The New Sudoku Players' Forum

[yzfwsf]

Code: Select all

,--------------------,--------------------,---------------------,
| 39    3678   4     | 137   15789  13579 | 13689  2      689   |
| 5     238    123   | 6     189    1239  | 7      13489  489   |
| 2369  23678  12367 | 1379  4      12379 | 13689  1389   5     |
:--------------------+--------------------+---------------------:
| 7     1      256   | 89    3      4     | 5689   589    2689  |
| 8     2346   236   | 5     179    1679  | 3469   3479   24679 |
| 36    3456   9     | 78    2      67    | 34568  34578  1     |
:--------------------+--------------------+---------------------:
| 13    357    8     | 3479  6      13579 | 2      14579  479   |
| 4     2357   2357  | 1239  1579   8     | 159    6      79    |
| 126   9      2567  | 1247  157    157   | 1458   14578  3     |
'--------------------'--------------------'---------------------'

There is a Rank 0 structure with 16 eliminations.

[Cenoman]

The solution I first posted was:

Hidden Text: Show

Kraken AAHS (64)r1356c2
(6)r1c2 - r1c9 = (62-8)r45c9 = (8)r12c9@
(6-8)r3c2 = (8)r3c78@
(64-5)r56c2 = (5-2)r4c3 = (2-8)r4c9 = (8)r12c9@

Nothing wrong in this, but the eliminations I inferred were wrong. I didn' pay attention the role of cell r4c9, preventing the corresponding matrix to be a pigeonhole matrix.

Updated version:
Kraken AAHS (64)r1356c2
(6)r1c2 - r1c9 = r45c9 - r4c7 = (62-8)r4c39 = (8)r12c9@
(6-8)r3c2 = (8)r3c78@
(64-5)r56c2 = (52-8)r4c39 = (8)r12c9@

8 truths: 26R4 46C2 68C9 8B3 5B4
8 links : 6r1 8b3 6b6 356n2 4n3 4n9
=> 12 eliminations

Code: Select all

,--------------------,--------------------,---------------------,
| 39    3678   4     | 137   15789  13579 | 139-68 2      689   |
| 5     238    13-2  | 6     189    1239  | 7      1349-8 489   |
| 2369  68-237 1367-2| 1379  4      12379 | 13689  1389   5     |
:--------------------+--------------------+---------------------:
| 7     1      256   | 89    3      4     | 5689   589    268-9 |
| 8     46-23  236   | 5     179    1679  | 349-6  3479   24679 |
| 36    456-3  9     | 78    2      67    | 3458-6 34578  1     |
:--------------------+--------------------+---------------------:
| 13    357    8     | 3479  6      13579 | 2      14579  479   |
| 4     2357   357-2 | 1239  1579   8     | 159    6      79    |
| 126   9      567-2 | 1247  157    157   | 1458   14578  3     |
'--------------------'--------------------'---------------------'

Main difference with yzfwsf's and totuan's solutions (see below): the basis is kraken column 6C2 instead of kraken row 6R3

[yzfwsf]

Hi Cenoman:
Your solution may be incorrect. EX: 9r5c9 is part of the final solution.


I input your solution to xsudo and the result is as follows:

[totuan]

I input your solution to xsudo and the result is as follows:

Maybe need more links/sets (using Xsudo v0.99):

Code: Select all

,--------------------,--------------------,---------------------,
| 39    3678   4     | 137   15789  13579 | 139-68 2      689   |
| 5     238    13-2  | 6     189    1239  | 7      1349-8 489   |
| 2369  68-237 1367-2| 1379  4      12379 | 13689  1389   5     |
:--------------------+--------------------+---------------------:
| 7     1      256   | 89    3      4     | 5689   589    268-9 |
| 8     46-23  236   | 5     179    1679  | 349-6  3479   24679 |
| 36    456-3  9     | 78    2      67    | 3458-6 34578  1     |
:--------------------+--------------------+---------------------:
| 13    357    8     | 3479  6      13579 | 2      14579  479   |
| 4     2357   357-2 | 1239  1579   8     | 159    6      79    |
| 126   9      567-2 | 1247  157    157   | 1458   14578  3     |
'--------------------'--------------------'---------------------'

Code: Select all

9 Sets = {2R4 6R34 8R3 6C2 8C9 245B4}
9 Links = {2c3 6c7 356n2 4n3 4n9 6b1 8b3}
16 Eliminations -->
(6c7) => r1c7<>6, (8b3) => r1c7<>8, (2c3) => r2c3<>2, (8b3) => r2c8<>8, (3n2) => r3c2<>2, (3n2) => r3c2<>3, (3n2) => r3c2<>7, (2c3) => r3c3<>2, (4n9) => r4c9<>9, (2B4*5n2) => r5c2<>2, (5n2) => r5c2<>3, (6c7) => r5c7<>6, (6n2) => r6c2<>3, (6c7) => r6c7<>6, (2c3) => r8c3<>2, (2c3) => r9c3<>2

Thanks for the puzzle!
totuan

[yzfwsf]

Region Type Blossom Loop: 6r3c1237 => r2389c3,r35c2 <> 2, r356c2 <> 3, r156c7 <> 6, r3c2 <> 7, b3p15 <> 8, r4c9 <> 9
Burring Loop: 6r3c1 - r13c2 = r56c2 - (6=235)b4p367 - (5=896)r4c478 - 6r3c7
Burr Branch 1: (6-8)r3c2 = r3c78 - r12c9 = 8r4c9

My solver did not implement AHS strong links and instead used ALS strong links. In some cases, it may result in more Truths than using AHS.

[totuan]

Code: Select all

,--------------------,--------------------,---------------------,
| 39    3678   4     | 137   15789  13579 | 139-68 2      689   |
| 5     238    123   | 6     189    1239  | 7      1349-8 489   |
| 2369  68-237 12367 | 1379  4      12379 | 13689  1389   5     |
:--------------------+--------------------+---------------------:
| 7     1      256   | 89    3      4     | 5689   589    268-9 |
| 8     46-23  236   | 5     179    1679  | 349-6  3479   24679 |
| 36    456-3  9     | 78    2      67    | 3458-6 34578  1     |
:--------------------+--------------------+---------------------:
| 13    357    8     | 3479  6      13579 | 2      14579  479   |
| 4     2357   2357  | 1239  1579   8     | 159    6      79    |
| 126   9      2567  | 1247  157    157   | 1458   14578  3     |
'--------------------'--------------------'---------------------'

On trying to present as diagram:

Code: Select all

                                ----------------------(26)r4c39=(6)r4c7-(6)r3c7
                               |                                         ||
(8)r3c2=(8)r3c78-r12c9=(8)r4c9-|                                        (6)r3c2 => loop
                               |                                         ||
                                -(2)r4c9=(2-5)r4c3=(45-6)r56c2=(6)r13c2-(6)r3c13

Code: Select all

8 Sets = {2R4 6R34 8R3 6C2 8C9 45B4}
8 Links = {6c7 356n2 4n3 4n9 6b1 8b3}
12 Eliminations -->
(6c7) => r1c7<>6, (8b3) => r1c7<>8, (8b3) => r2c8<>8, (3n2) => r3c2<>2, (3n2) => r3c2<>3, (3n2) => r3c2<>7, (4n9) => r4c9<>9, (5n2) => r5c2<>2, (5n2) => r5c2<>3, (6c7) => r5c7<>6, (6n2) => r6c2<>3, (6c7) => r6c7<>6

Then locked set 2’s B4 => more 4 eliminations: r2389c3<>2

totuan