The New Sudoku Players' Forum

[coloin]

Code: Select all

+---+---+---+
|59.|.87|6.4|
|6.8|9..|...|
|.74|65.|...|
+---+---+---+
|.56|8..|4.9|
|4.9|..6|...|
|7..|...|.6.|
+---+---+---+
|.4.|..5|...|
|..5|7.8|142|
|8.7|4..|.5.|
+---+---+---+  ATP2


SE11, TE2,B4B. And definitely no conventional tridagon...

[denis_berthier]

.
No tridagon, but a lot of degenerate cyclic ones.

Solution similar to previous puzzle:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 5     9     123   ! 123   8     7     ! 6     123   4     !
   ! 6     123   8     ! 9     1234  1234  ! 2357  1237  1357  !
   ! 123   7     4     ! 6     5     123   ! 2389  12389 138   !
   +-------------------+-------------------+-------------------+
   ! 123   5     6     ! 8     1237  123   ! 4     1237  9     !
   ! 4     1238  9     ! 1235  1237  6     ! 23578 12378 13578 !
   ! 7     1238  123   ! 1235  12349 12349 ! 2358  6     1358  !
   +-------------------+-------------------+-------------------+
   ! 1239  4     123   ! 123   12369 5     ! 3789  3789  3678  !
   ! 39    36    5     ! 7     369   8     ! 1     4     2     !
   ! 8     1236  7     ! 4     12369 1239  ! 39    5     36    !
   +-------------------+-------------------+-------------------+
171 candidates.

hidden-pairs-in-a-row: r6{n4 n9}{c5 c6} ==> r6c6≠3, r6c6≠2, r6c6≠1, r6c5≠3, r6c5≠2, r6c5≠1

Code: Select all

   +-------------------+-------------------+-------------------+
   ! 5     9     123   ! 123   8     7     ! 6     123   4     !
   ! 6     123   8     ! 9     1234  1234  ! 2357  1237  1357  !
   ! 123   7     4     ! 6     5     123   ! 2389  12389 138   !
   +-------------------+-------------------+-------------------+
   ! 123   5     6     ! 8     1237  123   ! 4     1237  9     !
   ! 4     1238  9     ! 1235  1237  6     ! 23578 12378 13578 !
   ! 7     1238  123   ! 1235  49    49    ! 2358  6     1358  !
   +-------------------+-------------------+-------------------+
   ! 1239  4     123   ! 123   12369 5     ! 3789  3789  3678  !
   ! 39    36    5     ! 7     369   8     ! 1     4     2     !
   ! 8     1236  7     ! 4     12369 1239  ! 39    5     36    !
   +-------------------+-------------------+-------------------+

***** STARTING ELEVEN_S REPLACEMENT TECHNIQUE *****
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.
Trying in block 1

AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to 3 digits 1, 2 and 3 in 3 cells r3c1, r2c2 and r1c3,
the resolution state is:

Code: Select all

   +----------------------+----------------------+----------------------+
   ! 5      9      3      ! 123    8      7      ! 6      123    4      !
   ! 6      2      8      ! 9      1234   1234   ! 12357  1237   12357  !
   ! 1      7      4      ! 6      5      123    ! 12389  12389  1238   !
   +----------------------+----------------------+----------------------+
   ! 123    5      6      ! 8      1237   123    ! 4      1237   9      !
   ! 4      1238   9      ! 1235   1237   6      ! 123578 12378  123578 !
   ! 7      1238   123    ! 1235   49     49     ! 12358  6      12358  !
   +----------------------+----------------------+----------------------+
   ! 1239   4      123    ! 123    12369  5      ! 123789 123789 123678 !
   ! 1239   1236   5      ! 7      12369  8      ! 123    4      123    !
   ! 8      1236   7      ! 4      12369  1239   ! 1239   5      1236   !
   +----------------------+----------------------+----------------------+

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

finned-x-wing-in-rows: n1{r1 r4}{c8 c4} ==> r6c4≠1, r5c4≠1
biv-chain[3]: r1c8{n2 n1} - c4n1{r1 r7} - r7c3{n1 n2} ==> r7c8≠2
biv-chain[4]: r1c8{n2 n1} - c4n1{r1 r7} - c3n1{r7 r6} - b4n2{r6c3 r4c1} ==> r4c8≠2
biv-chain[4]: b2n2{r3c6 r1c4} - c4n1{r1 r7} - c3n1{r7 r6} - b4n2{r6c3 r4c1} ==> r4c6≠2
biv-chain[2]: r4n2{c5 c1} - c3n2{r6 r7} ==> r7c5≠2
biv-chain[3]: r4c6{n1 n3} - r3c6{n3 n2} - r1c4{n2 n1} ==> r2c6≠1
whip[4]: r4n2{c1 c5} - c4n2{r5 r1} - c4n1{r1 r7} - r7c3{n1 .} ==> r7c1≠2
biv-chain[3]: r7c1{n3 n9} - r8n9{c1 c5} - r8n6{c5 c2} ==> r8c2≠3
whip[4]: r8n9{c5 c1} - r7c1{n9 n3} - r7c4{n3 n2} - b7n2{r7c3 .} ==> r8c5≠1
z-chain[3]: r8n1{c9 c2} - c2n6{r8 r9} - c9n6{r9 .} ==> r7c9≠1
whip[4]: r1n2{c8 c4} - c4n1{r1 r7} - c3n1{r7 r6} - r6n2{c3 .} ==> r5c8≠2
whip[1]: c8n2{r3 .} ==> r3c7≠2, r3c9≠2
z-chain[5]: r8n9{c5 c1} - r7c1{n9 n3} - r7c4{n3 n1} - r1c4{n1 n2} - c6n2{r3 .} ==> r8c5≠2
t-whip[3]: r8n2{c9 c1} - r8n9{c1 c5} - r9n9{c6 .} ==> r9c7≠2
whip[5]: r7c3{n2 n1} - r6c3{n1 n2} - c7n2{r6 r5} - c4n2{r5 r1} - c4n1{r1 .} ==> r7c9≠2
whip[5]: c3n2{r7 r6} - c3n1{r6 r7} - c4n1{r7 r1} - c4n2{r1 r5} - c9n2{r5 .} ==> r7c7≠2
whip[5]: r8n1{c9 c2} - r8n6{c2 c5} - r7n6{c5 c9} - r7n7{c9 c7} - r7n8{c7 .} ==> r7c8≠1
whip[5]: r8n1{c9 c2} - r8n6{c2 c5} - r7n6{c5 c9} - r7n7{c9 c8} - r7n8{c8 .} ==> r7c7≠1
z-chain[4]: r4n2{c5 c1} - r6c3{n2 n1} - r7n1{c3 c4} - b2n1{r1c4 .} ==> r4c5≠1
z-chain[4]: r7n1{c5 c3} - c3n2{r7 r6} - r4c1{n2 n3} - r4c6{n3 .} ==> r9c6≠1
hidden-single-in-a-column ==> r4c6=1
whip[4]: c8n9{r3 r7} - r7c1{n9 n3} - r4n3{c1 c5} - c4n3{r5 .} ==> r3c8≠3
z-chain[5]: r7c1{n3 n9} - r8n9{c1 c5} - r9c6{n9 n2} - b2n2{r3c6 r1c4} - c4n1{r1 .} ==> r7c4≠3
whip[1]: c4n3{r6 .} ==> r4c5≠3, r5c5≠3
naked-pairs-in-a-block: b5{r4c5 r5c5}{n2 n7} ==> r6c4≠2, r5c4≠2
whip[1]: b5n2{r5c5 .} ==> r9c5≠2
naked-pairs-in-a-row: r7{c3 c4}{n1 n2} ==> r7c5≠1
finned-swordfish-in-columns: n2{c1 c5 c7}{r8 r4 r5} ==> r5c9≠2
biv-chain[3]: r5n2{c7 c5} - r4n2{c5 c1} - r4n3{c1 c8} ==> r5c7≠3
biv-chain[3]: b8n2{r9c6 r7c4} - b7n2{r7c3 r8c1} - r8n9{c1 c5} ==> r9c6≠9
singles ==> r6c6=9, r6c5=4
hidden-single-in-a-block ==> r2c6=4
biv-chain[4]: r3c9{n8 n3} - r3c6{n3 n2} - r9n2{c6 c9} - b9n6{r9c9 r7c9} ==> r7c9≠8
biv-chain[4]: r9n9{c5 c7} - b3n9{r3c7 r3c8} - r3n2{c8 c6} - b2n3{r3c6 r2c5} ==> r9c5≠3
biv-chain[4]: r9c6{n3 n2} - r3n2{c6 c8} - c8n9{r3 r7} - r7c1{n9 n3} ==> r7c5≠3, r9c2≠3
whip[1]: c2n3{r6 .} ==> r4c1≠3
stte

[coloin]

Thanks for the analysis... of course the "feature" is the valid "tridagon" pattern [ in the solution grid] in B1245

Code: Select all

+---+---+---+
|..3|2..|...|
|.2.|.1.|...|
|1..|..3|...|
+---+---+---+
|2..|..1|...|
|.3.|.2.|...|
|..1|3..|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+


[denis_berthier]

Thanks for the analysis... of course the "feature" is the valid "tridagon" pattern [ in the solution grid] in B1245

Code: Select all

+---+---+---+
|..3|2..|...|
|.2.|.1.|...|
|1..|..3|...|
+---+---+---+
|2..|..1|...|
|.3.|.2.|...|
|..1|3..|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+


Except that this is not a tridagon pattern. The cells don't satisfy the right conditions. See http://forum.enjoysudoku.com/the-tridagon-rule-t39859.html.
.