The New Sudoku Players' Forum

[denis_berthier]

The B rating of a puzzle not solvable by braids is infinite. The question makes no sense.

Mauricio's puzzle is also in T&E(Single,2), but gB-Rating=2

If you speak of the gB rating, it makes sense.
But this example (B infinite, gB = 2) is not new. It was already in [CRT] in 2011.

Again: who's the author of the gB29 puzzle: 000009007004030010080100000001000002030080040700000500000005600090040030200900000 ER9.9/9.9/9.3

Don't you look at the original post? I have added notes on the author and source.

[/quote]
Ah, no, I hadn't seen the addition. Thanks.

[yzfwsf]

Code: Select all

005000000070006080200040009009100002020080040300002600100020004030800070000000500 9.7/9.7/9.7 t&e1 - JPF game 0441

After some steps, we get this RS.

Code: Select all

,---------------------,-------------------,--------------------,
| 4689   14689  5     | 2379  1379  13789 | 12347  1236   1367 |
| 49     7      134   | 239   139   6     | 1234   8      5    |
| 2      168    1368  | 357   4     13578 | 137    136    9    |
:---------------------+-------------------+--------------------:
| 45678  468    9     | 1     3567  3457  | 378    35     2    |
| 567    2      167   | 3679  8     3579  | 139    4      137  |
| 3      148    147   | 4579  579   2     | 6      159    78   |
:---------------------+-------------------+--------------------:
| 1      5      678   | 3679  2     379   | 389    369    4    |
| 469    3      246   | 8     1569  1459  | 129    7      16   |
| 678    689    24678 | 346   1367  13479 | 5      12369  1368 |
'---------------------'-------------------'--------------------'

Finding a valid g-Braid for r9c2<>8 has become an impossible task. Firstly, BFS may encounter the dilemma of insufficient memory, so I changed the algorithm to controlled DFS, which now leads to a situation of excessively long running time.

[denis_berthier]

Code: Select all

005000000070006080200040009009100002020080040300002600100020004030800070000000500 9.7/9.7/9.7 t&e1 - JPF game 0441

Firstly, BFS may encounter the dilemma of insufficient memory, so I changed the algorithm to controlled DFS, which now leads to a situation of excessively long running time.

SudoRules finds a solution with DFS or T&E(W1, 1), with no problem of memory or time.

[yzfwsf]

SudoRules finds a solution with DFS or T&E(W1, 1), with no problem of memory or time.

I'm not saying find a solution path, but rather find all the effective steps in the current state.In particular, as mentioned in the preamble post, find a valid path for r9c2<>8.Over 4 hours(Found 16 Steps. Time elapsed: 14480656.8 ms) of searching, my DFS algorithm found a path.

Code: Select all

g-Braid[23]: => r9c2<>8
8r9c2 - 8b9{r9c9=r7c7} - 8b4{r4c2=r4c1} - 9b7{r9c2=r8c1} - 5b4{r4c1=r5c1} - 8r1{r1c1=r1c6} - 9c7{r8c7=r5c7} - 7c1{r5c1=r9c1} - r7c3{n7=n6} - 6b4{r5c3=r4c2} - r3c2{n6=n1} - 4r4{r4c2=r4c6} - 4r8{r8c6=r8c3} - 2r8{r8c3=r8c7} - 2r2{r2c7=r2c4} - 9r2{r2c4=r2c5} - 1b2{r2c5=r1c5} - 9b5{r6c5=r6c4} - 5c4{r6c4=r3c4} - 7c5{r1c5=r46c5} - r5c6{n7=n3} - 3b2{r3c6=r1c4} - 3b8{r7c4=r9c5} - 3c9{r9c9=.}


[denis_berthier]

SudoRules finds a solution with DFS or T&E(W1, 1), with no problem of memory or time.

I'm not saying find a solution path, but rather find all the effective steps in the current state.In particular, as mentioned in the preamble post, find a valid path for r9c2<>8.
Over 10 hours of searching, my DFS algorithm found a path.

Code: Select all

g-Braid[23]: => r9c2<>8 ...

You were asking about DFS and BFS (i.e. more or less T&E) - which are purely procedural solutions.
You're now asking about a pattern-based g-braid solution, which is totally different. What I can tell is, SHC finds a full gB16 solution in 11,755 s (about 3.2 hrs), with never more than 2GB.
As SHC doesn't accept Kakuros as entries, I can't answer precisely your question about the elimination of n8r9c2; I can see no reason why one would try to eliminate this candidate in particular - especially if your program really shows it requires a g-Braid[23].
.

[yzfwsf]

My program found a full g-Braid solution in 89779.3 ms.

Hidden Text: Show

Code: Select all

g-Braid[11]: => r5c7<>7
7r5c7 - 9b6{r5c7=r6c8} - 1b6{r6c8=r56c9} - r8c9{n1=n6} - r7c8{n6=n3} - r4c8{n3=n5} - r9c9{n3=n8} - 8b6{r6c9=r4c7} - 8c1{r4c1=r1c1} - 8b2{r1c6=r3c6} - 5r3{r3c6=r3c4} - 7r3{r3c4=.}
Braid[11]: => r2c9<>3
3r2c9 - 3b1{r2c3=r3c3} - 5b3{r2c9=r3c8} - r4c8{n5=n3} - r3c4{n5=n7} - r3c7{n7=n1} - r5c7{n1=n9} - r6c8{n9=n1} - r8c7{n9=n2} - r2c7{n2=n4} - r2c3{n4=n1} - 1r5{r5c3=.}
Braid[16]: => r2c5<>5
5r2c5 - r2c9{n5=n1} - 5b3{r2c9=r3c8} - r8c9{n1=n6} - r4c8{n5=n3} - r7c8{n3=n9} - r6c8{n9=n1} - 1b9{r9c8=r8c7} - r8c5{n1=n9} - r6c5{n9=n7} - 9r6{r6c5=r6c4} - 4b5{r6c4=r4c6} - r8c6{n4=n5} - 5b5{r5c6=r5c4} - r5c9{n5=n7} - 5c1{r5c1=r4c1} - 7r4{r4c1=.}
Braid[4]: => r7c4<>5
5r7c4 - 5b7{r7c2=r8c1} - 5b2{r2c4=r3c6} - 5b3{r3c8=r2c9} - 5r5{r5c9=.}
g-Braid[7]: => r7c2<>9
9r7c2 - 5b7{r7c2=r8c1} - 5c5{r8c5=r46c5} - 5r5{r5c4=r5c9} - r2c9{n5=n1} - r4c8{n5=n3} - r7c8{n3=n6} - r8c9{n6=.}
Whip[4]: => r9c2<>4
4r9c2 - 4b8{r9c4=r8c6} - 4r4{r4c6=r4c1} - r2c1{n4=n9} - 9c2{r1c2=.}
Braid[10]: => r4c2<>5
5r4c2 - 5b7{r7c2=r8c1} - 5c5{r8c5=r6c5} - 5b6{r6c8=r5c9} - 5r2{r2c9=r2c4} - 2r2{r2c4=r2c7} - 2r8{r8c7=r8c3} - 4b3{r2c7=r1c7} - 4c2{r1c2=r6c2} - 4b5{r6c4=r4c6} - 4r8{r8c6=.}
Braid[11]: => r7c2<>8
8r7c2 - 5c2{r7c2=r6c2} - 5r7{r7c2=r7c6} - 5c5{r8c5=r4c5} - 5c8{r4c8=r3c8} - r2c9{n5=n1} - r8c9{n1=n6} - 6c5{r8c5=r9c5} - 6b7{r9c1=r7c3} - 7r7{r7c3=r7c4} - r3c4{n7=n3} - 3c5{r1c5=.}
Whip[2]: => r6c3<>8
8r6c3 - 8b6{r6c9=r4c7} - 8r7{r7c7=.}
Braid[8]: => r6c2<>5
5r6c2 - r7c2{n5=n6} - 5b7{r7c2=r8c1} - 5c5{r8c5=r4c5} - 6r4{r4c5=r4c1} - 8b4{r4c1=r4c2} - 4b4{r4c2=r6c3} - 4b7{r8c3=r9c1} - 4c4{r9c4=.}
Hidden Single: 5 in c2 => r7c2=5
Braid[5]: => r9c1<>9
9r9c1 - r2c1{n9=n4} - r8c1{n4=n6} - r1c1{n6=n8} - r9c2{n6=n8} - 8c3{r7c3=.}
Braid[6]: => r9c4<>7
7r9c4 - 4c4{r9c4=r6c4} - 7b7{r9c1=r7c3} - r6c3{n7=n1} - r6c2{n1=n8} - 8b6{r6c9=r4c7} - 8r7{r7c7=.}
Braid[9]: => r9c1<>4
4r9c1 - r2c1{n4=n9} - 4b8{r9c4=r8c6} - 4b5{r4c6=r6c4} - 5b8{r8c6=r8c5} - 9r8{r8c5=r8c7} - 1r8{r8c7=r8c9} - r2c9{n1=n5} - 5r6{r6c9=r6c8} - 9c8{r6c8=.}
Braid[9]: => r6c9<>1
1r6c9 - r8c9{n1=n6} - 8b6{r6c9=r4c7} - 8r7{r7c7=r7c3} - 6r7{r7c3=r7c4} - 6b5{r5c4=r4c5} - r4c2{n6=n4} - r6c3{n4=n7} - 7r4{r4c1=r4c6} - 7r7{r7c6=.}
Braid[10]: => r9c5<>9
9r9c5 - 9b7{r9c2=r8c1} - 9r2{r2c1=r2c4} - 2r2{r2c4=r2c7} - 5r2{r2c4=r2c9} - 2r8{r8c7=r8c3} - 4r8{r8c3=r8c6} - 5b8{r8c6=r8c5} - 4b5{r4c6=r6c4} - 5r6{r6c4=r6c8} - 9r6{r6c8=.}
Braid[11]: => r5c9<>5
5r5c9 - r2c9{n5=n1} - 5b4{r5c1=r4c1} - 5r2{r2c9=r2c4} - 2r2{r2c4=r2c7} - 5c6{r3c6=r8c6} - 2r8{r8c7=r8c3} - 4r8{r8c3=r8c1} - 4r2{r2c1=r2c3} - 3b1{r2c3=r3c3} - r3c4{n3=n7} - r3c7{n7=.}
Braid[12]: => r5c4<>5
5r5c4 - 5b4{r5c1=r4c1} - 5b2{r2c4=r3c6} - r4c8{n5=n3} - 8b2{r3c6=r1c6} - 3b5{r4c5=r5c6} - 8c1{r1c1=r9c1} - 8b9{r9c9=r7c7} - r4c7{n8=n7} - r4c6{n7=n4} - 3r7{r7c7=r7c4} - 4b8{r8c6=r9c4} - 6c4{r9c4=.}
Braid[12]: => r2c9<>1
1r2c9 - r8c9{n1=n6} - 5b3{r2c9=r3c8} - r4c8{n5=n3} - r5c9{n3=n7} - r1c9{n7=n3} - r3c7{n3=n7} - r3c4{n7=n3} - 3c5{r2c5=r9c5} - 6c5{r9c5=r4c5} - r5c4{n6=n9} - 9b6{r5c7=r6c8} - r7c8{n9=.}
Naked Single: r2c9=5
Braid[11]: => r9c4<>9
9r9c4 - 9b7{r9c2=r8c1} - 9b1{r1c1=r1c2} - 9c6{r1c6=r5c6} - 9c7{r5c7=r7c7} - 8b9{r7c7=r9c9} - 8r6{r6c9=r6c2} - 8c1{r4c1=r1c1} - 1c2{r6c2=r3c2} - 6b1{r3c2=r3c3} - r3c8{n6=n3} - 3b9{r7c8=.}
Braid[12]: => r7c7<>9
9r7c7 - 8b9{r7c7=r9c9} - 9b6{r5c7=r6c8} - r6c9{n8=n7} - r6c5{n7=n5} - r6c4{n5=n4} - r6c3{n4=n1} - 5b8{r8c5=r8c6} - 4b8{r8c6=r9c6} - 9b8{r9c6=r8c5} - 1b8{r8c5=r9c5} - 1r2{r2c5=r2c7} - 1c8{r1c8=.}
Braid[5]: => r5c7<>3
3r5c7 - 9b6{r5c7=r6c8} - 9b9{r7c8=r8c7} - 1b6{r6c8=r5c9} - 1b9{r8c9=r9c8} - 2b9{r9c8=.}
Braid[6]: => r2c7<>3
3r2c7 - r7c7{n3=n8} - 3b1{r2c3=r3c3} - 4b3{r2c7=r1c7} - 2b3{r1c7=r1c8} - 2r9{r9c8=r9c3} - 8c3{r9c3=.}
Braid[8]: => r1c7<>3
3r1c7 - r7c7{n3=n8} - r4c7{n8=n7} - r3c7{n7=n1} - r3c8{n1=n6} - r1c8{n6=n2} - r3c2{n6=n8} - 8c3{r3c3=r9c3} - 2r9{r9c3=.}
Braid[12]: => r8c3<>6
6r8c3 - r8c9{n6=n1} - 2b7{r8c3=r9c3} - 2b9{r9c8=r8c7} - 4b7{r9c3=r8c1} - 9b7{r8c1=r9c2} - 9b9{r9c8=r7c8} - 6r7{r7c8=r7c4} - 6r5{r5c4=r5c1} - 5b4{r5c1=r4c1} - 5b6{r4c8=r6c8} - 1b6{r6c8=r5c7} - 9c7{r5c7=.}
Braid[11]: => r1c7<>1
1r1c7 - 4b3{r1c7=r2c7} - 2c7{r2c7=r8c7} - r2c1{n4=n9} - r8c3{n2=n4} - r8c1{n4=n6} - r8c9{n6=n1} - 1b6{r5c9=r6c8} - r6c3{n1=n7} - r6c9{n7=n8} - r7c3{n7=n8} - 8r9{r9c1=.}
Braid[12]: => r1c7<>7
7r1c7 - 4b3{r1c7=r2c7} - r2c1{n4=n9} - 2c7{r2c7=r8c7} - r8c3{n2=n4} - 9c7{r8c7=r5c7} - r8c1{n4=n6} - r8c9{n6=n1} - 1b6{r5c9=r6c8} - r6c3{n1=n7} - r6c9{n7=n8} - r7c3{n7=n8} - 8r9{r9c1=.}
Whip[3]: => r3c7<>1
1r3c7 - 7c7{r3c7=r4c7} - 3c7{r4c7=r7c7} - 8c7{r7c7=.}
Braid[9]: => r1c1<>4
4r1c1 - r1c7{n4=n2} - r2c1{n4=n9} - 2r8{r8c7=r8c3} - 4r8{r8c3=r8c6} - 4b5{r4c6=r6c4} - 5b8{r8c6=r8c5} - 5r6{r6c5=r6c8} - 9b6{r6c8=r5c7} - 9r8{r8c7=.}
Braid[10]: => r4c1<>4
4r4c1 - r2c1{n4=n9} - 4b5{r4c6=r6c4} - 4c2{r4c2=r1c2} - r1c7{n4=n2} - 2r8{r8c7=r8c3} - 4r8{r8c3=r8c6} - 5b8{r8c6=r8c5} - 5r6{r6c5=r6c8} - 9b6{r6c8=r5c7} - 9r8{r8c7=.}
Braid[12]: => r4c6<>3
3r4c6 - r4c8{n3=n5} - 4b5{r4c6=r6c4} - 5r6{r6c4=r6c5} - 5b8{r8c5=r8c6} - 9r6{r6c5=r6c8} - 4b8{r8c6=r9c6} - r5c7{n9=n1} - 9b9{r7c8=r8c7} - 2r8{r8c7=r8c3} - 4c3{r8c3=r2c3} - 1r2{r2c3=r2c5} - 1c6{r1c6=.}
Braid[13]: => r5c1<>6
6r5c1 - 5b4{r5c1=r4c1} - 6b5{r5c4=r4c5} - r4c8{n5=n3} - 7c1{r4c1=r9c1} - 6r8{r8c5=r8c9} - 8c1{r9c1=r1c1} - 8b2{r1c6=r3c6} - 5b2{r3c6=r3c4} - r7c8{n6=n9} - 7r3{r3c4=r3c7} - 3c7{r3c7=r7c7} - r7c6{n3=n7} - 7r4{r4c6=.}
Braid[9]: => r9c4<>6
6r9c4 - 4c4{r9c4=r6c4} - 6r5{r5c4=r5c3} - 6b7{r7c3=r8c1} - r8c9{n6=n1} - 1r5{r5c9=r5c7} - 9b6{r5c7=r6c8} - 5r6{r6c8=r6c5} - r8c5{n5=n9} - 9r7{r7c4=.}
Braid[11]: => r9c8<>6
6r9c8 - r8c9{n6=n1} - 2b9{r9c8=r8c7} - r8c3{n2=n4} - 9c7{r8c7=r5c7} - 1r5{r5c7=r5c3} - 6r5{r5c3=r5c4} - 6r7{r7c4=r7c3} - r8c1{n6=n9} - 9b1{r1c1=r1c2} - 1b1{r1c2=r3c2} - 6r3{r3c2=.}
Braid[12]: => r9c3<>6
6r9c3 - 2r9{r9c3=r9c8} - 6r5{r5c3=r5c4} - 6r7{r7c4=r7c8} - 6b3{r1c8=r1c9} - 9b9{r7c8=r8c7} - 6c1{r1c1=r4c1} - 7b3{r1c9=r3c7} - 9r5{r5c7=r5c6} - 3b5{r5c6=r4c5} - 3c7{r4c7=r7c7} - r7c6{n3=n7} - 7r4{r4c6=.}
Braid[13]: => r8c6<>4
4r8c6 - r9c4{n4=n3} - 4b7{r8c1=r9c3} - 4b5{r4c6=r6c4} - 5b8{r8c6=r8c5} - 5r6{r6c5=r6c8} - r4c8{n5=n3} - 3b9{r7c8=r7c7} - 3b5{r4c5=r5c6} - 3r3{r3c6=r3c3} - r2c3{n3=n1} - r6c3{n1=n7} - r6c9{n7=n8} - 8c7{r4c7=.}
Whip[1]: => r9c3<>4
4r9c3 - 4r8{r8c1=.}
Braid[4]: => r2c4<>9
9r2c4 - r2c1{n9=n4} - 2r2{r2c4=r2c7} - 2r8{r8c7=r8c3} - 4r8{r8c3=.}
Braid[9]: => r8c1<>6
6r8c1 - r8c9{n6=n1} - 4b7{r8c1=r8c3} - 2r8{r8c3=r8c7} - 9c7{r8c7=r5c7} - 1b6{r5c7=r6c8} - r6c3{n1=n7} - r6c9{n7=n8} - r7c3{n7=n8} - 8r9{r9c1=.}
Whip[2]: => r1c1<>9
9r1c1 - r2c1{n9=n4} - r8c1{n4=.}
Braid[10]: => r6c4<>4
4r6c4 - r9c4{n4=n3} - 4b4{r6c2=r4c2} - r2c4{n3=n2} - 4r1{r1c2=r1c7} - 2c7{r1c7=r8c7} - r8c3{n2=n4} - r8c1{n4=n9} - 9r2{r2c1=r2c5} - 9r6{r6c5=r6c8} - 9c7{r5c7=.}
Hidden Single: 4 in c4 => r9c4=4
Hidden Single: 4 in c6 => r4c6=4
Braid[6]: => r5c4<>7
7r5c4 - r5c1{n7=n5} - 6b5{r5c4=r4c5} - r4c2{n6=n8} - r4c1{n8=n7} - 7b6{r4c7=r6c9} - 8r6{r6c9=.}
Braid[9]: => r4c7<>8
8r4c7 - r4c2{n8=n6} - r6c9{n8=n7} - 8r7{r7c7=r7c3} - 6b5{r4c5=r5c4} - r9c2{n8=n9} - 6r7{r7c4=r7c8} - 9c8{r7c8=r6c8} - r6c4{n9=n5} - r6c5{n5=.}
Hidden Single: 8 in c7 => r7c7=8
Hidden Single: 8 in c9 => r6c9=8
Whip[4]: => r3c3<>6
6r3c3 - r7c3{n6=n7} - r5c3{n7=n1} - r6c2{n1=n4} - r6c3{n4=.}
Whip[2]: => r7c8<>6
6r7c8 - 6c4{r7c4=r5c4} - 6c3{r5c3=.}
Whip[1]: => r1c9<>6
6r1c9 - 6c8{r1c8=.}
Whip[4]: => r5c6<>7
7r5c6 - 7b6{r5c9=r4c7} - 7b4{r4c1=r6c3} - 7r7{r7c3=r7c4} - 7r3{r3c4=.}
Whip[4]: => r9c3<>7
7r9c3 - r7c3{n7=n6} - r5c3{n6=n1} - r6c2{n1=n4} - r6c3{n4=.}
Whip[6]: => r3c8<>3
3r3c8 - 6b3{r3c8=r1c8} - r1c1{n6=n8} - r3c3{n8=n1} - 1b4{r5c3=r6c2} - 1c8{r6c8=r9c8} - 2c8{r9c8=.}
Braid[4]: => r1c6<>3
3r1c6 - 3b3{r1c8=r3c7} - 8b2{r1c6=r3c6} - 5b2{r3c6=r3c4} - 7r3{r3c4=.}
Braid[8]: => r4c5<>5
5r4c5 - r4c8{n5=n3} - r4c7{n3=n7} - r7c8{n3=n9} - 9b6{r6c8=r5c7} - r5c6{n9=n3} - r7c6{n3=n7} - 7r3{r3c6=r3c4} - 5c4{r3c4=.}
Braid[8]: => r3c6<>3
3r3c6 - r3c7{n3=n7} - r3c4{n7=n5} - 7b6{r4c7=r5c9} - r5c1{n7=n5} - r5c6{n5=n9} - r6c4{n9=n7} - 7c3{r6c3=r7c3} - r7c6{n7=.}
Braid[8]: => r1c5<>7
7r1c5 - 7b5{r4c5=r6c4} - 7c9{r1c9=r5c9} - r5c1{n7=n5} - 5b5{r5c6=r6c5} - 9r6{r6c5=r6c8} - 9b9{r7c8=r8c7} - 9c5{r8c5=r2c5} - 9c1{r2c1=.}
g-Braid[9]: => r1c8<>3
3r1c8 - r3c7{n3=n7} - r4c7{n7=n3} - 3r7{r7c8=r7c46} - r1c9{n7=n1} - 3c5{r9c5=r2c5} - 1b2{r2c5=r3c6} - 1c2{r3c2=r6c2} - 1c8{r6c8=r9c8} - 2c8{r9c8=.}
Whip[2]: => r1c9<>1
1r1c9 - 3b3{r1c9=r3c7} - 7b3{r3c7=.}
Braid[7]: => r8c5<>9
9r8c5 - r8c1{n9=n4} - r8c3{n4=n2} - r8c7{n2=n1} - r5c7{n1=n9} - 1c9{r8c9=r5c9} - r6c8{n1=n5} - 5c5{r6c5=.}
Whip[4]: => r1c6<>9
9r1c6 - 9b8{r7c6=r7c4} - 9b5{r5c4=r6c5} - 9c8{r6c8=r9c8} - 9c2{r9c2=.}
Braid[8]: => r7c4<>3
3r7c4 - 3c6{r7c6=r5c6} - 5r5{r5c6=r5c1} - 5r4{r4c1=r4c8} - 3b6{r4c8=r4c7} - 3c8{r4c8=r9c8} - 2r9{r9c8=r9c3} - 8c3{r9c3=r3c3} - 3r3{r3c3=.}
Braid[6]: => r9c8<>3
3r9c8 - r4c8{n3=n5} - r7c8{n3=n9} - 3b8{r9c5=r7c6} - 5b4{r4c1=r5c1} - r5c6{n5=n9} - 9r6{r6c4=.}
Braid[7]: => r2c5<>3
3r2c5 - 3c4{r1c4=r5c4} - 3r1{r1c4=r1c9} - 6c4{r5c4=r7c4} - 7c9{r1c9=r5c9} - r5c1{n7=n5} - r5c6{n5=n9} - 9b8{r7c6=.}
Whip[4]: => r2c3<>1
1r2c3 - r2c5{n1=n9} - r2c1{n9=n4} - 4c2{r1c2=r6c2} - 1c2{r6c2=.}
Braid[3]: => r3c6<>1
1r3c6 - r2c5{n1=n9} - 1b1{r3c2=r1c2} - 9r1{r1c2=.}
Whip[5]: => r1c6<>1
1r1c6 - r2c5{n1=n9} - r1c5{n9=n3} - r1c9{n3=n7} - r1c4{n7=n2} - r2c4{n2=.}
Whip[1]: => r8c5<>1
1r8c5 - 1c6{r8c6=.}
Whip[1]: => r9c5<>1
1r9c5 - 1c6{r8c6=.}
Whip[6]: => r9c8<>1
1r9c8 - r8c9{n1=n6} - r9c9{n6=n3} - 3c8{r7c8=r4c8} - 3c5{r4c5=r1c5} - 1b2{r1c5=r2c5} - 1b3{r2c7=.}
Whip[3]: => r9c6<>9
9r9c6 - 1r9{r9c6=r9c9} - 3b9{r9c9=r7c8} - 9r7{r7c8=.}
Braid[6]: => r9c2<>6
6r9c2 - 6c3{r7c3=r5c3} - 6r3{r3c2=r3c8} - 9r9{r9c2=r9c8} - 2c8{r9c8=r1c8} - 1c8{r1c8=r6c8} - 1r5{r5c7=.}
Whip[2]: => r9c1<>8
8r9c1 - 6b7{r9c1=r7c3} - 7b7{r7c3=.}
Whip[3]: => r9c6<>7
7r9c6 - r1c6{n7=n8} - r1c1{n8=n6} - r9c1{n6=.}
Whip[4]: => r4c1<>5
5r4c1 - r5c1{n5=n7} - 7c9{r5c9=r1c9} - r1c6{n7=n8} - 8c1{r1c1=.}
Hidden Single: 5 in r4 => r4c8=5
Hidden Single: 5 in c1 => r5c1=5
Hidden Single: 3 in c8 => r7c8=3
Whip[1]: => r8c6<>9
9r8c6 - 9r7{r7c4=.}
Whip[2]: => r1c5<>3
3r1c5 - 3b3{r1c9=r3c7} - 3r4{r4c7=.}
Whip[1]: => r5c4<>3
3r5c4 - 3b2{r1c4=.}
Whip[2]: => r1c4<>9
9r1c4 - r1c5{n9=n1} - r2c5{n1=.}
Whip[1]: => r6c5<>9
9r6c5 - 9b2{r1c5=.}
Whip[2]: => r5c9<>1
1r5c9 - r5c7{n1=n9} - r6c8{n9=.}
Whip[1]: => r8c7<>1
1r8c7 - 1c9{r8c9=.}
Whip[3]: => r4c1<>7
7r4c1 - r4c7{n7=n3} - 3c5{r4c5=r9c5} - 7r9{r9c5=.}
Hidden Single: 7 in c1 => r9c1=7
Hidden Single: 6 in b7 => r7c3=6
Hidden Single: 6 in r5 => r5c4=6
Whip[1]: => r6c4<>7
7r6c4 - 7c5{r4c5=.}
Braid[4]: => r1c4<>7
7r1c4 - r1c9{n7=n3} - r7c4{n7=n9} - 3r5{r5c9=r5c6} - 9c6{r5c6=.}
Whip[2]: => r3c4<>3
3r3c4 - r1c4{n3=n2} - r2c4{n2=.}
Whip[4]: => r3c6<>7
7r3c6 - r3c4{n7=n5} - 5b5{r6c4=r6c5} - 7b5{r6c5=r4c5} - 7c7{r4c7=.}
Whip[5]: => r1c2<>8
8r1c2 - r1c6{n8=n7} - r3c4{n7=n5} - r6c4{n5=n9} - 9c8{r6c8=r9c8} - r9c2{n9=.}
Whip[5]: => r1c4<>2
2r1c4 - 2b3{r1c7=r2c7} - r8c7{n2=n9} - 9r5{r5c7=r5c6} - 3r5{r5c6=r5c9} - 3r1{r1c9=.}
142 Steps! Time elapsed: 204373.1 ms


My program has a function to search for all possible steps currently available. I just found that searching for n8r9c2 takes a long time.If I remember correctly, you introduced similar features("try-to-eliminate-candidates") to SudoRules before.BFS and DFS are just the specific implementation process of my Braid solver, not the traditional brute force solving algorithm.

[denis_berthier]

My program has a function to search for all possible steps currently available. I just found that searching for n8r9c2 takes a long time.If I remember correctly, you introduced similar features("try-to-eliminate-candidates") to SudoRules before.

It's not similar.
Try-to-eliminate will only try the candidate(s) passed as arguments. If you want to try this function on your case, load g-Braids; then the specific commands are:

Code: Select all

(init-sukaku-grid
+---------------------+-------------------+--------------------+
! 4689   14689  5     ! 2379  1379  13789 ! 12347  1236   1367 !
! 49     7      134   ! 239   139   6     ! 1234   8      5    !
! 2      168    1368  ! 357   4     13578 ! 137    136    9    !
+---------------------+-------------------+--------------------+
! 45678  468    9     ! 1     3567  3457  ! 378    35     2    !
! 567    2      167   ! 3679  8     3579  ! 139    4      137  !
! 3      148    147   ! 4579  579   2     ! 6      159    78   !
+---------------------+-------------------+--------------------+
! 1      5      678   ! 3679  2     379   ! 389    369    4    !
! 469    3      246   ! 8     1569  1459  ! 129    7      16   !
! 678    689    24678 ! 346   1367  13479 ! 5      12369  1368 !
+---------------------+-------------------+--------------------+
)

(try-to-eliminate (nrc-to-label 8 9 2))

But the mere fact that the puzzle is in gB16 doesn't guarantee that n8r9c2 can be eliminated by a g-Braid in this RS.
.

[yzfwsf]

But the mere fact that the puzzle is in gB16 doesn't guarantee that n8r9c2 can be eliminated by a g-Braid in this RS.
.

My solver will first call the T&E algorithm to determine the elimination location and then find the corresponding Braid for it.
n8r9c2 is a T&E(BI 1) elimation in this RS, so there is a g-Braid for it. My solver finds a g-Braid[23].

[denis_berthier]

But the mere fact that the puzzle is in gB16 doesn't guarantee that n8r9c2 can be eliminated by a g-Braid in this RS.

My solver will first call the T&E algorithm to determine the elimination location and then find the corresponding Braid for it.
n8r9c2 is a T&E(BI 1) elimation in this RS, so there is a g-Braid for it. My solver finds a g-Braid[23].

OK.

[yzfwsf]

From GAME0449

Code: Select all

5..3..1...8.....2....6....76.45.3.......7.......4.63..4....16...2......8..7....9.   #  31    9.7/9.7/9.3 - JPF

Curious how long it will take SHC(or SudoRules) to get a gB rating?

[denis_berthier]

Code: Select all

5..3..1...8.....2....6....76.45.3.......7.......4.63..4....16...2......8..7....9.

Curious how long it will take SHC(or SudoRules) to get a gB rating?

Curious to know who created this puzzle.

[1to9only]

Code: Select all

5..3..1...8.....2....6....76.45.3.......7.......4.63..4....16...2......8..7....9.

Curious how long it will take SHC(or SudoRules) to get a gB rating?

Curious to know who created this puzzle.

http://forum.enjoysudoku.com/post315624.html#p315624
http://forum.enjoysudoku.com/patterns-game-t6290-50580.html#p315686

[yzfwsf]

My program provides the following solution，Most difficult rule: gBraid[20]

Hidden Text: Show

Code: Select all

Braid[9]: => r9c5<>8
8r9c5 - r9c4{n8=n2} - 8c4{r7c4=r5c4} - 8c1{r5c1=r6c1} - 7c1{r6c1=r2c1} - 7b2{r2c4=r1c6} - 8b2{r1c6=r3c6} - 2c6{r3c6=r5c6} - 2c7{r5c7=r4c7} - 8c7{r4c7=.}
g-Braid[11]: => r8c5<>9
9r8c5 - r8c4{n9=n7} - 6b8{r8c5=r9c5} - 9b5{r4c5=r5c46} - 7c7{r8c7=r4c7} - 6c2{r9c2=r1c2} - 6c8{r1c8=r5c8} - 9b6{r4c7=r46c9} - r1c9{n9=n4} - r1c8{n4=n8} - 4b6{r5c9=r5c7} - 8c7{r5c7=.}
Whip[11]: => r5c8<>8
8r5c8 - 8r4{r4c7=r4c5} - 8r1{r1c5=r1c6} - 7r1{r1c6=r1c2} - 7b4{r4c2=r6c1} - 8b4{r6c1=r6c3} - 8r7{r7c3=r7c4} - r9c4{n8=n2} - 2b9{r9c7=r7c9} - 2r4{r4c9=r4c7} - 7b6{r4c7=r4c8} - 7r7{r7c8=.}
Braid[12]: => r5c3<>8
8r5c3 - 8b7{r7c3=r9c1} - r9c4{n8=n2} - 8c4{r9c4=r7c4} - 7r7{r7c4=r7c8} - 7b6{r4c8=r4c7} - 8c7{r4c7=r3c7} - 2c7{r4c7=r5c7} - 8c6{r3c6=r1c6} - 2c6{r1c6=r3c6} - 2c1{r3c1=r6c1} - 7b4{r6c1=r6c2} - 7r1{r1c2=.}
g-Braid[14]: => r9c2<>3
3r9c2 - 6b7{r9c2=r8c3} - 6r2{r2c3=r2c9} - 3b3{r2c9=r3c8} - 3b9{r7c8=r7c9} - 2b9{r7c9=r9c79} - r9c4{n2=n8} - r9c1{n8=n1} - r8c1{n1=n9} - 1b9{r9c9=r8c8} - r3c1{n9=n2} - r1c3{n2=n9} - r1c9{n9=n4} - 4c8{r1c8=r5c8} - 6r5{r5c8=.}
g-Braid[14]: => r3c6<>4
4r3c6 - 4b1{r3c2=r1c2} - 6c2{r1c2=r9c2} - 7b1{r1c2=r2c1} - 6b8{r9c5=r8c5} - 4b8{r8c5=r9c5} - 3b8{r9c5=r7c5} - 5b8{r7c5=r89c6} - r2c6{n5=n9} - r2c4{n9=n1} - r2c5{n1=n5} - r2c7{n5=n4} - 4b9{r8c7=r8c8} - 1b9{r8c8=r9c9} - 3b9{r9c9=.}
Braid[16]: => r7c4<>8
8r7c4 - r9c4{n8=n2} - 7r7{r7c4=r7c8} - 8c3{r7c3=r6c3} - 7b6{r4c8=r4c7} - 2c7{r4c7=r5c7} - 2r4{r4c9=r4c5} - 8c7{r5c7=r3c7} - 9c7{r3c7=r2c7} - 2b4{r5c1=r6c1} - 7c1{r6c1=r2c1} - r2c4{n7=n1} - 1b5{r5c4=r6c5} - r6c8{n1=n5} - 5b3{r3c8=r2c9} - r2c5{n5=n4} - r2c6{n4=.}
Braid[10]: => r2c1<>1
1r2c1 - 1c4{r2c4=r5c4} - 7b1{r2c1=r1c2} - 8c4{r5c4=r9c4} - r9c1{n8=n3} - 2c4{r9c4=r7c4} - r8c1{n3=n9} - 9b8{r8c4=r7c5} - 3b8{r7c5=r8c5} - 6b8{r8c5=r9c5} - 6c2{r9c2=.}
Braid[13]: => r2c3<>1
1r2c3 - 1c4{r2c4=r5c4} - 6r2{r2c3=r2c9} - 8c4{r5c4=r9c4} - 3r2{r2c9=r2c1} - r9c1{n3=n1} - r8c1{n1=n9} - r3c1{n9=n2} - r8c4{n9=n7} - r3c3{n2=n9} - r2c4{n7=n9} - 9c6{r1c6=r5c6} - 9c7{r5c7=r4c7} - 7c7{r4c7=.}
Whip[1]: => r3c5<>1
1r3c5 - 1r2{r2c4=.}
Braid[15]: => r2c4<>7
7r2c4 - r8c4{n7=n9} - 1c4{r2c4=r5c4} - 7b8{r7c4=r8c6} - 7c1{r2c1=r6c1} - 8c4{r5c4=r9c4} - 7c7{r8c7=r4c7} - 8b7{r9c1=r7c3} - 8b4{r6c3=r5c1} - 2c1{r5c1=r3c1} - 9c1{r3c1=r2c1} - 8c7{r5c7=r3c7} - 9c7{r3c7=r5c7} - r5c6{n9=n2} - 2b4{r5c3=r6c3} - 9c3{r6c3=.}
Whip[1]: => r8c6<>7
7r8c6 - 7c4{r7c4=.}
g-Braid[15]: => r5c8<>1
1r5c8 - 1b9{r8c8=r9c9} - 6b6{r5c8=r5c9} - 4b6{r5c9=r5c7} - 6r2{r2c9=r2c3} - 6r8{r8c3=r8c5} - 4b9{r8c7=r8c8} - 3r8{r8c8=r8c13} - r9c1{n3=n8} - r9c4{n8=n2} - 8b8{r9c4=r7c5} - 2c7{r9c7=r4c7} - 8r4{r4c7=r4c8} - 7r4{r4c8=r4c2} - 7r1{r1c2=r1c6} - 8r1{r1c6=.}
g-Braid[11]: => r8c8<>7
7r8c8 - r8c4{n7=n9} - 1b9{r8c8=r9c9} - 7b8{r8c4=r7c4} - 7b6{r4c8=r4c7} - r2c4{n9=n1} - 1r5{r5c4=r5c123} - r4c2{n1=n9} - r4c9{n9=n2} - 2r7{r7c9=r7c5} - 8r7{r7c5=r7c3} - 9r7{r7c3=.}
Braid[15]: => r5c9<>2
2r5c9 - 2b9{r7c9=r9c7} - 6b6{r5c9=r5c8} - r9c4{n2=n8} - 2c4{r9c4=r7c4} - 4b6{r5c8=r5c7} - 7b8{r7c4=r8c4} - r8c7{n7=n5} - r2c7{n5=n9} - 9c4{r2c4=r5c4} - r5c6{n9=n8} - 8c1{r5c1=r6c1} - 2c1{r6c1=r3c1} - 2c6{r3c6=r1c6} - 7b2{r1c6=r2c6} - 7c1{r2c1=.}
g-Braid[15]: => r1c6<>4
4r1c6 - 4b1{r1c2=r3c2} - 7r1{r1c6=r1c2} - 7b4{r4c2=r6c1} - 6c2{r1c2=r9c2} - 6b8{r9c5=r8c5} - 4b8{r8c5=r9c5} - 3b8{r9c5=r7c5} - 8r7{r7c5=r7c3} - 8b4{r6c3=r5c1} - 8b5{r5c4=r46c5} - 8r1{r1c5=r1c8} - 6c8{r1c8=r5c8} - 4c8{r5c8=r8c8} - 1b9{r8c8=r9c9} - 3b9{r9c9=.}
Braid[17]: => r8c5<>4
4r8c5 - 6b8{r8c5=r9c5} - 3b8{r9c5=r7c5} - 6c2{r9c2=r1c2} - 6b3{r1c8=r2c9} - 8r7{r7c5=r7c3} - 4b1{r1c2=r3c2} - 6b6{r5c9=r5c8} - 3c2{r3c2=r5c2} - 3c9{r2c9=r9c9} - 4b9{r9c9=r9c7} - r9c1{n3=n1} - 4b6{r5c7=r5c9} - 1b1{r3c1=r3c3} - 1r5{r5c3=r5c4} - 8c4{r5c4=r9c4} - 2c4{r9c4=r7c4} - 2r9{r9c6=.}
g-Braid[17]: => r2c9<>9
9r2c9 - r2c4{n9=n1} - 3b3{r2c9=r3c8} - 6r2{r2c9=r2c3} - 3b1{r2c3=r2c1} - 6b7{r8c3=r9c2} - 6b8{r9c5=r8c5} - 3r8{r8c5=r8c3} - 1b7{r8c3=r89c1} - 5b7{r8c3=r7c23} - r7c8{n5=n7} - 7b6{r4c8=r4c7} - 9b6{r4c7=r5c7} - 2c7{r5c7=r9c7} - r9c4{n2=n8} - r5c4{n8=n2} - r5c1{n2=n8} - r5c6{n8=.}
g-Braid[17]: => r8c5<>5
5r8c5 - 6b8{r8c5=r9c5} - 3b8{r9c5=r7c5} - 6c2{r9c2=r1c2} - 6b3{r1c8=r2c9} - 4b1{r1c2=r3c2} - 6b6{r5c9=r5c8} - 3c2{r3c2=r5c2} - 3c9{r2c9=r9c9} - 1b9{r9c9=r8c8} - 4c8{r8c8=r1c8} - 4c5{r1c5=r2c5} - 4c9{r1c9=r5c9} - 1b2{r2c5=r2c4} - 1r5{r5c4=r5c13} - 1c2{r4c2=r9c2} - r9c1{n1=n8} - 8r7{r7c3=.}
g-Braid[18]: => r2c3<>9
9r2c3 - r2c4{n9=n1} - 6r2{r2c3=r2c9} - 3b3{r2c9=r3c8} - 3b1{r3c1=r2c1} - 6b6{r5c9=r5c8} - 7b1{r2c1=r1c2} - 4b1{r1c2=r3c2} - 6c2{r1c2=r9c2} - 6b8{r9c5=r8c5} - 3r8{r8c5=r8c3} - 3b4{r5c3=r5c2} - 1c2{r5c2=r46c2} - 1r5{r5c1=r5c9} - 1b9{r9c9=r8c8} - 4b6{r5c9=r5c7} - r2c7{n4=n5} - 4r8{r8c7=r8c6} - 5r8{r8c6=.}
g-Braid[15]: => r7c3<>3
3r7c3 - r2c3{n3=n6} - 8b7{r7c3=r9c1} - 6b7{r8c3=r9c2} - r9c4{n8=n2} - 8c4{r9c4=r5c4} - 2b9{r9c7=r7c9} - 1r9{r9c2=r9c9} - 1r5{r5c9=r5c123} - r4c9{n1=n9} - r4c2{n9=n7} - 7b6{r4c7=r6c8} - r7c8{n7=n5} - r7c2{n5=n9} - r6c2{n9=n5} - r6c9{n5=.}
g-Braid[18]: => r2c9<>4
4r2c9 - 3b3{r2c9=r3c8} - 6r2{r2c9=r2c3} - 5b3{r3c8=r23c7} - 3b1{r2c3=r2c1} - 6b7{r8c3=r9c2} - 6b8{r9c5=r8c5} - 7c1{r2c1=r6c1} - 3r8{r8c5=r8c3} - 5b7{r8c3=r7c23} - r7c8{n5=n7} - r8c7{n7=n4} - r9c7{n4=n2} - r9c4{n2=n8} - 8c1{r9c1=r5c1} - r5c7{n8=n9} - 9b3{r2c7=r1c9} - r1c3{n9=n2} - 2c1{r3c1=.}
g-Braid[20]: => r9c2<>1
1r9c2 - 1b9{r9c9=r8c8} - 6b7{r9c2=r8c3} - r8c5{n6=n3} - 6r2{r2c3=r2c9} - r8c1{n3=n9} - r8c4{n9=n7} - 7c7{r8c7=r4c7} - r4c2{n7=n9} - r4c8{n7=n8} - r1c8{n8=n4} - r1c9{n4=n9} - r1c3{n9=n2} - r1c5{n2=n8} - 8r7{r7c5=r7c3} - 5b7{r7c3=r7c2} - 8r6{r6c3=r6c1} - 2b4{r6c1=r5c1} - 2c4{r5c4=r79c4} - r7c5{n2=n9} - 9r6{r6c5=.}
Braid[10]: => r6c1<>1
1r6c1 - 1b7{r8c1=r8c3} - 1b9{r8c8=r9c9} - 1r5{r5c9=r5c4} - r2c4{n1=n9} - 8c4{r5c4=r9c4} - r9c1{n8=n3} - r8c1{n3=n9} - 9b8{r8c6=r7c5} - 3b8{r7c5=r8c5} - 6r8{r8c5=.}
g-Braid[12]: => r9c1<>8
8r9c1 - r9c4{n8=n2} - 1r9{r9c1=r9c9} - 8c4{r9c4=r5c4} - 2b9{r9c7=r7c9} - 1r5{r5c4=r5c123} - r4c9{n2=n9} - r4c2{n9=n7} - 7r1{r1c2=r1c6} - 8c6{r1c6=r3c6} - 2c6{r3c6=r5c6} - 2b6{r5c7=r4c7} - 8c7{r4c7=.}
Hidden Single: 8 in b7 => r7c3=8
Whip[6]: => r3c1<>3
3r3c1 - r9c1{n3=n1} - r8c1{n1=n9} - r8c4{n9=n7} - 7b9{r8c7=r7c8} - 3c8{r7c8=r8c8} - 1r8{r8c8=.}
Braid[10]: => r1c6<>9
9r1c6 - 7b2{r1c6=r2c6} - 7c1{r2c1=r6c1} - 8b4{r6c1=r5c1} - r5c6{n8=n2} - 8c4{r5c4=r9c4} - 2c4{r9c4=r7c4} - 7b8{r7c4=r8c4} - 7c7{r8c7=r4c7} - 8c7{r4c7=r3c7} - 8c6{r3c6=.}
Braid[11]: => r5c1<>3
3r5c1 - r9c1{n3=n1} - r8c1{n1=n9} - r3c1{n9=n2} - r2c1{n9=n7} - r8c4{n9=n7} - 7b2{r2c6=r1c6} - 7b9{r8c7=r7c8} - 2b2{r1c6=r1c5} - 8r1{r1c5=r1c8} - r4c8{n8=n1} - 1r8{r8c8=.}
Braid[5]: => r7c2<>3
3r7c2 - 3b4{r5c2=r5c3} - r2c3{n3=n6} - 3r3{r3c3=r3c8} - 3r8{r8c8=r8c5} - 6r8{r8c5=.}
g-Braid[9]: => r5c2<>9
9r5c2 - 3c2{r5c2=r3c2} - 9b5{r5c4=r46c5} - 9r7{r7c5=r7c4} - 7r7{r7c4=r7c8} - r2c4{n9=n1} - 3c8{r7c8=r8c8} - 1b9{r8c8=r9c9} - 1r5{r5c9=r5c13} - 1c2{r4c2=.}
Braid[11]: => r6c1<>2
2r6c1 - 7c1{r6c1=r2c1} - 8b4{r6c1=r5c1} - 7b2{r2c6=r1c6} - 8c4{r5c4=r9c4} - 8c6{r9c6=r3c6} - 8c7{r3c7=r4c7} - 7c7{r4c7=r8c7} - 7b8{r8c4=r7c4} - 2c4{r7c4=r5c4} - 2c7{r5c7=r9c7} - 2c6{r9c6=.}
Whip[2]: => r3c5<>2
2r3c5 - 2c1{r3c1=r5c1} - 2b5{r5c4=.}
Whip[6]: => r3c3<>2
2r3c3 - 2b4{r5c3=r5c1} - 8b4{r5c1=r6c1} - 7c1{r6c1=r2c1} - 7b2{r2c6=r1c6} - 2b2{r1c6=r1c5} - 2b5{r4c5=.}
Braid[10]: => r9c5<>2
2r9c5 - r9c4{n2=n8} - 2b9{r9c7=r7c9} - 2r6{r6c9=r6c3} - 2r4{r4c9=r4c7} - 2r1{r1c3=r1c6} - 7b2{r1c6=r2c6} - 7c1{r2c1=r6c1} - 8b4{r6c1=r5c1} - 8c7{r5c7=r3c7} - 8c6{r3c6=.}
Braid[11]: => r3c1<>1
1r3c1 - r9c1{n1=n3} - r8c1{n3=n9} - r7c2{n9=n5} - r9c2{n5=n6} - 6b8{r9c5=r8c5} - r8c4{n9=n7} - 7c7{r8c7=r4c7} - 3b8{r8c5=r7c5} - r7c9{n3=n2} - 2b6{r4c9=r5c7} - 2c1{r5c1=.}
g-Braid[9]: => r3c2<>9
9r3c2 - r3c1{n9=n2} - 4b1{r3c2=r1c2} - 9b7{r7c2=r8c13} - r1c3{n2=n6} - r8c4{n9=n7} - 7c7{r8c7=r4c7} - r1c8{n6=n8} - r4c2{n7=n1} - r4c8{n1=.}
Braid[9]: => r1c2<>9
9r1c2 - r3c1{n9=n2} - r1c3{n2=n6} - r1c9{n6=n4} - 6c8{r1c8=r5c8} - 4c8{r5c8=r8c8} - 1b9{r8c8=r9c9} - r9c1{n1=n3} - 3r8{r8c1=r8c5} - 6r8{r8c5=.}
Braid[11]: => r3c3<>9
9r3c3 - r3c1{n9=n2} - 1b1{r3c3=r3c2} - r1c3{n2=n6} - 3r3{r3c2=r3c8} - 4b1{r3c2=r1c2} - 6c8{r1c8=r5c8} - 4c8{r5c8=r8c8} - 1b9{r8c8=r9c9} - r9c1{n1=n3} - 3r8{r8c1=r8c5} - 6r8{r8c5=.}
Braid[11]: => r6c1<>9
9r6c1 - r3c1{n9=n2} - 7c1{r6c1=r2c1} - 7b2{r2c6=r1c6} - 2b2{r1c6=r1c5} - 8r1{r1c5=r1c8} - 8r6{r6c8=r6c5} - 8r4{r4c5=r4c7} - 2r4{r4c7=r4c9} - 2r7{r7c9=r7c4} - 7b8{r7c4=r8c4} - 7c7{r8c7=.}
g-Braid[11]: => r9c6<>2
2r9c6 - 2b9{r9c7=r7c9} - 2b2{r1c6=r1c5} - 2r6{r6c5=r6c3} - 2r4{r4c5=r4c7} - 7c7{r4c7=r8c7} - r8c4{n7=n9} - 9b7{r8c1=r7c2} - 9b4{r4c2=r5c13} - r5c6{n9=n8} - 8b2{r1c6=r3c5} - 8c7{r3c7=.}
Whip[11]: => r5c3<>2
2r5c3 - 2b1{r1c3=r3c1} - 2c6{r3c6=r1c6} - 7b2{r1c6=r2c6} - 7c1{r2c1=r6c1} - 8b4{r6c1=r5c1} - 8c4{r5c4=r9c4} - 2c4{r9c4=r7c4} - 7b8{r7c4=r8c4} - 7c7{r8c7=r4c7} - 8c7{r4c7=r3c7} - 8c6{r3c6=.}
Whip[11]: => r5c7<>2
2r5c7 - 2c1{r5c1=r3c1} - 2c6{r3c6=r1c6} - 7b2{r1c6=r2c6} - 7c1{r2c1=r6c1} - 8b4{r6c1=r5c1} - 8c4{r5c4=r9c4} - 2c4{r9c4=r7c4} - 7b8{r7c4=r8c4} - 7c7{r8c7=r4c7} - 8c7{r4c7=r3c7} - 8c6{r3c6=.}
Braid[9]: => r8c3<>1
1r8c3 - r3c3{n1=n3} - r9c1{n1=n3} - r8c1{n3=n9} - r7c2{n9=n5} - r8c4{n9=n7} - 7c7{r8c7=r4c7} - 2c7{r4c7=r9c7} - r7c9{n2=n3} - 3r2{r2c9=.}
Whip[1]: => r5c1<>1
1r5c1 - 1b7{r8c1=.}
g-Whip[9]: => r5c9<>9
9r5c9 - 9b5{r5c4=r46c5} - 9r1{r1c5=r1c3} - r3c1{n9=n2} - r5c1{n2=n8} - r5c6{n8=n2} - r5c4{n2=n1} - r2c4{n1=n9} - 9b8{r7c4=r8c6} - 9c1{r8c1=.}
Braid[9]: => r5c4<>8
8r5c4 - r9c4{n8=n2} - 2c7{r9c7=r4c7} - 8c7{r4c7=r3c7} - 8c5{r3c5=r1c5} - 2c5{r1c5=r6c5} - r5c6{n2=n9} - 2c3{r6c3=r1c3} - 9c7{r5c7=r2c7} - 9r1{r1c9=.}
Hidden Single: 8 in c4 => r9c4=8
Whip[1]: => r7c9<>2
2r7c9 - 2r9{r9c7=.}
Whip[4]: => r9c7<>5
5r9c7 - r7c9{n5=n3} - r7c8{n3=n7} - 7b6{r4c8=r4c7} - 2c7{r4c7=.}
Braid[6]: => r6c8<>7
7r6c8 - 7b4{r6c1=r4c2} - 7r7{r7c8=r7c4} - 2c4{r7c4=r5c4} - 2c1{r5c1=r3c1} - 2c6{r3c6=r1c6} - 7r1{r1c6=.}
Whip[1]: => r4c2<>7
7r4c2 - 7r6{r6c1=.}
Whip[5]: => r3c3<>3
3r3c3 - 1b1{r3c3=r3c2} - r4c2{n1=n9} - r7c2{n9=n5} - r7c9{n5=n3} - 3r2{r2c9=.}
Naked Single: r3c3=1
Whip[5]: => r5c2<>1
1r5c2 - r4c2{n1=n9} - r7c2{n9=n5} - r7c9{n5=n3} - 3b3{r2c9=r3c8} - 3c2{r3c2=.}
Whip[4]: => r3c8<>5
5r3c8 - 3r3{r3c8=r3c2} - r5c2{n3=n5} - 5b7{r7c2=r8c3} - 5c7{r8c7=.}
Whip[6]: => r9c7<>4
4r9c7 - 4b8{r9c5=r8c6} - 4r2{r2c6=r2c5} - 1b2{r2c5=r2c4} - 1r5{r5c4=r5c9} - 4b6{r5c9=r5c8} - 6r5{r5c8=.}
Naked Single: r9c7=2
Braid[5]: => r4c9<>1
1r4c9 - r4c2{n1=n9} - 2b6{r4c9=r6c9} - r6c3{n2=n5} - r5c2{n5=n3} - r5c3{n3=.}
g-Braid[7]: => r4c8<>1
1r4c8 - r4c2{n1=n9} - 1b9{r8c8=r9c9} - r7c2{n9=n5} - 4r9{r9c9=r9c56} - 5r9{r9c2=r9c56} - r8c6{n5=n9} - 9r7{r7c4=.}
Braid[5]: => r8c8<>3
3r8c8 - r7c9{n3=n5} - 1c8{r8c8=r6c8} - 3r3{r3c8=r3c2} - r5c2{n3=n5} - 5r6{r6c2=.}
Whip[5]: => r5c7<>8
8r5c7 - r4c8{n8=n7} - 7r7{r7c8=r7c4} - 2c4{r7c4=r5c4} - r5c1{n2=n9} - r5c6{n9=.}
Braid[6]: => r5c1<>9
9r5c1 - r3c1{n9=n2} - 8b4{r5c1=r6c1} - 7b4{r6c1=r6c2} - 7r1{r1c2=r1c6} - 2c6{r1c6=r5c6} - 8r5{r5c6=.}
Whip[6]: => r3c5<>8
8r3c5 - 8b5{r4c5=r5c6} - r5c1{n8=n2} - 2c4{r5c4=r7c4} - 7b8{r7c4=r8c4} - 7c7{r8c7=r4c7} - 8c7{r4c7=.}
Braid[6]: => r6c9<>2
2r6c9 - r4c9{n2=n9} - 2b4{r6c3=r5c1} - r3c1{n2=n9} - 8r5{r5c1=r5c6} - 8b2{r1c6=r1c5} - 9r1{r1c5=.}
Hidden Single: 2 in c9 => r4c9=2
Whip[6]: => r2c6<>5
5r2c6 - r9c6{n5=n4} - r8c6{n4=n9} - r8c4{n9=n7} - 7c7{r8c7=r4c7} - 8c7{r4c7=r3c7} - 5r3{r3c7=.}
g-Whip[6]: => r6c3<>5
5r6c3 - r5c2{n5=n3} - r5c3{n3=n9} - 9b5{r5c4=r46c5} - 9r1{r1c5=r1c9} - 9r6{r6c9=r6c5} - 2r6{r6c5=.}
Braid[5]: => r5c7<>5
5r5c7 - r5c2{n5=n3} - 5b3{r2c7=r2c9} - 5c3{r5c3=r8c3} - 3c3{r8c3=r2c3} - 6r2{r2c3=.}
g-Braid[5]: => r1c5<>4
4r1c5 - 4r2{r2c5=r2c7} - 2b2{r1c5=r13c6} - r5c7{n4=n9} - r5c6{n9=n8} - 8c5{r4c5=.}
Whip[5]: => r5c8<>5
5r5c8 - r5c2{n5=n3} - r5c3{n3=n9} - r6c3{n9=n2} - r1c3{n2=n6} - 6c8{r1c8=.}
Whip[5]: => r5c9<>5
5r5c9 - 1r5{r5c9=r5c4} - 2c4{r5c4=r7c4} - 7r7{r7c4=r7c8} - 5c8{r7c8=r8c8} - 5c3{r8c3=.}
Whip[1]: => r6c2<>5
5r6c2 - 5r5{r5c2=.}
Whip[2]: => r5c3<>9
9r5c3 - 3b4{r5c3=r5c2} - 5r5{r5c2=.}
g-Whip[4]: => r7c4<>7
7r7c4 - 2b8{r7c4=r7c5} - 2r6{r6c5=r6c3} - 9b4{r6c3=r46c2} - 9r7{r7c2=.}
Hidden Single: 7 in r7 => r7c8=7
Hidden Single: 7 in r4 => r4c7=7
Hidden Single: 7 in r8 => r8c4=7
Hidden Single: 8 in c7 => r3c7=8
Hidden Single: 3 in c8 => r3c8=3
Hidden Single: 3 in c2 => r5c2=3
Hidden Single: 5 in r5 => r5c3=5
Naked Single: r3c2=4
Naked Single: r4c8=8
Whip[1]: => r2c5<>5
5r2c5 - 5r3{r3c5=.}
Whip[1]: => r2c7<>4
4r2c7 - 4r1{r1c8=.}
Whip[2]: => r8c8<>4
4r8c8 - r1c8{n4=n6} - r5c8{n6=.}
Whip[2]: => r2c5<>9
9r2c5 - 9c7{r2c7=r5c7} - 9b5{r5c4=.}
Braid[3]: => r5c8<>4
4r5c8 - r5c7{n4=n9} - 4b3{r1c8=r1c9} - 9c9{r1c9=.}
Hidden Single: 4 in c8 => r1c8=4
Hidden Single: 6 in c8 => r5c8=6
Whip[3]: => r1c6<>2
2r1c6 - 2b1{r1c3=r3c1} - r5c1{n2=n8} - 8c6{r5c6=.}
Whip[2]: => r7c5<>2
2r7c5 - 2r6{r6c5=r6c3} - 2r1{r1c3=.}
Hidden Single: 2 in r7 => r7c4=2
Whip[2]: => r3c5<>9
9r3c5 - 9r7{r7c5=r7c2} - 9r4{r4c2=.}
Naked Single: r3c5=5
Whip[2]: => r6c2<>9
9r6c2 - 9r7{r7c2=r7c5} - 9r4{r4c5=.}
Whip[2]: => r2c1<>9
9r2c1 - 9c7{r2c7=r5c7} - 9c4{r5c4=.}
Whip[2]: => r1c3<>6
6r1c3 - 2b1{r1c3=r3c1} - 9b1{r3c1=.}
Whip[2]: => r8c3<>9
9r8c3 - r1c3{n9=n2} - r6c3{n2=.}
Whip[2]: => r8c1<>3
3r8c1 - r8c3{n3=n6} - r8c5{n6=.}
Whip[2]: => r2c6<>9
9r2c6 - 9c7{r2c7=r5c7} - 9c4{r5c4=.}
Whip[2]: => r6c5<>1
1r6c5 - r4c5{n1=n9} - r5c4{n9=.}
Whip[2]: => r5c6<>9
9r5c6 - r4c5{n9=n1} - r5c4{n1=.}
Whip[2]: => r6c5<>9
9r6c5 - r4c5{n9=n1} - r5c4{n1=.}
Whip[2]: => r1c5<>9
9r1c5 - 2c5{r1c5=r6c5} - 8c5{r6c5=.}
Whip[3]: => r7c5<>3
3r7c5 - r7c9{n3=n5} - 5r8{r8c7=r8c6} - 9b8{r8c6=.}
stte