The New Sudoku Players' Forum

[Mauriès Robert]

Hi all,
For the puzzle I propose below, I have not found a simple resolution in a few steps.
Your resolutions are therefore welcome.

513....7..6....13...2.1.6.8....81.........5.2.4.95....3.71.4......86......17..4..

puzzle: Show

solution: Show

Robert

[denis_berthier]

.
For a random puzzle with SER = 8.9, you can't expect a solution in few steps.

[Mauriès Robert]

Hi all,
While waiting for your resolutions, here is the one I propose, in three steps with TDP.

1) P'(2r6c1) : -2r6c1 => 2r6c6 ->34r45c4->3r9c5->37r8c79->1r6c9->68r6c38->... => -18r6c1 => r5c1=1 and r2c1=8 => -7r3c6.

step1: Show

2) P'(5r2c4) : -5r2c4 => [ 5r2c9 and 5r3c4->3r3c6->3r9c5 ]->{ [ 9r9c9->( 9r4c7 and 9r1c5) ]->9r7c2 }->9r5c3->... => No 9 possible on r2 => r2c4=5 and 4 validations by induction.

step2: Show

3) P'(4r1c5) : -4r1c5 => 9r1c5->3r3c6->3r9c5->5r9c9->5r7c2->5r4c3->6r4c9->... => no candidate possible in r7c9 => r1c5=4 and end of the puzzle by induction.

step3: Show

Robert

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 5     1     3     ! 6     49    8     ! 2     7     49    !
   ! 4789  6     489   ! 245   2479  279   ! 1     3     459   !
   ! 479   79    2     ! 345   1     379   ! 6     459   8     !
   +-------------------+-------------------+-------------------+
   ! 279   23579 569   ! 234   8     1     ! 379   469   34679 !
   ! 1789  379   689   ! 34    347   367   ! 5     14689 2     !
   ! 1278  4     68    ! 9     5     2367  ! 378   168   1367  !
   +-------------------+-------------------+-------------------+
   ! 3     2589  7     ! 1     29    4     ! 89    25689 569   !
   ! 249   259   459   ! 8     6     2359  ! 379   1259  13579 !
   ! 6     2589  1     ! 7     239   2359  ! 4     2589  359   !
   +-------------------+-------------------+-------------------+
165 candidates.

For a random puzzle with SER = 8.9, you can't expect a solution in few steps.

Of course, I meant, a few steps of reasonable lengths. (The puzzle is in W6, so "reasonable" is not more than 7 or 8.) Otherwise, here's one in 1 step:

FORCING[3]-T&E(W1) applied to trivalue candidates n3r9c9, n5r9c9 and n9r9c9 :
===> 11 values decided in the three cases: n4r5c4 n7r3c2 n4r3c1 n5r4c3 n4r8c3 n8r2c1 n8r9c2 n1r5c1 n9r2c3 n8r7c7 n4r4c8
===> 70 candidates eliminated in the three cases: n4r2c1 n7r2c1 n9r2c1 n4r2c3 n8r2c3 n4r2c4 n2r2c5 n9r2c5 n9r2c6 n9r2c9 n7r3c1 n9r3c1 n9r3c2 n4r3c4 n7r3c6 n4r3c8 n2r4c1 n9r4c1 n5r4c2 n7r4c2 n6r4c3 n9r4c3 n4r4c4 n3r4c7 n7r4c7 n6r4c8 n9r4c8 n3r4c9 n4r4c9 n9r4c9 n7r5c1 n8r5c1 n9r5c1 n7r5c2 n9r5c3 n3r5c4 n4r5c5 n3r5c6 n1r5c8 n4r5c8 n6r5c8 n1r6c1 n8r6c1 n7r6c6 n8r6c7 n3r6c9 n6r6c9 n8r7c2 n9r7c7 n2r7c8 n8r7c8 n9r7c8 n4r8c1 n9r8c2 n5r8c3 n9r8c3 n2r8c6 n9r8c7 n5r8c8 n9r8c8 n5r8c9 n9r8c9 n2r9c2 n5r9c2 n9r9c2 n9r9c5 n2r9c6 n3r9c6 n5r9c8 n8r9c8
stte

[P.O.]

Code: Select all

after singles and intersections:

r1n9{c9 c5} - r7c5{n9 n2} - r9c5{n2n9 n3} - c9{r2r9}{n5n9} => r4c9 r7c9 r8c9 <> 9

       / n5r2c9
r3c8{n5         } - c4n3{r3 r4r5} - c5n3{r5 r9} - r9c9{n3n5 n9} -  r1c9{n9 n4} => r3c8 <> 4
       \ n5r3c4

c3n4{r8 r2} - r3{c1c2c6}{n3n7n9} - b8n3{r8c6r9c6 r9c5} - c9{r1r2r9}{n4n5n9} - b2{r1c5r2c5r2c6}{n2n7n9} - c4{r2r3r5}{n3n4n5} - c2n3{r5 r4} - r4n5{c2 c3} => r8c3 <> 5

single: ( r4c3b4 n5 )
intersections: c8n4{r4r5} => r4c9 <> 4
               r4n6{c8c9} => r5c8 r6c8 r6c9 <> 6
               
r1n9{c9 c5} - r7c5{n9 n2} - r9c5{n2n9 n3} - c9{r2r9}{n5n9} - r7c9{n5 n6} - r4n6{c9 c8} - r4n4{c8 c4} - r5{c2c4c5}{n3n7n9} - r7n9{c2 c7c8} => r9c9 <> 9

intersection: c9n9{r1r2} => r3c8 <> 9
ste.


[DEFISE]

Initial basics :
Single(s): 8r1c6, 6r1c4, 2r1c7, 6r9c1
Box/Line: 5c4b2 => -5r2c6 -5r3c6
Box/Line: 8b7c2 => -8r5c2

As I didn't find anything interesting with chains of length <=8 here is my solution with a T&E(S2):

3r3c6 true =>
Single 3r3c6, 3r9c5
Box/Line: 7r3b1 => -7r2c1
Box/Line: 3r6b6 => -3r4c7 -3r4c9
Hidden pairs: 37r8c79 => -9r8c7 -1r8c9 -5r8c9 -9r8c9
Single(s): 1r8c8, 1r5c1, 1r6c9, 3r6c7, 7r8c7, 9r4c7, 8r7c7, 3r8c9, 8r9c2, 7r4c9, 2r4c1, 2r6c6, 7r6c1, 7r3c2, 2r8c2, 2r9c8, 2r7c5, 2r2c4, 5r2c9, 9r9c9, 4r1c9, 9r1c5, 7r2c6, 4r2c5, 5r3c4, 9r3c8, 4r3c1, 7r5c5, 6r5c6, 6r7c9, 5r7c8, 9r7c2
=> r8c1 empty

=> -3r3c6
STTE

[DEFISE]

Nevertheless, to respond to Robert's challenge, here is what I propose:

Single(s): 8r1c6, 6r1c4, 2r1c7, 6r9c1
Box/Line: 5c4b2 => -5r2c6 -5r3c6
Box/Line: 8b7c2 => -8r5c2

whip[9]: c6n5{r8 r9}- c2n5{r9 r4}- c2n3{r4 r5}- c5n3{r5 r9}- r9c9{n3 n9}- b3n9{r1c9 r3c8}- r3c2{n9 n7}- r3c1{n7 n4}- r8n4{c1 .} => -5r8c3
Single(s): 5r4c3
Box/Line: 6r4b6 => -6r5c8 -6r6c8 -6r6c9

whip[10]: r5c4{n4 n3}- c5n3{r5 r9}- r5c5{n3 n7}- b5n4{r5c5 r4c4}- r3c4{n4 n5}- r2n5{c4 c9}- r9c9{n5 n9}- r1n9{c9 c5}- r7n9{c5 c2}- r5c2{n9 .} => -4r5c8
Box/Line: 4r5b5 => -4r4c4
Hidden pairs: 46r4c89 => -9r4c8 -3r4c9 -7r4c9 -9r4c9
Hidden pairs: 17c9r68 => -3r6c9 -3r8c9 -5r8c9 -9r8c9
STTE