The New Sudoku Players' Forum

[Leren]

Code: Select all

*-----------*
|..4|..5|..6|
|8..|1..|.7.|
|.6.|...|...|
|---+---+---|
|1..|7..|.8.|
|..6|..4|.35|
|...|...|...|
|---+---+---|
|...|...|...|
|..5|..9|..4|
|7..|2..|.1.|
*-----------*
..4..5..68..1...7..6.......1..7...8...6..4.35....................5..9..47..2...1.

[pjb]

Four fishes:
Swordfish of 1s (r158\c257) => -1 r3c7, r6c57, r7c25
Swordfish of 4s (r249\c257) => -4 r3c57, r6c27, r7c25
Swordfish of 5s (r249\c257) => -5 r3c7, r6c25, r7c57
Mutant swordfish of 6s (r9c48\r6b89) => -6 from r6c567, r7c567, r8c57 => btte
Also 4 MSLSs, but fish simpler

Phil

[denis_berthier]

.
Solved using only Subsets:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------------+-------------------------+-------------------------+
   ! 239     12379   4       ! 389     23789   5       ! 12389   29      6       !
   ! 8       2359    239     ! 1       23469   236     ! 23459   7       239     !
   ! 2359    6       12379   ! 3489    234789  2378    ! 1234589 2459    12389   !
   +-------------------------+-------------------------+-------------------------+
   ! 1       23459   239     ! 7       23569   236     ! 2469    8       29      !
   ! 29      2789    6       ! 89      1289    4       ! 1279    3       5       !
   ! 23459   2345789 23789   ! 35689   1235689 12368   ! 124679  2469    1279    !
   +-------------------------+-------------------------+-------------------------+
   ! 23469   123489  12389   ! 34568   1345678 13678   ! 2356789 2569    23789   !
   ! 236     1238    5       ! 368     13678   9       ! 23678   26      4       !
   ! 7       3489    389     ! 2       34568   368     ! 35689   1       389     !
   +-------------------------+-------------------------+-------------------------+

hidden-pairs-in-a-block: b1{n1 n7}{r1c2 r3c3} ==> r3c3 ≠ 9, r3c3 ≠ 3, r3c3 ≠ 2, r1c2 ≠ 9, r1c2 ≠ 3, r1c2 ≠ 2
swordfish-in-columns: n6{c1 c4 c8}{r8 r7 r6} ==> r8c7 ≠ 6, r8c5 ≠ 6, r7c7 ≠ 6, r7c6 ≠ 6, r7c5 ≠ 6, r6c7 ≠ 6, r6c6 ≠ 6, r6c5 ≠ 6
swordfish-in-columns: n7{c3 c6 c9}{r6 r3 r7} ==> r7c7 ≠ 7, r7c5 ≠ 7, r6c7 ≠ 7, r6c2 ≠ 7, r3c5 ≠ 7
swordfish-in-columns: n4{c1 c4 c8}{r6 r7 r3} ==> r7c5 ≠ 4, r7c2 ≠ 4, r6c7 ≠ 4, r6c2 ≠ 4, r3c7 ≠ 4, r3c5 ≠ 4
hidden-pairs-in-a-block: b6{n4 n6}{r4c7 r6c8} ==> r6c8 ≠ 9, r6c8 ≠ 2, r4c7 ≠ 9, r4c7 ≠ 2
swordfish-in-columns: n1{c3 c6 c9}{r3 r7 r6} ==> r7c5 ≠ 1, r7c2 ≠ 1, r6c7 ≠ 1, r6c5 ≠ 1, r3c7 ≠ 1
naked-pairs-in-a-block: b6{r4c9 r6c7}{n2 n9} ==> r6c9 ≠ 9, r6c9 ≠ 2, r5c7 ≠ 9, r5c7 ≠ 2
hidden-pairs-in-a-block: b8{n1 n7}{r7c6 r8c5} ==> r8c5 ≠ 8, r8c5 ≠ 3, r7c6 ≠ 8, r7c6 ≠ 3
swordfish-in-columns: n5{c1 c4 c8}{r3 r6 r7} ==> r7c7 ≠ 5, r7c5 ≠ 5, r6c5 ≠ 5, r6c2 ≠ 5, r3c7 ≠ 5
hidden-pairs-in-a-block: b3{n4 n5}{r2c7 r3c8} ==> r3c8 ≠ 9, r3c8 ≠ 2, r2c7 ≠ 9, r2c7 ≠ 3, r2c7 ≠ 2
hidden-pairs-in-a-block: b4{n4 n5}{r4c2 r6c1} ==> r6c1 ≠ 9, r6c1 ≠ 3, r6c1 ≠ 2, r4c2 ≠ 9, r4c2 ≠ 3, r4c2 ≠ 2
hidden-pairs-in-a-block: b8{n4 n5}{r7c4 r9c5} ==> r9c5 ≠ 8, r9c5 ≠ 6, r9c5 ≠ 3, r7c4 ≠ 8, r7c4 ≠ 6, r7c4 ≠ 3
hidden-triplets-in-a-column: c7{n4 n5 n6}{r4 r2 r9} ==> r9c7 ≠ 9, r9c7 ≠ 8, r9c7 ≠ 3
hidden-triplets-in-a-row: r6{n4 n5 n6}{c8 c1 c4} ==> r6c4 ≠ 9, r6c4 ≠ 8, r6c4 ≠ 3
hidden-triplets-in-a-column: c5{n4 n5 n6}{r2 r9 r4} ==> r4c5 ≠ 9, r4c5 ≠ 3, r4c5 ≠ 2, r2c5 ≠ 9, r2c5 ≠ 3, r2c5 ≠ 2
naked-pairs-in-a-block: b5{r4c5 r6c4}{n5 n6} ==> r4c6 ≠ 6
hidden-triplets-in-a-row: r7{n4 n5 n6}{c1 c4 c8} ==> r7c8 ≠ 9, r7c8 ≠ 2, r7c1 ≠ 9, r7c1 ≠ 3, r7c1 ≠ 2
Singles + 1 whip[1] to the end

[RSW]

Tatooine Tosche Station

[Leren]

Tatooine Tosche Station

Well spotted ! Leren

[denis_berthier]

.
Surprisingly, there are also 1-step (and only one elimination) solutions with (very long) whips. Starting from the same PM as in my first answer:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------------+-------------------------+-------------------------+
   ! 239     12379   4       ! 389     23789   5       ! 12389   29      6       !
   ! 8       2359    239     ! 1       23469   236     ! 23459   7       239     !
   ! 2359    6       12379   ! 3489    234789  2378    ! 1234589 2459    12389   !
   +-------------------------+-------------------------+-------------------------+
   ! 1       23459   239     ! 7       23569   236     ! 2469    8       29      !
   ! 29      2789    6       ! 89      1289    4       ! 1279    3       5       !
   ! 23459   2345789 23789   ! 35689   1235689 12368   ! 124679  2469    1279    !
   +-------------------------+-------------------------+-------------------------+
   ! 23469   123489  12389   ! 34568   1345678 13678   ! 2356789 2569    23789   !
   ! 236     1238    5       ! 368     13678   9       ! 23678   26      4       !
   ! 7       3489    389     ! 2       34568   368     ! 35689   1       389     !
   +-------------------------+-------------------------+-------------------------+

There are 15 W1-anti-backdoors:
n5r2c2 n4r2c7 n4r3c4 n5r3c8 n4r4c2 n5r4c5 n6r4c7 n5r6c1 n6r6c4 n4r6c8 n4r7c1 n5r7c4 n6r8c1 n4r9c5 n5r9c7
14 of which give rise to a 1-step solution with whips of length ≤ 16.
Here are the two simplest ones, using only typed whips in cn-space:

Code: Select all

whip-cn[14]: c1n5{r3 r6} - c4n5{r6 r7} - c4n4{r7 r3} - c8n4{r3 r6} - c1n4{r6 r7} - c1n6{r7 r8} - c4n6{r8 r6} - c8n6{r6 r7} - c8n9{r7 r1} - c4n9{r1 r5} - c1n9{r5 r3} - c5n9{r3 r2} - c5n6{r2 r9} - c5n4{r9 .} ==> r3c8 ≠ 5
stte

OR:

Code: Select all

whip-cn[14]: c4n5{r6 r7} - c4n4{r7 r3} - c8n4{r3 r6} - c1n4{r6 r7} - c1n6{r7 r8} - c4n6{r8 r6} - c8n6{r6 r7} - c8n5{r7 r3} - c8n9{r3 r1} - c4n9{r1 r5} - c1n9{r5 r3} - c5n9{r3 r2} - c5n6{r2 r9} - c5n4{r9 .} ==> r6c1 ≠ 5
stte

As they are in a fixed space, maybe someone can find a set covering interpretation of these, with 14 base sets made only of 14 cn-cells each, respectively:
- c1n4, c4n4, c5n4, c8n4, c1n5, c4n5, c1n6, c4n6, c5n6, c8n6, c1n9, c4n9, c5n9, c8n9
- c1n4, c4n4, c5n4, c8n4, c4n5, c8n5, c1n6, c4n6, c5n6, c8n6, c1n9, c4n9, c5n9, c8n9
Notice that they would differ by only one base set.




P.S.: there are also two similar whip-cn[15]:
whip-cn[15]: c1n5{r3 r6} - c4n5{r6 r7} - c4n4{r7 r3} - c8n4{r3 r6} - c1n4{r6 r7} - c1n6{r7 r8} - c4n6{r8 r6} - c8n6{r6 r7} - c8n5{r7 r3} - c8n9{r3 r1} - c4n9{r1 r5} - c1n9{r5 r3} - c5n9{r3 r2} - c5n6{r2 r9} - c5n4{r9 .} ==> r2c2 ≠ 5
stte

whip-cn[15]: c8n5{r7 r3} - c1n5{r3 r6} - c4n5{r6 r7} - c4n4{r7 r3} - c8n4{r3 r6} - c1n4{r6 r7} - c1n6{r7 r8} - c4n6{r8 r6} - c8n6{r6 r7} - c8n9{r7 r1} - c4n9{r1 r5} - c1n9{r5 r3} - c5n9{r3 r2} - c5n6{r2 r9} - c5n4{r9 .} ==> r9c7 ≠ 5
stte

The other 1-step solutions mix the 2D-spaces.