The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | 2 . . | . . 3 |
| . 4 . | . 5 . | . 6 . |
+-------+-------+-------+
| . 7 . | 8 4 . | . 5 . |
| . . 2 | 3 . . | . . 8 |
| . . . | . . 7 | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 3 | 1 . . | . . 2 |
| . 5 . | . 7 . | . 4 . | <-- Alderaan
+-------+-------+-------+
...........12....3.4..5..6..7.84..5...23....8.....7..............31....2.5..7..4.

[Cenoman]

Anglers, bring your fishing rods !

[pjb]

Using fish alone, and looking each time for simplest fish, I needed 15 :

Swordfish of 2s (r349\c167) => -2 r1c17, r6c7, r7c16
Swordfish of 3s (r349\c167) => -3 r1c16, r6c17, r7c67
basics
Swordfish of 4s (r258\c167) => -4 r1c67, r6c17, r7c16
Swordfish of 5s (r258\c167) => -5 r1c17, r6c1, r7c67
basics
Finned X-wing of 7s (r28\c18), fr8c7 => -7 r7c8
Swordfish of 7s (r258\c178) => -7 r1c78, r3c7, r7c17
basics
Finned X-wing of 6s (r82\c25), fr2c6 => -6 r1c5
Finned X-wing of 6s (r85\c25), fr5c6 => -6 r6c5
Sashimi X-wing of 6s (c34\r49), fr4c3, r6c4 => -6 r4c6, r6c12
Finned X-wing of 6s (c47\r69), fr7c7 => -6r9c9
basics
Swordfish of 6s (r258\c256 => -6 r1c6, r7c26
basics
Swordfish of 9s (r258\c258) => -9 r1c58, r6c25, r7c28
Swordfish of 9s (r167\c167) => -9 r3c67, r4c16, r9c17
Sashimi franken swordfish of 1s (r345\c68b4), fr3c79 => -1 r1c8
Sashimi franken swordfish of 9s (r127\c26b3), fr7c1 => -9 r8c2; stte

Phil

[mith]

Nice. I hadn't noticed all the non-basic X-Wings, since I deal with basic Swordfish first.

What struck me about this one is where the first few digits are placed:

Code: Select all

+-------+-------+-------+
| 6 . . | . . . | . . . |
| . 9 1 | 2 . . | . . 3 |
| . 4 8 | . 5 . | . 6 . |
+-------+-------+-------+
| . 7 . | 8 4 . | . 5 . |
| . . 2 | 3 9 . | . . 8 |
| . . . | . . 7 | . . . |
+-------+-------+-------+
| . . . | . . . | 6 . . |
| . . 3 | 1 . . | . 9 2 |
| . 5 . | . 7 . | . 4 1 | <-- Formerly Alderaan
+-------+-------+-------+

[denis_berthier]

Using only Subsets (no Franken Fish) and a short hidden xy-chain (biv-chain-cn[3]), we get a total of 32 Subsets:

Code: Select all

(solve "...........12....3.4..5..6..7.84..5...23....8.....7..............31....2.5..7..4.")
***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = TyBC+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
270 candidates, 2204 csp-links and 2204 links. Density = 6.07%
swordfish-in-columns: n7{c3 c4 c9}{r7 r3 r1} ==> r7c8 ≠ 7, r7c7 ≠ 7, r7c1 ≠ 7, r3c7 ≠ 7, r3c1 ≠ 7, r1c8 ≠ 7, r1c7 ≠ 7, r1c1 ≠ 7
swordfish-in-columns: n4{c3 c4 c9}{r6 r7 r1} ==> r7c6 ≠ 4, r7c1 ≠ 4, r6c7 ≠ 4, r6c1 ≠ 4, r1c7 ≠ 4, r1c6 ≠ 4
hidden-pairs-in-a-block: b7{r7c3 r8c1}{n4 n7} ==> r8c1 ≠ 9, r8c1 ≠ 8, r8c1 ≠ 6, r7c3 ≠ 9, r7c3 ≠ 8, r7c3 ≠ 6
swordfish-in-columns: n3{c2 c5 c8}{r6 r1 r7} ==> r7c7 ≠ 3, r7c6 ≠ 3, r6c7 ≠ 3, r6c1 ≠ 3, r1c6 ≠ 3, r1c1 ≠ 3
swordfish-in-rows: n2{r3 r4 r9}{c1 c7 c6} ==> r7c6 ≠ 2, r7c1 ≠ 2, r6c7 ≠ 2, r1c7 ≠ 2, r1c1 ≠ 2
hidden-pairs-in-a-block: b1{r1c2 r3c1}{n2 n3} ==> r3c1 ≠ 9, r3c1 ≠ 8, r1c2 ≠ 9, r1c2 ≠ 8, r1c2 ≠ 6
hidden-pairs-in-a-block: b6{r4c7 r6c8}{n2 n3} ==> r6c8 ≠ 9, r6c8 ≠ 1, r4c7 ≠ 9, r4c7 ≠ 6, r4c7 ≠ 1
hidden-pairs-in-a-block: b8{r7c5 r9c6}{n2 n3} ==> r9c6 ≠ 9, r9c6 ≠ 8, r9c6 ≠ 6, r7c5 ≠ 9, r7c5 ≠ 8, r7c5 ≠ 6
swordfish-in-rows: n5{r2 r5 r8}{c7 c1 c6} ==> r7c7 ≠ 5, r7c6 ≠ 5, r6c1 ≠ 5, r1c7 ≠ 5, r1c1 ≠ 5
hidden-pairs-in-a-block: b3{r1c9 r2c7}{n4 n5} ==> r2c7 ≠ 9, r2c7 ≠ 8, r2c7 ≠ 7, r1c9 ≠ 9, r1c9 ≠ 7, r1c9 ≠ 1
hidden-pairs-in-a-block: b4{r5c1 r6c3}{n4 n5} ==> r6c3 ≠ 9, r6c3 ≠ 8, r6c3 ≠ 6, r5c1 ≠ 9, r5c1 ≠ 6, r5c1 ≠ 1
hidden-pairs-in-a-block: b8{r7c4 r8c6}{n4 n5} ==> r8c6 ≠ 9, r8c6 ≠ 8, r8c6 ≠ 6, r7c4 ≠ 9, r7c4 ≠ 6
hidden-triplets-in-a-column: c1{n4 n5 n7}{r8 r5 r2} ==> r2c1 ≠ 9, r2c1 ≠ 8, r2c1 ≠ 6
hidden-triplets-in-a-row: r1{n4 n5 n7}{c4 c9 c3} ==> r1c4 ≠ 9, r1c4 ≠ 6, r1c3 ≠ 9, r1c3 ≠ 8, r1c3 ≠ 6
naked-pairs-in-a-block: b1{r1c3 r2c1}{n5 n7} ==> r3c3 ≠ 7
finned-x-wing-in-columns: n6{c3 c4}{r9 r4} ==> r4c6 ≠ 6
finned-x-wing-in-columns: n6{c4 c3}{r9 r6} ==> r6c2 ≠ 6, r6c1 ≠ 6
hidden-triplets-in-a-column: c7{n4 n5 n7}{r5 r2 r8} ==> r8c7 ≠ 9, r8c7 ≠ 8, r8c7 ≠ 6, r5c7 ≠ 9, r5c7 ≠ 6, r5c7 ≠ 1
finned-x-wing-in-columns: n6{c4 c7}{r6 r9} ==> r9c9 ≠ 6
finned-x-wing-in-rows: n6{r8 r5}{c2 c5} ==> r6c5 ≠ 6
finned-x-wing-in-rows: n6{r8 r2}{c2 c5} ==> r1c5 ≠ 6
naked-triplets-in-a-row: r8{c1 c6 c7}{n7 n4 n5} ==> r8c8 ≠ 7
hidden-pairs-in-a-block: b9{r7c9 r8c7}{n5 n7} ==> r7c9 ≠ 9, r7c9 ≠ 6, r7c9 ≠ 1
whip[1]: b9n6{r9c7 .} ==> r6c7 ≠ 6
hidden-triplets-in-a-row: r6{n4 n5 n6}{c9 c3 c4} ==> r6c9 ≠ 9, r6c9 ≠ 1, r6c4 ≠ 9
swordfish-in-columns: n9{c3 c4 c9}{r4 r9 r3} ==> r9c7 ≠ 9, r9c1 ≠ 9, r4c6 ≠ 9, r4c1 ≠ 9, r3c7 ≠ 9, r3c6 ≠ 9
swordfish-in-columns: n6{c3 c4 c9}{r4 r9 r6} ==> r9c7 ≠ 6, r9c1 ≠ 6, r4c1 ≠ 6
singles ==> r7c7 = 6, r1c1 = 6
hidden-pairs-in-a-row: r4{n6 n9}{c3 c9} ==> r4c9 ≠ 1
hidden-triplets-in-a-column: c6{n4 n5 n6}{r2 r8 r5} ==> r5c6 ≠ 9, r5c6 ≠ 1, r2c6 ≠ 9, r2c6 ≠ 8
whip[1]: b5n9{r6c5 .} ==> r1c5 ≠ 9, r2c5 ≠ 9, r8c5 ≠ 9
naked-pairs-in-a-column: c5{r2 r8}{n6 n8} ==> r5c5 ≠ 6, r1c5 ≠ 8
x-wing-in-rows: n9{r2 r8}{c2 c8} ==> r7c8 ≠ 9, r7c2 ≠ 9, r6c2 ≠ 9, r5c8 ≠ 9, r5c2 ≠ 9, r1c8 ≠ 9
hidden-single-in-a-row ==> r5c5 = 9
biv-chain-cn[3]: c1n9{r7 r6} - c7n9{r6 r1} - c8n9{r2 r8} ==> r8c2 ≠ 9
singles ==> r2c2 = 9, r3c3 = 8, r8c8 = 9, r9c9 = 1
naked-pairs-in-a-block: b2{r1c5 r3c6}{n1 n3} ==> r1c6 ≠ 1
finned-x-wing-in-columns: n1{c5 c8}{r1 r6} ==> r6c7 ≠ 1
stte

[Ajò Dimonios]

Only two step with TDP

Code: Select all

+---------------------+--------------------+---------------------+
| 2356789 23689 56789 | 4679 13689 134689  | 1245789 12789 14579 |
| 56789   689   1     | 2    689   4689    | 45789   789   3     |
| 23789   4     789   | 79   5     1389    | 12789   6     179   |
+---------------------+--------------------+---------------------+
| 1369    7     69    | 8    4     1269    | 12369   5     169   |
| 14569   169   2     | 3    169   1569    | 14679   179   8     |
| 1345689 13689 45689 | 569  1269  7       | 123469  1239  1469  |
+---------------------+--------------------+---------------------+
| 1246789 12689 46789 | 4569 23689 2345689 | 1356789 13789 15679 |
| 46789   689   3     | 1    689   45689   | 56789   789   2     |
| 12689   5     689   | 69   7     23689   | 13689   4     169   |
+---------------------+--------------------+---------------------+


The conjugated tracks T (5r6c4) and T (5r5c6) cross and produce numerous eliminations until the elimination of 5r6c4 because track T (5r6c4) is invalid.

Code: Select all

+-----------------+----------------+----------------+
| 23689 23689 7   | 4  13689 13689 | 1289  1289 5   |
| 5     689   1   | 2  689   689   | 4     7    3   |
| 2389  4     89  | 7  5     1389  | 1289  6    19  |
+-----------------+----------------+----------------+
| 1369  7     69  | 8  4     1269  | 12369 5    169 |
| 4     169   2   | 3  169   5     | 7     19   8   |
| 13689 13689 5   | 69 1269  7     | 12369 1239 4   |
+-----------------+----------------+----------------+
| 12689 12689 4   | 5  23689 23689 | 13689 1389 7   |
| 7     689   3   | 1  689   4     | 5     89   2   |
| 12689 5     689 | 69 7     23689 | 13689 4    169 |
+-----------------+----------------+----------------+


6r6c4=r9c4-r9c3=r4c3-r4c9=r9c9-r9c4=6r6c4=>+6r6c4=>stte

Paolo

[Leren]

Just for fun here is an outline of a crazy solution with no single digit fish at all, but plenty of loops.

Double Kite Loop (57) Box 3, r2c1, r7c9 => 11 eliminations.

Multifish 1: Truths 20 Base 4567 Rows 12578; Links 20 Cols 125678 Cells r1c3 r1c4 r1c9 r7c3 r7c4 r7c9.

Multifish 2: Truths 26 Base 12389 Rows 13479 Cells r6c1 r6c7 ; Links 26 Cols 134679 Cells r1c2 r1c5 r1c8 r7c2 r7c5 r7c8. A total of 53 eliminations for these 2 but no solved cells.

Some basics.

L2 Wing Loop: (4) r2c6 = r2c7 - r5c7 = (4-5) r5c1 = (5-6) r5c6 = (6) r2c6 loop => - 4 r1c7.

More basics.

L3 Wing: (8) r3c3 = (8-6) r9c3 = (6-9) r9c4 = (9) r3c4 => - 9 r3c3.

More basics.

L2 Wing Loop: (2) r3c1 = r3c7 - r4c7 = (2-1) r4c6 = (1-3) r3c6 = (3) r3c1 loop => - 2 r16c7.

L2 Wing Loop: (2) r1c2 = r7c2 - r7c5 = (2-1) r6c5 = (1-3) r1c5 = (3) r1c2 loop=> - 2 r7c16.

L2 Wing Loop: (3) r4c7 = r4c1 - r3c1 = (3-1) r3c6 = (1-2) r3c7 = (2) r4c7 loop => - 1 r4c7, - 3 r6c1.

L2 Wing Loop: (3) r9c6 = r9c7 - r4c7 = (3-1) r4c1 = (1-2) r4c6 = (2) r9c6 loop => - 3 r6c7, - 8 r9c6.

More basics.

L2 Wing: (8) r7c6 = r1c6 - r1c7 = (8-3) r9c7 = (3) r7c8 => - 8 r7c8; stte

The single digit fish were all undersize so I threw them back

Leren

[pjb]

A no-fish approach: 5 MSLSs (57 eliminations) and 2 simple chains

Base: 234; 18 cell Truths: r167 c258 +r2c2 r5c2 r8c2 r2c5 r5c5 r8c5 r2c8 r5c8 r8c8, 18 links: 23r1, 23r6, 23r7, 1689c2, 1689c5, 1789c8, 11 eliminations
basics
Base: 234; 18 cell Truths: r258 c167 +r2c2 r2c5 r2c8 r5c2 r5c5 r5c8 r8c2 r8c5 r8c8, 18 links: 56789r2, 15679r5, 56789r8, 4c1, 4c6, 4c7, 6 eliminations
Base: 1289; 12 cell Truths: r2582 c568; 12 links: 89r2, 19r5, 89r8, 6c2, 6c5, 456c6, 7c8; 22 eliminations
basics
Base: 457; 14 cell Truths: r136 c349 +r4c3 r9c3 r9c4 r4c9 r9c9; 14 links: 457r1, 7r3, 45r6, 689c3, 69c4, 169c9; 12 eliminations
basics
Base: 1238; 12 cell Truths: r2581 c258; 12 links: 8r2, 1r5, 8r8, 457c1, 69c2, 69c5, 79c8; 6 eliminations =>

Code: Select all

 6       23      57     | 47     138    189    | 189    128    45     
 57      89      1      | 2      689    46     | 45     789    3     
 23      4       89     | 79     5      1389   | 1289   6      179   
------------------------+----------------------+---------------------
 139     7       69     | 8      4      129    | 23     5      169   
 45      169     2      | 3      19     56     | 47     179    8     
 189     138     45     | 56     12     7      | 19     23     46     
------------------------+----------------------+---------------------
 189     128     47     | 45     23     89     | 6      138    57     
 47      689     3      | 1      689    45     | 57     89     2     
 1289    5       689    | 69     7      23     | 1389   4      19     


Then:
(1=9)r9c9 - (9)r9c4 = (9-7)r3c4 = (7-1)r3c9 => -1 r3c9
basics
(1=3)r1c5 - (3=2)r7c5 - (2=1)r6c5 - (1)r6c7 = (1)r5c8 => -1 r1c8; stte

Phil