The New Sudoku Players' Forum

[coloin]

Code: Select all

+---+---+---+
|..3|45.|.89|
|...|.89|23.|
|..9|3.2|4.5|
+---+---+---+
|...|...|8.3|
|...|...|95.|
|9..|8.5|.24|
+---+---+---+
|392|...|54.|
|.18|..4|...|
|7.4|...|...|
+---+---+---+


a new BxB 11, with SE 11.7.11.7/9.5
at any rate not a simple tridagon insertion....
edit
although if you guess that the 3 goes at r6c5 then this implies the 2 goes into r5c4 ..... is this assumptive technique valid ?

[denis_berthier]

.
Not the simplest tridagon but the next simplest case: with 2 guardians.

As in many cases, replacement leads to an easy solution:

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 126    267    3      ! 4      5      167    ! 167    8      9      !
   ! 1456   4567   1567   ! 167    8      9      ! 2      3      167    !
   ! 168    678    9      ! 3      167    2      ! 4      167    5      !
   +----------------------+----------------------+----------------------+
   ! 12456  24567  1567   ! 12679  124679 167    ! 8      167    3      !
   ! 12468  234678 167    ! 1267   123467 1367   ! 9      5      167    !
   ! 9      367    167    ! 8      1367   5      ! 167    2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      1678   !
   ! 56     1      8      ! 25679  23679  4      ! 367    679    267    !
   ! 7      56     4      ! 12569  12369  1368   ! 136    169    1268   !
   +----------------------+----------------------+----------------------+
178 candidates.

Code: Select all

Trid-OR2-relation for digits 1, 7 and 6 in blocks:
        b2, with cells (marked #): r1c6, r2c4, r3c5
        b3, with cells (marked #): r1c7, r2c9, r3c8
        b5, with cells (marked #): r4c6, r5c4, r6c5
        b6, with cells (marked #): r4c8, r5c9, r6c7
with 2 guardians (in cells marked @): n2r5c4 n3r6c5
   +----------------------+----------------------+----------------------+
   ! 126    267    3      ! 4      5      167#   ! 167#   8      9      !
   ! 1456   4567   1567   ! 167#   8      9      ! 2      3      167#   !
   ! 168    678    9      ! 3      167#   2      ! 4      167#   5      !
   +----------------------+----------------------+----------------------+
   ! 12456  24567  1567   ! 12679  124679 167#   ! 8      167#   3      !
   ! 12468  234678 167    ! 1267#@ 123467 1367   ! 9      5      167#   !
   ! 9      367    167    ! 8      1367#@ 5      ! 167#   2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      1678   !
   ! 56     1      8      ! 25679  23679  4      ! 367    679    267    !
   ! 7      56     4      ! 12569  12369  1368   ! 136    169    1268   !
   +----------------------+----------------------+----------------------+

Trid-OR2-whip[2]: OR2{{n2r5c4 | n3r6c5}} - c2n3{r6 .} ==> r5c2≠2
Trid-OR2-whip[3]: OR2{{n2r5c4 | n3r6c5}} - c2n3{r6 r5} - r5n8{c2 .} ==> r5c1≠2
whip[1]: r5n2{c5 .} ==> r4c4≠2, r4c5≠2
Trid-OR2-whip[4]: OR2{{n2r5c4 | n3r6c5}} - c6n3{r5 r9} - r9n8{c6 c9} - r9n2{c9 .} ==> r8c4≠2
Trid-OR2-whip[4]: OR2{{n2r5c4 | n3r6c5}} - r5n3{c6 c2} - r5n4{c2 c1} - r5n8{c1 .} ==> r5c5≠2
hidden-single-in-a-block ==> r5c4=2
z-chain[3]: r9n2{c5 c9} - c9n8{r9 r7} - r7n6{c9 .} ==> r9c5≠6
z-chain[3]: r9n2{c5 c9} - c9n8{r9 r7} - r7n1{c9 .} ==> r9c5≠1
z-chain[4]: r9n2{c5 c9} - r9n8{c9 c6} - b8n3{r9c6 r8c5} - c5n2{r8 .} ==> r9c5≠9

***** STARTING ELEVEN_S REPLACEMENT TECHNIQUE *****
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.
Trying in block 6

AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to 3 digits 1, 6 and 7 in 3 cells r6c7, r5c9 and r4c8,
the resolution state is:

Code: Select all

   +----------------------+----------------------+----------------------+
   ! 1672   2167   3      ! 4      5      167    ! 167    8      9      !
   ! 16745  45167  1675   ! 167    8      9      ! 2      3      167    !
   ! 1678   1678   9      ! 3      167    2      ! 4      167    5      !
   +----------------------+----------------------+----------------------+
   ! 167245 245167 1675   ! 1679   16749  167    ! 8      7      3      !
   ! 16748  341678 167    ! 2      16734  1673   ! 9      5      6      !
   ! 9      3167   167    ! 8      1673   5      ! 1      2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      1678   !
   ! 5167   167    8      ! 51679  231679 4      ! 3167   1679   2167   !
   ! 167    5167   4      ! 16759  23     16738  ! 1673   1679   16728  !
   +----------------------+----------------------+----------------------+

THIS IS THE PUZZLE THAT WILL NOW BE SOLVED.
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.

Code: Select all

Resolution state after Singles:
   +----------------------+----------------------+----------------------+
   ! 1267   1267   3      ! 4      5      167    ! 67     8      9      !
   ! 14567  14567  1567   ! 167    8      9      ! 2      3      17     !
   ! 1678   1678   9      ! 3      167    2      ! 4      16     5      !
   +----------------------+----------------------+----------------------+
   ! 12456  12456  156    ! 169    1469   16     ! 8      7      3      !
   ! 1478   13478  17     ! 2      1347   137    ! 9      5      6      !
   ! 9      367    67     ! 8      367    5      ! 1      2      4      !
   +----------------------+----------------------+----------------------+
   ! 3      9      2      ! 167    167    1678   ! 5      4      178    !
   ! 1567   167    8      ! 15679  123679 4      ! 367    169    127    !
   ! 167    1567   4      ! 15679  23     13678  ! 367    169    1278   !
   +----------------------+----------------------+----------------------+

whip[1]: r7n6{c6 .} ==> r9c6≠6, r8c4≠6, r8c5≠6, r9c4≠6
z-chain[3]: c3n7{r6 r2} - r3n7{c2 c5} - r6n7{c5 .} ==> r5c1≠7
z-chain[3]: c3n7{r6 r2} - r3n7{c1 c5} - r6n7{c5 .} ==> r5c2≠7
whip[4]: r5c3{n1 n7} - r6n7{c3 c5} - r3c5{n7 n6} - r7c5{n6 .} ==> r5c5≠1
z-chain[3]: r5n1{c3 c6} - r1n1{c6 c1} - c3n1{r2 .} ==> r4c2≠1
z-chain[3]: r5n1{c3 c6} - r1n1{c6 c2} - c3n1{r2 .} ==> r4c1≠1
whip[5]: r5c3{n7 n1} - r5c6{n1 n3} - r6c5{n3 n6} - r3c5{n6 n1} - r7c5{n1 .} ==> r5c5≠7
whip[5]: r4c6{n6 n1} - r1c6{n1 n7} - r5n7{c6 c3} - c3n1{r5 r2} - r1n1{c1 .} ==> r7c6≠6
z-chain[6]: b5n7{r6c5 r5c6} - c6n3{r5 r9} - c6n8{r9 r7} - r7c9{n8 n1} - r2c9{n1 n7} - c4n7{r2 .} ==> r7c5≠7
t-whip[5]: c6n6{r4 r1} - b3n6{r1c7 r3c8} - b3n1{r3c8 r2c9} - b2n1{r2c4 r3c5} - r7c5{n1 .} ==> r6c5≠6, r4c5≠6
whip[1]: b5n6{r4c6 .} ==> r4c1≠6, r4c2≠6, r4c3≠6
z-chain[5]: r3n7{c2 c5} - r6n7{c5 c3} - c3n6{r6 r2} - r2c4{n6 n1} - r2c9{n1 .} ==> r2c2≠7
z-chain[5]: r3n8{c2 c1} - r3n7{c1 c5} - r6c5{n7 n3} - c2n3{r6 r5} - c2n8{r5 .} ==> r3c2≠1, r3c2≠6
t-whip[5]: c5n6{r7 r3} - b3n6{r3c8 r1c7} - b3n7{r1c7 r2c9} - b2n7{r2c4 r1c6} - r7n7{c6 .} ==> r7c4≠6
hidden-single-in-a-block ==> r7c5=6
biv-chain[3]: r3c5{n7 n1} - r3c8{n1 n6} - r1c7{n6 n7} ==> r1c6≠7
naked-pairs-in-a-column: c6{r1 r4}{n1 n6} ==> r9c6≠1, r7c6≠1, r5c6≠1
whip[1]: r5n1{c3 .} ==> r4c3≠1
naked-single ==> r4c3=5
naked-pairs-in-a-block: b4{r4c1 r4c2}{n2 n4} ==> r5c2≠4, r5c1≠4
hidden-single-in-a-row ==> r5c5=4
hidden-pairs-in-a-block: b1{n4 n5}{r2c1 r2c2} ==> r2c2≠6, r2c2≠1, r2c1≠7, r2c1≠6, r2c1≠1
biv-chain[3]: r1c6{n1 n6} - r1c7{n6 n7} - r2c9{n7 n1} ==> r2c4≠1
biv-chain[3]: r6c3{n7 n6} - r2n6{c3 c4} - b2n7{r2c4 r3c5} ==> r6c5≠7
easy end in BC3
.