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[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . 1 2 |
| . . . | . . 3 | 4 . 5 |
| . . 5 | . 2 . | . 6 . |
+-------+-------+-------+
| . . . | . 6 . | . . 3 |
| . 1 . | 3 5 . | 6 . . |
| . 3 . | 2 . 4 | 5 . . |
+-------+-------+-------+
| . 6 3 | 1 4 . | . . . |
| 7 . 1 | . . . | 2 . . |
| 8 . 9 | . . . | . . . |
+-------+-------+-------+
.......12.....34.5..5.2..6.....6...3.1.35.6...3.2.45...6314....7.1...2..8.9......

[Cenoman]

My first try with the pattern...

Code: Select all

 +------------------------+--------------------------+------------------------+
 |  3469   789     4678   |  456789  <789    56789   | <3789   1       2      |
 |  1269   2789    2678   | <6789     1789   3       |  4     <789     5      |
 |  1349   789     5      |  4789     2     <1789    |  3789   6      <789    |
 +------------------------+--------------------------+------------------------+
 |  2459   25789   2478   | <789      6      1789    | <1789   24789   3      |
 |  249    1       2478   |  3        5     <789     |  6      24789  <4789   |
 |  69     3       678    |  2       <1789   4       |  5     <789     1789   |
 +------------------------+--------------------------+------------------------+
 |  25     6       3      |  1        4      25789   |  789    5789    789    |
 |  7      45      1      |  5689     389    5689    |  2      34589   689-4  |
 |  8      245     9      |  567      37     2567    |  17     3457    167-4  |
 +------------------------+--------------------------+------------------------+

TH (789)b2356 having six guardians. The three guardians 1r3c6, 1r4c7, 1r6c5 have the same parity (all are conjugates of 1r4c6). Whichever one to be considered:
(1)r4c7 - r6c9 = (16)r89c9
(3)r1c7 - r3c7 = (3-1)r3c1 = r2c1 - r2c5 = r6c5 - r6c9 = (16)r89c9
(6)r2c4 - (6=27891)b1p24568 - r2c5 = r6c5 - r6c9 = (16)r89c9
(4)r5c9
=>-4r89c9; lclste [HP (34)r89c8; ste]

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 3469   789    4678   ! 456789 789    56789  ! 3789   1      2      !
   ! 1269   2789   2678   ! 6789   1789   3      ! 4      789    5      !
   ! 1349   789    5      ! 4789   2      1789   ! 3789   6      789    !
   +----------------------+----------------------+----------------------+
   ! 2459   25789  2478   ! 789    6      1789   ! 1789   24789  3      !
   ! 249    1      2478   ! 3      5      789    ! 6      24789  4789   !
   ! 69     3      678    ! 2      1789   4      ! 5      789    1789   !
   +----------------------+----------------------+----------------------+
   ! 25     6      3      ! 1      4      25789  ! 789    5789   789    !
   ! 7      45     1      ! 5689   389    5689   ! 2      34589  4689   !
   ! 8      245    9      ! 567    37     2567   ! 17     3457   1467   !
   +----------------------+----------------------+----------------------+
199 candidates.

Code: Select all

t-whip[3]: r4n1{c6 c7} - r9c7{n1 n7} - r7n7{c9 .} ==> r4c6≠7
biv-chain[4]: r9c7{n7 n1} - r4n1{c7 c6} - r3n1{c6 c1} - r3n3{c1 c7} ==> r3c7≠7
whip[6]: r3n4{c4 c1} - c1n1{r3 r2} - c5n1{r2 r6} - c5n7{r6 r9} - r9c7{n7 n1} - r4n1{c7 .} ==> r3c4≠7
whip[8]: c8n2{r5 r4} - b6n4{r4c8 r5c9} - r5c1{n4 n2} - b7n2{r7c1 r9c2} - r9n4{c2 c8} - c8n3{r9 r8} - c8n5{r8 r7} - r7c1{n5 .} ==> r5c8≠9
t-whip[9]: c1n3{r1 r3} - r3n1{c1 c6} - c5n1{r2 r6} - c9n1{r6 r9} - r9c7{n1 n7} - r7n7{c9 c6} - c6n2{r7 r9} - r9n6{c6 c4} - c6n6{r8 .} ==> r1c1≠6
whip[8]: r1n5{c6 c4} - r1n6{c4 c3} - r1n4{c3 c1} - c1n3{r1 r3} - r3n1{c1 c6} - r4n1{c6 c7} - r9c7{n1 n7} - b8n7{r9c4 .} ==> r1c6≠7
whip[9]: c1n3{r1 r3} - c1n1{r3 r2} - c5n1{r2 r6} - c9n1{r6 r9} - c9n6{r9 r8} - c9n4{r8 r5} - c1n4{r5 r4} - r4n5{c1 c2} - c2n9{r4 .} ==> r1c1≠9
whip[9]: r1n5{c6 c4} - b2n6{r1c4 r2c4} - r9c4{n6 n7} - r9c7{n7 n1} - r4n1{c7 c6} - r3n1{c6 c1} - c1n3{r3 r1} - r1n4{c1 c3} - r1n6{c3 .} ==> r1c6≠8
whip[9]: r1n5{c6 c4} - b2n6{r1c4 r2c4} - r9c4{n6 n7} - r9c7{n7 n1} - r4n1{c7 c6} - r3n1{c6 c1} - c1n3{r3 r1} - r1n4{c1 c3} - r1n6{c3 .} ==> r1c6≠9
whip[9]: r1n5{c4 c6} - r1n6{c6 c3} - r1n4{c3 c1} - c1n3{r1 r3} - r3n1{c1 c6} - b5n1{r4c6 r6c5} - c5n7{r6 r9} - r9c7{n7 n1} - r4n1{c7 .} ==> r1c4≠7
whip[9]: c1n1{r3 r2} - c5n1{r2 r6} - c9n1{r6 r9} - c9n6{r9 r8} - c9n4{r8 r5} - r5c1{n4 n2} - b4n9{r5c1 r4c2} - r4n5{c2 c1} - r7c1{n5 .} ==> r3c1≠9
t-whip[10]: r3n1{c1 c6} - c5n1{r2 r6} - c9n1{r6 r9} - r9c7{n1 n7} - r7n7{c9 c6} - c6n2{r7 r9} - r9n6{c6 c4} - c6n6{r8 r1} - r1n5{c6 c4} - c4n4{r1 .} ==> r3c1≠4
hidden-single-in-a-row ==> r3c4=4
t-whip[7]: r1n4{c3 c1} - c1n3{r1 r3} - r3n1{c1 c6} - c5n1{r2 r6} - c9n1{r6 r9} - c9n6{r9 r8} - c9n4{r8 .} ==> r5c3≠4
whip[9]: r4n1{c6 c7} - r9c7{n1 n7} - r7n7{c9 c6} - r5c6{n7 n9} - r3c6{n9 n1} - r3c1{n1 n3} - r1c1{n3 n4} - r5c1{n4 n2} - r7n2{c1 .} ==> r4c6≠8
whip[9]: r1n4{c3 c1} - c1n3{r1 r3} - r3n1{c1 c6} - b5n1{r4c6 r6c5} - c9n1{r6 r9} - r9c7{n1 n7} - b8n7{r9c4 r7c6} - b5n7{r5c6 r4c4} - c2n7{r4 .} ==> r1c3≠7
z-chain[10]: r8n3{c8 c5} - r9c5{n3 n7} - r9c7{n7 n1} - r4n1{c7 c6} - r3n1{c6 c1} - c1n3{r3 r1} - r1n4{c1 c3} - r4n4{c3 c1} - c1n5{r4 r7} - r8c2{n5 .} ==> r8c8≠4
t-whip[10]: r1n6{c6 c3} - r1n4{c3 c1} - c1n3{r1 r3} - r3n1{c1 c6} - b5n1{r4c6 r6c5} - c9n1{r6 r9} - r9c7{n1 n7} - b8n7{r9c4 r7c6} - c6n2{r7 r9} - r9n6{c6 .} ==> r2c4≠6
whip[1]: r2n6{c3 .} ==> r1c3≠6
hidden-pairs-in-a-row: r1{n5 n6}{c4 c6} ==> r1c4≠9, r1c4≠8
whip[7]: r6n1{c9 c5} - r2n1{c5 c1} - b1n6{r2c1 r2c3} - r6c3{n6 n8} - r1c3{n8 n4} - r1c1{n4 n3} - r3c1{n3 .} ==> r6c9≠7
whip[8]: c8n2{r4 r5} - c8n4{r5 r9} - c8n3{r9 r8} - c8n5{r8 r7} - c1n5{r7 r4} - r4n4{c1 c3} - r1c3{n4 n8} - b4n8{r4c3 .} ==> r4c8≠8
whip[9]: c5n1{r2 r6} - c9n1{r6 r9} - r9c7{n1 n7} - c5n7{r9 r1} - r2c4{n7 n8} - r2c8{n8 n7} - c9n7{r3 r5} - c9n4{r5 r8} - c9n6{r8 .} ==> r2c5≠9
whip[9]: c5n1{r2 r6} - c9n1{r6 r9} - r9c7{n1 n7} - c5n7{r9 r1} - r2c4{n7 n9} - r2c8{n9 n7} - c9n7{r3 r5} - c9n4{r5 r8} - c9n6{r8 .} ==> r2c5≠8
whip[7]: r3n3{c7 c1} - r3n1{c1 c6} - r2c5{n1 n7} - r2c8{n7 n8} - b2n8{r2c4 r1c5} - r1c3{n8 n4} - r1c1{n4 .} ==> r3c7≠9
t-whip[7]: b6n1{r6c9 r4c7} - c6n1{r4 r3} - r3c1{n1 n3} - c7n3{r3 r1} - c7n9{r1 r7} - c7n7{r7 r9} - r7c9{n7 .} ==> r6c9≠8
whip[9]: c8n2{r4 r5} - c8n4{r5 r9} - c8n3{r9 r8} - c8n5{r8 r7} - c1n5{r7 r4} - r4n4{c1 c3} - r1c3{n4 n8} - b4n8{r4c3 r4c2} - r4n2{c2 .} ==> r4c8≠7
whip[9]: c8n2{r4 r5} - c8n4{r5 r9} - c8n3{r9 r8} - c8n5{r8 r7} - c1n5{r7 r4} - r4n4{c1 c3} - r1c3{n4 n8} - b4n8{r4c3 r4c2} - r4n2{c2 .} ==> r4c8≠9

Code: Select all

   +-------------------+-------------------+-------------------+
   ! 34    789   48    ! 56    789   56    ! 3789  1     2     !
   ! 1269  2789  2678  ! 789   17    3     ! 4     789   5     !
   ! 13    789   5     ! 4     2     1789  ! 38    6     789   !
   +-------------------+-------------------+-------------------+
   ! 2459  25789 2478  ! 789   6     19    ! 1789  24    3     !
   ! 249   1     278   ! 3     5     789   ! 6     2478  4789  !
   ! 69    3     678   ! 2     1789  4     ! 5     789   19    !
   +-------------------+-------------------+-------------------+
   ! 25    6     3     ! 1     4     25789 ! 789   5789  789   !
   ! 7     45    1     ! 5689  389   5689  ! 2     3589  4689  !
   ! 8     245   9     ! 567   37    2567  ! 17    3457  1467  !
   +-------------------+-------------------+-------------------+

OR5-anti-tridagon[12] (type diag) for digits 7, 8 and 9 in blocks:
        b2, with cells: r1c5, r2c4, r3c6
        b3, with cells: r1c7, r2c8, r3c9
        b5, with cells: r6c5, r4c4, r5c6
        b6, with cells: r6c8, r4c7, r5c9
with 5 guardians: n3r1c7 n1r3c6 n1r4c7 n4r5c9 n1r6c5

OR5-forcing-whip-elim[9] based on OR5-anti-tridagon[12] for n4r5c9, n1r4c7, n1r6c5, n1r3c6 and  n3r1c7:
   || n4r5c9 -
   || n1r4c7 - partial-whip[1]: r6c9{n1 n9} -
   || n1r6c5 - partial-whip[1]: r6c9{n1 n9} -
   || n1r3c6 - partial-whip[2]: c5n1{r2 r6} - r6c9{n1 n9} -
   || n3r1c7 - partial-whip[4]: r3n3{c7 c1} - r3n1{c1 c6} - c5n1{r2 r6} - r6c9{n1 n9} -
 ==> r5c9≠9

whip[8]: c3n7{r6 r2} - c3n6{r2 r6} - r6c1{n6 n9} - b6n9{r6c9 r4c7} - r4c4{n9 n8} - r2c4{n8 n9} - r2c8{n9 n8} - r6n8{c8 .} ==> r4c2≠7
whip[1]: b4n7{r6c3 .} ==> r2c3≠7

OR5-forcing-whip-elim[8] based on OR5-anti-tridagon[12] for n4r5c9, n3r1c7, n1r3c6, n1r4c7 and  n1r6c5:
   || n4r5c9 -
   || n3r1c7 - partial-whip[1]: r1c1{n3 n4} -
   || n1r3c6 - partial-whip[2]: r3c1{n1 n3} - r1c1{n3 n4} -
   || n1r4c7 - partial-whip[2]: r4c6{n1 n9} - r5n9{c6 c1} -
   || n1r6c5 - partial-whip[2]: r4c6{n1 n9} - r5n9{c6 c1} -
 ==> r5c1≠4

whip[1]: r5n4{c9 .} ==> r4c8≠4
naked-single ==> r4c8=2
biv-chain[3]: r2n6{c1 c3} - c3n2{r2 r5} - r5c1{n2 n9} ==> r2c1≠9
whip[1]: c1n9{r6 .} ==> r4c2≠9
biv-chain[4]: r6c1{n9 n6} - c3n6{r6 r2} - c3n2{r2 r5} - r5c1{n2 n9} ==> r4c1≠9
biv-chain[4]: c3n6{r2 r6} - r6c1{n6 n9} - r5c1{n9 n2} - c3n2{r5 r2} ==> r2c3≠8
biv-chain[6]: r7n2{c6 c1} - c1n5{r7 r4} - c1n4{r4 r1} - b1n3{r1c1 r3c1} - r3n1{c1 c6} - r4c6{n1 n9} ==> r7c6≠9
whip[1]: r7n9{c9 .} ==> r8c8≠9, r8c9≠9
t-whip[7]: c1n5{r7 r4} - c1n4{r4 r1} - c1n3{r1 r3} - r3n1{c1 c6} - r4n1{c6 c7} - r9c7{n1 n7} - b8n7{r9c4 .} ==> r7c6≠5
t-whip[7]: r7n7{c9 c6} - r7n2{c6 c1} - r5c1{n2 n9} - r6c1{n9 n6} - r2c1{n6 n1} - c5n1{r2 r6} - c9n1{r6 .} ==> r9c9≠7
t-whip[7]: c2n2{r9 r2} - r2c3{n2 n6} - r2c1{n6 n1} - c5n1{r2 r6} - c9n1{r6 r9} - c9n6{r9 r8} - r8n4{c9 .} ==> r9c2≠4
hidden-single-in-a-block ==> r8c2=4
z-chain[8]: r9c7{n7 n1} - r4n1{c7 c6} - r3n1{c6 c1} - c1n3{r3 r1} - c1n4{r1 r4} - c1n5{r4 r7} - c8n5{r7 r8} - c8n3{r8 .} ==> r9c8≠7
t-whip[8]: r7n2{c6 c1} - b4n2{r5c1 r5c3} - r2c3{n2 n6} - r2c1{n6 n1} - b2n1{r2c5 r3c6} - r4n1{c6 c7} - r9c7{n1 n7} - b8n7{r9c4 .} ==> r7c6≠8
whip[1]: r7n8{c9 .} ==> r8c8≠8, r8c9≠8
naked-single ==> r8c9=6

OR5-forcing-whip-elim[5] based on OR5-anti-tridagon[12] for n1r3c6, n1r4c7, n1r6c5, n3r1c7 and  n4r5c9:
   || n1r3c6 -
   || n1r4c7 -
   || n1r6c5 -
   || n3r1c7 - partial-whip[2]: r3n3{c7 c1} - r3n1{c1 c6} -
   || n4r5c9 - partial-whip[2]: r9c9{n4 n1} - b6n1{r6c9 r4c7} -
 ==> r4c6≠1
stte