The New Sudoku Players' Forum

[urhegyi]

A member at the sudoku puzzle group posted this "hard" sudoku and asked to solve it. No one was capable. It has SE 11.1. Now a computer program found the trick: it has a MSLS. But the question is as a human solver how can you find this?

Code: Select all

.-----------------------.--------------------------.--------------------.
| 235689  23789  235679 | 2345689  123468  1234569 | 14579  1257  4579  |
| 2569    279    1      | 24569    246     24569   | 8      257   3     |
| 4       2389   2359   | 23589    7       12359   | 159    6     59    |
:-----------------------+--------------------------+--------------------:
| 3569    349    34569  | 1        346     8       | 2      357   45679 |
| 23569   2349   8      | 234679   2346    234679  | 45679  357   1     |
| 7       12349  23469  | 23469    5       23469   | 469    38    4689  |
:-----------------------+--------------------------+--------------------:
| 189     14789  479    | 45678    1468    14567   | 3      1578  2     |
| 1238    6      237    | 23578    9       12357   | 157    4     578   |
| 1238    5      2347   | 234678   123468  123467  | 167    9     678   |
'-----------------------'--------------------------'--------------------'

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...........1...8.34...7..6....1.82....8.....17...5..........3.2.6..9..4..5.....9.

[yzfwsf]

Coffee+green=5x rows, while blue+green=5x columns, so the final solution contained in coffee and blue should be the same. Coffee currently has 10 clues for 1238, while blue does not have 1238, but it has 10 blank cells that must be filled with 1238, 45679 can be deleted. Blue has 10 clues for 45679, so all 10 blank cells in coffee must be filled with 45679, 1238 can be deleted.

[Leren]

There was also a Multifish pattern available : Truths 15 Base 1238 Rows 3689; Links 15 Cols 34679 Cells r3c2 r6c8 r8c1 r9c1 r9c5 ; 19 eliminations get you to here.

Code: Select all

*---------------------------------------------------------------*
| 235689  23789  5679  | 569   12368  569   | 4579  1257  4579  |
| 2569    279    1     | 4569  246    4569  | 8     257   3     |
| 4      #238   *2359  |*23589 7     *12359 |*159   6     59    |
|----------------------+--------------------+-------------------|
| 3569    349    4569  | 1     346    8     | 2     357   45679 |
| 23569   2349   8     | 4679  2346   4679  | 4569  35    1     |
| 7       1     *23469 |*23469 5     *23469 | 469  #38    4689  |
|----------------------+--------------------+-------------------|
| 189     4789   479   | 4567  1468   4567  | 3     1578  2     |
|#1238    6     *237   |*23578 9     *12357 |*157   4    *578   |
|#1238    5     *2347  |*23478 1238  *12347 |*167   9    *678   |
*---------------------------------------------------------------*

Follow on basics get you to here, which AFAIK is where all the available Rank 0 patterns will end up.

Code: Select all

*----------------------------------------------*
| 38  38  5679 | 569   1   569  | 4579 2  4579 |
| 56  79  1    | 4569  2   4569 | 8    57 3    |
| 4   2   59   | 8     7   3    | 1    6  59   |
|--------------+----------------+--------------|
| 56  349 4569 | 1     346 8    | 2    37 4679 |
| 2   349 8    | 4679  346 4679 | 4569 35 1    |
| 7   1   3469 | 23469 5   2469 | 469  8  469  |
|--------------+----------------+--------------|
| 9   478 47   | 4567  468 4567 | 3    1  2    |
| 138 6   237  | 237   9   127  | 57   4  578  |
| 138 5   2347 | 2347  38  1247 | 67   9  678  |
*----------------------------------------------*

A few easy moves will finish the puzzle. Leren

[urhegyi]

Today I studied the MSLS technique here by watching the first video about the basic concept:https://www.reddit.com/r/sudoku/comments/p4m8mb/the_sudokult_discussion_set_equivalence_theory/
I think I understood it enough to modify the last posted example.

Code: Select all

...........1...8.34...9..6....1.82....8.....15...4..........3.2.9..5..7..7.....4.

After the MSLS the finishing part is easier than in the first one I think.
If yzfwsf and/or Leren would be so kind to check this and confirm my opinion?
I would like to thank both of them for commenting my first post, that has encouraged me to study this theory.

[yzfwsf]

Code: Select all

,-----------------------,------------------------,--------------------,
| 236789  23568  235679 | 235678  123678  123567 | 14579  1259  4579  |
| 2679    256    1      | 24567   267     24567  | 8      259   3     |
| 4       2358   2357   | 23578   9       12357  | 157    6     57    |
:-----------------------+------------------------+--------------------:
| 3679    346    34679  | 1       367     8      | 2      359   45679 |
| 23679   2346   8      | 235679  2367    235679 | 4679   39    1     |
| 5       1      23679  | 23679   4       23679  | 679    389   6789  |
:-----------------------+------------------------+--------------------:
| 168     4568   456    | 46789   1678    14679  | 3      1589  2     |
| 12368   9      2346   | 23468   5       12346  | 16     7     68    |
| 12368   7      2356   | 23689   12368   12369  | 1569   4     5689  |
'-----------------------'------------------------'--------------------'

MSLS:16 Cells r2457c1258, 16 Links 2r2,3r4,23r5,18r7,679c1,456c2,67c5,59c8
23 Eliminations:r7c6<>1,r25c46<>2,r5c46,r4c3<>3,r1c28,r3c2<>5,r1c125,r9c15,r8c1<>6,r1c15<>7,r7c4<>8,r1c18,r6c8<>9

or

Multi-Fish: 15 Trueth:1238c1,238c2,1238c5,1238c8,15 Links:1238r1,2r2,3r4,23r5,18r7+r9c15,r3c2,r6c8,r8c1 => 32 eliminations
r3c2<>5, r6c8<>9, r8c1<>6, r9c1<>6, r9c5<>6, r1c3<>23, r1c4<>238, r1c6<>123, r1c7<>1, r1c1<>679, r1c2<>56, r1c5<>67, r1c8<>59, r2c4<>2, r2c6<>2, r4c3<>3, r5c4<>23, r5c6<>23, r7c4<>8, r7c6<>1

[Leren]

MSLS : Base 1238; r12457 c1258 : 20 Links; 1238r1 2r2 3r4 23r5 18r7 ; 679c1 456c2 67c5 59c8 ; Get's you to here with 23 eliminations.

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*--------------------------------------------------------------------------------*
| 236789  23568   5679     | 567     123678  567      | 4579    1259    4579     |
| 2679    256     1        | 4567    267     4567     | 8       259     3        |
| 4       238     2357     | 23578   9       12357    | 157     6       57       |
|--------------------------+--------------------------+--------------------------|
| 3679    346     4679     | 1       367     8        | 2       359     45679    |
| 23679   2346    8        | 5679    2367    5679     | 4679    39      1        |
| 5       1       23679    | 23679   4       23679    | 679     38      6789     |
|--------------------------+--------------------------+--------------------------|
| 168     4568    456      | 4679    1678    4679     | 3       1589    2        |
| 1238    9       2346     | 23468   5       12346    | 16      7       68       |
| 1238    7       2356     | 23689   1238    12369    | 1569    4       5689     |
*--------------------------------------------------------------------------------*

Follow on eliminations get you to here. The finish is easier than for the previous puzzle.

Code: Select all

*-----------------------------------------------*
| 38  38  5679 | 567  1   567  | 4579 2   4579  |
| 79  56  1    | 4567 2   4567 | 8    59  3     |
| 4   2   57   | 8    9   3    | 1    6   57    |
|--------------+---------------+----------------|
| 79  346 4679 | 1    367 8    | 2    359 45679 |
| 2   346 8    | 579  367 579  | 479  39  1     |
| 5   1   3679 | 2379 4   279  | 79   8   679   |
|--------------+---------------+----------------|
| 6   458 45   | 479  78  479  | 3    1   2     |
| 13  9   234  | 234  5   124  | 6    7   8     |
| 138 7   23   | 236  38  126  | 59   4   59    |
*-----------------------------------------------*

So far these are "well behaved" MSLS in that none of the cells in the MSLS grid are solved. When that occurs some extra truth balancing tricks are required to get the rank to 0.

I see that I cross posted with yzfwsf who found different MSLS but I'm pretty sure the post basics elimination positions will be the same in each case.

Leren