The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| 1 . . | . . 2 | 3 . . |
| . 4 . | . 5 . | . 6 . |
+-------+-------+-------+
| . 5 . | . 7 . | . 4 . |
| 3 . . | . . 8 | 2 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| 2 . . | . . 3 | 1 . . |
| . 9 . | . 4 . | . 5 . |
| . . 1 | 6 . . | . . . |
+-------+-------+-------+
.........1....23...4..5..6..5..7..4.3....82...........2....31...9..4..5...16.....


[RSW]

Swordfish (5)r257c349 => -5 r1c3 r6c4 r1c9 r6c9
Swordfish (4)r257c349 => -4 r6c3 r1c4 r6c4 r1c9 r9c9.
Swordfish (3)r348c349 => -3 r1c3 r1c4 r6c4 r6c9 r9c9.
Swordfish (2)r348c349 => -2 r1c3 r6c3 r6c4 r1c9 r9c9.
Finned-X-Wing (1)r34c(4)69 Fin: r3c4 => -1r1c6
Finned-X-Wing (1)c58r15(6) Fin: r6c8 => -1r5c9
Swordfish (1)r348c469 => -1 r1c4 r6c4 r1c9 r6c9.
First solved cell: 9r6c4
Finned-X-Wing (8)r34c1(3)7, Fin: r4c3 => -8r6c1
Finned-X-Wing (8)c48r(1)27, Fin: r1c4 => -8r2c5
Swordfish (8)r348c137 => -8 r1c1 r1c3 r2c3 r6c3 r6c7 r9c7.
Finned-X-Wing (6)r68c1(3)7, Fin: r6c3 => -6r4c1
Swordfish (9)r257c358 => -9 r1c3.
XYZ-wing: (579)r3c6 r7c4 r9c6 => -7 r8c6
ste


Edit: On further examination, if I'd disabled finned fish in my solver, it would have still solved with the 7 swordfish and the xyz-wing.

[rjamil]

Let me try from start:

1) HP: 45 @ r7c3 r9c1 in Box 7;
2) SF: 1 @ r348c469 Row wise;
3) SF: 2 @ r348c349 Row wise;
4) HP: 12 @ r1c8 r3c9 in Box 3;
5) SF: 3 @ r348c349 Row wise;
6) HT: 123 @ r1c258 in Row 1;
7) HT: 123 @ r6c258 in Row 6;
8) HT: 123 @ r348c4 in Column 4;
9) HT: 123 @ r348c9 in Column 9;
10) HP: 23 @ r1c2 r3c3 in Box 1;
11) HT: 789 @ r3c167 in Row 3;
12) HP: 23 @ r4c4 r6c5 in Box 5;
13) NP: 13 @ r4c9 r6c8 in Box 6;
14) HT: 123 @ r169c8 in Column 8;
15) SF: 4 @ r257c349 Row wise;
16) SF: 5 @ r257c349 Row wise;
17) NS: 9 @ r6c4;
18) HP: 45 @ r1c7 r2c9 in Box 3;
19) NP: 16 @ r4c6 r5c5 in Box 5;
20) SF: 8 @ r348c137 Row wise;
21) HS: 8 @ r6c9 in Row 6;
22) HS: 8 @ r1c4 in Row 1;
23) HT: 238 @ r9c258 in Row 9;
24) HT: 238 @ r348c3 in Column 3;
25) NP: 79 @ r19c9 in Column 9;
26) HP: 67 @ r7c2 r8c1 in Box 7;
27) HP: 89 @ r7c58 in Row 7;
28) JF: 6 @ r1468c1367 Row wise;
29) SF: 9 @ r257c358 Row wise;
30) NP: 67 @ r16c3 in Column 3;

Code: Select all

 +------------------+--------------+----------------+
 | 5679   23   67   | 8   13  4679 | 45     12   79 |
 | 1      678  59   | 47  69  2    | 3      789  45 |
 | 789    4    23   | 13  5   79   | 789    6    12 |
 +------------------+--------------+----------------+
 | 89-6   5    28   | 23  7   16   | 69     4    13 |
 | 3      167  49   | 45  16  8    | 2      79   56 |
 | 4(6)7  12   (6)7 | 9   23  45   | 5(6)7  13   8  |
 +------------------+--------------+----------------+
 | 2      67   45   | 57  89  3    | 1      89   46 |
 | (6)7   9    38   | 12  4   17   | (6)78  5    23 |
 | 45     38   1    | 6   28  579  | 479    23   79 |
 +------------------+--------------+----------------+

31) GSS: Base 6 @ r68c7 Cover 6 @ r6c13 r8c1 => -6 @ r4c1;

Code: Select all

 +------------------+----------------+--------------+
 | 5679  23      67 | 8   3-1   4679 | 45   12   79 |
 | 1     (6)8-7  59 | 47  (6)9  2    | 3    789  45 |
 | 789   4       23 | 13  5     79   | 789  6    12 |
 +------------------+----------------+--------------+
 | 89    5       28 | 23  7     16   | 69   4    13 |
 | 3     (167)   49 | 45  (16)  8    | 2    79   56 |
 | 467   12      67 | 9   23    45   | 567  13   8  |
 +------------------+----------------+--------------+
 | 2     (67)    45 | 57  89    3    | 1    89   46 |
 | 67    9       38 | 12  4     17   | 678  5    23 |
 | 45    38      1  | 6   28    579  | 479  23   79 |
 +------------------+----------------+--------------+

32) XYZ-Transport (Ring): 167 @ r5c25 r7c2 ERI 6 @ b1r1c2 ERI 6 @ b2r1c5 (or SL 6 @ r2c25) => -1 @ r5c1 => -7 @ r2c2;

Code: Select all

 +--------------------+-----------------+--------------+
 | (5679)  23    6[7] | 8     13  469-7 | 45   12   79 |
 | 1       68    59   | 47    69  2     | 3    789  45 |
 | [7]89   4     23   | 13    5   79    | 789  6    12 |
 +--------------------+-----------------+--------------+
 | 89      5     28   | 23    7   16    | 69   4    13 |
 | 3       167   49   | 45    16  8     | 2    79   56 |
 | 467     12    67   | 9     23  45    | 567  13   8  |
 +--------------------+-----------------+--------------+
 | (2)     6[7]  45   | 5[7]  89  (3)   | 1    89   46 |
 | 6[7]    9     38   | 12    4   1[7]  | 678  5    23 |
 | 45      38    1    | 6     28  5[7]9 | 479  23   79 |
 +--------------------+-----------------+--------------+

33) G(T)ER: ERI 7 @ b1r1c1 ERI 7 @ b7r7c1 ERI 7 @ b8r7c6 => -7 @ r1c6;

Code: Select all

 +---------------+----------------+-------------------+
 | 5679  23   67 | 8     13  46-9 | 45    12     (79) |
 | 1     68   59 | 4(7)  69  2    | 3     (7)89  45   |
 | 789   4    23 | 13    5   (79) | 78-9  6      12   |
 +---------------+----------------+-------------------+
 | 89    5    28 | 23    7   16   | 69    4      13   |
 | 3     167  49 | 45    16  8    | 2     79     56   |
 | 467   12   67 | 9     23  45   | 567   13     8    |
 +---------------+----------------+-------------------+
 | 2     67   45 | 57    89  3    | 1     89     46   |
 | 67    9    38 | 12    4   17   | 678   5      23   |
 | 45    38   1  | 6     28  579  | 479   23     79   |
 +---------------+----------------+-------------------+

34) WW: 79 @ r1c9 r3c6 SL 7 @ r2c48 => -9 @ r1c6 r3c7;

Code: Select all

 +-------------------+-------------+--------------+
 | 5679  23     67   | 8   13  46  | 45   12   79 |
 | 1     68     59   | 47  69  2   | 3    789  45 |
 | 789   4      23   | 13  5   79  | 78   6    12 |
 +-------------------+-------------+--------------+
 | 89    5      28   | 23  7   16  | 69   4    13 |
 | 3     16(7)  49   | 45  16  8   | 2    79   56 |
 | 47-6  12     (67) | 9   23  45  | 567  13   8  |
 +-------------------+-------------+--------------+
 | 2     6(7)   45   | 57  89  3   | 1    89   46 |
 | (67)  9      38   | 12  4   17  | 678  5    23 |
 | 45    38     1    | 6   28  579 | 479  23   79 |
 +-------------------+-------------+--------------+

35) WW: 67 @ r6c3 r8c1 SL 7 @ r57c2 => -6 @ r6c1;
36) XY-Wing: 479 @ r5c38 r6c1 => -7 @ r5c2 r6c7; stte

R. Jamil

[pjb]

With various locked sets along the way:
Swordfish of 1s (r348\c469)
Swordfish of 2s (r348\c349)
Swordfish of 3s (r348\c349)
Swordfish of 4s (r257\c349)
Swordfish of 5s (r257\c349)
Swordfish of 8s (r348\c137)
(1=6)r5c5 - (6=9)r2c5 - (9=7)r3c6 - (7=1)r8c6 => -1 r4c6; stte

Phil

[mith]

What's interesting about this one is that SE (without the new ordering) will solve it with swordfish on all nine digits. (With hidden triplets processed first, SE and Hodoku both lose the swordfish on 9s.)

(My solution was RSW's; there is more than one way to do it with 7 swordfish, not sure if it can be reduced to 6? Without something stronger than the XYZ-Wing anyway.)

[denis_berthier]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| 1 . . | . . 2 | 3 . . |
| . 4 . | . 5 . | . 6 . |
+-------+-------+-------+
| . 5 . | . 7 . | . 4 . |
| 3 . . | . . 8 | 2 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| 2 . . | . . 3 | 1 . . |
| . 9 . | . 4 . | . 5 . |
| . . 1 | 6 . . | . . . |
+-------+-------+-------+
.........1....23...4..5..6..5..7..4.3....82...........2....31...9..4..5...16.....


As fish and finned-fish are not enough, I added bivalue-chains:
(solve ".........1....23...4..5..6..5..7..4.3....82...........2....31...9..4..5...16.....")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = Z+SFin
*** Using CLIPS 6.32-r770
***********************************************************************************************
261 candidates, 2028 csp-links and 2028 links. Density = 5.98%
hidden-pairs-in-a-block: b7{r7c3 r9c1}{n4 n5} ==> r9c1 ≠ 8, r9c1 ≠ 7, r7c3 ≠ 8, r7c3 ≠ 7, r7c3 ≠ 6
swordfish-in-columns: n3{c2 c5 c8}{r9 r1 r6} ==> r9c9 ≠ 3, r6c9 ≠ 3, r6c4 ≠ 3, r1c4 ≠ 3, r1c3 ≠ 3
swordfish-in-columns: n4{c1 c6 c7}{r9 r6 r1} ==> r9c9 ≠ 4, r6c4 ≠ 4, r6c3 ≠ 4, r1c9 ≠ 4, r1c4 ≠ 4
swordfish-in-columns: n1{c2 c5 c8}{r6 r5 r1} ==> r6c9 ≠ 1, r6c6 ≠ 1, r6c4 ≠ 1, r5c9 ≠ 1, r5c4 ≠ 1, r1c9 ≠ 1, r1c6 ≠ 1, r1c4 ≠ 1
swordfish-in-rows: n2{r3 r4 r8}{c9 c3 c4} ==> r9c9 ≠ 2, r6c4 ≠ 2, r6c3 ≠ 2, r1c9 ≠ 2, r1c3 ≠ 2
hidden-pairs-in-a-block: b1{r1c2 r3c3}{n2 n3} ==> r3c3 ≠ 9, r3c3 ≠ 8, r3c3 ≠ 7, r1c2 ≠ 8, r1c2 ≠ 7, r1c2 ≠ 6
hidden-pairs-in-a-block: b3{r1c8 r3c9}{n1 n2} ==> r3c9 ≠ 9, r3c9 ≠ 8, r3c9 ≠ 7, r1c8 ≠ 9, r1c8 ≠ 8, r1c8 ≠ 7
hidden-pairs-in-a-block: b5{r4c4 r6c5}{n2 n3} ==> r6c5 ≠ 9, r6c5 ≠ 6, r6c5 ≠ 1, r4c4 ≠ 9, r4c4 ≠ 1
hidden-pairs-in-a-block: b9{r8c9 r9c8}{n2 n3} ==> r9c8 ≠ 9, r9c8 ≠ 8, r9c8 ≠ 7, r8c9 ≠ 8, r8c9 ≠ 7, r8c9 ≠ 6
hidden-triplets-in-a-row: r1{n1 n2 n3}{c5 c8 c2} ==> r1c5 ≠ 9, r1c5 ≠ 8, r1c5 ≠ 6
hidden-triplets-in-a-column: c9{n1 n2 n3}{r4 r3 r8} ==> r4c9 ≠ 9, r4c9 ≠ 8, r4c9 ≠ 6
hidden-triplets-in-a-row: r6{n1 n2 n3}{c8 c2 c5} ==> r6c8 ≠ 9, r6c8 ≠ 8, r6c8 ≠ 7, r6c2 ≠ 8, r6c2 ≠ 7, r6c2 ≠ 6
naked-pairs-in-a-block: b6{r4c9 r6c8}{n1 n3} ==> r5c8 ≠ 1
finned-x-wing-in-columns: n8{c8 c5}{r2 r7} ==> r7c4 ≠ 8
hidden-triplets-in-a-column: c4{n1 n2 n3}{r3 r8 r4} ==> r8c4 ≠ 8, r8c4 ≠ 7, r3c4 ≠ 9, r3c4 ≠ 8, r3c4 ≠ 7
whip[1]: c4n8{r2 .} ==> r2c5 ≠ 8
naked-pairs-in-a-block: b2{r1c5 r3c4}{n1 n3} ==> r3c6 ≠ 1
finned-x-wing-in-rows: n8{r3 r4}{c7 c1} ==> r6c1 ≠ 8
swordfish-in-rows: n8{r3 r4 r8}{c1 c7 c3} ==> r9c7 ≠ 8, r6c7 ≠ 8, r6c3 ≠ 8, r2c3 ≠ 8, r1c7 ≠ 8, r1c3 ≠ 8, r1c1 ≠ 8
hidden-single-in-a-row ==> r6c9 = 8
hidden-single-in-a-row ==> r1c4 = 8
hidden-triplets-in-a-row: r9{n2 n3 n8}{c5 c8 c2} ==> r9c5 ≠ 9, r9c2 ≠ 7
hidden-triplets-in-a-column: c3{n2 n3 n8}{r4 r3 r8} ==> r8c3 ≠ 7, r8c3 ≠ 6, r4c3 ≠ 9, r4c3 ≠ 6
naked-pairs-in-a-block: b7{r8c3 r9c2}{n3 n8} ==> r8c1 ≠ 8, r7c2 ≠ 8
swordfish-in-columns: n7{c2 c4 c8}{r5 r2 r7} ==> r7c9 ≠ 7, r5c9 ≠ 7, r5c3 ≠ 7, r2c9 ≠ 7, r2c3 ≠ 7
swordfish-in-columns: n6{c2 c5 c9}{r7 r2 r5} ==> r5c3 ≠ 6, r2c3 ≠ 6
hidden-pairs-in-a-column: c3{n6 n7}{r1 r6} ==> r6c3 ≠ 9, r1c3 ≠ 9, r1c3 ≠ 5
swordfish-in-columns: n9{c3 c5 c8}{r2 r5 r7} ==> r7c9 ≠ 9, r7c4 ≠ 9, r5c9 ≠ 9, r5c4 ≠ 9, r2c9 ≠ 9, r2c4 ≠ 9
hidden-single-in-a-column ==> r6c4 = 9
naked-pairs-in-a-block: b5{r4c6 r5c5}{n1 n6} ==> r6c6 ≠ 6
hidden-pairs-in-a-column: c9{n7 n9}{r1 r9} ==> r1c9 ≠ 5
hidden-pairs-in-a-block: b3{r1c7 r2c9}{n4 n5} ==> r1c7 ≠ 9, r1c7 ≠ 7
hidden-pairs-in-a-row: r7{n8 n9}{c5 c8} ==> r7c8 ≠ 7
finned-x-wing-in-columns: n6{c6 c3}{r1 r4} ==> r4c1 ≠ 6
biv-chain[3]: b9n4{r9c7 r7c9} - b9n6{r7c9 r8c7} - r4c7{n6 n9} ==> r9c7 ≠ 9
biv-chain[3]: r1n4{c6 c7} - r9c7{n4 n7} - c9n7{r9 r1} ==> r1c6 ≠ 7
biv-chain[3]: r3c6{n7 n9} - r9n9{c6 c9} - c9n7{r9 r1} ==> r3c7 ≠ 7
biv-chain[3]: b9n8{r7c8 r8c7} - r3c7{n8 n9} - b6n9{r4c7 r5c8} ==> r7c8 ≠ 9
stte

[Cenoman]

Three step solution, including a huge MSLS (combining five sworfishes), an X-chain in the 8s (that must have a complex fish name, SpAce would have named it accurately...) and one M2-Wing.

Code: Select all

 +----------------------------+---------------------------+----------------------------+
 |  56789   23678   6789-235  |  789-134  13689   4679-1  |  45789   12789   789-1245  |
 |  1      <678    <56789     | <4789    <689     2       |  3      <789    <45789     | 6789
 | <789     4      <23789     | <13789    5      <179     | <789     6      <12789     | 789
 +----------------------------+---------------------------+----------------------------+
 | <689     5      <2689      | <1239     7      <169     | <689     4      <13689     | 689
 |  3      <167    <4679      | <1459    <169     8       |  2      <179    <15679     | 1679
 |  46789   12678   6789-24   |  9-12345  12369   4569-1  |  56789   13789   6789-135  |
 +----------------------------+---------------------------+----------------------------+
 |  2      <678    <45        | <5789    <89      3       |  1      <789    <46789     | 6789
 | <678     9      <3678      | <1278     4      <17      | <678     5      <23678     | 678
 |  45      378     1         |  6        289     579     |  4789    23789   789-234   |
 +----------------------------+---------------------------+----------------------------+
                    2345         12345            1                          12345

1. MSLS (combining 5 sworfishes in 1, 2, 3, 4, 5)
36 cell truths: r257 c234589, r348 c134679
36 links: 2345c3, 12345c4, 1c6, 12345c9, 6789r2, 789r3, 689r4, 1679r5, 6789r7, 678r8
25 eliminations: -235 r1c3, -24 r6c3, 134 r1c4, -12345 r6c4, -1 r16c6, -1245 r1c9, -135 r6c9, -234 r9c9

Code: Select all

 +------------------------+---------------------+-----------------------+
 |  5679-8  23    679-8   | B78    13    4679   |  45     12    789     |
 |  1      f678   5679-8  | B478   689   2      |  3      789   45      |
 | a789     4     23      |  13    5    A79     | b789    6     12      |
 +------------------------+---------------------+-----------------------+
 |  689     5     2689    |  23    7     16     |  69-8   4     13689   |
 |  3       167   4679    |  45    16    8      |  2      79    15679   |
 |  4678    12    678     |  9     23    45     |  567-8  13    678     |
 +------------------------+---------------------+-----------------------+
 |  2      e678   45      | C578   89    3      |  1      789   46789   |
 | d678     9    d3678    |  12    4     17     | c678    5     23      |
 |  45     e378   1       |  6     289  D57-9   |  479-8  23    789     |
 +------------------------+---------------------+-----------------------+

2. X-loop (8)r3c1 = r3c7 - r8c7 = r8c13 - r79c2 = r8c2@ => -8 r1c13, r2c3, r469c7; basics (locked 8r46c9; +8r1c4)
3. M2-Wing (9=7)r3c6 - r12c4 = (7-5)r7c4 = (5)r9c6 => -9 r9c6; singles to the end

[SpAce]

Hi Cenoman,

an X-chain in the 8s (that must have a complex fish name, SpAce would have named it accurately...)

Thanks for the compliment.

2. X-loop (8)r3c1 = r3c7 - r8c7 = r8c13 - r79c2 = r2c2@ => -8 r1c13, r2c3, r469c7

<=> Mutant Swordfish: (8)r38c2\c7b17 => the same

A basic transformation would yield:

Code: Select all

r38c2   \ c7b17   | +b4
r38c2b4 \ c7b147  |  b147 -> c123
r38c2b4 \ c1237   | -c2
r38b4   \ c137

<=>

Code: Select all

.-----------------------.----------------.--------------------.
|  5679-8  23    679-8  | 78   13   4679 |  45     12   789   |
|  1       678   5679-8 | 478  689  2    |  3      789  45    |
| *789     4     23     | 13   5    79   | *789    6    12    |
:-----------------------+----------------+--------------------:
| *689     5    *2689   | 23   7    16   |  69-8   4    13689 |
|  3       167   4679   | 45   16   8    |  2      79   15679 |
| *4678    12   *678    | 9    23   45   |  567-8  13   678   |
:-----------------------+----------------+--------------------:
|  2       678   45     | 578  89   3    |  1      789  46789 |
| *678     9    *3678   | 12   4    17   | *678    5    23    |
|  45      378   1      | 6    289  579  |  479-8  23   789   |
'-----------------------'----------------'--------------------'

Franken Swordfish: (8)r38b4\c137 => -8 r1c1,r12c3,r469c7

The UFG considers a Franken simpler than a Mutant, but personally I think anything expressible as a basic chain/loop is always simpler. Thus I prefer your original. The simplest chain form for the latter fish needs a Franken X-Wing (or something much uglier) as a node:

(8)r3c1 = r3c7 - r8c7 = (8)b47\c13 - loop => the same