The New Sudoku Players' Forum

[Mauriès Robert]

Hi all,
A friend suggested that I solve the following puzzle and I confess that I can't find a satisfactory resolution.
What would be your best resolution?

89....26.2......575.12.....1.5.376.....8.6......12.7.......45..954.....2.1.....46

puzzle: Show

Robert

[DEFISE]

Hi Robert,
I did not find anything exceptional:

Single(s): 2r9c6
Box/Line: 6r8b8 => -6r7c4 -6r7c5
Box/Line: 4c1b4 => -4r4c2 -4r5c2 -4r6c2
Hidden pairs: 67r3c25 => -3r3c2 -4r3c2 -4r3c5 -8r3c5 -9r3c5
Single(s): 4r2c2
Box/Line: 4r3b3 => -4r1c9
Box/Line: 3b1c3 => -3r5c3 -3r6c3 -3r7c3 -3r9c3

If you allow me only one joker:
try 3r1c3 using singles and box/lines => contradiction => -3r1c3
Single(s): 7r1c3, 6r3c2, 3r2c3, 7r3c5, 8r9c3

whip[4]: r1c9{n1 n3}- r1c6{n3 n5}- b5n5{r6c6 r5c5}- c5n4{r5 .} => -1r1c5
Naked triplets: 459c5r159 => -9r2c5 -9r7c5
whip[7]: r1n1{c9 c6}- c6n5{r1 r6}- r5n5{c5 c9}- c9n1{r5 r7}- r7c5{n1 n8}- r8c6{n8 n3}- r3n3{c6 .} => -3r1c9
Single(s): 1r1c9
Box/Line: 3r1b2 => -3r3c6
whip[7]: r7n9{c8 c4}- r2n9{c4 c6}- c6n1{r2 r8}- r7c5{n1 n8}- r7c9{n8 n3}- r8c7{n3 n8}- r2c7{n8 .} => -9r9c7
Single(s): 3r9c7, 7r9c1, 7r5c2
Box/Line: 3r8b8 => -3r7c4
Box/Line: 9r9b8 => -9r7c4
Single(s): 7r7c4, 7r8c8
whip[7]: r5c1{n3 n4}- r6n4{c1 c9}- r6n8{c9 c8}- r4c9{n8 n9}- r5c7{n9 n1}- r8c7{n1 n8}- r7c9{n8 .} => -3r6c2
STTE

[denis_berthier]

.
At the request of Robert.
SER = 8.9, W = 7, nothing noticeable.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 8     9     37    ! 3457  1457  135   ! 2     6     134   !
   ! 2     346   36    ! 3469  14689 1389  ! 13489 5     7     !
   ! 5     3467  1     ! 2     46789 389   ! 3489  389   3489  !
   +-------------------+-------------------+-------------------+
   ! 1     28    5     ! 49    3     7     ! 6     289   489   !
   ! 347   237   2379  ! 8     459   6     ! 1349  1239  13459 !
   ! 346   368   3689  ! 1     2     59    ! 7     389   34589 !
   +-------------------+-------------------+-------------------+
   ! 367   23678 23678 ! 379   1789  4     ! 5     13789 1389  !
   ! 9     5     4     ! 367   1678  138   ! 138   1378  2     !
   ! 37    1     378   ! 3579  5789  2     ! 389   4     6     !
   +-------------------+-------------------+-------------------+
180 candidates.

Simplest first solution:

Code: Select all

hidden-pairs-in-a-row: r3{n6 n7}{c2 c5} ==> r3c5≠9, r3c5≠8, r3c5≠4, r3c2≠4, r3c2≠3
hidden-single-in-a-block ==> r2c2=4
whip[1]: b1n3{r2c3 .} ==> r5c3≠3, r6c3≠3, r7c3≠3, r9c3≠3
whip[1]: b2n4{r1c5 .} ==> r1c9≠4
biv-chain[3]: r5n5{c9 c5} - r6c6{n5 n9} - b4n9{r6c3 r5c3} ==> r5c9≠9
z-chain[4]: c5n4{r1 r5} - b5n5{r5c5 r6c6} - r1n5{c6 c4} - r1n4{c4 .} ==> r1c5≠1, r1c5≠7
biv-chain[3]: r1n1{c9 c6} - c6n5{r1 r6} - b6n5{r6c9 r5c9} ==> r5c9≠1
t-whip[5]: r1c3{n7 n3} - r1c9{n3 n1} - r1c6{n1 n5} - r6c6{n5 n9} - c3n9{r6 .} ==> r5c3≠7
biv-chain[4]: c1n6{r7 r6} - b4n4{r6c1 r5c1} - r5n7{c1 c2} - r3c2{n7 n6} ==> r7c2≠6
t-whip[6]: r1c3{n7 n3} - r1c9{n3 n1} - r1c6{n1 n5} - r6c6{n5 n9} - c3n9{r6 r5} - c3n2{r5 .} ==> r7c3≠7
finned-x-wing-in-columns: n7{c3 c4}{r1 r9} ==> r9c5≠7
t-whip[6]: r9n7{c3 c4} - r9n5{c4 c5} - r1c5{n5 n4} - r5c5{n4 n9} - r5c3{n9 n2} - c2n2{r5 .} ==> r7c2≠7
z-chain[4]: r5n7{c2 c1} - r9c1{n7 n3} - r7c2{n3 n8} - r4c2{n8 .} ==> r5c2≠2
z-chain[4]: r5c2{n3 n7} - r5c1{n7 n4} - r6n4{c1 c9} - c9n5{r6 .} ==> r5c9≠3
t-whip[5]: c2n3{r6 r7} - c2n2{r7 r4} - c8n2{r4 r5} - r5n1{c8 c7} - r5n3{c7 .} ==> r6c1≠3
t-whip[7]: r9c3{n8 n7} - r1c3{n7 n3} - r1c9{n3 n1} - r1c6{n1 n5} - r6c6{n5 n9} - c3n9{r6 r5} - c3n2{r5 .} ==> r7c3≠8
biv-chain[5]: b4n4{r5c1 r6c1} - c1n6{r6 r7} - r7c3{n6 n2} - r5n2{c3 c8} - b6n1{r5c8 r5c7} ==> r5c7≠4
hidden-single-in-a-column ==> r3c7=4
z-chain[5]: r6n4{c9 c1} - c1n6{r6 r7} - r7c3{n6 n2} - b4n2{r5c3 r4c2} - r4n8{c2 .} ==> r6c9≠8
z-chain[5]: b6n8{r6c8 r4c9} - r4c2{n8 n2} - c8n2{r4 r5} - c8n1{r5 r8} - c8n7{r8 .} ==> r7c8≠8
z-chain[5]: b6n8{r6c8 r4c9} - r4c2{n8 n2} - c8n2{r4 r5} - c8n1{r5 r7} - c8n7{r7 .} ==> r8c8≠8
z-chain[6]: r4n9{c9 c4} - r4n4{c4 c9} - r6n4{c9 c1} - c1n6{r6 r7} - r7c3{n6 n2} - r5c3{n2 .} ==> r5c8≠9, r5c7≠9
whip[6]: r2n1{c6 c7} - r1c9{n1 n3} - r3n3{c9 c6} - r8c6{n3 n8} - c7n8{r8 r9} - c7n9{r9 .} ==> r1c6≠1
hidden-single-in-a-row ==> r1c9=1
t-whip[6]: c7n9{r9 r2} - r3n9{c9 c6} - r6c6{n9 n5} - r1c6{n5 n3} - r1c3{n3 n7} - r9c3{n7 .} ==> r9c7≠8
finned-x-wing-in-columns: n8{c7 c6}{r8 r2} ==> r2c5≠8
whip[1]: c5n8{r9 .} ==> r8c6≠8
biv-chain[3]: r8c6{n3 n1} - r7n1{c5 c8} - b9n7{r7c8 r8c8} ==> r8c8≠3
biv-chain[3]: b2n1{r2c5 r2c6} - r2n8{c6 c7} - r8n8{c7 c5} ==> r8c5≠1
biv-chain[4]: r7n1{c8 c5} - r2n1{c5 c6} - r2n8{c6 c7} - c7n9{r2 r9} ==> r7c8≠9
biv-chain[4]: r8n8{c5 c7} - r2n8{c7 c6} - c6n1{r2 r8} - r8c8{n1 n7} ==> r8c5≠7
biv-chain[4]: r1n7{c3 c4} - r3c5{n7 n6} - r8c5{n6 n8} - r9n8{c5 c3} ==> r9c3≠7
singles ==> r9c3=8, r1c3=7, r3c2=6, r2c3=3, r3c5=7, r5c2=7, r3c6≠3
naked-triplets-in-a-column: c5{r1 r5 r9}{n5 n4 n9} ==> r7c5≠9, r2c5≠9
finned-x-wing-in-rows: n9{r7 r4}{c4 c9} ==> r6c9≠9
biv-chain[2]: c7n9{r2 r9} - r7n9{c9 c4} ==> r2c4≠9
stte

[Mauriès Robert]

Hi Denis and François,
Thank you for your resolutions. I will advise my friend who submitted this puzzle to look at them, possibly adapting them in terms of TDP if he is not familiar with Denis' theory and notations.
Robert

[denis_berthier]

.
Notice that there's a single (BRT or W1) anti-backdoor: n4r4c4. Unfortunately, there's no easy way of eliminating this candidate.

[DEFISE]

I forgot to specify that I did not implement the exotic patterns (MSLS, Exocet, etc) nor even the loops.
I don't know if this is the case with SudokuRules by Denis.

[denis_berthier]

I forgot to specify that I did not implement the exotic patterns (MSLS, Exocet, etc) nor even the loops.
I don't know if this is the case with SudokuRules by Denis.

SudoRules allows to activate some exotic patterns: sk-loops, J-Exocets (as per David P. Bird, but not the more general, partly undefined exocets) and the more recent Tridagons and Tridagon-Forcing-Whips. It doesn't have MSLS. I didn't try any of these on this puzzle.
Nor did I try any rule based on uniqueness.