The New Sudoku Players' Forum

[denis_berthier]

.
Diagonal cross 9.1
Here is a hard puzzle with the same pattern as here: http://forum.enjoysudoku.com/diagonal-cross-5-6-t38788.html
It's on the hard side of the 9.1s.

Code: Select all

   +-------+-------+-------+
   ! . . 9 ! . . . ! 5 . . !
   ! . 4 . ! 7 . 9 ! . 8 . !
   ! 1 . . ! . 3 . ! . . 2 !
   +-------+-------+-------+
   ! . 9 . ! . . . ! . 3 . !
   ! . . 4 ! . . . ! 8 . . !
   ! . 5 . ! . . . ! . 6 . !
   +-------+-------+-------+
   ! 3 . . ! . 9 . ! . . 8 !
   ! . 6 . ! 5 . 2 ! . 7 . !
   ! . . 7 ! . . . ! 6 . . !
   +-------+-------+-------+

..9...5...4.7.9.8.1...3...2.9.....3...4...8...5.....6.3...9...8.6.5.2.7...7...6.. # 96092 FNBTHYK C24.m/S8.f

24 givens, SER = 9.1

[DEFISE]

By applying "simplest first" I obtain solutions with whips [<= 10], g-whips [<= 10] and
s2-whips [<= 10], but all boring because having a lot of steps.
By trying to reduce the number of steps I found the following 2 solutions:

1) In gW[10] :

Hidden Text: Show

Singles: 7r7c6, 6r7c4
Alignment: 4r7b9 => -4r8c7 -4r8c9 -4r9c8 -4r9c9
Alignment: 3r8b9 => -3r9c9
Hidden pair: 56r3c36 => -8r3c3 -4r3c6 -8r3c6
Hidden pair: 49c1r89 => -8r8c1 -2r9c1 -5r9c1 -8r9c1
Singles: 5r2c1, 6r3c3, 5r3c6, 5r7c3
Alignment: 2b7c2 => -2r1c2 -2r5c2

whip[7]: r3n7{c7 c2}- r1n7{c1 c9}- r1n3{c9 c2}- c2n8{r1 r9}- r9n2{c2 c8}- c8n5{r9 r5}- c8n9{r5 .} => -9r3c7
Single: 9r3c8

whip[10]: r2c7{n3 n1}- r1c8{n1 n4}- r7n4{c8 c7}- r3c7{n4 n7}- r4c7{n7 n2}- c3n2{r4 r6}- r6c7{n2 n9}- r5n9{c9 c4}- r5n2{c4 c5}- r2n2{c5 .} => -3r2c3
Singles: 2r2c3, 3r6c3, 3r1c2

whip[10]: r3n7{c7 c2}- c2n8{r3 r9}- b1n8{r3c2 r1c1}- r1n7{c1 c9}- c9n6{r1 r2}- r2c5{n6 n1}- r9c5{n1 n4}- r8c5{n4 n8}- r6c5{n8 n2}- r6c1{n2 .} => -7r6c7

g-whip[10]: r1n7{c1 c9}- c7n7{r3 r4}- c5n7{r4 r5}- c5n5{r5 r4}- c5n6{r4 r12} – r1n6{c6 c5} – c5n2{r1 r6}
- c7n2{r6 r7}- r7c2{n2 n1}- r5c2{n1 .} => -7r6c1

whip[7]: r3c2{n8 n7}- c7n7{r3 r4}- c1n7{r4 r5}- r1c1{n7 n8}- r6c1{n8 n2}- c7n2{r6 r7}- c2n2{r7 .} => -8r9c2
Singles: 8r3c2, 7r1c1, 4r3c4, 7r3c7, 7r5c2, 1r4c3, 8r8c3
Hidden pair: 57r4c59 => -2r4c5 -4r4c5 -6r4c5 -8r4c5 -4r4c9

whip[10]: r4c7{n4 n2}- r4c4{n2 n8}- r6c6{n8 n1}- r6c7{n1 n9}- r6c4{n9 n2}- r1c4{n2 n1}- r2c5{n1 n6}- r5c5{n6 n5}- r4c5{n5 n7}- c9n7{r4 .} => -4r6c9
STTE

2) In S2-whip[14]

Hidden Text: Show

The same basics as for the 1st solution, and then:

S2-whip[14]: r1n3{c9 c2}- r2c3{n3 n2}- r1c1{n2 n8}- c2n8{r1 r9}- r9n2{c2 c8}- {n2r7c7 HP :n27r46c7} –
{n1r6c7 NP :n27r6c17} – {n2r6c5 HP :n57r45c5} – c5n2{r4 r1} – r1n6{c5 c6} – c5n6{r2 .} => -7r1c9

Singles: 7r3c7, 8r3c2, 4r3c4, 9r3c8, 8r8c3
Alignment: 1c3b4 => -1r5c2

whip[9]: r2c3{n2 n3}- r2c7{n3 n1}- r1c8{n1 n4}- r7n4{c8 c7}- r4c7{n4 n2}- r6c7{n2 n9}- r5n9{c9 c4}- r5n2{c4 c1}- r1n2{c1 .} => -2r2c5

Singles: 2r2c3, 7r1c1, 3r1c2, 1r4c3, 7r5c2, 3r6c3
Hidden pair: 57r4c59 => -2r4c5 -4r4c5 -6r4c5 -8r4c5 -4r4c9

whip[10]: r4c7{n4 n2}- r4c4{n2 n8}- r6c6{n8 n1}- r6c7{n1 n9}- r6c4{n9 n2}- r1c4{n2 n1}- r2c5{n1 n6}- r5c5{n6 n5}- r4c5{n5 n7}- c9n7{r4 .} => -4r6c9

STTE

 

[ghfick]

Hi DEFISE,

I see you are using SudoRules. Can you help us to understand the whips? In particular, can you give an explanation of the first whip ? :

whip[7]: r3n7{c7 c2}- r1n7{c1 c9}- r1n3{c9 c2}- c2n8{r1 r9}- r9n2{c2 c8}- c8n5{r9 r5}- c8n9{r5 .} => -9r3c7

I think that one needs to see the grids [with candidates] in all 4 formats [rc, rn, cn and bn] to follow the notation. Maybe you can help us. Many forum members would like help here and in terms that are specific to the 9x9 Sudoku and using [when possible] the terms most widely used on this forum.

Gordon

[DEFISE]

Hi DEFISE,
I see you are using SudoRules. Can you help us to understand the whips? In particular, can you give an explanation of the first whip ? :

whip[7]: r3n7{c7 c2}- r1n7{c1 c9}- r1n3{c9 c2}- c2n8{r1 r9}- r9n2{c2 c8}- c8n5{r9 r5}- c8n9{r5 .} => -9r3c7

I think that one needs to see the grids [with candidates] in all 4 formats [rc, rn, cn and bn] to follow the notation.
Gordon

Hi Gordon,
First of all, to understand this whip you just need to see the grid with candidates in classic format.
9r3c7 is the target of the whip. The demonstration that 9r3c7 is false is this one :

If we assume 9r3c7 to be true,
then 7r3c7 (r3n7c7) is false => 7r3c2 (r3n7c2) is true because it’s the only 7 of r3 compatible with the target.
Then 7r1c1 (r1n7c1) is false => 7r1c9 (r1n7c9) is true because it’s the only 7 of r1 compatible with the target and 7r3c2
etc… and last step is:
then 9r5c8 (c8n9r5) is false => there is no 9 in c8 which is compatible with the target and all the candidates deduced as true (i.e 7r3c2, 7r1c9, 3r1c2, 8r9c2, 2r9c8, 5r5c8).
So we conclude that the target 9r3c7 cannot be true.