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[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| 9 . . | . . 8 | 7 . . |
| . 6 . | . 5 . | . 4 . |
+-------+-------+-------+
| . 3 . | . 2 . | . 5 . |
| 8 . . | . . 9 | 1 . . |
| . . . | 8 . . | . . . |
+-------+-------+-------+
| . . 2 | . . 1 | 9 . . |
| . 5 . | . 3 . | . 6 . |
| . . 3 | . . . | . 2 . |
+-------+-------+-------+
.........9....87...6..5..4..3..2..5.8....91.....8.......2..19...5..3..6...3....2.

[SpAce]

Code: Select all

        *1789    *1789               *1789                     *1789
.------------------------.---------------------------.-------------------------.
| 235   \178-24  \178-45 | 2346-179  \179-46  2346-7 | 2356-8  \189-3  2356-89 | \1789,n2358
| 9^     124      145    | 2346-1     146     8^     | 7^       13     2356    | \1
| 23     6       \178    | 12379      5       237    | 238      4      2389    | \n3
:------------------------+---------------------------+-------------------------:
| 147    3       \179-46 | 1467       2       467    | 468      5      46789   | \n3
| 8^     247      4567   | 35         467     9^     | 1^       37     2346-7  | \7
| 25     12479    145679 | 8^         1467    35     | 2346     379    2346-79 | \179
:------------------------+---------------------------+-------------------------:
| 46-7   478      2      | 456-7      4678    1^     | 9^       378    345-78  | \78
| 147    5       \1789-4 | 2479       3       247    | 48       6      1478    | \n3
| 1467  \1789-4   3      | 45679     \789-46  4567   | 458      2      14578   | \n25
'------------------------'---------------------------'-------------------------'

Step 1. Force Lightning:

MF (1789 C): 16x16 {1789C2358 \ [1789r1|1n2358] 1r2 7r5 179r6 78r7 348n3 9n25} => 28 elims

Then I noticed it was not stte: Show

Hmm... I may have a mistake. The row-based variant doesn't yield stte, which is weird. I'll investigate. Added. Yes, I do have a mistake. Those eliminations don't yield stte. I must have misclicked something. Let's see what next then...

Added: Step 2.

grid: Show

Code: Select all

  \4                  \4            \4      \4
.-------------------.---------------------.-------------------.
|  235   178   178  | *2346   179   *2346 |  2356   189  2356 | *4
|  9     24    45   |  236    16     8    |  7      13   2356 |
|  23    6     178  |  12379  5      237  |  238    4    89   |
:-------------------+---------------------+-------------------:
| *147   3     179  | *1467   2     *467  | *468    5    789  | *4
|  8     247   456  |  35     467    9    |  1      37   2346 |
|  25    179   456  |  8      17     35   |  236-4  79   2346 |
:-------------------+---------------------+-------------------:
|  6-4   478   2    |  56-4   4678   1    |  9      378  345  |
| *147   5     1789 | *2479   3     *247  | *48     6    178  | *4
| *1467  1789  3    | *45679  789   *4567 | *458    2    178  | *4
'-------------------'---------------------'-------------------'

Jediscumfish: (4)r1489\c1467 => -4 r6c7,r7c14; stte

Hope it works now...

--
Edit. Added the second step. For some weird reason I thought the first one did the trick alone.

[mith]

The only stte one steppers I found in the solvers are nasty dynamic chains, but that doesn't mean there isn't one. I can do it in two (with basics in between).

[SpAce]

The only stte one steppers I found in the solvers are nasty dynamic chains, but that doesn't mean there isn't one. I can do it in two (with basics in between).

Ok. I think I know what happened. I probably had the right answer already but then somehow thought the simplified version worked also. Too bad I deleted the first version, so I have to redo it to see what extra eliminations it had. I'll be back...

Added. No, it wasn't what I thought. I actually have no idea what happened. All I know is that Hodoku showed a white ball after those eliminations. And then it didn't. Well, glad I noticed it myself when I did the row-based variant for fun. It should have had the same result but didn't, so I suspected something was off.

Added 2. I found it. I had mistakenly eliminated 8r1c8. I remembered that the ball turned white very early when I started taking the eliminations from the top row. I kind of wondered about it but not enough. Well, even I get boarded sometimes

[denis_berthier]

It requires only the most classical Subsets:

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
***  Using CLIPS 6.32-r770
***********************************************************************************************
252 candidates, 1872 csp-links and 1872 links. Density = 5.92%
whip[1]: c3n6{r6 .} ==> r6c1 ≠ 6, r4c1 ≠ 6
whip[1]: c8n1{r2 .} ==> r3c9 ≠ 1, r1c9 ≠ 1, r2c9 ≠ 1
hidden-pairs-in-a-block: b5{r5c4 r6c6}{n3 n5} ==> r6c6 ≠ 7, r6c6 ≠ 6, r6c6 ≠ 4, r5c4 ≠ 7, r5c4 ≠ 6, r5c4 ≠ 4
hidden-triplets-in-a-column: c1{n2 n3 n5}{r6 r3 r1} ==> r6c1 ≠ 7, r6c1 ≠ 4, r6c1 ≠ 1, r3c1 ≠ 7, r3c1 ≠ 1, r1c1 ≠ 7, r1c1 ≠ 4, r1c1 ≠ 1
swordfish-in-columns: n9{c2 c5 c8}{r6 r9 r1} ==> r9c4 ≠ 9, r6c9 ≠ 9, r6c3 ≠ 9, r1c9 ≠ 9, r1c4 ≠ 9
swordfish-in-rows: n8{r3 r4 r8}{c3 c9 c7} ==> r9c9 ≠ 8, r9c7 ≠ 8, r7c9 ≠ 8, r1c9 ≠ 8, r1c7 ≠ 8, r1c3 ≠ 8
hidden-pairs-in-a-row: r9{n8 n9}{c2 c5} ==> r9c5 ≠ 7, r9c5 ≠ 6, r9c5 ≠ 4, r9c2 ≠ 7, r9c2 ≠ 4, r9c2 ≠ 1
swordfish-in-columns: n1{c2 c5 c8}{r1 r6 r2} ==> r6c3 ≠ 1, r2c4 ≠ 1, r2c3 ≠ 1, r1c4 ≠ 1, r1c3 ≠ 1
hidden-triplets-in-a-column: c3{n1 n8 n9}{r4 r3 r8} ==> r8c3 ≠ 7, r8c3 ≠ 4, r4c3 ≠ 7, r4c3 ≠ 6, r4c3 ≠ 4, r3c3 ≠ 7
whip[1]: r3n7{c6 .} ==> r1c4 ≠ 7, r1c5 ≠ 7, r1c6 ≠ 7
hidden-triplets-in-a-row: r1{n1 n8 n9}{c5 c2 c8} ==> r1c8 ≠ 3, r1c5 ≠ 6, r1c5 ≠ 4, r1c2 ≠ 7, r1c2 ≠ 4, r1c2 ≠ 2
hidden-single-in-a-block ==> r1c3 = 7
whip[1]: r1n4{c6 .} ==> r2c4 ≠ 4, r2c5 ≠ 4
naked-pairs-in-a-block: b1{r1c2 r3c3}{n1 n8} ==> r2c2 ≠ 1
swordfish-in-columns: n7{c2 c5 c8}{r5 r6 r7} ==> r7c9 ≠ 7, r7c4 ≠ 7, r7c1 ≠ 7, r6c9 ≠ 7, r5c9 ≠ 7
hidden-triplets-in-a-row: r6{n1 n7 n9}{c2 c5 c8} ==> r6c8 ≠ 3, r6c5 ≠ 6, r6c5 ≠ 4, r6c2 ≠ 4, r6c2 ≠ 2
swordfish-in-columns: n3{c1 c6 c7}{r3 r1 r6} ==> r6c9 ≠ 3, r3c9 ≠ 3, r3c4 ≠ 3, r1c9 ≠ 3, r1c4 ≠ 3
swordfish-in-rows: n5{r2 r5 r7}{c9 c3 c4} ==> r9c9 ≠ 5, r9c4 ≠ 5, r6c3 ≠ 5, r1c9 ≠ 5
hidden-quads-in-a-column: c9{n1 n7 n9 n8}{r8 r9 r4 r3} ==> r9c9 ≠ 4, r8c9 ≠ 4, r4c9 ≠ 6, r4c9 ≠ 4, r3c9 ≠ 2
jellyfish-in-rows: n4{r1 r9 r4 r8}{c6 c4 c7 c1} ==> r7c4 ≠ 4, r7c1 ≠ 4, r6c7 ≠ 4
stte

[mith]

So, my favorite two stepper:

MSLS:19 Cells r12567c2358 or MSLS:20 Cells r3489c14679
Hidden Quad: 1789r1
Hidden Quad: 1789c9
Jellyfish: 4r1489, stte

Most of the MSLS/MF steps take care of one of the hidden quads in the process, but that particular pair of duals leaves them both intact (and have the most eliminations from the start) - and also makes them rather obvious.

I've found a few that have this progression of MF/MSLS into hidden quad into jellyfish, but this one is the nicest I think.

[Cenoman]

Code: Select all

 +--------------------------+----------------------------+--------------------------+
 | B235    12478   14578    |  1234679   14679   23467   |  23568   1389   235689   |
 |  9     B124    B145      |  12346  wAa146     8       |  7     Cb13     2356     |
 | B23     6       178      |  12379     5       237     |  238     4      2389     |
 +--------------------------+----------------------------+--------------------------+
 |  147    3       14679    | y1467      2      y467     | z468     5      46789    |
 |  8      247     4567     |  35       x467     9       |  1       37     23467    |
 |  25     12479   145679   |  8        x1467    35      |  2346    379    234679   |
 +--------------------------+----------------------------+--------------------------+
 |  467    478     2        |  4567      4678    1       |  9     Dc378  Ed3478-5   |
 |  147    5       14789    |  2479      3       247     | z48      6      1478     |
 |  1467   14789   3        |  45679     46789   4567    | z458     2      14578    |
 +--------------------------+----------------------------+--------------------------+

Kraken cell (146)r2c5
(1)r2c5 - (1=3)r2c8 - r7c8 = (3)r7c9
(4)r2c5 - (4=2351)b1p1567 - (1=3)r2c8 - r7c8 = (3)r7c9
(6)r2c5 - r56c5 = r4c46 - (6=485)r489c7
---------------
=> -5 r7c9; ste

[SpAce]

Does this count as a one-stepper?

Code: Select all

 \147    \9n      \348n    \1479      \9n     \47      \48              \3489n
         *1789    *1789               *1789                     *1789
.-------------------------.---------------------------.--------------------------.
| 235    \1478-2  \1478-5 | 2346-179  \1479-6  2346-7 | 2356-8  \189-3   235689  | *4      \n2358
| 9^      124      145    | 236-14     146     8^     | 7^       13      2356    |         \1
| 23      6      \\178    | 12379      5       237    | 238      4      \89-23   | *1789   \n3
:-------------------------+---------------------------+--------------------------:
| 147     3      \\179-46 | 1467       2       467    | 468      5      \4789-6  | *14789  \n3
| 8^      247      4567   | 35         467     9^     | 1^       37      2346-7  |         \7
| 25      12479    145679 | 8^         1467    35     | 236-4    379     2346-79 |         \179
:-------------------------+---------------------------+--------------------------:
| 6-47    478      2      | 56-47      4678    1^     | 9^       378     345-78  |         \78
| 147     5      \\1789-4 | 2479       3       247    | 48       6      \1478    | *14789  \n3
| 1467  \\1789-4   3      | 45679    \\789-46  4567   | 458      2      \1478-5  | *14789  \n25
'-------------------------'---------------------------'--------------------------'

Dark Side Storm:

36x36 {1789R3489 4R1489 1789C2358 \ 147c1 1479c4 47c6 48c7 3489n9 1n2358 1r2 7r5 179r6 78r7 348n33 99n25} => 31 elims; stte

The critical eliminations are -47 r7c14.

[SpAce]

Most of the MSLS/MF steps take care of one of the hidden quads in the process

My original Multifish leaves both intact if the optional cell-covers [1n2358] aren't used. The same with the row-based variant [3489n9]. Both yield the same exact eliminations (21) if only the corresponding row or column cover is used. The extra (or alternate) cell-covers yield 7 more eliminations each, which are the same eliminations as the hidden quads would get. On the other hand, my other monster fish must use both sets of cell covers because they're needed to cover the extra digit 4.

Btw, I've stopped using MSLS almost completely because I recently figured that MF are much nicer for a manual solver. They're usually smaller and way simpler and faster to work with in almost all cases. You only have to deal with 3-5 digits (instead of all 9) in either rows or columns (instead of both). The mandatory cell covers seemed like an ugly feature at first, but they actually make truth balancing much easier. I think champagne had the right idea all along.

[mith]

When I've been doing them manually recently, I think I am doing more MF style than MSLS style. I just end up referencing MSLS when I'm checking against yzf's solver.

[rjamil]

Here's my two cents' worth solution (from start): (similar to denis_berthier's solution)

Code: Select all

 +-----------------------+-----------------------+----------------------+
 | 123457  12478  14578  | 1234679  14679  23467 | 23568  1389  1235689 |
 | 9       124    145    | 12346    146    8     | 7      13    12356   |
 | 1237    6      178    | 12379    5      237   | 238    4     12389   |
 +-----------------------+-----------------------+----------------------+
 | 1467    3      14679  | 1467     2      467   | 468    5     46789   |
 | 8       247    4567   | 34567    467    9     | 1      37    23467   |
 | 124567  12479  145679 | 8        1467   34567 | 2346   379   234679  |
 +-----------------------+-----------------------+----------------------+
 | 467     478    2      | 4567     4678   1     | 9      378   34578   |
 | 147     5      14789  | 2479     3      247   | 48     6     1478    |
 | 1467    14789  3      | 45679    46789  4567  | 458    2     14578   |
 +-----------------------+-----------------------+----------------------+

1) LC Type 1: 6 @ r789c1;
2) LC Type 2: 1 @ r123c8;
3) HT (Col): 235 @ r136c1;
4) HP (Box): 35 @ r5c4 r6c6;
5) SF (Row): 3 @ r257c489;
6) SF (Row): 5 @ r257c349;
7) SF (Row): 8 @ r348c379;
8) SF (Row): 9 @ r348c349;
9) HP (Row): 89 @ r9c25;
10) JF (Row): 1 @ r3489c1349;
11) HT (Row): 189 @ r1c258;
12) LC Type 1: 7 @ r123c3;
13) NT (Col): 456 @ r256c3;
14) NS: 7 @ r1c3;
15) LC Type 2: 4 @ r1c456;
16) NP (Box): 18 @ r1c2 r3c3;
17) JF (Row):7 @ r3489c1469;
18) HT (Row): 179 @ r6c258;
19) HQ (Col): 1789 @ r3489c9; and
20) JF (Row): 4 @ r1489c1467; stte

R. Jamil