Anti-Tridagon-Puzzle

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Anti-Tridagon-Puzzle

Postby coloin » Wed May 28, 2025 7:29 pm

Code: Select all
+---+---+---+
|98.|..5|.67|
|7.4|6..|8..|
|.6.|87.|9..|
+---+---+---+
|.78|.6.|4..|
|4.9|...|..6|
|65.|..4|..8|
+---+---+---+
|8.7|..6|5..|
|.4.|..7|683|
|.96|...|712|
+---+---+---+  ATP   ED=10.4 

Tried to make a better puzzle with this feature but struggled....
coloin
 
Posts: 2580
Joined: 05 May 2005
Location: Devon

Re: Anti-Tridagon-Puzzle

Postby denis_berthier » Thu May 29, 2025 3:41 am

.
98...5.677.46..8...6.87.9...78.6.4..4.9.....665...4..88.7..65...4...7683.96...712

Not sure what "this feature" means for you. But here's my solution. It has something noticeable: a non-degenerate tridagon with 7 guardians, which is not used in the solution - except for launching eleven's digit replacement technique.

The puzzle is in T&E(2), B2B.

Resolution state after Singles and whips[1]:
Code: Select all
   +-------------------+-------------------+-------------------+
   ! 9     8     123   ! 1234  1234  5     ! 123   6     7     !
   ! 7     123   4     ! 6     1239  1239  ! 8     235   15    !
   ! 1235  6     1235  ! 8     7     123   ! 9     234   14    !
   +-------------------+-------------------+-------------------+
   ! 123   7     8     ! 12359 6     1239  ! 4     2359  159   !
   ! 4     123   9     ! 12357 12358 1238  ! 123   2357  6     !
   ! 6     5     123   ! 12379 1239  4     ! 123   2379  8     !
   +-------------------+-------------------+-------------------+
   ! 8     123   7     ! 123   123   6     ! 5     49    49    !
   ! 125   4     125   ! 1259  1259  7     ! 6     8     3     !
   ! 35    9     6     ! 345   3458  38    ! 7     1     2     !
   +-------------------+-------------------+-------------------+
146 candidates.


Code: Select all
Trid-OR7-relation for digits 1, 2 and 3 in blocks:
        b1, with cells (marked #): r1c3, r2c2, r3c1
        b2, with cells (marked #): r1c4, r2c5, r3c6
        b4, with cells (marked #): r6c3, r5c2, r4c1
        b5, with cells (marked #): r6c5, r5c4, r4c6
with 7 guardians (in cells marked @): n4r1c4 n9r2c5 n5r3c1 n9r4c6 n5r5c4 n7r5c4 n9r6c5
   +-------------------------+-------------------------+-------------------------+
   ! 9       8       123#    ! 1234#@  1234    5       ! 123     6       7       !
   ! 7       123#    4       ! 6       1239#@  1239    ! 8       235     15      !
   ! 1235#@  6       1235    ! 8       7       123#    ! 9       234     14      !
   +-------------------------+-------------------------+-------------------------+
   ! 123#    7       8       ! 12359   6       1239#@  ! 4       2359    159     !
   ! 4       123#    9       ! 12357#@ 12358   1238    ! 123     2357    6       !
   ! 6       5       123#    ! 12379   1239#@  4       ! 123     2379    8       !
   +-------------------------+-------------------------+-------------------------+
   ! 8       123     7       ! 123     123     6       ! 5       49      49      !
   ! 125     4       125     ! 1259    1259    7       ! 6       8       3       !
   ! 35      9       6       ! 345     3458    38      ! 7       1       2       !
   +-------------------------+-------------------------+-------------------------+


z-chain[3]: r9n4{c4 c5} - c5n8{r9 r5} - c5n5{r5 .} ==> r9c4≠5
whip[7]: c5n8{r5 r9} - r9c6{n8 n3} - c4n3{r9 r1} - c7n3{r1 r6} - c3n3{r6 r3} - c3n5{r3 r8} - b8n5{r8c4 .} ==> r5c5≠3

Code: Select all
   +-------------------+-------------------+-------------------+
   ! 9     8     123   ! 1234  1234  5     ! 123   6     7     !
   ! 7     123   4     ! 6     1239  1239  ! 8     235   15    !
   ! 1235  6     1235  ! 8     7     123   ! 9     234   14    !
   +-------------------+-------------------+-------------------+
   ! 123   7     8     ! 12359 6     1239  ! 4     2359  159   !
   ! 4     123   9     ! 12357 1258  1238  ! 123   2357  6     !
   ! 6     5     123   ! 12379 1239  4     ! 123   2379  8     !
   +-------------------+-------------------+-------------------+
   ! 8     123   7     ! 123   123   6     ! 5     49    49    !
   ! 125   4     125   ! 1259  1259  7     ! 6     8     3     !
   ! 35    9     6     ! 34    3458  38    ! 7     1     2     !
   +-------------------+-------------------+-------------------+


***** STARTING ELEVEN_S REPLACEMENT TECHNIQUE *****
RELEVANT DIGIT REPLACEMENTS WILL BE NECESSARY AT THE END, based on the original givens.
Trying in block 4
AFTER APPLYING ELEVEN''S REPLACEMENT METHOD to 3 digits 1, 2 and 3 in 3 cells r6c3, r5c2 and r4c1,
the resolution state is:
Code: Select all
   +----------------------+----------------------+----------------------+
   ! 9      8      123    ! 1234   1234   5      ! 123    6      7      !
   ! 7      123    4      ! 6      1239   1239   ! 8      1235   1235   !
   ! 1235   6      1235   ! 8      7      123    ! 9      1234   1234   !
   +----------------------+----------------------+----------------------+
   ! 3      7      8      ! 12359  6      1239   ! 4      12359  12359  !
   ! 4      2      9      ! 12357  12358  1238   ! 123    12357  6      !
   ! 6      5      1      ! 12379  1239   4      ! 123    12379  8      !
   +----------------------+----------------------+----------------------+
   ! 8      123    7      ! 123    123    6      ! 5      49     49     !
   ! 1235   4      1235   ! 12359  12359  7      ! 6      8      123    !
   ! 1235   9      6      ! 1234   123458 1238   ! 7      123    123    !
   +----------------------+----------------------+----------------------+

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

;;; solution in W7, with nothing noticeable
whip[1]: r7n2{c5 .} ==> r9c6≠2, r8c4≠2, r8c5≠2, r9c4≠2, r9c5≠2
z-chain[6]: c5n4{r1 r9} - r9n8{c5 c6} - c6n3{r9 r5} - c7n3{r5 r6} - c7n2{r6 r1} - r1c3{n2 .} ==> r1c5≠3
whip[6]: c7n1{r5 r1} - r3n1{c9 c1} - r2c2{n1 n3} - r1n3{c3 c4} - r7n3{c4 c5} - b5n3{r5c5 .} ==> r5c6≠1
whip[4]: r5c6{n3 n8} - r9c6{n8 n1} - r7n1{c4 c2} - c2n3{r7 .} ==> r2c6≠3
z-chain[6]: c5n4{r1 r9} - r9n8{c5 c6} - r5c6{n8 n3} - r5c7{n3 n1} - r1n1{c7 c4} - r1n4{c4 .} ==> r1c5≠2
whip[6]: c5n8{r9 r5} - r5c6{n8 n3} - b2n3{r3c6 r1c4} - r1n4{c4 c5} - r1n1{c5 c7} - r5c7{n1 .} ==> r9c5≠3
whip[6]: r6n7{c4 c8} - r6n9{c8 c5} - c6n9{r4 r2} - c6n2{r2 r3} - b1n2{r3c3 r1c3} - c7n2{r1 .} ==> r6c4≠2
whip[6]: r1n1{c5 c7} - r5c7{n1 n3} - r5c6{n3 n8} - r9c6{n8 n3} - r7n3{c5 c2} - c2n1{r7 .} ==> r2c6≠1
whip[7]: r7n1{c5 c2} - c1n1{r9 r3} - c6n1{r3 r4} - c6n9{r4 r2} - c6n2{r2 r3} - r2c5{n2 n3} - r2c2{n3 .} ==> r9c5≠1
whip[7]: r7n1{c5 c2} - c1n1{r9 r3} - c6n1{r3 r4} - c6n9{r4 r2} - c6n2{r2 r3} - r2c5{n2 n3} - r2c2{n3 .} ==> r8c5≠1
whip[6]: b1n1{r2c2 r3c1} - r8n1{c1 c4} - r1n1{c4 c5} - c5n4{r1 r9} - b8n5{r9c5 r8c5} - r8n9{c5 .} ==> r2c9≠1
whip[7]: c3n5{r3 r8} - r9n5{c1 c5} - c5n8{r9 r5} - r5c6{n8 n3} - r3c6{n3 n1} - r1n1{c5 c7} - r5c7{n1 .} ==> r3c3≠2
whip[7]: b9n3{r9c9 r9c8} - c6n3{r9 r5} - c7n3{r5 r6} - c7n2{r6 r1} - b1n2{r1c3 r3c1} - r3c6{n2 n1} - r1n1{c4 .} ==> r3c9≠3
whip[7]: r7n1{c5 c2} - c1n1{r9 r3} - r2c2{n1 n3} - c3n3{r3 r8} - c9n3{r8 r9} - c9n1{r9 r4} - c6n1{r4 .} ==> r8c4≠1
whip[7]: r1c3{n3 n2} - r1c7{n2 n1} - r5c7{n1 n3} - c6n3{r5 r9} - b9n3{r9c9 r8c9} - r8n1{c9 c1} - r8n2{c1 .} ==> r1c4≠3
z-chain[3]: r2c2{n1 n3} - r1n3{c3 c7} - r1n1{c7 .} ==> r2c5≠1
z-chain[5]: b2n3{r2c5 r3c6} - r5c6{n3 n8} - r9n8{c6 c5} - b8n5{r9c5 r8c4} - r8n9{c4 .} ==> r8c5≠3
t-whip[5]: b2n3{r2c5 r3c6} - r5c6{n3 n8} - r9c6{n8 n1} - r7n1{c4 c2} - c2n3{r7 .} ==> r2c9≠3, r2c8≠3
whip[1]: c9n3{r9 .} ==> r9c8≠3
z-chain[3]: r2c9{n2 n5} - r2c8{n5 n1} - r9c8{n1 .} ==> r3c8≠2
z-chain[4]: b1n2{r1c3 r3c1} - b1n1{r3c1 r2c2} - r2c8{n1 n5} - r2c9{n5 .} ==> r1c7≠2
hidden-single-in-a-column ==> r6c7=2
biv-chain[3]: c5n2{r7 r2} - r2n3{c5 c2} - c2n1{r2 r7} ==> r7c5≠1
x-wing-in-columns: n1{c5 c7}{r1 r5} ==> r5c8≠1, r5c4≠1, r1c4≠1
naked-triplets-in-a-column: c5{r2 r6 r7}{n2 n9 n3} ==> r8c5≠9, r5c5≠3
singles ==> r8c5=5, r9c1=5, r3c3=5, r8c4=9
whip[1]: r9n2{c9 .} ==> r8c9≠2
hidden-pairs-in-a-row: r5{n5 n7}{c4 c8} ==> r5c8≠3, r5c4≠3
finned-x-wing-in-rows: n3{r5 r3}{c6 c7} ==> r1c7≠3
stte
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