Forcing T&E

Advanced methods and approaches for solving Sudoku puzzles

Re: Forcing T&E

Postby denis_berthier » Fri Jan 15, 2021 5:31 am

Mauriès Robert wrote:
denis_berthier wrote:But the discussion was not between whips and antitracks; it was between a whip and a pair of conjugated tracks. You keep repeating that the latter have an easier to find starting point. I've shown that this claim is false.

I didn't say anything like that, read what I wrote again.

You have written in every possible thread that the starting point for a whip was its target, but it was easier to start with conjugated track. I'm certainly not going to search all this site for that.

But I'm glad to hear that, at last, you admit it's a false claim.
denis_berthier
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Re: Forcing T&E

Postby Mauriès Robert » Fri Jan 15, 2021 2:57 pm

denis_berthier wrote:You have written in every possible thread that the starting point for a whip was its target, but it was easier to start with conjugated track. I'm certainly not going to search all this site for that.
But I'm glad to hear that, at last, you admit it's a false claim.

Indeed, don't search all over the site you wouldn't find such a statement from me. What I have been able to say about a target concerns the anti-tracks I compare to whips and braids and not the conjuguated tracks.
I said that with an anti-track P'(E) the target is found as a consequence of its development among all the candidates who see E, whereas for whips and braids it is not, the target is chosen as a starting point. On this last point, I have admitted being wrong, the starting point for the whips/braids and the antitracks are the same, we have agreed on this, which for me implies that the target is found with the whips/braids as a consequence of their development among the candidates who see the candidate on the left of the variable CSP V1. But as you pointed out to me before, we are off-topic, the thread being devoted to forcing-T&E to which I have nothing to add.
Having said that, I have some questions to ask you, which I will do in private because it is not a question of debating but of understanding.

Cordialy
Robert
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Re: Forcing T&E

Postby denis_berthier » Fri Jan 15, 2021 3:18 pm

Mauriès Robert wrote:I have some questions to ask you, which I will do in private because it is not a question of debating but of understanding.

Questions of understanding are probably more interesting to the silent readers of this forum than the usual pointless debates.
denis_berthier
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Location: Paris

Re: Forcing T&E

Postby Mauriès Robert » Fri Jan 15, 2021 4:52 pm

denis_berthier wrote:
Mauriès Robert wrote:I have some questions to ask you, which I will do in private because it is not a question of debating but of understanding.

Questions of understanding are probably more interesting to the silent readers of this forum than the usual pointless debates.

Ok, so I'm going to create a topic to ask you questions with the objective of better understanding your theories.
Robert
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Location: France

Forcing{3}-T&E

Postby denis_berthier » Tue Feb 16, 2021 11:49 am

.
Forcing{3}-T&E

Forcing-T&E is very inelegant and it is not a panacea.
In the following example (Ref.: http://forum.enjoysudoku.com/sudokus-with-a-nice-form-t38506-15.html#p300739)

JPF wrote:Here is an other example with the same pattern:
Code: Select all
 . . 1 | . 2 . | 3 . .
 . 4 . | . 1 . | . 5 .
 6 . . | 3 . 5 | . . 1
-------+-------+-------
 . . 6 | . . . | 7 . .
 2 1 . | . . . | . 6 3
 . . 5 | . . . | 1 . .
-------+-------+-------
 5 . . | 1 . 8 | . . 9
 . 9 . | . 6 . | . 3 .
 . . 8 | . 9 . | 5 . .    ED=9.8/1.2/1.2


there is a solution in gW13, obtainable with the usual SudoRules rules and simplest-first strategy:
solution in gW13: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = gW+SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
singles ==> r9c8 = 1, r8c1 = 1, r8c4 = 5, r5c5 = 5, r4c9 = 5, r4c6 = 1, r1c2 = 5
177 candidates, 1002 csp-links and 1002 links. Density = 6.43%
Code: Select all
RESOLUTION STATE RS1:
   789       5         1         46789     2         4679      3         4789      4678     
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         2489      24789     1         
   3489      38        6         2489      348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      2347      1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       2367      8         247       9         2347      5         1         2467     


whip[2]: r5n8{c7 c4} - b2n8{r1c4 .} ==> r3c7 ≠ 8
122 g-candidates, 816 csp-glinks and 474 non-csp glinks
whip[9]: r5n8{c4 c7} - r8n8{c7 c9} - r2n8{c9 c1} - c2n8{r3 r6} - r4c2{n8 n3} - c1n3{r6 r9} - c6n3{r9 r6} - r6n6{c6 c4} - b5n2{r6c4 .} ==> r4c4 ≠ 8
whip[9]: c2n8{r6 r3} - r4c2{n8 n3} - r4c5{n3 n4} - c5n8{r4 r6} - r5n8{c4 c7} - r5n4{c7 c3} - c1n4{r6 r9} - r9n3{c1 c6} - r6n3{c6 .} ==> r4c1 ≠ 8
g-whip[11]: b4n3{r6c2 r456c1} - r2n3{c1 c3} - r7n3{c3 c5} - c6n3{r9 r6} - r6n6{c6 c4} - b5n2{r6c4 r4c4} - b5n9{r4c4 r5c456} - c3n9{r5 r3} - c7n9{r3 r2} - c7n6{r2 r7} - c2n6{r7 .} ==> r9c2 ≠ 3
g-whip[10]: r3n4{c8 c5} - b2n8{r3c5 r123c4} - r5n8{c4 c7} - c8n8{r6 r3} - c8n7{r3 r7} - c5n7{r7 r6} - r3n7{c5 c123} - c1n7{r2 r9} - r9n3{c1 c6} - r7c5{n3 .} ==> r1c8 ≠ 4
whip[12]: r5n7{c6 c3} - r8n7{c3 c9} - r8n8{c9 c7} - r5n8{c7 c4} - c5n8{r6 r3} - c5n7{r3 r7} - b8n3{r7c5 r9c6} - c6n2{r9 r8} - r9c4{n2 n4} - b2n4{r1c4 r1c6} - r5n4{c6 c7} - c9n4{r6 .} ==> r6c6 ≠ 7
whip[12]: r6n6{c4 c6} - c6n3{r6 r9} - c6n2{r9 r8} - r9c4{n2 n4} - r9c1{n4 n7} - r8c3{n7 n4} - r8c7{n4 n8} - r5n8{c7 c4} - c5n8{r6 r3} - b2n4{r3c5 r1c6} - r5n4{c6 c7} - c9n4{r6 .} ==> r6c4 ≠ 7
whip[12]: r6n6{c4 c6} - c6n3{r6 r9} - c6n2{r9 r8} - r9c4{n2 n7} - r9c1{n7 n4} - c3n4{r8 r5} - c6n4{r5 r1} - c9n4{r1 r8} - r8c7{n4 n8} - r5c7{n8 n9} - b5n9{r5c6 r4c4} - c4n2{r4 .} ==> r6c4 ≠ 4
g-whip[12]: b4n7{r5c3 r6c123} - c5n7{r6 r3} - c5n8{r3 r456} - r5n8{c4 c7} - r8n8{c7 c9} - b9n7{r8c9 r9c9} - c8n7{r7 r1} - c8n8{r1 r3} - r3c2{n8 n2} - c3n2{r3 r8} - r8c7{n2 n4} - r3n4{c7 .} ==> r7c3 ≠ 7
g-whip[12]: r9n3{c6 c1} - r2n3{c1 c3} - r7n3{c3 c5} - b5n3{r4c5 r6c6} - r6n6{c6 c4} - b5n2{r6c4 r4c4} - b5n9{r4c4 r5c456} - c3n9{r5 r3} - c3n2{r3 r789} - r9n2{c2 c9} - r2n2{c9 c7} - c7n9{r2 .} ==> r9c6 ≠ 7
g-whip[12]: r9n3{c6 c1} - r2n3{c1 c3} - r7n3{c3 c5} - b5n3{r4c5 r6c6} - r6n6{c6 c4} - b5n2{r6c4 r4c4} - b5n9{r4c4 r5c456} - c3n9{r5 r3} - c3n2{r3 r789} - r9n2{c2 c9} - r2n2{c9 c7} - c7n9{r2 .} ==> r9c6 ≠ 4
g-whip[10]: c3n4{r5 r789} - r9n4{c1 c9} - r1n4{c9 c6} - b8n4{r8c6 r7c5} - b8n3{r7c5 r9c6} - r9c1{n3 n7} - r9c4{n7 n2} - r8c6{n2 n7} - r5c6{n7 n9} - r4c4{n9 .} ==> r5c4 ≠ 4
g-whip[13]: b2n4{r3c5 r1c456} - c9n4{r1 r789} - r7n4{c8 c3} - r5n4{c3 c7} - r5n8{c7 c4} - c5n8{r6 r3} - c5n7{r3 r7} - b8n3{r7c5 r9c6} - r9c1{n3 n7} - r8c3{n7 n2} - c6n2{r8 r6} - r4n2{c4 c8} - r7c8{n2 .} ==> r6c5 ≠ 4
g-whip[11]: r4c2{n3 n8} - r6c2{n8 n7} - r6c5{n7 n8} - r3n8{c5 c8} - c9n8{r1 r8} - b6n8{r6c9 r5c7} - b6n9{r5c7 r456c8} - r1c8{n9 n7} - r7n7{c8 c5} - r3n7{c5 c3} - r8n7{c3 .} ==> r6c1 ≠ 3
g-whip[12]: r9n3{c6 c1} - r4n3{c1 c2} - b4n8{r4c2 r6c123} - r6c5{n8 n7} - b4n7{r6c1 r5c3} - b7n7{r8c3 r789c2} - r6c2{n7 n8} - r3c2{n8 n2} - r3c3{n2 n9} - r3c7{n9 n4} - c5n4{r3 r4} - r5n4{c6 .} ==> r7c5 ≠ 3
hidden-single-in-a-block ==> r9c6 = 3
whip[5]: r7c5{n7 n4} - r7c8{n4 n2} - r4n2{c8 c4} - r9n2{c4 c2} - c2n6{r9 .} ==> r7c2 ≠ 7
whip[6]: r9c1{n4 n7} - r8c3{n7 n2} - c6n2{r8 r6} - b6n2{r6c8 r4c8} - r7c8{n2 n7} - r7c5{n7 .} ==> r7c3 ≠ 4
whip[7]: r5n8{c4 c7} - r8n8{c7 c9} - r2n8{c9 c1} - c1n3{r2 r4} - r4c2{n3 n8} - c5n8{r4 r6} - r6n3{c5 .} ==> r1c4 ≠ 8
whip[7]: r3n4{c8 c5} - b2n8{r3c5 r2c4} - r5n8{c4 c7} - r6c9{n8 n2} - c6n2{r6 r8} - r8c7{n2 n4} - r7n4{c7 .} ==> r1c9 ≠ 4
whip[1]: b3n4{r3c8 .} ==> r3c5 ≠ 4
whip[4]: r7c5{n4 n7} - r7c8{n7 n2} - b6n2{r4c8 r6c9} - c9n4{r6 .} ==> r7c7 ≠ 4
hidden-pairs-in-a-row: r7{n4 n7}{c5 c8} ==> r7c8 ≠ 2
whip[4]: r7n4{c5 c8} - c9n4{r8 r6} - c1n4{r6 r4} - c5n4{r4 .} ==> r9c4 ≠ 4
whip[5]: r4n2{c8 c4} - r4n9{c4 c1} - r4n4{c1 c5} - r7c5{n4 n7} - r9c4{n7 .} ==> r4c8 ≠ 8
whip[5]: r4n2{c8 c4} - r9c4{n2 n7} - r7c5{n7 n4} - r4n4{c5 c1} - r9c1{n4 .} ==> r4c8 ≠ 9
whip[6]: c1n3{r2 r4} - r4c2{n3 n8} - r4c5{n8 n4} - b8n4{r7c5 r8c6} - c3n4{r8 r5} - c3n9{r5 .} ==> r2c1 ≠ 9
whip[6]: r3c5{n8 n7} - r7n7{c5 c8} - r1c8{n7 n9} - b6n9{r6c8 r5c7} - r5n8{c7 c4} - b2n8{r2c4 .} ==> r3c8 ≠ 8
x-wing-in-rows: n8{r3 r4}{c2 c5} ==> r6c5 ≠ 8, r6c2 ≠ 8
naked-pairs-in-a-row: r6{c2 c5}{n3 n7} ==> r6c1 ≠ 7
biv-chain[3]: b4n7{r6c2 r5c3} - c3n4{r5 r8} - r9c1{n4 n7} ==> r9c2 ≠ 7
hidden-pairs-in-a-block: b7{n4 n7}{r8c3 r9c1} ==> r8c3 ≠ 2
biv-chain[3]: b7n7{r8c3 r9c1} - r9n4{c1 c9} - r7c8{n4 n7} ==> r8c9 ≠ 7
whip[3]: r8n7{c3 c6} - r5n7{c6 c4} - b2n7{r1c4 .} ==> r3c3 ≠ 7
swordfish-in-rows: n7{r3 r6 r7}{c8 c2 c5} ==> r1c8 ≠ 7
whip[6]: c6n2{r6 r8} - r9c4{n2 n7} - r9c1{n7 n4} - r6c1{n4 n8} - b6n8{r6c8 r5c7} - b6n9{r5c7 .} ==> r6c6 ≠ 9
whip[3]: r4n9{c4 c1} - r1n9{c1 c8} - r6n9{c8 .} ==> r2c4 ≠ 9
whip[5]: c4n4{r1 r4} - c5n4{r4 r7} - b8n7{r7c5 r8c6} - r5c6{n7 n9} - c4n9{r6 .} ==> r1c4 ≠ 7
whip[5]: b2n4{r1c6 r1c4} - b2n9{r1c4 r2c6} - r5c6{n9 n4} - c3n4{r5 r8} - r8n7{c3 .} ==> r1c6 ≠ 7
whip[4]: c1n3{r2 r4} - r4c2{n3 n8} - c5n8{r4 r3} - b2n7{r3c5 .} ==> r2c1 ≠ 7
whip[5]: r1n8{c9 c1} - r1n7{c1 c9} - c9n6{r1 r9} - r9n4{c9 c1} - c1n7{r9 .} ==> r2c9 ≠ 8
whip[6]: r5n8{c4 c7} - r2n8{c7 c1} - c1n3{r2 r4} - r4n9{c1 c4} - b5n2{r4c4 r6c6} - r6n6{c6 .} ==> r6c4 ≠ 8
whip[4]: r3c5{n7 n8} - c4n8{r2 r5} - r5n7{c4 c3} - r8n7{c3 .} ==> r2c6 ≠ 7
hidden-pairs-in-a-block: b2{n7 n8}{r2c4 r3c5} ==> r2c4 ≠ 6
whip[4]: r6n6{c4 c6} - b5n2{r6c6 r4c4} - c4n4{r4 r1} - c4n6{r1 .} ==> r6c4 ≠ 9
biv-chain[3]: r6n9{c8 c1} - r4n9{c1 c4} - r4n2{c4 c8} ==> r6c8 ≠ 2
whip[5]: r8n8{c9 c7} - r5n8{c7 c4} - r2c4{n8 n7} - r9c4{n7 n2} - r8n2{c6 .} ==> r8c9 ≠ 4
biv-chain[4]: r9c4{n2 n7} - r9c1{n7 n4} - c9n4{r9 r6} - b6n2{r6c9 r4c8} ==> r4c4 ≠ 2
hidden-single-in-a-row ==> r4c8 = 2
hidden-pairs-in-a-row: r6{n2 n6}{c4 c6} ==> r6c6 ≠ 4
biv-chain[4]: c1n7{r1 r9} - r9n4{c1 c9} - r6c9{n4 n8} - c8n8{r6 r1} ==> r1c1 ≠ 8
whip[1]: r1n8{c9 .} ==> r2c7 ≠ 8
biv-chain[3]: c1n3{r4 r2} - r2n8{c1 c4} - b5n8{r5c4 r4c5} ==> r4c5 ≠ 3
singles ==> r6c5 = 3, r6c2 = 7
biv-chain[3]: r5c3{n9 n4} - r8c3{n4 n7} - c6n7{r8 r5} ==> r5c6 ≠ 9
whip[1]: c6n9{r2 .} ==> r1c4 ≠ 9
biv-chain[3]: r5c6{n4 n7} - r8n7{c6 c3} - c3n4{r8 r5} ==> r5c7 ≠ 4
whip[1]: b6n4{r6c9 .} ==> r6c1 ≠ 4
biv-chain[4]: r9n4{c1 c9} - r6c9{n4 n8} - c1n8{r6 r2} - c1n3{r2 r4} ==> r4c1 ≠ 4
singles ==> r5c3 = 4, r5c6 = 7, r8c3 = 7, r9c1 = 4, r6c9 = 4, r1c1 = 7
naked-pairs-in-a-column: c8{r1 r6}{n8 n9} ==> r3c8 ≠ 9
biv-chain[3]: c7n6{r7 r2} - r1c9{n6 n8} - r8c9{n8 n2} ==> r7c7 ≠ 2
singles ==> r7c7 = 6, r9c2 = 6
biv-chain[3]: r1n9{c8 c6} - c6n4{r1 r8} - c7n4{r8 r3} ==> r3c7 ≠ 9
hidden-single-in-a-row ==> r3c3 = 9
biv-chain[4]: r4c4{n9 n4} - b2n4{r1c4 r1c6} - r1n9{c6 c8} - r6n9{c8 c1} ==> r4c1 ≠ 9
stte


However, there is no solution using only Forcing-T&E as defined until now.
Starting from the same resolution state RS1 as in the gW13 solution, one can get the following eliminations:

applying Forcing-T&E: Show
FORCING-T&E(S) applied to bivalue candidates n3r6c6 and n3r9c6 :
===> 0 values decided in both cases:
===> 3 candidates eliminated in both cases: n3r9c2 n4r9c6 n7r9c6
Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         4789      4678     
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         2489      24789     1         
   3489      38        6         2489      348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      2347      1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       267       8         247       9         23        5         1         2467     


FORCING-T&E(S) applied to bivalue candidates n8r5c4 and n8r5c7 :
===> 0 values decided in both cases:
===> 1 candidates eliminated in both cases: n8r3c7

Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         4789      4678     
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         249       24789     1         
   3489      38        6         2489      348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      2347      1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       267       8         247       9         23        5         1         2467     

And that's all. No more Forcing-T&E can be applied successfully.


I therefore coded a generalisation of Forcing-T&E, Forcing{3}-T&E where trivalue cells can be used as starting points instead of bivalue ones. Needless to say, this is still more inelegant than starting with bivalue cells, but I wanted to try.
The rules are obvious: start a separate T&E procedure for each of the 3 candidates in a trivalue cell; any candidate deleted (resp. asserted as a value) in the three procedures can be deleted (resp. asserted) in the solution.
It works in the present case, providing a solution in six steps (still starting from RS1):

Solution with Forcing{3}-T&E: Show
Forcing{3}-T&ES) applied to trivalue candidates n3r7c2, n3r7c3 and n3r7c3 :
===> 0 values decided in the three cases:
===> 4 candidates eliminated in the three cases: n8r4c4 n3r9c2 n4r9c6 n7r9c6

Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         4789      4678     
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         2489      24789     1         
   3489      38        6         249       348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      2347      1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       267       8         247       9         23        5         1         2467     


Forcing{3}-T&E(S) applied to trivalue candidates n2r6c6, n2r8c6 and n2r8c6 :
===> 0 values decided in the three cases:
===> 2 candidates eliminated in the three cases: n4r7c3 n7r7c3

Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         4789      4678     
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         2489      24789     1         
   3489      38        6         249       348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      23        1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       267       8         247       9         23        5         1         2467     


Forcing{3}-T&E(S) applied to trivalue candidates n4r3c5, n7r3c5 and n7r3c5 :
===> 0 values decided in the three cases:
===> 2 candidates eliminated in the three cases: n4r1c9 n8r3c7

Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         4789      678       
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         249       24789     1         
   3489      38        6         249       348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      23        1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       267       8         247       9         23        5         1         2467     


Forcing{3}-T&E(S) applied to trivalue candidates n3r7c5, n4r7c5 and n4r7c5 :
===> 0 values decided in the three cases:
===> 6 candidates eliminated in the three cases: n4r1c8 n4r3c5 n8r4c1 n8r4c8 n4r6c5 n4r7c7

Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         789       678       
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         78        5         249       24789     1         
   349       38        6         249       348       1         7         249       5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    378       234679    1         2489      248       
   5         2367      23        1         347       8         26        247       9         
   1         9         247       5         6         247       248       3         2478     
   347       267       8         247       9         23        5         1         2467     


Forcing{3}-T&E(S) applied to trivalue candidates n4r5c3, n7r5c3 and n7r5c3 :
===> 1 values decided in the three cases: n3r9c6
===> 11 candidates eliminated in the three cases: n9r2c1 n4r5c4 n4r5c7 n4r6c1 n7r6c4 n3r6c6 n7r6c6 n3r7c5 n3r9c1 n4r9c4 n2r9c6

Code: Select all
CURRENT RESOLUTION STATE:
   789       5         1         46789     2         4679      3         789       678       
   378       4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         78        5         249       24789     1         
   349       38        6         249       348       1         7         249       5         
   2         1         479       789       5         479       89        6         3         
   3789      378       5         24689     378       2469      1         2489      248       
   5         2367      23        1         47        8         26        247       9         
   1         9         247       5         6         247       248       3         2478     
   47        267       8         27        9         3         5         1         2467     


Forcing{3}-T&E(S) applied to trivalue candidates n3r4c1, n4r4c1 and n4r4c1 :
===> 4 values decided in the three cases: n6r9c2 n6r7c7 n2r2c7 n2r4c8
===> 51 candidates eliminated in the three cases: n9r1c1 n6r1c4 n7r1c4 n8r1c4 n9r1c4 n7r1c6 n7r1c8 n7r1c9 n7r2c1 n2r2c3 n7r2c3 n6r2c4 n9r2c4 n7r2c6 n6r2c7 n8r2c7 n9r2c7 n2r2c9 n8r2c9 n7r3c3 n2r3c7 n2r3c8 n8r3c8 n2r4c4 n4r4c8 n9r4c8 n9r5c3 n7r5c4 n9r5c6 n3r6c1 n7r6c1 n8r6c2 n4r6c4 n8r6c4 n9r6c4 n8r6c5 n4r6c6 n9r6c6 n2r6c8 n2r6c9 n6r7c2 n7r7c2 n2r7c7 n2r7c8 n2r8c3 n2r8c7 n4r8c9 n7r8c9 n2r9c2 n7r9c2 n6r9c9

Code: Select all
CURRENT RESOLUTION STATE:
   78        5         1         4         2         469       3         89        68       
   38        4         39        78        1         69        2         5         67       
   6         278       29        3         78        5         49        479       1         
   349       38        6         49        348       1         7         2         5         
   2         1         47        89        5         47        89        6         3         
   89        37        5         26        37        26        1         489       48       
   5         23        23        1         47        8         6         47        9         
   1         9         47        5         6         247       48        3         28       
   47        6         8         27        9         3         5         1         247       

stte


I haven't yet tried to mix the above two variants of Forcing-T&E.
denis_berthier
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Location: Paris

Re: Forcing{3}-T&E

Postby creint » Tue Feb 16, 2021 8:56 pm

denis_berthier wrote:.
there is a solution in gW13, obtainable with the usual SudoRules rules and simplest-first strategy:
[hidden=solution in gW13]***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = gW+SFin
*** Using CLIPS 6.32-r779
*** Download from: https://github.com/denis-berthier/CSP-Rules-V2.1
***********************************************************************************************
singles ==> r9c8 = 1, r8c1 = 1, r8c4 = 5, r5c5 = 5, r4c9 = 5, r4c6 = 1, r1c2 = 5
177 candidates, 1002 csp-links and 1002 links. Density = 6.43%
Code: Select all
RESOLUTION STATE RS1:
   789       5         1         46789     2         4679      3         4789      4678     
   3789      4         2379      6789      1         679       2689      5         2678     
   6         278       279       3         478       5         2489      24789     1         
   3489      38        6         2489      348       1         7         2489      5         
   2         1         479       4789      5         479       489       6         3         
   34789     378       5         246789    3478      234679    1         2489      248       
   5         2367      2347      1         347       8         246       247       9         
   1         9         247       5         6         247       248       3         2478     
   347       2367      8         247       9         2347      5         1         2467     


solution in gW13:
How fast should this solve? I takes a while on my pc > 3 min.

Code: Select all
whip[2]: r5n8{c7 c4} - b2n8{r1c4 .} ==> r3c7 ≠ 8

It looks its missing r2c4 from the false set, shouldn't it be:
Code: Select all
whip[2]: r5n8{c7 c4} - b2n8{r12c4 .} ==> r3c7 ≠ 8


Code: Select all
r5n8{c4 c7} - r8n8{c7 c9} - r2n8{c9 c1} - c2n8{r3 r6} - r4c2{n8 n3} - c1n3{r6 r9} - c6n3{r9 r6} - r6n6{c6 c4} - b5n2{r6c4 .} ==> r4c4 ≠ 8

It looks like c2n8{r3 r6} is skipping 8r4c2, at that point you could see it as and OR chain: 8r4c2 -> -5r4c4 OR 8r6c2 and then the remaining logic. Does it skip that because it can directly see the target? Why does the chain already know which target it is excluding?
Also there is no mention that -8r2c36 is used from previous steps at step: r2n8{c9 c1}
Why is there . inside b5n2{r6c4 .}, shouldn't is be b5n2{r6c4 r4c4}? Following the logic -2r6c4 what should follow: any placement that could be made that exclude 8 in r4c4?

Code: Select all
g-whip[11]: b4n3{r6c2 r456c1} - r2n3{c1 c3} - r7n3{c3 c5} - c6n3{r9 r6} - r6n6{c6 c4} - b5n2{r6c4 r4c4} - b5n9{r4c4 r5c456} - c3n9{r5 r3} - c7n9{r3 r2} - c7n6{r2 r7} - c2n6{r7 .} ==> r9c2 ≠ 3

b4n3{r6c2 r456c1} should be b4n3{r6c2 r46c1} because r5c1 is already filled with 2.
creint
 
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Joined: 20 January 2018

Re: Forcing{3}-T&E

Postby denis_berthier » Wed Feb 17, 2021 2:29 am

creint wrote:solution in gW13:
How fast should this solve? I takes a while on my pc > 3 min.

On my Mac, it takes 3.5 mins. Notice that only an infinitesimal proportion of puzzles need so long chains.

As for the rest of your questions, before commenting what whips, g-whips... are or how they should look, read their definitions.
z and t- candidates are not written (not "skipped"); they are not part of the pattern.
denis_berthier
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Location: Paris

Re: Forcing T&E

Postby Leren » Wed Feb 17, 2021 9:42 am

Couldn't resist trying Hodoku for it's time to solve this one. Essentially no time, but uses 6 long forcing chains and one Brute force (T&E ) for a large "score" of 18,194, but a long way from 3 minutes. Leren
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Re: Forcing T&E

Postby denis_berthier » Wed Feb 17, 2021 9:53 am

Leren wrote:Couldn't resist trying Hodoku for it's time to solve this one. Essentially no time, but uses 6 long forcing chains and one Brute force (T&E ) for a large "score" of 18,194, but a long way from 3 minutes. Leren

Using T&E, any 9x9 puzzle can be solved in a tiny fraction of a second. The more resolution rules you use, the longer it will take to have a pattern-based solution.
Hodoku using brute force (i.e. Guessing, worse than T&E) means it is unable to solve it using only resolution rules.
denis_berthier
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