The New Sudoku Players' Forum

[pjb]

Code: Select all

*-----------*
|..1|...|7..|
|.5.|9.7|.8.|
|6..|...|..5|
|---+---+---|
|.1.|4.6|.9.|
|...|...|...|
|.6.|3.9|.2.|
|---+---+---|
|4..|...|..8|
|.9.|5.4|.3.|
|..3|...|6..|
*-----------*
..1...7...5.9.7.8.6.......5.1.4.6.9...........6.3.9.2.4.......8.9.5.4.3...3...6..

Phil
Apologies for typo at r4c8, thanks eleven

[Leren]

Code: Select all

*----------------------------------------------------------------*
| 2389   2348  1      | 268  234568 2358 | 7      P46     239-46 |
|P23     5     4-2    | 9    146-23 7    |B1234    8     B12346  |
| 6      23478 24789  | 128  12348  1238 | 239-14 P14     5      |
|---------------------+------------------+-----------------------|
| 23578  1     2578   | 4    2578   6    | 358     9      37     |
| 235789 23478 245789 | 1278 12578  1258 | 13458   14567  13467  |
| 578    6     4578   | 3    1578   9    | 1458    2      147    |
|---------------------+------------------+-----------------------|
| 4      27    2567   | 1267 123679 123  | 1259    157    8      |
| 1278   9     2678   | 5    12678  4    | 12      3      127    |
| 12578  278   3      | 1278 12789  128  | 6       1457   12479  |
*----------------------------------------------------------------*

Sue de Coq: Base Cells r2c79 {12346} Pincer Cells r2c1 {23} + r13c8 {146} => - 46 r1c9, - 14 r3c7, - 2 r2c3, - 23 r2c5; stte

Leren

[eleven]

Another view of the Sue de Coq:

Code: Select all

 *---------------------------------------------------------------------------------*
 |  2389     2348    1        |  268    234568   2358   |  7      #46      239-46  |
 | #23       5      #4-2      |  9      146-23   7      | #1234    8      #12346   |
 |  6        23478   24789    |  128    12348    1238   |  239-14 #14      5       |
 |----------------------------+-------------------------+--------------------------|
 |  23578    1       2578     |  4      2578     6      |  358     9       37      |
 |  235789   23478   245789   |  1278   12578    1258   |  13458   1567-4  13467   |
 |  578      6       4578     |  3      1578     9      |  1458    2       147     |
 |----------------------------+-------------------------+--------------------------|
 |  4        27      2567     |  1267   123679   123    |  1259    157     8       |
 |  1278     9       2678     |  5      12678    4      |  12      3       127     |
 |  12578    278     3        |  1278   12789    128    |  6       157-4   12479   |
 *---------------------------------------------------------------------------------*

12346 in 6 cells, 4 must be twice, therefore in r2c3 (and r13c8), the others in the pattern -> -23r2c5, -146b3p37, -4r5c8,r9c8

[rjamil]

Code: Select all

 +-----------------------+--------------------+---------------------+
 | 2389    2348   1      | 268   234568  2358 | 7     +46     239-46|
 | 23      5     +4-2    | 9    +146-23  7    |*1234   8     *12346 |
 | 6       23478  24789  | 128   12348   1238 | 1239-4 1+4    5     |
 +-----------------------+--------------------+---------------------+
 | 23578   1      2578   | 4     2578    6    | 358    9      37    |
 | 235789  23478  245789 | 1278  12578   1258 | 13458  14567  13467 |
 | 578     6      4578   | 3     1578    9    | 1458   2      147   |
 +-----------------------+--------------------+---------------------+
 | 4       27     2567   | 1267  123679  123  | 1259   157    8     |
 | 1278    9      2678   | 5     12678   4    | 12     3      127   |
 | 12578   278    3      | 1278  12789   128  | 6      1457   12479 |
 +-----------------------+--------------------+---------------------+

Almost Locked Triple: 146 @ r2c79 r2c35 r13c8 => -46 @ r1c9 -4 @ r3c7 -2 @ r2c3 -23 @ r2c5; stte

R. Jamil
Edit 20210621: Typo

[eleven]

You do not mention the 23 in r2c1. Can you explain the "almost locked triple" without it ?

[yzfwsf]

The number 146 is in the second row. Except for r2c79, it only appears in r2c35. Therefore, r2c79 must have at least one 146, and the candidates of r13c8 in the third box is only from 146, so r2c79 can only have one cell of 146 at most. There is one and only one 146 in r2c79, so there is Hidden Triple in the 2nd row and Naked Triple in the 3rd box.
Rank logic:5 truths 146r2,r13c8; 5 links r2c35,146b3

[eleven]

Ah yes, clear - thanks (just looked in again, if he meant a hidden triple).

[pjb]

Are SDC and double ALS measuring the same thing? I had in mind the following:

(2=3)r2c1 - (3=2)r2c79, r13c8 - loop => same eliminations as Leren's SDC.

Are they ever non-equivalent? (I removed SDC from my solver because I thought they were)

Phil

[jco]

Code: Select all

.-------------------------------------------------------------------.
| 2389    2348   1      | 268   234568  2358 | 7     ea46     239-46|
| 23      5      24     | 9    c16-234  7    | 123-4   8     d1236-4|
| 6       23478  24789  |b128  b12348  b1238 | 239-14 a14     5     |
|-----------------------+--------------------+----------------------|
| 23578   1      2578   | 4     2578    6    | 358     9      37    |
| 235789  23478  245789 | 1278  12578   1258 | 13458   1567-4 13467 |
| 578     6      4578   | 3     1578    9    | 1458    2      147   |
|-----------------------+--------------------+----------------------|
| 4       27     2567   | 1267  123679  123  | 1259    157    8     |
| 1278    9      2678   | 5     12678   4    | 12      3      127   |
| 12578   278    3      | 1278  12789   128  | 6       157-4  12479 |
'-------------------------------------------------------------------'

Loop (6=41)r13c8 - r3c456 = (1-6)r2c5 = r2c9 - (6)r1c8
=> -4 b3p3467, -4 r59c8, -1 r3c7, -(234)r2c5, -6 r1c9; ste

[eleven]

Are SDC and double ALS measuring the same thing? I had in mind the following:

(2=3)r2c1 - (3=2)r2c79, r13c8 - loop => same eliminations as Leren's SDC.

Are they ever non-equivalent? (I removed SDC from my solver because I thought they were)

Phil

I thought so either, but don't know, if it is proved. What i like is, that there are rather different ways to spot it, as shown here.

[Leren]

This is the puzzle : 3.9...5.........29.6.....3..3.2...6.7....5.8225.7.4....7.......19.4.3......5..3..

Here is a Sue de Coq Move for 12 eliminations, similar to Hodoku:

Code: Select all

*-----------------------------------------------------*
| 3   2  9  |P168   P1478     P1678  | 5    14  14678 |
| 458 48 17 |B1368   35-1478  P1678  | 168  2   9     |
| 458 6  17 |B189    259-1478 29-178 | 18   3   1478  |
|-----------+------------------------+----------------|
| 9   3  4  | 2      18        18    | 7    6   5     |
| 7   1  6  |P39     39        5     | 4    8   2     |
| 2   5  8  | 7      6         4     | 19   19  3     |
|-----------+------------------------+----------------|
| 468 7  3  | 168-9  1289      12689 | 1289 5   148   |
| 1   9  5  | 4      28        3     | 268  7   68    |
| 468 48 2  | 5      1789      16789 | 3    149 148   |
*-----------------------------------------------------*
Sue de Coq: Base Cells r23c4 {13689}  Pincer Cells r5c4 {39} + r1c456, r2c6 {14678}

and here is an ALS loop for 14 eliminations:

Code: Select all

*------------------------------------------------------*
| 3    2   9  |B168    4-178   B1678  | 5    14  14678 |
| 458  48  17 |B1368   345-178 B1678  | 168  2   9     |
| 458  6   17 |B189    2459-178 29-178| 18   3   1478  |
|-------------+-----------------------+----------------|
| 9    3   4  | 2      18      18     | 7    6   5     |
| 7    1   6  |A39     39      5      | 4    8   2     |
| 2    5   8  | 7      6       4      | 19   19  3     |
|-------------+-----------------------+----------------|
| 468  7   3  | 168-9  1289    12689  | 1289 5   148   |
| 1    9   5  | 4      28      3      | 268  7   68    |
| 468  48  2  | 5      1789    1689-7 | 3    149 148   |
*------------------------------------------------------*
ALS XZ Rule Loop : ALS 1 r5c4; ALS 2 r1c46, r2c46, r3c4; Z = 3 & 9

The difference seems to be that in Sue de Coq logic, r1c5 has to be in the pattern, for the 4 eliminations, whereas in ALS logic you don't get the 4 eliminations, but more overall.

Maybe there is a Sue de Coq without r1c5, but neither I nor Hodoku played it.

It's been so long since I've looked at Sue de Coq logic I've long since forgotten the details of just how it works. My money is on the ALS logic being simpler to understand and giving at least as many eliminations as Sue de Coq.

Leren

[yzfwsf]

Maybe there is a Sue de Coq without r1c5, but neither I nor Hodoku played it.
Leren

My solver does it.

Code: Select all

Sue de Coq: r23c4 - {13689} (r1c46,r2c6 - {1678}, r5c4 -{39}) =>  r1c5<>1 r2c5<>1 r3c5<>1 r3c6<>1 r1c5<>7 r2c5<>7 r3c5<>7 r3c6<>7 r9c6<>7 r1c5<>8 r2c5<>8 r3c5<>8 r3c6<>8 r7c4<>9

[marek stefanik]

Are SDC and double ALS measuring the same thing? I had in mind the following:

(2=3)r2c1 - (3=2)r2c79, r13c8 - loop => same eliminations as Leren's SDC.

Are they ever non-equivalent? (I removed SDC from my solver because I thought they were)

Phil

That's an interesting question, I had never thought about it before reading your post.

Obviously, there are cases of doubly-linked ALSs that SDC doesn't cover, since it's limited to one line and one box and therefore cannot detect for example doubly-linked ALSs in two rows.

While most SDCs I've encountered (or at least those I was able to spot) consist of an AALS at the intersection and ALSs in its box and line (and can therefore be expressed as doubly-linked ALSs in two different ways), there are examples with more 'A's and more links.

Consider an intersection with three 1234 cells in its line and three 56789 cells in its box.
If you were to discribe this as two ALSs, you would have to use either 3ALS –(5 links)– 2ALS or 3ALS –(4 links)– ALS.
I don't think any solver is programmed to consider anything else than regular ALSs, therefore SDC can provide eliminations they wouldn't find otherwise.

Marek

[denis_berthier]

.
Resolution state at the start and also after Singles and whips[1]:

Code: Select all

   +----------------------+----------------------+----------------------+
   ! 2389   2348   1      ! 268    234568 2358   ! 7      46     23469  !
   ! 23     5      24     ! 9      12346  7      ! 1234   8      12346  !
   ! 6      23478  24789  ! 128    12348  1238   ! 12349  14     5      !
   +----------------------+----------------------+----------------------+
   ! 23578  1      2578   ! 4      2578   6      ! 358    9      37     !
   ! 235789 23478  245789 ! 1278   12578  1258   ! 13458  14567  13467  !
   ! 578    6      4578   ! 3      1578   9      ! 1458   2      147    !
   +----------------------+----------------------+----------------------+
   ! 4      27     2567   ! 1267   123679 123    ! 1259   157    8      !
   ! 1278   9      2678   ! 5      12678  4      ! 12     3      127    !
   ! 12578  278    3      ! 1278   12789  128    ! 6      1457   12479  !
   +----------------------+----------------------+----------------------+

229 candidates, 1607 csp-links and 1607 links. Density = 6.16%

Code: Select all

whip[4]: r3c8{n4 n1} - r2n1{c9 c5} - r2n6{c5 c9} - r1c8{n6 .} ==> r9c8 ≠ 4
w1-tte

[Leren]

pjb wrote : Are SDC and double ALS measuring the same thing?

With this example, possibly not. This is the puzzle : 3....9742...5..6.........1........611.986.........3.....1.2..3..4...5..75......28

Code: Select all

*---------------------------------------------------------*
| 3      1568  568    |P16     P18     9     | 7    4  2  |
| 2479   1279  247    | 5       347-1 B1247  | 6    8  39 |
| 246789 26789 24678  | 2347-6  347-8 B24678 | 39   1  5  |
|---------------------+----------------------+------------|
| 2478   23578 234578 | 2479    4579  P247   | 2389 6  1  |
| 1      2357  9      | 8       6     P247   | 23   57 34 |
| 24678  25678 245678 | 12479   14579  3     | 289  57 49 |
|---------------------+----------------------+------------|
| 789    789   1      | 479     2      8-47  | 5    3  6  |
| 268    4     2368   | 36      38     5     | 1    9  7  |
| 5      3679  367    | 13679   1379   16-7  | 4    2  8  |
*---------------------------------------------------------*
Sue de Coq: Base Cells r23c6  {124678} Pincer Cells r45c6 {247}  + r1c45 {168} => - 1 r2c5, - 6 r3c4, - 8 r3c5, -47 r7c6, - 7 r9c6; stte

Code: Select all

*---------------------------------------------------------*
| 3      156-8 56-8   |A16     A18     9     | 7    4  2  |
| 2479   1279  247    | 5       347-1 B1247  | 6    8  39 |
| 246789 26789 24678  | 2347-6  347-8 B24678 | 39   1  5  |
|---------------------+----------------------+------------|
| 2478   23578 234578 | 2479    4579  B247   | 2389 6  1  |
| 1      2357  9      | 8       6     B247   | 23   57 34 |
| 24678  25678 245678 | 12479   14579  3     | 289  57 49 |
|---------------------+----------------------+------------|
| 789    789   1      | 479     2     B478   | 5    3  6  |
| 268    4     2368   | 36      3-8    5     | 1    9  7  |
| 5      3679  367    | 13679   1379   16-7  | 4    2  8  |
*---------------------------------------------------------*
ALS XZ Rule Loop : ALS 1 r1c45; ALS 2 r23457c6; Z = 1 & 6 => - 8 r1c23, - 1 r2c5, - 6 r3c4, - 8 r3c5, - 8 r8c5, - 7 r9c6; stte

The main difference is that, with the SDC you can get - 47 r7c6. With double ALS I can't see how you can get it, even though there were a number of double ALS moves available.

<Edit> Fixed typo as pointed out by Cenoman - Leren