The New Sudoku Players' Forum

[yzfwsf]

Code: Select all

,---------------------,---------------------,--------------------,
| 12569   129   3     | 4       567    679  | 1679   8     679   |
| 569     7     5689  | 35689   1      689  | 4      2359  2369  |
| 1469    1469  15689 | 356789  5678   2    | 13679  1359  3679  |
:---------------------+---------------------+--------------------:
| 135679  1369  5679  | 6789    678    4    | 2      139   3789  |
| 2679    2369  4     | 1       2678   6789 | 3789   39    5     |
| 129     8     179   | 279     3      5    | 179    6     4     |
:---------------------+---------------------+--------------------:
| 13469   5     169   | 268     2468   168  | 3689   7     23689 |
| 8       1346  167   | 267     9      167  | 5      234   236   |
| 4679    469   2     | 5678    45678  3    | 689    49    1     |
'---------------------'---------------------'--------------------'

There is a Blossom Loop with 14 eliminations. There are also MSLS and Multi-fish available.But they need more truth than Blossom Loop.
This puzzle is the last question in this series
Program Algorithm:Find a burr loop and then find a branch for each burr. The endpoint of a branch is the preparatory elimination of a loop or other branch (weak chain eliminations). All truths in the structure do not overlap.

[totuan]

Code: Select all

,---------------------,---------------------,--------------------,
| 12569   129   3     | 4       567    679  | 1679   8     679   |
| 569     7     5689  | 35689   1      689  | 4      25-39 2369  |
| 1469    1469  5689-1| 356789  5678   2    | 13679  15-39 3679  |
:---------------------+---------------------+--------------------:
| 135679  1369  5679  | 6789    678    4    | 2      139   3789  |
| 2679    2369  4     | 1       2678   6789 | 3789   39    5     |
| 12-9    8     179   | 279     3      5    | 179    6     4     |
:---------------------+---------------------+--------------------:
| 134-69  5     169   | 268     24-68  168  | 3689   7     23689 |
| 8       134-6 167   | 267     9      167  | 5      24-3  236   |
| 4679    469   2     | 5678    45678  3    | 689    49    1     |
'---------------------'---------------------'--------------------'

All 1's on R6 lead to 24r8c8

Code: Select all

                        -------------------(1)r7c1,r8c2=r78c3-(1)r6c2
                       |                                       ||
(4)r8c8=(34)r7c1,r8c2 -|                                      (1)r6c7-r4c8=(1-5)r3c8=(5-2)r2c8=(2)r8c8 => loop
                       |                                       ||
                        -(4)r7c1=(4-2)r7c5=r78c4-r6c4=(2)r6c1-(1)r6c1

Code: Select all

10 Sets = {1R6 2R6 4R78 12C8 5B3 13B7 2B8}
10 Links = {1c3 2c4 67n1 8n2 7n5 238n8 1b6}
12 Eliminations -->
(2n8) => r2c8<>3, (2n8) => r2c8<>9, (1c3) => r3c3<>1, (3n8) => r3c8<>3, (3n8) => r3c8<>9, (6n1) => r6c1<>9, (7n1) => r7c1<>6, (7n1) => r7c1<>9, (7n5) => r7c5<>6, (7n5) => r7c5<>8, (8n2) => r8c2<>6, (8n8) => r8c8<>3

Then locked set 3’s B6 => 2 eliminations: r4c9,r5c7<>3

Thanks for the puzzle!
totuan

[yzfwsf]

Then locked set 3’s B6 => 2 eliminations: r4c9,r5c7<>3

Hi totuan:
If you use ALS instead of AHS in the eighth column, you will get those two additional eliminations in one step.Thank you for your excellent solution.

[yzfwsf]

Region Type Blossom Loop: 1r6c137 => r3c3 <> 1, r238c8,r4c9,r5c7 <> 3, r7c15,r8c2 <> 6, r7c5 <> 8, r23c8,r67c1 <> 9
Burring Loop: (1-2)r6c1 = r6c4 - r5c5 = (2-4)r7c5 = r7c1 - (4=6791)b7p3678 - 1r6c3
Burr Branch 1: 1r6c7 - (1=394)r459c8 - r8c8 = 4r8c2

Thank you for your participation. This series has come to a complete end.

[Cenoman]

Sorry for being late. I stick to my presentation using Kraken Loops (with conflicting endpoints) I have found one for each of your ten puzzles, and it is the way I could implement it in my solver.

Kraken row(1)r6c137
(1-2)r6c1 = r6c4 - r5c5 = (2)r7c5@
(1)r6c3 - r78c3 = (13-4)b7p15 = r9c12 - r9c5 = (4)r7c5@
(1)r6c7 - r4c8 = (125-4)r238c8 = r9c8 - r9c5 = (4)r7c5@

ALS version

Hidden Text: Show

Kraken row(1)r6c137
(1-2)r6c1 = r6c4 - r5c5 = (2)r7c5@
(1)r6c3 - (1=6794)b7p3678 - r9c5 = (4)r7c5@
(1)r6c7 - (1=394)r459c8 - r9c5 = (4)r7c5@

11 truths: 12R6 24C5 1245C8 134B7
11 links: 4r9 1c3 2b5 1b6 6n1 7n5 7n1 8n2 238n8

Code: Select all

,---------------------,---------------------,--------------------,
| 12569   129   3     | 4       567    679  | 1679   8     679   |
| 569     7     5689  | 35689   1      689  | 4      25-39 2369  |
| 1469    1469  5689-1| 356789  5678   2    | 13679  15-39 3679  |
:---------------------+---------------------+--------------------:
| 135679  1369  5679  | 6789    678    4    | 2      139   3789  |
| 2679    2369  4     | 1       2678   6789 | 3789   39    5     |
| 12-9    8     179   | 279     3      5    | 179    6     4     |
:---------------------+---------------------+--------------------:
| 134-69  5     169   | 268     24-68  168  | 3689   7     23689 |
| 8       134-6 167   | 267     9      167  | 5      24-3  236   |
| 4679    469   2     | 5678    45678  3    | 689    49    1     |
'---------------------'---------------------'--------------------'

12 eliminations (+ pointing 3r45c8 =>-3b6p34)

Thanks for the puzzles.

Edit: corrected a typo in the PM (Thanks Leren !)

[yzfwsf]

Sorry for being late. I stick to my presentation using Kraken Loops (with conflicting endpoints) I have found one for each of your ten puzzles, and it is the way I could implement it in my solver.

Hi Cenoman:
Kraken is the method used by manual players to discover this technique. Kraken a strong region, with all branches ending in the same weak region.I think this is not easy to implement with code, so I used the method of finding burr loop and adding branches. Of course, the strong and weak regions mentioned above may not necessarily be physically meaningful, but can also be logically meaningful.