c8 = r5c8 - (6=3)r5c3 => - 3 r56c2; stte

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Re: April 5, 2017

Postby Leren » Wed Apr 05, 2017 9:17 am

Ngsia wrote : Almost like Leren (3)r4c2 = (3-8)r4c5 = (8-6)r4c8 = r5c8 - (6=3)r5c3 => - 3 r56c2

I think you'll find this is the same loop as mine, just notated differently, so you can have - 2 in r4c8 as well.

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Re: April 5, 2017

Postby Cenoman » Wed Apr 05, 2017 8:20 pm

Code: Select all
 +-------------------+---------------------+-------------------+
 | 27    1237   8    | 12      4    123    | 6     5     9     |
 | 26    123    36   | 5       9    123    | 8     4     7     |
 | 9     4      5    | 68      7    68     | 3     1     2     |
 +-------------------+---------------------+-------------------+
 |b67-2 a379-2  4    |a1279    38  a1279   |a12    68-2  5     |
 | 5     79-23 b36   | 12479   38   1279   | 124   268   348   |
 | 8    b23     1    | 246     5    26     | 9     7     34    |
 +-------------------+---------------------+-------------------+
 | 3     6      2    | 789     1    5      | 47    89    48    |
 | 4     5      79   | 3       6    789    | 27    289   1     |
 | 1     8      79   | 79      2    4      | 5     3     6     |
 +-------------------+---------------------+-------------------+

Doubly linked ALS-XZ rule (12379)r4c2467 -37- (2367)b4p168 =>-2r4c128,-23r5c2; stte

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Re: April 5, 2017

Postby eleven » Wed Apr 05, 2017 9:05 pm

Code: Select all
 *-----------------------------------------------------*
 | 27   1237  8   | 12     4   123   |  6    5    9    |
 | 26   123   36  | 5      9   123   |  8    4    7    |
 | 9    4     5   | 68     7   68    |  3    1    2    |
 |----------------+------------------+-----------------|
 | 267  2379  4   | 1279   38  1279  | b12   268  5    |
 | 5    2379 a36  | 12479 a38  1279  | b124 a268 a348  |
 | 8    23    1   | 246    5   26    |  9    7    3-4  |
 |----------------+------------------+-----------------|
 | 3    6     2   | 789    1   5     |  47   89   48   |
 | 4    5     79  | 3      6   789   |  27   289  1    |
 | 1    8     79  | 79     2   4     |  5    3    6    |
 *-----------------------------------------------------*

(4=2)r5c3589-(2=4)r45c7 => -4r6c9, stte
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Re: April 5, 2017

Postby SteveG48 » Wed Apr 05, 2017 9:38 pm

Cenoman wrote:
Code: Select all
 +-------------------+---------------------+-------------------+
 | 27    1237   8    | 12      4    123    | 6     5     9     |
 | 26    123    36   | 5       9    123    | 8     4     7     |
 | 9     4      5    | 68      7    68     | 3     1     2     |
 +-------------------+---------------------+-------------------+
 |b67-2 a379-2  4    |a1279    38  a1279   |a12    68-2  5     |
 | 5     79-23 b36   | 12479   38   1279   | 124   268   348   |
 | 8    b23     1    | 246     5    26     | 9     7     34    |
 +-------------------+---------------------+-------------------+
 | 3     6      2    | 789     1    5      | 47    89    48    |
 | 4     5      79   | 3       6    789    | 27    289   1     |
 | 1     8      79   | 79      2    4      | 5     3     6     |
 +-------------------+---------------------+-------------------+

Doubly linked ALS-XZ rule (12379)r4c2467 -37- (2367)b4p168 =>-2r4c128,-23r5c2; stte

Cenoman


Cenoman, I think I follow what's going on in your solution, but perhaps you can explain the notation. Both end terms evaluate as Boolean "not true", since they have more candidates than cells.
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Re: April 5, 2017

Postby eleven » Thu Apr 06, 2017 6:26 am

Good question.
What i saw is, that you have 6 digits for 7 cells. So one must be there twice, this only can be 2, which must be both in r6c2 and one of r4c467. Then the others must be there and 3 can only be in r4c2 or r5c3,.
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Re: April 5, 2017

Postby pjb » Thu Apr 06, 2017 7:24 am

Code: Select all
 27      1237    8      | 12     4      123    | 6      5      9     
 26      123     36     | 5      9      123    | 8      4      7     
 9       4       5      | 68     7      68     | 3      1      2     
------------------------+----------------------+---------------------
b267    b2379    4      |b1279   38    b1279   |b12     268    5     
 5       279-3  a36     | 12479  38     1279   | 124    268    348   
 8       2-3     1      | 246    5      26     | 9      7      34     
------------------------+----------------------+---------------------
 3       6       2      | 789    1      5      | 47     89     48     
 4       5       79     | 3      6      789    | 27     289    1     
 1       8       79     | 79     2      4      | 5      3      6     

(3=6)r5c3 - (6=3)r4c12467 => -3 r56c2; stte

also a slightly different loop: (8)r4c5 - (8=3)r5c5 - (3=6)r5c3 - r4c1 = (6-8)r4c8 = r4c5 => -3r5c2, -3r5c9, -2r4c8; stte

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Re: April 5, 2017

Postby eleven » Thu Apr 06, 2017 7:58 pm

Cenoman wrote:Doubly linked ALS-XZ rule (12379)r4c2467 -37- (2367)b4p168 =>-2r4c128,-23r5c2; stte

Code: Select all
     +-------------------+---------------------+-------------------+
     | 27    1237   8    | 12      4    123    | 6     5     9     |
     | 26    123    36   | 5       9    123    | 8     4     7     |
     | 9     4      5    | 68      7    68     | 3     1     2     |
     +-------------------+---------------------+-------------------+
     |a67-2 a379-2  4    |a1279    38  a1279   |a12    68-2  5     |
     | 5     79-23 b36   | 12479   38   1279   | 124   268   348   |
     | 8    b23     1    | 246     5    26     | 9     7     34    |
     +-------------------+---------------------+-------------------+
     | 3     6      2    | 789     1    5      | 47    89    48    |
     | 4     5      79   | 3       6    789    | 27    289   1     |
     | 1     8      79   | 79      2    4      | 5     3     6     |
     +-------------------+---------------------+-------------------+


There is a double link 36 between the ALS's 123679r4c12467 and 236r5c3,r6c2.
They share their 3's and 6'S in box 4. So 3 must be in the one ALS and 6 in the other. And 36 can be eliminated from the rest of box 4.
All other digits must be true in both ALS's. This gives 2r6c2, then 2r4c467.
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Re: April 5, 2017

Postby Cenoman » Thu Apr 06, 2017 9:52 pm

I try to answer 'Steve's question and eleven's comments

Code: Select all
2r4c2 3r4c2 7r4c2 9r4c2
2r4c4       7r4c4 9r4c4 1r4c4
2r4c6       7r4c6 9r4c6 1r6c6
2r4c7                   1r4c7
-----------------------------------------
            7r4c1             2r4c1 6r4c1
      3r5C3                         6r5c3
      3r6c2                   2r6c2


The best way to explain the eliminations in the doubly linked ALS-XZ pattern is to look at its PM (Pigeonhole Matrix). The dotted line is to show each ALS, but plays no role. The restricted commons are shown by columns 2 & 3 that are common to both ALS's (digits 3 & 7) As in the first column all candidates are in a weak link with each other, the matrix is said to be symetric, i.e. the order of columns has no importance.

Any candidate in sight of all candidates of one column is eliminated (even if it is part of one ALS):
- 1st col. eliminates 2r4c1 and 2r4c8,
- 2nd col. eliminates 3r5c2
- 6th col. eliminates 2r4c2 and 2r5c2
- other col. eliminates nothing.
Note that the stte finish is due to -2 r4c12, r5c2 leading to +2r6c2 (stte) as noted by eleven.

The above matrix is that of a "rank 0 logic" exactly as the matrix of a swordfish.
Doubly linked ALS's can't lose any of their digits, so any candidate in sight of all instances of one of their digits is eliminated. This is also true for restricted commons, provided all instances in both ALS's are seen.

Eleven has proposed another assembly of cells in ALS's (r4c1 in a instead of b). The matrix is the same, and therefore the eliminations too, but the RC are changed to 3 & 6
Code: Select all
2r4c2 3r4c2 7r4c2 9r4c2
2r4c4       7r4c4 9r4c4 1r4c4
2r4c6       7r4c6 9r4c6 1r6c6
2r4c7                   1r4c7
            7r4c1             2r4c1 6r4c1
-----------------------------------------
      3r5C3                         6r5c3
      3r6c2                   2r6c2


And now back to Steve's question:
Cenoman, I think I follow what's going on in your solution, but perhaps you can explain the notation. Both end terms evaluate as Boolean "not true", since they have more candidates than cells.

I understand the question more as a matter of notation than a matter of logics.
I have noted that way Doubly linked ALS-XZ rule (12379)r4c2467 -37- (2367)b4p168 =>-2r4c128,-23r5c2; stte
i.e. giving all digits and cells of each ALS, separated with the two restricted commons between "-".
I guess Steve tried to read this as a chain, which it is not. I don't know how to write this logic as a chain, as well as I don't know to write a full swordfish as a chain. Any suggestion ?

I considered the elimination rules of the pattern as a theorem. Maybe should I have written a few words in English, as eleven did in its two posts ?

Any advice is welcomed.
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Re: April 5, 2017

Postby SteveG48 » Fri Apr 07, 2017 5:15 pm

Thanks, Big C. I don't claim to understand all that yet, but I will.

Yes, my question was more about the notation than the logic, and I don't know how I would notate such a thing.
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