The New Sudoku Players' Forum

[SCLT]

Here's a puzzle I created with a specific solution in mind. I'm curious to see what you come up with - have fun!

Code: Select all

+-------+-------+-------+
| 7 . 1 | . 3 . | . . . |
| . 8 . | 7 . 6 | . . . |
| . . 3 | . 5 . | 9 . . |
+-------+-------+-------+
| . . . | 4 . 2 | . 9 . |
| . . . | . 7 . | 1 . 5 |
| . . . | . . 5 | . 8 . |
+-------+-------+-------+
| 1 . . | . . . | 3 . 9 |
| . 3 . | . . . | . 6 . |
| 9 . 5 | . . . | . . 1 |
+-------+-------+-------+
7.1.3.....8.7.6.....3.5.9.....4.2.9.....7.1.5.....5.8.1.....3.9.3.....6.9.5.....1


[ghfick]

Excellent... impressive... however...
MSLS :13579 : r13579 c2468: 59r1, 1r3, 39r5, 57r7, 37r9, 246c2, 268c4, 48c6, 247c8
Exclusions: -5 r1c7, -3 r5c1, -9 r5c3, -7 r7c3, -7 r9c7, -6 r4c2, -2 r6c2, -4 r6c2, -6 r6c2, -6 r6c4, -2 r8c4, -8 r8c4, -4 r8c6, -8 r8c6, -2 r2c8, -4 r2c8 more?
Nice pattern... maybe for the Patterns Game?

[pjb]

One step: Multi-Fish: Base 2468
20 Truths = {2468R1, 2468R3, 2468R5, 2468R7, 2468R9}
20 Links = {246c2, 268c4, 48c6, 24c8, 1n7, 1n9, 3n1, 3n9, 5n1, 5n3, 7n3, 7n5, 9n5, 9n7}
17 Eliminations: -5 r1c7, -7 r3c9, -3r 5c1, -9 r5c3, -7 r7c3, -7 r9c7, -24 r2c8, -6 r4c2, -24 r6c2, -6 r6c24, -28 r8c4, -48 r8c6; stte

Phil

[SCLT]

Excellent... impressive... however...
MSLS :13579 : r13579 c2468: 59r1, 1r3, 39r5, 57r7, 37r9, 246c2, 268c4, 48c6, 247c8
Exclusions: -5 r1c7, -3 r5c1, -9 r5c3, -7 r7c3, -7 r9c7, -6 r4c2, -2 r6c2, -4 r6c2, -6 r6c2, -6 r6c4, -2 r8c4, -8 r8c4, -4 r8c6, -8 r8c6, -2 r2c8, -4 r2c8 more?
Nice pattern... maybe for the Patterns Game?

Weird, why do you break the odd-even partition by using the link set 7c8 instead of 7r3?

By the way, your MSLS also has the eliminations -7r7c8 and -7r9c8 since those candidates are covered by two link sets. The modification I suggested gives -7r3c9 instead. Both lead to the same next step (hidden single 7 in r3c8) and stte.

One step: Multi-Fish: Base 2468
20 Truths = {2468R1, 2468R3, 2468R5, 2468R7, 2468R9}
20 Links = {246c2, 268c4, 48c6, 24c8, 1n7, 1n9, 3n1, 3n9, 5n1, 5n3, 7n3, 7n5, 9n5, 9n7}
17 Eliminations: -5 r1c7, -7 r3c9, -3r 5c1, -9 r5c3, -7 r7c3, -7 r9c7, -24 r2c8, -6 r4c2, -24 r6c2, -6 r6c24, -28 r8c4, -48 r8c6; stte

Phil

Yes Phil, that's exactly what I had in mind. And of course equivalent to the (modified) MSLS given by ghfick.

[SpAce]

The first solution I found used only 13x13 sets, but it's btte:

Code: Select all

               *159               *1359           *139              *135
      \35               \9                \19              \5               \3
     .--------------------------.-------------------------.------------------------.
     | 7        24569    1^     |  289     3^      489    | 2468-5   245     2468  |        \59
\n8  | 245      8        249    |  7       1249    6      | 245     \135-24  234   | *1359
     | 246      246      3^     |  128     5^      148    | 9^       1247    24678 |        \1
     :--------------------------+-------------------------+------------------------:
\n2  | 3568    \15-67    678    |  4       168     2      | 67       9^      367   | *135
     | 2468-3   2469     2468-9 |  3689    7       389    | 1^       234     5^    |        \39
\n24 | 2346    \19-2467  24679  | \139-6   169     5^     | 2467     8       23467 | *139
     :--------------------------+-------------------------+------------------------:
     | 1^       2467     24678  |  2568    2468    478    | 3^       2457    9^    |        \5
\n46 | 248      3^       2478   | \159-28  12489  \19-478 | 24578    6       2478  | *159
     | 9^       2467     5^     |  2368    2468    3478   | 2478     247     1^    |        \3
     '--------------------------'-------------------------'------------------------'

MF (1359): 13x13 {1359R2 135R4 139R6 159R8 \ 35c1 9c3 19c5 5c7 3c9 46n2 68n4 8n6 2n8} => 17 elims; btte

Column-based MF (1359): Show

MF (1359): 13x13 {159C2 1359C4 139C6 135C8 \ 59r1 1r3 39r5 5r7 3r9 2n8 4n2 6n24 8n46} => 17 elims; btte

16x16 is enough for stte (just add 7 to the digits):

Code: Select all

              *1579              *1359           *1379             *1357
      \35               \79               \19              \57              \37
     .--------------------------.-------------------------.-------------------------.
     | 7^       24569    1^     |  289     3^      489    | 2468-5   245     2468   |        \59
\n8  | 245      8        249    |  7^      1249    6      | 245     \135-24  234    | *1359
     | 246      246      3^     |  128     5^      148    | 9^       1247    2468-7 |        \17
     :--------------------------+-------------------------+-------------------------:
\n2  | 3568    \15-67    678    |  4       168     2      | 67       9^      367    | *1357
     | 2468-3   2469     2468-9 |  3689    7^      389    | 1^       234     5^     |        \39
\n24 | 2346    \19-2467  24679  | \139-6   169     5^     | 2467     8       23467  | *1379
     :--------------------------+-------------------------+-------------------------:
     | 1^       2467     24678  |  2568    2468    478    | 3^       2457    9^     |        \57
\n46 | 248      3^       248-7  | \159-28  12489  \19-478 | 24578    6       2478   | *1579
     | 9^       2467     5^     |  2368    2468    3478   | 248-7    247     1^     |        \37
     '--------------------------'-------------------------'-------------------------'

MF (13579): 16x16 {1359R2 1357R4 1379R6 1579R8 \ 35c1 79c3 19c5 57c7 37c9 46n2 68n4 8n6 2n8} => 20 elims; stte

Column-based MF (13579): Show

MF (13579): 16x16 {1579C2 1359C4 1379C6 1357C8 \ 59r1 17r3 39r5 57r7 37r9 2n8 4n2 6n24 8n46} => 20 elims; stte

Other options:

Multifish (2468): Show

Code: Select all

       *2468             *2468             *2468            *2468            *2468
               \246               \268            \48               \24
     .---------------------------.------------------------.--------------------------.
\n79 |  7       24569     1      | 289      3      489    | \2468-5  245     \2468   | *2468
     |  245     8^        249    | 7        1249   6^     |  245     135-24   234    |        \24
\n19 | \246     246       3      | 128      5      148    |  9       1247    \2468-7 | *2468
     :---------------------------+------------------------+--------------------------:
     |  3568    157-6     678    | 4^       168    2^     |  67      9        367    |        \68
\n13 | \2468-3  2469     \2468-9 | 3689     7      389    |  1       234      5      | *2468
     |  2346    179-246   24679  | 139-6    169    5      |  2467    8^       23467  |        \246
     :---------------------------+------------------------+--------------------------:
\n35 |  1       2467     \2468-7 | 2568    \2468   478    |  3       2457     9      | *2468
     |  248     3         2478   | 159-28   12489  179-48 |  24578   6^       2478   |        \248
\n57 |  9       2467      5      | 2368    \2468   3478   | \248-7   247      1      | *2468
     '---------------------------'------------------------'--------------------------'

MF (2468): 20x20 {2468R13579 \ 246c2 268c4 48c6 24c8 35n1 57n3 79n5 19n7 13n9} => 17 elims; stte

MF (2468): 20x20 {2468C13579 \ 24r2 68r4 246r6 248r8 1n79 3n39 5n13 7n35 9n57} => the same

MSLS 4x5: Show

Code: Select all

  \35               \79               \19              \57              \37
.---------------------------.------------------------.--------------------------.
|  7       24569     1      | 289      3      489    |  2468-5  245      2468   |
| *245     8        *249    | 7       *1249   6      | *245     135-24  *234    | \24
|  246     246       3      | 128      5      148    |  9       1247     2468-7 |
:---------------------------+------------------------+--------------------------:
| *3568    157-6    *678    | 4       *168    2      | *67      9       *367    | \68
|  2468-3  2469      2468-9 | 3689     7      389    |  1       234      5      |
| *2346    179-246  *24679  | 139-6   *169    5      | *2467    8       *23467  | \246
:---------------------------+------------------------+--------------------------:
|  1       2467      2468-7 | 2568     2468   478    |  3       2457     9      |
| *248     3        *2478   | 159-28  *12489  179-48 | *24578   6       *2478   | \248
|  9       2467      5      | 2368     2468   3478   |  248-7   247      1      |
'---------------------------'------------------------'--------------------------'

MSLS (4x5): 20x20 {2468N13579 \ 1c5 2r268 3c19 4r268 5c17 6r46 7c379 8r48 9c35} => 17 elims; stte

MSLS 5x4: Show

Code: Select all

         \246[7]            \268            \48[7]            \24[7]
.--------------------------.-------------------------.-------------------------.
| 7       *24569    1      | *289     3      *489    | 2468-5  *245     2468   | \59
| 245      8        249    |  7       1249    6      | 245      135-24  234    |
| 246     *246      3      | *128     5      *148    | 9       *1247    2468-7 | \1[7]
:--------------------------+-------------------------+-------------------------:
| 3568     15-67    678    |  4       168     2      | 67       9       367    |
| 2468-3  *2469     2468-9 | *3689    7      *389    | 1       *234     5      | \39
| 2346     19-2467  24679  |  139-6   169     5      | 2467     8       23467  |
:--------------------------+-------------------------+-------------------------:
| 1       *2467     2468-7 | *2568    2468   *478    | 3       *2457    9      | \5[7]
| 248      3        2478   |  159-28  12489   19-478 | 24578    6       2478   |
| 9       *2467     5      | *2368    2468   *3478   | 248-7   *247     1      | \3[7]
'--------------------------'-------------------------'-------------------------'

MSLS (5x4): 20x20 {24579N2468 \ 1r3 2c248 3r59 4c268 5r17 6c24 7[r379|c268] 8c46 9r15} => 20 elims; stte

What's interesting about the MSLS variants is that the row/column covers alternate with digits: 1c,2r,3c,...9c or 1r,2c,3r,...9r. Is that by design?

By the way, your MSLS also has the eliminations -7r7c8 and -7r9c8 since those candidates are covered by two link sets.

Indeed. They're Rank 1 cannibal eliminations. It works, but the modification you suggested (using 7r3 instead of 7c8) is cleaner because it's pure Rank 0.

[SCLT]

What's interesting about the MSLS variants is that the row/column covers alternate with digits: 1c,2r,3c,...9c or 1r,2c,3r,...9r. Is that by design?

Yes, this is by design. The puzzle was created by considering a partition between odd givens and even givens, so this is entirely unsurprising. To spell it out, you'll notice that the givens naturally fall into two sets, denoted by X and Y here:

Code: Select all

+-------+-------+-------+
| X . X | . X . | . . . |
| . Y . | Y . Y | . . . |
| . . X | . X . | X . . |
+-------+-------+-------+
| . . . | Y . Y | . Y . |
| . . . | . X . | X . X |
| . . . | . . Y | . Y . |
+-------+-------+-------+
| X . . | . . . | X . X |
| . Y . | . . . | . Y . |
| X . X | . . . | . . X |
+-------+-------+-------+


The positions marked X are in odd rows/columns, and the positions marked Y are in even rows/columns. By deciding that all the givens in the X positions would be odd, and that exactly 6 of the givens in the Y positions would be even, this guarantees that there will be an MSLS (you can use either an MSNS or an MSHS/Multifish depending on your point of view) that proves the parity of several of the unclued cells, marked here with O and E for odd and even:

Code: Select all

+-------+-------+-------+
| X . X | . X . | E . E |
| . Y . | Y . Y | . O . |
| E . X | . X . | X . E |
+-------+-------+-------+
| . O . | Y . Y | . Y . |
| E . E | . X . | X . X |
| . O . | O . Y | . Y . |
+-------+-------+-------+
| X . E | . E . | X . X |
| . Y . | O . O | . Y . |
| X . X | . E . | E . X |
+-------+-------+-------+


So it was just a matter of looking for a puzzle of this form that (a) had a unique solution and (b) was singles-only after the MSLS step and (c) had no basic steps available at the start (this puzzle has nothing less than SE 7.1 available at the beginning).