The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . 1 | 2 . . | . 3 . |
| . . . | . 4 . | 5 . . |
| . . . | . . 7 | . . . |
+-------+-------+-------+
| . 4 . | . . . | 7 . . |
| . . 6 | . . . | . 1 3 |
| 1 . 8 | . . . | . . 6 |
+-------+-------+-------+
| . 1 . | 8 . . | . . 5 |
| . 9 . | . 7 5 | . . . |
| 8 . . | 6 . . | . 2 . |
+-------+-------+-------+
..12...3.....4.5.......7....4....7....6....131.8.....6.1.8....5.9..75...8..6...2.

(As a reminder, these are puzzles which are rated 11+ by SE, but fall to some advanced technique not implemented by SE. Like last week's, I don't think this one reduces to basics, but does get much easier.)

[Leren]

Code: Select all

*---------------------------------------------------------------------------------*
| 4579   *5678    1        | 2      *5689    *689      |*4689    3       479-8    |
| 2379    2368-7  2379     | 139     4        1368-9   | 5       6789    12789    |
| 23459   2368-5  23459    | 1359    1368-59  7        | 1268-49 4689    12489    |
|--------------------------+---------------------------+--------------------------|
| 2359    4       2359     | 1359    12368-59 12368-9  | 7       589     289      |
| 579-2  *257     6        | 4579   *2589    *2489     |*2489    1       3        |
| 1      *2357    8        | 4579-3 *2359    *2349     |*249     459     6        |
|--------------------------+---------------------------+--------------------------|
| 3467    1       347      | 8       23-9     23-49    | 36-49   4679    5        |
| 2346    9       234      | 134     7        5        | 1368-4  468     148      |
| 8      *357     457-3    | 6      *139     *1349     |*1349    2       479-1    |
*---------------------------------------------------------------------------------*

MSLS  : 16 Cell Truths ; c2567 r1569 : 16 Links; 57c2 59c5 49c6 49c7 ; 68r1 28r5 23r6 13r9 ;

21 Eliminations : r1c9 <> 8, r2c2 <> 7, r2c6 <> 9, r3c2 <> 5, r3c5 <> 59, r3c7 <> 49, r4c5 <> 59, r4c6 <> 9, r5c1 <> 2, r6c4 <> 3, r7c5 <> 9, r7c67 <> 49, r8c7 <> 4, r9c3 <> 3, r9c9 <> 1

Leren

[Ajò Dimonios]

Code: Select all

+-------------------+----------------------+-------------------+
| 4579  5678  1     | 2     5689    689    | 4689   3    4789  |
| 2379  23678 2379  | 139   4       13689  | 5      6789 12789 |
| 23459 23568 23459 | 1359  135689  7      | 124689 4689 12489 |
+-------------------+----------------------+-------------------+
| 2359  4     2359  | 1359  1235689 123689 | 7      589  289   |
| 2579  257   6     | 4579  2589    2489   | 2489   1    3     |
| 1     2357  8     | 34579 2359    2349   | 249    459  6     |
+-------------------+----------------------+-------------------+
| 3467  1     347   | 8     239     2349   | 3469   4679 5     |
| 2346  9     234   | 134   7       5      | 13468  468  148   |
| 8     357   3457  | 6     139     1349   | 1349   2    1479  |
+-------------------+----------------------+-------------------+


MSLS
Base 12368
T16={1569n2 1569n5 1569n6 1569n7} L16={57c2 59c5 49c6 49c7 68r1 28 r5 23r6 13r9}
21 Eliminations: -8 r1c9, -2 r5c1, -3 r6c4, -3 r9c3, -1 r9c9, -7 r2c2, -5 r3c2, -5 r3c5, -9 r3c5, -5 r4c5, -9 r4c5, -9 r7c5, -9 r2c6, -9 r4c6, -4 r7c6, -9 r7c6, -4 r3c7, -9 r3c7, -4 r7c7, -9 r7c7, -4 r8c7,

Code: Select all

+-------------+------------------+-----------+
| 579  567 1  | 2     569   69   | 8   3  4  |
| 239  68  39 | 139   4     68   | 5   7  12 |
| 35   28  4  | 35    18    7    | 12  6  9  |
+-------------+------------------+-----------+
| 2359 4   39 | 159   16    126  | 7   58 28 |
| 579  257 6  | 4579  2589  2489 | 249 1  3  |
| 1    257 8  | 4579  2359  2349 | 249 45 6  |
+-------------+------------------+-----------+
| 4    1   7  | 8     23    23   | 6   9  5  |
| 6    9   2  | 14    7     5    | 3   48 18 |
| 8    3   5  | 6     19    149  | 14  2  7  |
+-------------+------------------+-----------+


4r9c6=r9c7-r8c8=r6c8=>-4r6c6
8r3c2=(8-1)r3c5=r3c7-(1=4)r9c7-r9c6=(4-8)r5c6=8r5c5=>-8r3c5=>stte

Paolo

[SpAce]

Step 1.

Code: Select all

         \57                      \59       \49       \49
.-----------------------.----------------------------.-----------------------.
| \4579   5678    1     |  2       5689      689     | 4689     3     \479-8 | *4579  \n19
|  2379   2368-7  2379  |  139     4         1368-9  | 5        6789   12789 |
|  23459  2368-5  23459 |  1359    1368-59   7       | 1268-49  4689   12489 |
:-----------------------+----------------------------+-----------------------:
|  2359   4       2359  |  1359    12368-59  12368-9 | 7        589    289   |
| \579-2  257     6     | \4579    2589      2489    | 2489     1      3     | *4579  \n14
|  1      2357    8     | \4579-3  2359      2349    | 249     \459    6     | *4579  \n48
:-----------------------+----------------------------+-----------------------:
|  3467   1       347   |  8       23-9      23-49   | 36-49    4679   5     |
|  2346   9       234   |  134     7         5       | 1368-4   468    148   |
|  8      357    \457-3 |  6       139       1349    | 1349     2     \479-1 | *4579  \n39
'-----------------------'----------------------------'-----------------------'

Multifish (4579): 16x16 {4579R1569 \ 57c2 59c5 49c67 1n19 5n14 6n48 9n39} => 21 elims


Step 2.

Code: Select all

.---------------.--------------------.-------------.
| 579   567  1  | 2      569   a69   | 8    3   4  |
| 239   68   39 | 139    4     a68   | 5    7   12 |
| 35    28   4  | 35    c1-8    7    | 12   6   9  |
:---------------+--------------------+-------------:
| 2359  4    39 | 159   c126   b126  | 7    58  28 |
| 579   257  6  | 4579   2589   2489 | 249  1   3  |
| 1     257  8  | 4579   2359   2349 | 249  45  6  |
:---------------+--------------------+-------------:
| 4     1    7  | 8      23     23   | 6    9   5  |
| 6     9    2  | 14     7      5    | 3    48  18 |
| 8     3    5  | 6     c19    b149  | 14   2   7  |
'---------------'--------------------'-------------'

(8=69)r21c6 - (6|9)r49c6 = (691)r493c5 => -8 r3c5; stte


[Cenoman]

Code: Select all

 +--------------------------+-----------------------------+--------------------------+
 |  4579    5678    1       |  2       5689      689      |  4689     3      479-8   |
 | <2379    2368-7 <2379    | <139     4         1368-9   |  5       <6789  <12789   |79
 | <23459   2368-5 <23459   | <1359    1368-59   7        |  1268-49 <4689  <12489   |459
 +--------------------------+-----------------------------+--------------------------+
 | <2359    4      <2359    | <1359    12368-59  12368-9  |  7       <589   <289     |59
 |  579-2   257     6       |  4579    2589      2489     |  2489     1      3       |
 |  1       2357    8       |  4579-3  2359      2349     |  249      459    6       |
 +--------------------------+-----------------------------+--------------------------+
 | <3467    1      <347     |  8       23-9      23-49    |  36-49   <4679   5       |479
 | <2346    9      <234     | <134     7         5        |  1368-4  <468   <148     |4
 |  8       357     457-3   |  6       139       1349     |  1349     2      479-1   |
 +--------------------------+-----------------------------+--------------------------+
    236             23         13                                     68     128

1. MSLS
23 cell truths: r23478 c138 & r2348 c49;
23 links: 79r2, 459r3, 59r4, 479r7, 4r8, 236c1, 23c3, 13c4, 68c8, 128c9
21 eliminations: -7 r2c2, -9 r2c6, -5r3c2, -59 r3c5, -49 r3c7, -59 r4c5, -9 r4c6, -9 r7c5, -49 r7c67, -4r8c7, -2 r5c1, -3 r9c3, -3 r6c4, -8 r1c9, - 1r9c9

Code: Select all

 +--------------------+-----------------------+------------------+
 |  579    567   1    |  2      569   a69     |  8     3    4    |
 |  239*  c68    39   |  139    4      8-6    |  5     7    12*  |
 |  35    c28    4    |  35     18     7      | b12    6    9    |
 +--------------------+-----------------------+------------------+
 |  2359*  4     39   |  159    16-2  a16-2   |  7     58   28*  |
 |  579    257   6    |  4579   2589   2489   |  249   1    3    |
 |  1      257   8    |  4579   2359   2349   |  249   45   6    |
 +--------------------+-----------------------+------------------+
 |  4      1     7    |  8      23     23     |  6     9    5    |
 |  6      9     2    |  14     7      5      |  3     48   18   |
 |  8      3     5    |  6      19    a149    | b14    2    7    |
 +--------------------+-----------------------+------------------+

2. X-Wing (2)c19\r24 => -2 r4c56
3. (6=194)r149c6 - (4=12)r39c7 - (2=86)r23c2 => -6 r2c6; ste

[mith]

There is another MSLS that gives a few more eliminations, but the solution from there isn't significantly different. Either way, SER goes down to 4.5 (it can be solved with, for example, a UR type 4, X-Wing, and Skyscraper).

[SpAce]

There is another MSLS that gives a few more eliminations

Can you show that? I can't find any that would give more eliminations with the normal cover sets. I can see that Cenoman's 23-cell variant could get these additional eliminations in row 7, but it requires siamese logic (alternate bases\covers) and gains nothing significant:

-36 r7c1, -3 r7c37, -467 r7c8

The same eliminations are available through a naked or hidden triple right after, and I think it's much clearer that way. Did you mean something else?

[mith]

This is from yzf's solver, of course:

MSLS:19 Cells r15679c2567, 19 Links 68r1,28r5,23r6,236r7,13r9,57c2,59c5,49c6,49c7
24 Eliminations:r9c9<>1,r5c1<>2,r7c13,r6c4,r9c3<>3,r38c7<>4,r3c25,r4c5<>5,r7c18,r8c78,r13c7<>6,r2c2<>7,r1c9<>8,r3c57,r4c56,r2c6<>9

[SpAce]

This is from yzf's solver, of course:

MSLS:19 Cells r15679c2567, 19 Links 68r1,28r5,23r6,236r7,13r9,57c2,59c5,49c6,49c7
24 Eliminations:r9c9<>1,r5c1<>2,r7c13,r6c4,r9c3<>3,r38c7<>4,r3c25,r4c5<>5,r7c18,r8c78,r13c7<>6,r2c2<>7,r1c9<>8,r3c57,r4c56,r2c6<>9

Ok, thanks. It's just like I suspected. YZF is using unlisted siamese covers to get extra eliminations. That's a bit confusing for those who don't know it. In this case these four eliminations aren't explained by the listed links:

Code: Select all

-6 r1c7  (6r1+6c7, Rank 1, cannibalistic)
-6 r38c7 (6c7)
-6 r8c8  (6b9)

What makes those possible is the lone 6r7c7 that can be covered in three ways: 6r7,6c7,6b9. If all of them are used, that should be clearly expressed in the list of covers to avoid confusion. For example:

MSLS:19 Cells r15679c2567, 19 Links 68r1,28r5,23r6,23r7,6(r7|c7|b9),13r9,57c2,59c5,49c6,49c7 => 24 elims

As usual, the extra eliminations don't make any difference to the end result, because the same eliminations are available through basics right after. There's nothing wrong with taking them immediately, but then the reasoning should be explained. Personally I'd rather keep things simple unless there's something valuable to gain.