The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|...|...|
 |.6.|189|.5.|
 |9..|7.4|..1|
 |---+---+---|
 |.93|648|51.|
 |...|...|...|
 |.56|327|49.|
 |---+---+---|
 |7..|4.6|..2|
 |.1.|872|.4.|
 |...|...|...|
 *-----------*


Play/Print this puzzle online

[eleven]

Code: Select all

 *-------------------------------------------------*
 | 5   d478  1    | 2   6   3   | 789    78    49  |
 |*34   6   c27   | 1   8   9   |b27     5     34  |
 | 9    238 *28   | 7   5   4   |a2368   2368  1   |
 |----------------+-------------+------------------|
 | 2    9    3    | 6   4   8   | 5      1     7   |
 |#48   478 #478  | 59  19  15  |a236    236   36  |
 | 1    5    6    | 3   2   7   | 4      9     8   |
 |----------------+-------------+------------------|
 | 7    38   5    | 4   19  6   | 19     38    2   |
 | 36   1    9    | 8   7   2   |a36     4     5   |
 |#468  248 #248  | 59  3   15  | 16789  678   69  |
 *-------------------------------------------------*

Dp 48 r59c13, external candidates 4r2c1=8r3c3
r3c3=8->r358c7=236->r2c7=7->r2c3=2->r1c2=7->r2c1=4

[pjb]

(6=3)r8c7 - (3=8)r7c8 - (8=6)r19c8 => r9c79 <> 6; stte

Phil

[ArkieTech]

Code: Select all

 *--------------------------------------------------------------------*
 | 5      47-8   1      | 2      6      3      | 789    78     49     |
 | 34     6      27     | 1      8      9      | 27     5      34     |
 | 9     *238   *28     | 7      5      4      | 2368   2368   1      |
 |----------------------+----------------------+----------------------|
 | 2      9      3      | 6      4      8      | 5      1      7      |
 | 48     478    478    | 59     19     15     | 236    236    36     |
 | 1      5      6      | 3      2      7      | 4      9      8      |
 |----------------------+----------------------+----------------------|
 | 7     *38     5      | 4      19     6      | 19     38     2      |
 | 36     1      9      | 8      7      2      | 36     4      5      |
 | 468    248    248    | 59     3      15     | 16789  678    69     |
 *--------------------------------------------------------------------*
xyz-wing
(8=3)r7c2-(3=28)r3c23 => -8r1c2; lclste

[tlanglet]

(6=9)r9c9-(9=4)r1c9-r2c9=r2c1-(48=6)r59c1 => r9c78<>6

Ted

[Marty R.]

Code: Select all

+-------------+----------+---------------+
| 5   478 1   | 2  6  3  | 789   78   49 |
| 34  6   27  | 1  8  9  | 27    5    34 |
| 9   238 28  | 7  5  4  | 2368  2368 1  |
+-------------+----------+---------------+
| 2   9   3   | 6  4  8  | 5     1    7  |
| 48  478 478 | 59 19 15 | 236   236  36 |
| 1   5   6   | 3  2  7  | 4     9    8  |
+-------------+----------+---------------+
| 7   38  5   | 4  19 6  | 19    38   2  |
| 36  1   9   | 8  7  2  | 36    4    5  |
| 468 248 248 | 59 3  15 | 16789 678  69 |
+-------------+----------+---------------+


Play this puzzle online at the Daily Sudoku site

R9c9=6=>contradiction

(9=6)r9c9-(6=3)r8c7-(3=8)r7c8-(78=6)r19c8; contradiction=>r9c9<>6

Is this shortened form valid?

(9=6)r9c9-(78=6)r19c8; contradiction=>r9c9<>6

[Leren]

Code: Select all

*---------------------------------------------------------------------------------*
| 5       478     1        | 2       6       3        |b789     a78      49       |
| 34      6       27       | 1       8       9        |b27       5       34       |
| 9       238     28       | 7       5       4        |b2368     236-8   1        |
|--------------------------+--------------------------+---------------------------|
| 2       9       3        | 6       4       8        | 5        1       7        |
| 48      478     478      | 59      19      15       |b236      236     36       |
| 1       5       6        | 3       2       7        | 4        9       8        |
|--------------------------+--------------------------+---------------------------|
| 7       38      5        | 4       9-1     6        |b19       38      2        |
| 36      1       9        | 8       7       2        |b36       4       5        |
| 468     248     248      | 59      3       15       | 78-1-6-9 678     69       |
*---------------------------------------------------------------------------------*

Doubly linked als-xz rule r1c8 r123578c7 x = 7,8 = > r3c8 <> 8, r7c5 <> 1, r9c7 <> 1,6,9; stte

Leren

[Luke]

Code: Select all

*---------------------------------------------------------------------------------*
| 5       478     1        | 2       6       3        |b789     a78      49       |
| 34      6       27       | 1       8       9        |b27       5       34       |
| 9       238     28       | 7       5       4        |b2368     236-8   1        |
|--------------------------+--------------------------+---------------------------|
| 2       9       3        | 6       4       8        | 5        1       7        |
| 48      478     478      | 59      19      15       |b236      236     36       |
| 1       5       6        | 3       2       7        | 4        9       8        |
|--------------------------+--------------------------+---------------------------|
| 7       38      5        | 4       9-1     6        |b19       38      2        |
| 36      1       9        | 8       7       2        |b36       4       5        |
| 468     248     248      | 59      3       15       | 78-1-6-9 678     69       |
*---------------------------------------------------------------------------------*

Doubly linked als-xz rule r1c8 r123578c7 x = 7,8 = > r3c8 <> 8, r7c5 <> 1, r9c7 <> 1,6,9; stte

Leren

Beautiful, love it. We're you able to see that manually? I have the hardest time finding these.

[JC Van Hay]

The following 2 Sue de Coq are 2 possible interpretations of the solution of the puzzle by solving the column 9 (r1c9=9->contradiction :=> r1c9=4;ste).

Code: Select all

Marty's Sue de Coq ...
+---------------+------------+--------------------+
| 5    478  1   | 2   6   3  | 789     (78)   49  |
| 34   6    27  | 1   8   9  | 27      5      34  |
| 9    238  28  | 7   5   4  | 2368    236-8  1   |
+---------------+------------+--------------------+
| 2    9    3   | 6   4   8  | 5       1      7   |
| 48   478  478 | 59  19  15 | 236     236    36  |
| 1    5    6   | 3   2   7  | 4       9      8   |
+---------------+------------+--------------------+
| 7    38   5   | 4   19  6  | 19      (38)   2   |
| 36   1    9   | 8   7   2  | (36)    4      5   |
| 468  248  248 | 59  3   15 | 1789-6  (678)  9-6 |
+---------------+------------+--------------------+
r1c8=7->r79c8.r8c7=368 or r1c8=8->r79c8.r8c7=367
:=> -8r1c3,-6r9c79

Leren's Sue de Coq ...
+---------------+------------+-------------------+
| 5    478  1   | 2   6   3  | 9-78    (78)   49 |
| 34   6    27  | 1   8   9  | (27)    5      34 |
| 9    238  28  | 7   5   4  | (2368)  236-8  1  |
+---------------+------------+-------------------+
| 2    9    3   | 6   4   8  | 5       1      7  |
| 48   478  478 | 59  19  15 | (236)   236    36 |
| 1    5    6   | 3   2   7  | 4       9      8  |
+---------------+------------+-------------------+
| 7    38   5   | 4   19  6  | 19      38     2  |
| 36   1    9   | 8   7   2  | (36)    4      5  |
| 468  248  248 | 59  3   15 | 1789-6  678    69 |
+---------------+------------+-------------------+
r1c8=7->r2358c7=2368 or r1c8=8->r2358c7=2367
:=> -78r1c7,-8r3c8,-6r9c7

[David P Bird]

Code: Select all

*---------------------------------------------------------------------------------*
| 5       478     1        | 2       6       3        | 789      78      49       |
| 34      6       27       | 1       8       9        | 27       5       34       |
| 9       238     28       | 7       5       4        | 2368     2368    1        |
|--------------------------+--------------------------+---------------------------|
| 2       9       3        | 6       4       8        | 5        1       7        |
| 48      478     478      | 59      19      15       | 236      236     36       |
| 1       5       6        | 3       2       7        | 4        9       8        |
|--------------------------+--------------------------+---------------------------|
| 7       38      5        | 4       9-1     6        | 19       38      2        |
| 36      1       9        | 8       7       2        | 36       4       5        |
| 468     248     248      | 59      3       15       | 16789    678     69       |
*---------------------------------------------------------------------------------*

Expressing these column 7 box 3 interactions as 2-Sector Naked and Hidden Sets there are a variety of options:

As before:
Multi-sector Naked Set:(12369)c7,(78)b3: 7 digits/constrained cells => r3c8 <> 8, r9c7 <> 169

Multi-sector Naked Set:(236)c7,(78)b3: 5 digits/constrained cells => r1c7 <> 78, r3c8 <> 8, r9c7 <> 6

Additionally:
Multi-sector Hidden Set: (1789)c7,(236)b3: 7 digits/available cells => r2c9 <> 4, r3c8 <> 8, r9c7 <> 6

Multi-sector Hidden Set: (1789)c7,(36)b3: 6 digits/available cells => r3c7 <> 3, r3c8 <> 38, r9c7 <> 6

Constrained cells are those that only contain member candidates
Available cells are those capable of holding member candidates

I'm never quite sure which ones should be called Sue de Coqs, but the different variations are quite challenging to find in a well populated puzzle.

[Luke]

Code: Select all

*---------------------------------------------------------------------------------*
| 5       478     1        | 2       6       3        | 789      78      49       |
| 34      6       27       | 1       8       9        | 27       5       34       |
| 9       238     28       | 7       5       4        | 2368     2368    1        |
|--------------------------+--------------------------+---------------------------|
| 2       9       3        | 6       4       8        | 5        1       7        |
| 48      478     478      | 59      19      15       | 236      236     36       |
| 1       5       6        | 3       2       7        | 4        9       8        |
|--------------------------+--------------------------+---------------------------|
| 7       38      5        | 4       9-1     6        | 19       38      2        |
| 36      1       9        | 8       7       2        | 36       4       5        |
| 468     248     248      | 59      3       15       | 16789    678     69       |
*---------------------------------------------------------------------------------*

Expressing these column 7 box 3 interactions as 2-Sector Naked and Hidden Sets there are a variety of options:

As before:
Multi-sector Naked Set:(12369)c7,(78)b3: 7 digits/constrained cells => r3c8 <> 8, r9c7 <> 169

It's always curious to me that this approach (same as "disjoint subsets"?) only find certain eliminations by extrapolation. Leren's DL-als takes out (1)r7c5 directly. I suspect that carrying forward all SdQ eliminations will always take out those that the DL-als finds directly, but I don't know for sure.

[daj95376]

[Withdrawn: a poor example easily replaced by an M-Ring.]

[David P Bird]

Luke457 It's always curious to me that this approach (same as "disjoint subsets"?) only find certain eliminations by extrapolation. Leren's DL-als takes out (1)r7c5 directly. I suspect that carrying forward all SdQ eliminations will always take out those that the DL-als finds directly, but I don't know for sure.

Yes, Multi-sector Naked Sets include patterns that have previously been called 'disjoint subsets', 'doubly linked ALSs', and 'cannibalistic ALS chains'. However the term also covers Multi-fish where the underlying logic is the same, which is why I choose to use it.

I only notated the eliminations available in the two covering houses as that was all that was needed. However, once a locked set has been found, it will eliminate any candidate that sees all the internal instances of itself in one of the houses used by the pattern, so additional eliminations may also 'belong' to the pattern.

In a single house if an ANS is found there will always be a complementary AHS, but with multiple houses there may or may not be a simple complement (ie one where no candidate is covered more than once), and this applies in reverse too. Colouring focus digits I find AHSs easier to spot than ANSs. In either case, it's the ones that overlap that are of interest, but for a manual solver that requires committing them to memory as and when they are identified. So far it seems to me that that MSNSs are more common then MSHSs, but that may be because of I haven't developed an eye for them yet.

[eleven]

In my eyes the als, Sue de Coq, base/cover and ring interpretations are more of theoretical interest.
All you have to spot is a simple forcing chain:
r1c8=7->r9c7=7
r1c8=8->r9c7=8
The rest falls into place.
7r9c7=7r123c7-(7=8)r1c8-8r13c7=8r9c7 => r9c7<>169, and if you want r3c8<>8

[aran]

In my eyes the als, Sue de Coq, base/cover and ring interpretations are more of theoretical interest.
All you have to spot is a simple forcing chain:
r1c8=7->r9c7=7
r1c8=8->r9c7=8
The rest falls into place.
7r9c7=7r123c7-(7=8)r1c8-8r13c7=8r9c7 => r9c7<>169, and if you want r3c8<>8

Eleven
It all becomes very subjective at some point.
DL-ALS are intrinsically for some - of whom me - admirable objects in a way that forcing chains could never be.
In these simple puzzles with more or less one stop solutions, almost anything goes.
But in more complicated puzzles, a Dl-ALS will or may work wonders without any easy transcription as a forcing chain or other.
To that extent looking out for them has merit.

As an aside, reference to DL-ALS as doubly-linked ALS-XZ rule is imo not the best.
For whereas in a standard ALS-XZ there are minimal Z in play, in a DL-ALS the Z are potentially numerous : indeed the concept is different. As can be seen if one thinks in base cover terms : a DL-ALS has rank 0 and is therefore a beautiful object per se...surely unarguable...whilst a ALS-XY is "merely" at move, and at best a beautiful move.