The New Sudoku Players' Forum

[yzfwsf]

Code: Select all

.2......34..2..8....7.8..2.1...3.5.......5..4..64...8..3...1..9..57...6.6...9.4..

It's relatively easier than previous ones
SE Rate:8.4 \ Hodoku Rate: 15996 \ YZF_SUDOKU Rate:10526

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
|T59-8    2       189      |T1569    1567    679      | 1679    4       3        |
| 4       1569    139      | 2       1567    3679     | 8       1579    1567     |
| 359     1569    7        | 13569   8       4        |B169     2      B156      |
|--------------------------+--------------------------+--------------------------|
| 1       4789    2489     | 689     3       26789    | 5       79      267      |
| 23789   789     2389     | 1689    1267    5        | 123679  1379    4        |
| 23579   579     6        | 4       127     279      | 12379   8       127      |
|--------------------------+--------------------------+--------------------------|
| 278     3       248      | 568     2456    1        | 27      57      9        |
| 289     1489    5        | 7       24      238      | 123     6       128      |
| 6       178     128      | 358     9       238      | 4       1357    12578    |
*--------------------------------------------------------------------------------*

Exocet 1: r3c7 r3c9 r1c1 r1c4 1569 => - 8 r1c1

Code: Select all

*--------------------------------------------------------------------------------*
| 59      2       8        | 1569    1567    679      |T167-9   4       3        |
| 4       1569    139      | 2       1567    3679     | 8       1579    1567     |
| 359     1569    7        | 13569   8       4        | 169     2       156      |
|--------------------------+--------------------------+--------------------------|
| 1       4789    249      | 689     3       26789    | 5       79     B267      |
| 23789   789     239      | 1689    1267    5        | 123679  1379    4        |
| 23579   579     6        | 4       127     279      | 12379   8      B127      |
|--------------------------+--------------------------+--------------------------|
| 278     3       24       | 568     2456    1        | 27      57      9        |
| 289     1489    5        | 7       24      238      |T12-3    6       128      |
| 6       178     12       | 358     9       238      | 4       1357    12578    |
*--------------------------------------------------------------------------------*

Exocet 2: r4c9 r6c9 r1c7 r8c7 1267 => - 9, r1c7, - 3 r8c7. Some basics followed by :

Code: Select all

*--------------------------------------------------------------------------------*
| 59      2       8        | 1569    1567    679      | 167     4       3        |
| 4       16      3        | 2       1567   b679      | 8      a1579    1567     |
| 59      16      7        | 3       8       4        | 16-9    2       156      |
|--------------------------+--------------------------+--------------------------|
| 1       4       29       | 689     3       26789    | 5       7-9     267      |
| 378     78      29       | 169     1267    5        | 123679  17-9    4        |
| 37      5       6        | 4       127    c279      |d12379   8       127      |
|--------------------------+--------------------------+--------------------------|
| 278     3       4        | 568     256     1        | 27      57      9        |
| 28      9       5        | 7       4       3        | 12      6       128      |
| 6       78      1        | 58      9       28       | 4       3       2578     |
*--------------------------------------------------------------------------------*

Skyscraper : (9) r2c8 = r2c6 - r6c6 = (9) r6c7 => - 9 r3c7, r45c8; stte

Leren

[denis_berthier]

Yes, easier. In W6. And much can be done with typed-whips.

Hidden Text: Show

(solve ".2......34..2..8....7.8..2.1...3.5.......5..4..64...8..3...1..9..57...6.6...9.4..")
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin+JE
*** using CLIPS 6.31-r761
***********************************************************************************************
singles ==> r3c6 = 4, r1c8 = 4
193 candidates, 1085 csp-links and 1085 links. Density = 5.86%
finned-swordfish-in-rows: n3{r6 r8 r3}{c1 c7 c6} ==> r2c6 ≠ 3
singles ==> r3c4 = 3, r2c3 = 3
finned-swordfish-in-columns: n9{c3 c4 c8}{r4 r5 r1} ==> r1c7 ≠ 9
biv-chain[3]: b7n9{r8c2 r8c1} - r3c1{n9 n5} - b4n5{r6c1 r6c2} ==> r6c2 ≠ 9
whip-rn[3]: r5n8{c3 c4} - r7n8{c4 c1} - r1n8{c1 .} ==> r4c3 ≠ 8
whip-cn[3]: c6n6{r2 r4} - c9n6{r4 r3} - c2n6{r3 .} ==> r2c5 ≠ 6
whip-cn[3]: c3n1{r1 r9} - c8n1{r9 r5} - c4n1{r5 .} ==> r1c7 ≠ 1
whip-rn[3]: r3n9{c2 c7} - r2n9{c8 c6} - r6n9{c6 .} ==> r1c1 ≠ 9
whip-rn[4]: r8n1{c9 c2} - r3n1{c2 c7} - r2n1{c9 c5} - r6n1{c5 .} ==> r9c9 ≠ 1
whip-rc[4]: r7c8{n5 n7} - r7c7{n7 n2} - r9c9{n2 n8} - r9c4{n8 .} ==> r9c8 ≠ 5
whip-rn[4]: r8n9{c2 c1} - r3n9{c1 c7} - r2n9{c8 c6} - r6n9{c6 .} ==> r5c2 ≠ 9
whip-rn[4]: r8n9{c1 c2} - r3n9{c2 c7} - r2n9{c8 c6} - r6n9{c6 .} ==> r5c1 ≠ 9
whip-rn[4]: r8n9{c2 c1} - r3n9{c1 c7} - r2n9{c8 c6} - r6n9{c6 .} ==> r4c2 ≠ 9
whip-cn[4]: c3n1{r9 r1} - c4n1{r1 r5} - c5n1{r6 r2} - c8n1{r2 .} ==> r9c2 ≠ 1
naked-pairs-in-a-column: c2{r5 r9}{n7 n8} ==> r8c2 ≠ 8, r6c2 ≠ 7, r4c2 ≠ 8, r4c2 ≠ 7
singles ==> r4c2 = 4, r6c2 = 5, r7c3 = 4, r8c5 = 4
whip[1]: r4n8{c6 .} ==> r5c4 ≠ 8
biv-chain[3]: r1c1{n5 n8} - r7n8{c1 c4} - r9c4{n8 n5} ==> r1c4 ≠ 5
whip[1]: c4n5{r9 .} ==> r7c5 ≠ 5
biv-chain[3]: r7c5{n6 n2} - r7c7{n2 n7} - r1c7{n7 n6} ==> r1c5 ≠ 6
biv-chain[4]: r3n5{c9 c1} - r1c1{n5 n8} - r7n8{c1 c4} - c4n5{r7 r9} ==> r9c9 ≠ 5
singles ==> r7c8 = 5, r9c4 = 5
biv-chain[2]: r7n7{c7 c1} - c2n7{r9 r5} ==> r5c7 ≠ 7
biv-chain[3]: c5n6{r5 r7} - r7c4{n6 n8} - r4n8{c4 c6} ==> r4c6 ≠ 6
whip[1]: c6n6{r2 .} ==> r1c4 ≠ 6
whip-rc[3]: r9c2{n7 n8} - r9c9{n8 n2} - r7c7{n2 .} ==> r9c8 ≠ 7
biv-chain[3]: b9n7{r9c9 r7c7} - r1c7{n7 n6} - b6n6{r5c7 r4c9} ==> r4c9 ≠ 7
biv-chain[4]: r4n7{c8 c6} - r4n8{c6 c4} - r7n8{c4 c1} - r7n7{c1 c7} ==> r6c7 ≠ 7
t-whip[4]: b7n2{r8c1 r9c3} - r9n1{c3 c8} - b9n3{r9c8 r8c7} - r6n3{c7 .} ==> r6c1 ≠ 2
biv-chain[5]: r8n3{c6 c7} - r9c8{n3 n1} - c3n1{r9 r1} - b1n8{r1c3 r1c1} - r7n8{c1 c4} ==> r8c6 ≠ 8
whip[5]: b3n9{r2c8 r3c7} - r3c1{n9 n5} - r1n5{c1 c5} - r1n7{c5 c6} - r4n7{c6 .} ==> r2c8 ≠ 7
whip[1]: c8n7{r5 .} ==> r6c9 ≠ 7
biv-chain[3]: r2c8{n9 n1} - r9n1{c8 c3} - r8c2{n1 n9} ==> r2c2 ≠ 9
whip-rn[4]: r4n7{c8 c6} - r6n7{c6 c1} - r6n9{c1 c6} - r2n9{c6 .} ==> r4c8 ≠ 9
naked-single ==> r4c8 = 7
biv-chain[5]: r1n8{c3 c1} - b1n5{r1c1 r3c1} - b3n5{r3c9 r2c9} - c9n7{r2 r9} - r9c2{n7 n8} ==> r9c3 ≠ 8
t-whip[5]: r2c2{n6 n1} - c3n1{r1 r9} - c8n1{r9 r5} - r6c9{n1 n2} - r4c9{n2 .} ==> r2c9 ≠ 6
whip-rn[6]: r2n9{c8 c6} - r1n9{c4 c3} - r4n9{c3 c4} - r4n6{c4 c9} - r3n6{c9 c2} - r2n6{c2 .} ==> r3c7 ≠ 9
hidden-single-in-a-block ==> r2c8 = 9
whip[1]: b2n9{r1c6 .} ==> r1c3 ≠ 9
whip[1]: c3n9{r5 .} ==> r6c1 ≠ 9
swordfish-in-columns: n1{c3 c4 c8}{r9 r1 r5} ==> r5c7 ≠ 1, r5c5 ≠ 1, r1c5 ≠ 1
biv-chain[3]: r2n5{c9 c5} - r1c5{n5 n7} - b3n7{r1c7 r2c9} ==> r2c9 ≠ 1
whip[1]: b3n1{r3c9 .} ==> r3c2 ≠ 1
biv-chain[3]: r3c7{n1 n6} - r3c2{n6 n9} - r8c2{n9 n1} ==> r8c7 ≠ 1
naked-pairs-in-a-row: r8{c6 c7}{n2 n3} ==> r8c9 ≠ 2, r8c1 ≠ 2
naked-triplets-in-a-column: c1{r1 r3 r8}{n8 n5 n9} ==> r7c1 ≠ 8, r5c1 ≠ 8
singles ==> r7c4 = 8, r4c6 = 8, r7c5 = 6
whip[1]: b8n2{r9c6 .} ==> r6c6 ≠ 2
hidden-pairs-in-a-row: r9{n7 n8}{c2 c9} ==> r9c9 ≠ 2
whip[1]: c9n2{r6 .} ==> r5c7 ≠ 2, r6c7 ≠ 2
biv-chain[3]: c1n2{r7 r5} - r5c5{n2 n7} - c2n7{r5 r9} ==> r7c1 ≠ 7
stte

[eleven]

Exocet 1: r3c7 r3c9 r1c1 r1c4 1569 => - 8 r1c1

I can't see that. Please explain.

[Leren]

eleven wrote : I can't see that. Please explain.

Hi eleven. Yes, it's an "ugly" Exocet, in that I appear to have used to used the method of last resort (for all four digits) to prove that if a digit is in the base it must be in a target cell, using a contradiction argument.

I remember that this was considered fair game when I wrote this all up about 7 years ago. Still, if you feel that I've crossed a line of reasonableness in proving the Exocet, I wouldn't argue with you.

Also fixed a minor typo in the diagram. Leren

[RSW]

My solver also had two exocets and a skyscraper, but they are different from Leren's.

Sorry. Solver output is very verbose: Show

Code: Select all

* Cell r3c6 is the only valid location in row 3 for digit 4
 - Removing candidate 4 from r1c6 r8c6 r1c5
* Cell r1c8 is the only valid location in column 8 for digit 4
   1     2    3      4     5    6       7      8    9     
 +-----------------+------------------+-------------------+
1| 589   2    189  | 1569  1567 679   | 1679   4    3     |
2| 4     1569 139  | 2     1567 3679  | 8      1579 1567  |
3| 359   1569 7    | 13569 8    4     | 169    2    156   |
 +-----------------+------------------+-------------------+
4| 1     4789 2489 | 689   3    26789 | 5      79   267   |
5| 23789 789  2389 | 1689  1267 5     | 123679 1379 4     |
6| 23579 579  6    | 4     127  279   | 12379  8    127   |
 +-----------------+------------------+-------------------+
7| 278   3    248  | 568   2456 1     | 27     57   9     |
8| 289   1489 5    | 7     24   238   | 123    6    128   |
9| 6     178  128  | 358   9    238   | 4      1357 12578 |
 +-----------------+------------------+-------------------+

Testing Exocet: (2348)R8C56, r7c3 r9c8
M1: r9c7 r9c9; M2: r7c1 r7c2
S-Cell Cols: 438 Rows: 123456
Digit: 2 failed cover line test.
Exocet failed JE test.

Proof of Almost Junior Exocet:
+2r8c5, -2r7c3, -2r9c8 -> Leads to contradiction using basics.
+4r8c5, -4r7c3, -4r9c8 -> Leads to contradiction using singles.
+2r8c6, -2r7c3, -2r9c8 -> Leads to contradiction using basics.
+3r8c6, -3r7c3, -3r9c8 -> Leads to contradiction using singles.
+8r8c6, -8r7c3, -8r9c8 -> Leads to contradiction using basics.
All Base/Target mutual exclusions lead to contradiction.
Almost Junior Exocet is proven.

Rule 3: Nonbase candidate 157 is invalid in target cells.
Eliminating 1 5 7 from target r9c8.

Summary AJE2: (2348)R8C56, r7c3 r9c8 -> -157r9c8

* Cell r9c8=3 by simple elimination.
* Cell r8c6 is the only valid location in row 8 for digit 3
 - Removing candidate 3 from r2c6
* Cell r3c4 is the only valid location in column 4 for digit 3
 - Removing candidate 3 from r3c1
* Cell r2c3 is the only valid location in block 1 for digit 3
 - Removing candidate 3 from r5c3
   1     2    3      4    5    6       7      8    9     
 +-----------------+-----------------+-------------------+
1| 589   2    189  | 1569 1567 679   | 1679   4    3     |
2| 4     1569 3    | 2    1567 679   | 8      1579 1567  |
3| 59    1569 7    | 3    8    4     | 169    2    156   |
 +-----------------+-----------------+-------------------+
4| 1     4789 2489 | 689  3    26789 | 5      79   267   |
5| 23789 789  289  | 1689 1267 5     | 123679 179  4     |
6| 23579 579  6    | 4    127  279   | 12379  8    127   |
 +-----------------+-----------------+-------------------+
7| 278   3    248  | 568  2456 1     | 27     57   9     |
8| 289   1489 5    | 7    24   3     | 12     6    128   |
9| 6     178  128  | 58   9    28    | 4      3    12578 |
 +-----------------+-----------------+-------------------+
Skyscraper: Candidate 1 in cells r1c4 r2c8, linked by r5c4 r5c8
At least one of r1c4 r2c8 must be 1. Therefore, 1 can be eliminated from all cells in sight of both r1c4 & r2c8.
 - Removing candidate 1 from r1c7 r2c5
Box/Line: In block 2, the only valid positions for digit 1 are r1c4 r1c5
 - Removing candidate 1 from row 1 r1c3
Box/Line: In block 1, the only valid positions for digit 1 are r2c2 r3c2
 - Removing candidate 1 from column 2 r8c2 r9c2
Sparse Subset: In column 2, the digits 4 7 8 9 must go in cells r4c2 r5c2 r8c2 r9c2 (unspecified order)
These digits can then be eliminated from the other cells in column 2
 - Removing candidate(s) 9 from cell r2c2
 - Removing candidate(s) 9 from cell r3c2
 - Removing candidate(s) 7 9 from cell r6c2
Sparse Subset: In column 2, the digits 4 5 7 8 9 must go in cells r4c2 r5c2 r6c2 r8c2 r9c2 (unspecified order)
These digits can then be eliminated from the other cells in column 2
 - Removing candidate(s) 5 from cell r2c2
 - Removing candidate(s) 5 from cell r3c2
Sparse Subset: In column 3, the digits 2 4 8 9 must go in cells r1c3 r4c3 r5c3 r7c3 (unspecified order)
These digits can then be eliminated from the other cells in column 3
 - Removing candidate(s) 2 8 from cell r9c3
* Cell r6c2 now has only one possible value: 5
 - Removing candidate 5 from r6c1
* Cell r9c3 now has only one possible value: 1
 - Removing candidate 1 from r9c9
   1     2    3      4    5    6       7      8    9     
 +-----------------+-----------------+------------------+
1| 589   2    89   | 1569 1567 679   | 679    4    3    |
2| 4     16   3    | 2    567  679   | 8      1579 1567 |
3| 59    16   7    | 3    8    4     | 169    2    156  |
 +-----------------+-----------------+------------------+
4| 1     4789 2489 | 689  3    26789 | 5      79   267  |
5| 23789 789  289  | 1689 1267 5     | 123679 179  4    |
6| 2379  5    6    | 4    127  279   | 12379  8    127  |
 +-----------------+-----------------+------------------+
7| 278   3    248  | 568  2456 1     | 27     57   9    |
8| 289   489  5    | 7    24   3     | 12     6    128  |
9| 6     78   1    | 58   9    28    | 4      3    2578 |
 +-----------------+-----------------+------------------+

Testing Exocet: (579)R3C13, r1c6 r2c9
M1: r2c7 r2c8; M2: r1c4 r1c5
S-Cell Cols: 269 Rows: 456789
Digit: 5 failed cover line test.
Exocet failed JE test.

Proof of Almost Junior Exocet:
+5r3c1, -5r1c6, -5r2c9 -> Leads to contradiction using basics.
+9r3c1, -9r1c6, -9r2c9 -> Leads to contradiction using basics.
+7r3c3, -7r1c6, -7r2c9 -> *1st non contradiction.
All Base/Target mutual exclusions, except one, lead to contradiction.
Almost Junior Exocet is proven.

Rule 3: Nonbase candidate 6 is invalid in target cells.
Eliminating 6 from target r1c6.
Rule 3: Nonbase candidate 16 is invalid in target cells.
Eliminating 1 6 from target r2c9.
Rule 7: If one cell of a mirror node has only nonbase candidates, then all nonbase candidates can be removed from the other cell of the mirror node.
Eliminating 1 from mirror r2c8.
Rule 9: Mirror node 2 has locked nonbase digit 1. All other nonbase digits can be eliminated from the mirror node.
Eliminating 6 from mirror r1c4.
Rule 9: Mirror node 2 has locked nonbase digit 1. All other nonbase digits can be eliminated from the mirror node.
Eliminating 6 from mirror r1c5.
Rule 13: If one cell in a mirror node contains only non base candidates, then any base candidate absent from the corresponding target, may be removed from the other cell in the mirror node.
Eliminating 5 from mirror r2c8.

Summary AJE2: (579)R3C13, r1c6 r2c9 -> -15r2c8 -16r2c9 -6r1c456

<stte>