The New Sudoku Players' Forum

[denis_berthier]

here is only a summary of my resolution at depth 2, because my program does not output the exact syntax of whips (only right links):
1) I prove that (puzzle + hint 7L3C5) has no solution, using several whips[n], n <= 10.
2) I delete the candidate 7L3C5
3) I solve the puzzle using several whips[n], n <= 10.

OK, I can reproduce this with SudoRules, with the same max lengths.
As of now, it seems to be the simplest solution - n8r3c5 is a whip[10]-backdoor. But one may ask, why should you try precisely this candidate?

[DEFISE]

As of now, it seems to be the simplest solution - n7r3c5 is a whip[10]-backdoor. But one may ask, why should you try precisely this candidate?

I chose the 78r3c5 pair because it was the best start found by my DFS optimization program (with criterion = minimum number of tree ends). See Robert's post above.
This is not a very rational justification, especially because the branches of my DFS tree are developed using “basic techniques” i.e. alignements (whip [1]) and subsets.
Let's say I'm lucky !
N.B: I suppose you wanted to write "n8r3c5 is a whip[10]-backdoor" (not n7r3c5).

[denis_berthier]

I suppose you wanted to write "n8r3c5 is a whip[10]-backdoor" (not n7r3c5).

OK, thanks. I corrected.

[yzfwsf]

My Braid engine provides a Braid [18] solution path for this puzzle at a speed of 1.7 seconds.

Hidden Text: Show

Code: Select all

Hidden Single: 7 in r8 => r8c7=7
Hidden Single: 3 in r9 => r9c6=3
Hidden Single: 1 in r9 => r9c5=1
Hidden Single: 1 in r7 => r7c1=1
Whip[1]: => r1c9<>8
8r1c9 - 8c7{r1c7=.}
Whip[1]: => r2c9<>8
8r2c9 - 8c7{r1c7=.}
Whip[1]: => r3c9<>8
8r3c9 - 8c7{r1c7=.}
Whip[2]: => r4c6<>1
1r4c6 - 1b6{r4c7=r6c9} - 1r3{r3c9=.}
Braid[11]: => r5c4<>2
2r5c4 - 2b8{r7c4=r7c5} - r7c7{n2=n9} - 2c7{r7c7=r4c7} - r5c7{n9=n3} - 1r4{r4c7=r4c4} - r1c7{n3=n8} - 3b5{r4c4=r6c4} - 3b4{r6c3=r4c1} - 8c4{r6c4=r2c4} - 8c1{r2c1=r8c1} - 2c1{r8c1=.}
Braid[13]: => r9c9<>9
9r9c9 - r7c7{n9=n2} - 9b7{r9c2=r7c2} - r9c8{n2=n6} - r9c2{n6=n8} - 6b7{r9c2=r8c1} - r3c2{n8=n7} - r3c5{n7=n8} - r2c1{n7=n8} - r1c1{n8=n3} - 3b3{r1c7=r3c8} - 8r4{r4c1=r4c4} - 1r4{r4c4=r4c7} - 3r4{r4c7=.}
Braid[13]: => r4c7<>9
9r4c7 - r7c7{n9=n2} - 1b6{r4c7=r6c9} - 1b5{r6c4=r4c4} - r5c7{n2=n3} - 2r9{r9c8=r9c3} - 1r3{r3c9=r3c6} - 3r4{r4c8=r4c1} - 3b1{r1c1=r3c3} - 2b4{r4c1=r5c1} - 9c3{r3c3=r2c3} - 2c9{r5c9=r3c9} - 9b2{r2c4=r1c4} - 9c9{r1c9=.}
Braid[15]: => r8c9<>2
2r8c9 - r7c7{n2=n9} - 2b7{r8c1=r9c3} - 2b3{r3c9=r3c8} - 5r8{r8c9=r8c6} - r9c8{n9=n6} - 3r3{r3c8=r3c3} - 9c3{r3c3=r2c3} - 5b1{r2c3=r1c2} - 6c2{r1c2=r7c2} - r8c1{n6=n8} - 8b1{r1c1=r3c2} - r4c2{n8=n4} - r4c6{n4=n9} - 9b6{r4c8=r5c9} - 9r3{r3c9=.}
Braid[17]: => r2c7<>9
9r2c7 - r7c7{n9=n2} - r5c7{n2=n3} - 2b8{r7c4=r8c4} - 2b7{r8c1=r9c3} - 9c3{r9c3=r3c3} - 3b1{r3c3=r1c1} - 3b3{r1c8=r3c8} - 9b2{r3c6=r1c4} - 2b3{r3c8=r3c9} - 3r4{r4c1=r4c4} - 1b3{r3c9=r2c9} - 1c4{r2c4=r6c4} - 8c4{r6c4=r2c4} - r2c3{n8=n5} - r5c3{n5=n4} - 4b7{r8c3=r7c2} - 4c4{r7c4=.}
Braid[10]: => r2c1<>8
8r2c1 - r2c7{n8=n1} - 8b3{r2c7=r1c7} - 1r4{r4c7=r4c4} - 8c4{r4c4=r6c4} - 3b5{r6c4=r5c4} - 3c7{r5c7=r4c7} - 3c1{r4c1=r1c1} - 6b1{r1c1=r1c2} - 5c2{r1c2=r4c2} - 8r4{r4c2=.}
Braid[17]: => r3c6<>7
7r3c6 - r3c5{n7=n8} - 1r3{r3c6=r3c9} - r3c2{n8=n9} - r2c7{n1=n8} - 1b6{r6c9=r4c7} - 2b3{r3c9=r3c8} - 9b7{r7c2=r9c3} - 2r9{r9c3=r9c9} - 8b9{r9c9=r8c9} - 2b6{r5c9=r5c7} - 8c3{r8c3=r6c3} - 2b4{r6c3=r4c1} - r8c1{n2=n6} - 6b1{r1c1=r1c2} - r1c5{n6=n4} - r4c5{n4=n5} - 5c2{r4c2=.}
Braid[18]: => r4c7<>2
2r4c7 - r7c7{n2=n9} - 1r4{r4c7=r4c4} - r5c7{n9=n3} - r1c7{n3=n8} - 3b5{r5c4=r6c4} - 3b4{r6c3=r4c1} - 3r1{r1c1=r1c8} - 8c4{r6c4=r2c4} - 8c1{r4c1=r8c1} - r3c5{n8=n7} - 2c1{r8c1=r5c1} - 7b3{r3c8=r2c8} - r2c1{n7=n6} - 5c8{r2c8=r7c8} - r8c9{n5=n6} - 6b6{r5c9=r6c8} - 6c6{r6c6=r5c6} - 7r5{r5c6=.}
Whip[2]: => r5c3<>2
2r5c3 - 2c7{r5c7=r7c7} - 2r9{r9c8=.}
Braid[17]: => r1c2<>6
6r1c2 - r2c1{n6=n7} - 5c2{r1c2=r4c2} - 7b4{r5c1=r6c2} - 7c6{r6c6=r5c6} - 4c2{r6c2=r7c2} - 5b5{r5c6=r5c5} - 5r7{r7c5=r7c8} - 9r7{r7c8=r7c7} - 2c7{r7c7=r5c7} - r5c1{n2=n3} - r1c1{n3=n8} - r3c2{n8=n9} - 8r3{r3c2=r3c5} - r3c6{n9=n1} - 8r4{r4c5=r4c4} - 1b5{r4c4=r6c4} - 3c4{r6c4=.}
Whip[1]: => r8c1<>6
6r8c1 - 6c2{r7c2=.}
Braid[10]: => r4c8<>2
2r4c8 - 2b3{r3c8=r3c9} - 1r3{r3c9=r3c6} - 2r9{r9c9=r9c3} - r8c1{n2=n8} - r4c1{n8=n3} - 3b1{r1c1=r3c3} - 9c3{r3c3=r2c3} - 9r3{r3c2=r3c8} - 9b9{r7c8=r7c7} - 2c7{r7c7=.}
Braid[9]: => r5c1<>2
2r5c1 - r8c1{n2=n8} - 2c7{r5c7=r7c7} - 7b4{r5c1=r6c2} - r4c1{n8=n3} - 2b8{r7c4=r8c4} - r8c3{n2=n4} - 4b4{r5c3=r4c2} - r4c8{n4=n9} - 9b9{r7c8=.}
Braid[11]: => r1c7<>9
9r1c7 - r7c7{n9=n2} - r5c7{n2=n3} - 2b8{r7c4=r8c4} - r5c1{n3=n7} - r8c1{n2=n8} - r8c3{n8=n4} - r5c3{n4=n5} - 5b1{r2c3=r1c2} - 7b1{r1c2=r3c2} - r3c5{n7=n8} - 8r1{r1c4=.}
Whip[2]: => r5c7<>3
3r5c7 - 2c7{r5c7=r7c7} - 9c7{r7c7=.}
Braid[12]: => r1c2<>8
8r1c2 - r1c7{n8=n3} - 5b1{r1c2=r2c3} - r4c7{n3=n1} - 3b1{r1c1=r3c3} - 9b1{r3c3=r3c2} - 7c2{r3c2=r6c2} - r3c6{n9=n1} - r5c1{n7=n3} - 1b5{r6c6=r6c4} - 3b5{r6c4=r4c4} - 8c4{r4c4=r2c4} - r2c7{n8=.}
Braid[9]: => r5c5<>7
7r5c5 - r3c5{n7=n8} - r5c1{n7=n3} - 7b2{r1c5=r2c6} - 7c1{r2c1=r1c1} - 8b1{r1c1=r2c3} - r2c7{n8=n1} - 1r4{r4c7=r4c4} - 3b5{r4c4=r6c4} - 8c4{r6c4=.}
Braid[17]: => r6c4<>2
2r6c4 - 2b4{r6c3=r4c1} - 2r8{r8c1=r8c3} - 4b7{r8c3=r7c2} - r7c4{n4=n6} - 6r8{r8c4=r8c9} - r8c4{n6=n4} - 6b6{r5c9=r6c8} - 3r6{r6c8=r6c3} - 3b1{r3c3=r1c1} - 4b4{r6c3=r5c3} - 3c7{r1c7=r4c7} - 6r1{r1c1=r1c5} - 5c3{r5c3=r2c3} - 5c9{r2c9=r1c9} - 4b2{r1c5=r2c6} - 4c9{r2c9=r6c9} - 1b6{r6c9=.}
Braid[17]: => r9c9<>2
2r9c9 - 2b3{r3c9=r3c8} - 8b9{r9c9=r8c9} - 3r3{r3c8=r3c3} - r8c1{n8=n2} - 5b9{r8c9=r7c8} - r8c3{n2=n4} - r5c3{n4=n5} - 5r2{r2c3=r2c9} - 5c5{r5c5=r4c5} - 2r4{r4c5=r4c4} - 1r4{r4c4=r4c7} - 1b3{r2c7=r3c9} - r3c6{n1=n9} - 9b5{r4c6=r5c4} - 3b5{r5c4=r6c4} - 3b6{r6c8=r4c8} - 9r4{r4c8=.}
Braid[9]: => r7c5<>2
2r7c5 - 2b9{r7c7=r9c8} - 2b5{r4c5=r4c4} - 2b3{r3c8=r3c9} - 2b4{r4c1=r6c3} - 1r3{r3c9=r3c6} - 1b5{r6c6=r6c4} - 3r6{r6c4=r6c8} - 6c8{r6c8=r7c8} - 5r7{r7c8=.}
Whip[1]: => r4c4<>2
2r4c4 - 2c5{r4c5=.}
Braid[11]: => r6c6<>6
6r6c6 - 6b6{r6c8=r5c9} - r9c9{n6=n8} - 6r8{r8c9=r8c4} - r8c9{n8=n5} - 2b8{r8c4=r7c4} - 5b8{r8c6=r7c5} - 2c7{r7c7=r5c7} - 4r7{r7c5=r7c2} - r5c5{n2=n4} - 4r4{r4c4=r4c8} - 9b6{r4c8=.}
Braid[8]: => r1c1<>7
7r1c1 - r2c1{n7=n6} - 7r5{r5c1=r5c6} - 6c6{r5c6=r8c6} - 5b8{r8c6=r7c5} - 5b9{r7c8=r8c9} - 5r5{r5c5=r5c3} - 5r2{r2c3=r2c8} - 7r2{r2c8=.}
Braid[8]: => r1c8<>3
3r1c8 - 3b6{r4c8=r4c7} - 1r4{r4c7=r4c4} - 3c1{r4c1=r5c1} - 3b5{r5c4=r6c4} - 7b4{r5c1=r6c2} - 7r1{r1c2=r1c5} - r3c5{n7=n8} - 8c4{r1c4=.}
Braid[12]: => r2c6<>1
1r2c6 - r3c6{n1=n9} - 1b3{r2c7=r3c9} - 1r6{r6c9=r6c4} - 2b3{r3c9=r3c8} - 2b9{r7c8=r7c7} - r5c7{n2=n9} - 2b8{r7c4=r8c4} - 2c1{r8c1=r4c1} - 9b5{r5c4=r4c4} - 3b5{r4c4=r5c4} - 3b4{r5c1=r6c3} - 3r3{r3c3=.}
Braid[11]: => r2c4<>6
6r2c4 - r2c1{n6=n7} - r5c1{n7=n3} - 7r5{r5c1=r5c6} - 3r1{r1c1=r1c7} - 6c6{r5c6=r8c6} - 8b3{r1c7=r2c7} - 5c6{r8c6=r4c6} - 5b4{r4c2=r5c3} - r2c3{n5=n9} - 9c6{r2c6=r3c6} - 1b2{r3c6=.}
Braid[12]: => r3c9<>1
1r3c9 - 1c6{r3c6=r6c6} - 2b3{r3c9=r3c8} - 2r9{r9c8=r9c3} - 3r3{r3c8=r3c3} - r8c1{n2=n8} - r8c3{n8=n4} - r1c1{n8=n6} - 6b2{r1c4=r2c6} - 7c6{r2c6=r5c6} - 4c6{r5c6=r4c6} - 4b4{r4c2=r6c2} - 7r6{r6c2=.}
Hidden Single: 1 in r3 => r3c6=1
Whip[4]: => r4c8<>3
3r4c8 - r4c7{n3=n1} - 1b5{r4c4=r6c4} - 3r6{r6c4=r6c3} - 3r3{r3c3=.}
Braid[6]: => r7c4<>6
6r7c4 - 6r8{r8c4=r8c9} - 6b6{r5c9=r6c8} - 5b9{r8c9=r7c8} - 2r7{r7c8=r7c7} - 2c8{r9c8=r3c8} - 3c8{r3c8=.}
Braid[7]: => r4c4<>4
4r4c4 - r4c8{n4=n9} - r4c6{n9=n5} - r4c2{n5=n8} - 5b8{r8c6=r7c5} - 4r7{r7c5=r7c2} - r6c2{n4=n7} - r6c6{n7=.}
Braid[7]: => r4c4<>9
9r4c4 - r4c8{n9=n4} - 1r4{r4c4=r4c7} - r4c6{n4=n5} - r2c7{n1=n8} - 5b4{r4c2=r5c3} - r2c3{n5=n9} - 9c6{r2c6=.}
Whip[7]: => r1c5<>8
8r1c5 - r1c7{n8=n3} - r1c1{n3=n6} - r2c1{n6=n7} - r5c1{n7=n3} - 3r4{r4c1=r4c4} - 8b5{r4c4=r6c4} - 1c4{r6c4=.}
Braid[7]: => r3c8<>2
2r3c8 - r3c9{n2=n9} - 2r9{r9c8=r9c3} - r8c1{n2=n8} - 9c3{r9c3=r2c3} - 9b2{r2c4=r1c4} - 8r1{r1c4=r1c7} - 3b3{r1c7=.}
Hidden Single: 2 in r3 => r3c9=2
Braid[7]: => r6c9<>4
4r6c9 - r4c8{n4=n9} - r6c6{n4=n7} - 1b6{r6c9=r4c7} - 3b6{r4c7=r6c8} - r3c8{n3=n7} - 7b2{r3c5=r1c5} - 7c2{r1c2=.}
Whip[7]: => r5c6<>4
4r5c6 - 7r5{r5c6=r5c1} - r2c1{n7=n6} - 6c6{r2c6=r8c6} - 5c6{r8c6=r4c6} - 5b4{r4c2=r5c3} - 3r5{r5c3=r5c4} - 9b5{r5c4=.}
Braid[6]: => r7c7<>2
2r7c7 - r5c7{n2=n9} - r7c4{n2=n4} - r4c8{n9=n4} - 4b7{r7c2=r8c3} - 4r5{r5c3=r5c5} - 2r5{r5c5=.}
Hidden Single: 2 in c7 => r5c7=2
Hidden Single: 9 in c7 => r7c7=9
Braid[6]: => r6c5<>6
6r6c5 - r6c9{n6=n1} - 2r6{r6c5=r6c3} - r4c7{n1=n3} - r4c1{n3=n8} - 3r6{r6c8=r6c4} - 8r6{r6c4=.}
Braid[8]: => r1c4<>8
8r1c4 - r1c7{n8=n3} - r3c5{n8=n7} - r3c8{n7=n9} - r4c8{n9=n4} - 9r1{r1c8=r1c2} - 5b1{r1c2=r2c3} - r2c8{n5=n7} - 7r1{r1c8=.}
Whip[2]: => r1c1<>6
6r1c1 - 3r1{r1c1=r1c7} - 8r1{r1c7=.}
Hidden Single: 6 in c1 => r2c1=6
Hidden Single: 7 in c1 => r5c1=7
Whip[2]: => r4c4<>3
3r4c4 - 3c7{r4c7=r1c7} - 3c1{r1c1=.}
Whip[5]: => r8c6<>4
4r8c6 - 4b7{r8c3=r7c2} - r6c2{n4=n8} - r4c2{n8=n5} - 5c6{r4c6=r5c6} - 6c6{r5c6=.}
Whip[5]: => r6c4<>4
4r6c4 - 4b8{r7c4=r7c5} - 4c2{r7c2=r4c2} - r4c8{n4=n9} - r4c6{n9=n5} - 5c5{r4c5=.}
Braid[6]: => r5c4<>6
6r5c4 - 3b5{r5c4=r6c4} - 6c6{r5c6=r8c6} - 1r6{r6c4=r6c9} - 5r8{r8c6=r8c9} - 6c9{r6c9=r9c9} - 8c9{r9c9=.}
Braid[7]: => r5c4<>4
4r5c4 - 3r5{r5c4=r5c3} - 4b8{r7c4=r7c5} - 4b2{r1c5=r2c6} - 5b8{r7c5=r8c6} - 4c9{r2c9=r1c9} - 5c9{r1c9=r2c9} - 5c3{r2c3=.}
Braid[7]: => r2c3<>9
9r2c3 - 5b1{r2c3=r1c2} - 9r3{r3c2=r3c8} - r4c8{n9=n4} - r4c2{n4=n8} - r4c4{n8=n1} - r4c7{n1=n3} - 3c8{r6c8=.}
Whip[6]: => r2c9<>5
5r2c9 - r2c3{n5=n8} - r1c1{n8=n3} - r3c3{n3=n9} - r9c3{n9=n2} - 2b9{r9c8=r7c8} - 5c8{r7c8=.}
Whip[3]: => r4c5<>5
5r4c5 - 5b8{r7c5=r8c6} - 5c9{r8c9=r1c9} - 5c2{r1c2=.}
Braid[5]: => r2c8<>4
4r2c8 - 5r2{r2c8=r2c3} - 7r2{r2c8=r2c6} - r6c6{n7=n4} - 4r4{r4c5=r4c2} - 5c2{r4c2=.}
Whip[4]: => r1c4<>4
4r1c4 - 4b8{r7c4=r7c5} - 4b7{r7c2=r8c3} - 4r5{r5c3=r5c9} - 4r2{r2c9=.}
Whip[5]: => r4c2<>8
8r4c2 - r6c2{n8=n4} - r6c6{n4=n7} - 7r2{r2c6=r2c8} - 5r2{r2c8=r2c3} - 5c2{r1c2=.}
Whip[3]: => r4c5<>4
4r4c5 - r4c2{n4=n5} - r4c6{n5=n9} - r4c8{n9=.}
Braid[4]: => r6c4<>8
8r6c4 - r4c5{n8=n2} - r6c2{n8=n4} - r6c5{n4=n7} - r6c6{n7=.}
Whip[3]: => r2c3<>8
8r2c3 - r2c7{n8=n1} - 1r4{r4c7=r4c4} - 8c4{r4c4=.}
Naked Single: r2c3=5
Hidden Single: 5 in c2 => r4c2=5
Whip[2]: => r5c6<>9
9r5c6 - 5c6{r5c6=r8c6} - 6c6{r8c6=.}
Whip[2]: => r2c9<>9
9r2c9 - 9b6{r5c9=r4c8} - 9c6{r4c6=.}
Braid[3]: => r1c8<>4
4r1c8 - r4c8{n4=n9} - 5b3{r1c8=r1c9} - 9c9{r1c9=.}
Whip[1]: => r5c9<>4
4r5c9 - 4c8{r4c8=.}
Whip[2]: => r7c5<>4
4r7c5 - 4b7{r7c2=r8c3} - 4r5{r5c3=.}
Whip[1]: => r2c4<>4
4r2c4 - 4b8{r7c4=.}
Whip[2]: => r8c4<>6
6r8c4 - r7c5{n6=n5} - r8c6{n5=.}
Whip[2]: => r8c9<>8
8r8c9 - 5r8{r8c9=r8c6} - 6r8{r8c6=.}
Hidden Single: 8 in c9 => r9c9=8
Whip[3]: => r1c4<>9
9r1c4 - 6c4{r1c4=r6c4} - 6b6{r6c8=r5c9} - 9r5{r5c9=.}
Naked Single: r1c4=6
Whip[1]: => r2c8<>9
9r2c8 - 9b2{r2c4=.}
Naked Single: r2c8=7
Hidden Single: 7 in c6 => r6c6=7
Whip[1]: => r5c9<>6
6r5c9 - 6r6{r6c8=.}
stte
127 Steps!Time elapsed: 1655.0 ms