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[denis_berthier]

.

Code: Select all

+-------+-------+-------+
! . . . ! . 5 6 ! . . . !
! . . . ! 1 8 . ! 2 3 . !
! . . 9 ! 2 3 7 ! . . . !
+-------+-------+-------+
! 2 . . ! . . . ! 8 . 3 !
! 3 . 4 ! 8 . . ! 1 9 . !
! . . . ! 3 . . ! . 2 4 !
+-------+-------+-------+
! . 4 . ! . . 3 ! . . . !
! 8 . . ! . . . ! 9 4 . !
! 9 . 1 ! . 4 8 ! 3 . . !
+-------+-------+-------+
....56......18.23...9237...2.....8.33.48..19....3...24.4...3...8.....94.9.1.483..;258;45965;mith
SER = 11.7

[Edit]: I completed the name. I didn't want to provide initial information before seeing your solutions.

[P.O.]

the puzzle has a 'tridagon profile', a POM solution:

Hidden Text: Show

Code: Select all

....56......18.23...9237...2.....8.33.48..19....3...24.4...3...8.....94.9.1.483..

#VT: (30 7 2 3 122 129 134 6 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2
#VT: (30 7 2 3 113 114 125 6 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3
#VT: (22 7 2 3 100 107 110 2 5)
Cells: nil nil nil nil nil nil nil (20 48) nil
SetVC: ( n8r3c2   n8r6c3 )

#VT: (25 7 2 3 101 107 114 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2
#VT: (25 7 2 3 95 96 108 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3
#VT: (17 7 2 3 83 89 83 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:(2 46) nil nil nil nil nil (2 3) nil nil
2 3
#VT: (17 7 2 3 49 57 53 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil (29 47) (29 47) (29 47) nil nil
2 3
#VT: (17 7 2 3 45 52 50 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3 4
#VT: (17 5 2 3 24 27 16 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil (63) nil nil (31 63 69) (31 59 63 68) (1 18 63) nil nil
2
#VT: (17 5 2 3 23 25 16 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3
#VT: (17 5 2 3 18 19 14 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil (59) nil nil
2 3
#VT: (17 5 2 3 18 17 14 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil nil nil nil nil nil nil nil nil
2 3 4
#VT: (17 4 2 3 6 5 3 2 5)
Cells: nil nil nil nil nil nil nil nil nil
Candidates:nil (66) nil nil (25 57 58 62 72 81) (12 25 45 46 65 81) (9 35 38 50 55 57 65 67 80 81) nil nil
EraseCC: ( n4r3c7   n2r9c9   n7r1c7   n7r7c8   n7r5c9   n7r6c1
           n8r1c8   n8r7c9   n1r8c9   n1r3c8   n1r7c5   n2r7c3
           n9r7c4   n3r1c3   n4r1c4   n9r1c9   n9r2c6   n7r4c4
           n2r8c6   n1r1c1   n2r1c2   n5r5c6   n1r6c6   n7r8c5
           n4r4c6   n6r5c2   n2r5c5   n9r6c2   n6r6c5   n5r6c7
           n6r7c7   n5r9c8   n1r4c2   n5r4c3   n9r4c5   n6r4c8
           n5r7c1   n3r8c2   n6r8c3   n5r8c4   n7r9c2   n6r9c4
           n5r2c2   n7r2c3   n6r2c9   n6r3c1   n5r3c9   n4r2c1 )
1 2 3   4 5 6   7 8 9
4 5 7   1 8 9   2 3 6
6 8 9   2 3 7   4 1 5
2 1 5   7 9 4   8 6 3
3 6 4   8 2 5   1 9 7
7 9 8   3 6 1   5 2 4
5 4 2   9 1 3   6 7 8
8 3 6   5 7 2   9 4 1
9 7 1   6 4 8   3 5 2

(2 2 3 2 2 3 2 3 2 3 2 3 4 2 2 3 2 3 2 3 4)


[yzfwsf]

Code: Select all

Hidden Pair: 23 in r1c2,r1c3 => r1c2<>178,r1c3<>78
Hidden Single: 8 in c3 => r6c3=8
Hidden Single: 8 in c2 => r3c2=8
Locked Candidates 1 (Pointing): 1 in b1 => r6c1<>1
Hidden Pair: 19 in r4c2,r6c2 => r4c2<>567,r6c2<>567
Triplet Oddagon Forcing Chain: Each true guardian of Triplet Oddagon will all lead To: r7c5<>6,r7c5<>7,r14c4,r7c5<>9
               2r8c3 - (2=5679)r7c1347
              3r8c3 - (3=2)r1c3 - (2=5679)r7c1347
              2r9c2 - (2=5679)r7c1347
              1r8c9 - (1=25679)b8p14567
              2r8c9 - (2=15679)b8p14567
Hidden Single: 9 in r1 => r1c9=9
Hidden Single: 8 in r1 => r1c8=8
Hidden Single: 1 in r1 => r1c1=1
Hidden Single: 7 in r1 => r1c7=7
Hidden Single: 4 in r1 => r1c4=4
Full House: r2c6=9
Hidden Single: 4 in r2 => r2c1=4
Hidden Single: 4 in r3 => r3c7=4
Hidden Single: 4 in r4 => r4c6=4
Hidden Single: 8 in r7 => r7c9=8
Hidden Single: 9 in r7 => r7c4=9
Whip[8]: Supposing 5r5c9 would causes 5 to disappear in Column 6 => r5c9<>5
5r5c9 - 5c7(r6=r7) - 5c8(r9=r3) - 5c1(r3=r6) - 7r6(c1=c5) - 7r5(c5=c2) - 7r2(c2=c3) - 5c3(r2=r8) - 5c6(r8=.)
Hidden Pair: 19 in r4c2,r4c5 => r4c5<>67
AIC Type 2: 5r5c2 = (5-2)r5c6 = r5c5 - r7c5 = r7c3 - r1c3 = (2-3)r1c2 = 3r8c2 => r8c2<>5
Grouped AIC Type 2: (7=6)r5c9 - r23c9 = (6-1)r3c8 = r7c8 - (1=2)r7c5 - r5c5 = (2-5)r5c6 = 5r5c2 => r5c2<>7
Grouped AIC Type 2: 3r8c2 = r8c3 - (3=2)r1c3 - r7c3 = (2-1)r7c5 = (1-7)r7c8 = 7r7c13 => r8c2<>7
Whip[3]: Supposing 7r8c3 would causes 7 to disappear in Box 8 => r8c3<>7
7r8c3 - 7r7(c1=c8) - 7r4(c8=c4) - 7b8(p7=.)
Whip[4]: Supposing 6r9c9 would causes 6 to disappear in Box 8 => r9c9<>6
6r9c9 - 2r9(c9=c2) - r1c2(2=3) - r8c2(3=6) - 6b8(p5=.)
Whip[5]: Supposing 7r4c8 would causes 7 to disappear in Box 4 => r4c8<>7
7r4c8 - r5c9(7=6) - 6c7(r6=r7) - 6c8(r9=r3) - 6c1(r3=r6) - 7b4(p7=.)
Hidden Single: 7 in b6 => r5c9=7
Locked Candidates 2 (Claiming): 7 in r8 => r9c4<>7
Whip[4]: Supposing 6r7c3 would causes 6 to disappear in Column 7 => r7c3<>6
6r7c3 - 2r7(c3=c5) - r5c5(2=6) - 6r4(c4=c8) - 6c7(r6=.)
Whip[4]: Supposing 6r8c5 would causes 7 to disappear in Column 5 => r8c5<>6
6r8c5 - 6r5(c5=c2) - 6b7(p8=p1) - 7c1(r7=r6) - 7c5(r6=.)
Locked Candidates 1 (Pointing): 6 in b8 => r4c4<>6
AIC Type 2: 5r6c7 = r4c8 - (5=7)r4c4 - r4c3 = 7r6c1 => r6c1<>5
AIC Type 2: 6r7c7 = (6-5)r6c7 = (5-1)r6c6 = r8c6 - r8c9 = 1r7c8 => r7c8<>6
AIC Type 2: 6r4c8 = (6-5)r6c7 = (5-1)r6c6 = r8c6 - r8c9 = (1-7)r7c8 = 7r9c8 => r9c8<>6
Whip[4]: Supposing 5r2c3 would causes 6 to disappear in Column 8 => r2c3<>5
5r2c3 - r3c1(5=6) - r6c1(6=7) - r4c3(7=6) - 6c8(r4=.)
Discontinuous Nice Loop: 1r4c2 = r4c5 - r7c5 = (1-7)r7c8 = r9c8 - r9c2 = r2c2 - (7=6)r2c3 - r4c3 = r4c8 - (6=5)r6c7 - (5=1)r6c6 - r6c2 = 1r4c2 => r4c2=1
Hidden Single: 9 in r4 => r4c5=9
Hidden Single: 9 in r6 => r6c2=9
Discontinuous Nice Loop: 6r4c8 = r4c3 - (6=7)r2c3 - r2c2 = r9c2 - (7=5)r9c8 - (5=6)r4c8 => r4c8=6
Full House: r6c7=5
Full House: r7c7=6
Naked Single: r6c6=1
X-Chain: 5r8c6 = r5c6 - r5c2 = 5r4c3 => r8c3<>5
XY-Chain: (6=7)r2c3 - (7=5)r4c3 - (5=6)r5c2 => r2c2<>6
XY-Chain: (7=5)r7c1 - (5=6)r3c1 - (6=7)r2c3 => r7c3<>7
XY-Chain: (1=2)r7c5 - (2=5)r7c3 - (5=7)r7c1 - (7=6)r6c1 - (6=5)r3c1 - (5=1)r3c8 => r7c8<>1
stte


[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 147    12378  2378   ! 49     5      6      ! 47     178    1789   !
   ! 4567   567    567    ! 1      8      49     ! 2      3      5679   !
   ! 1456   1568   9      ! 2      3      7      ! 456    1568   1568   !
   +----------------------+----------------------+----------------------+
   ! 2      15679  567    ! 45679  1679   1459   ! 8      567    3      !
   ! 3      567    4      ! 8      267    25     ! 1      9      567    !
   ! 1567   156789 5678   ! 3      1679   159    ! 567    2      4      !
   +----------------------+----------------------+----------------------+
   ! 567    4      2567   ! 5679   12679  3      ! 567    15678  125678 !
   ! 8      23567  23567  ! 567    1267   125    ! 9      4      12567  !
   ! 9      2567   1      ! 567    4      8      ! 3      567    2567   !
   +----------------------+----------------------+----------------------+
186 candidates

Code: Select all

hidden-pairs-in-a-row: r1{n2 n3}{c2 c3} ==> r1c3≠8, r1c3≠7, r1c2≠8, r1c2≠7, r1c2≠1
silngles ==> r3c2=8, r6c3=8
whip[1]: c2n1{r6 .} ==> r6c1≠1
hidden-pairs-in-a-block: b4{n1 n9}{r4c2 r6c2} ==> r6c2≠7, r6c2≠6, r6c2≠5, r4c2≠7, r4c2≠6, r4c2≠5
biv-chain[3]: r1c7{n7 n4} - b2n4{r1c4 r2c6} - r2n9{c6 c9} ==> r2c9≠7
whip[1]: r2n7{c3 .} ==> r1c1≠7
z-chain[5]: c9n8{r7 r1} - r1n9{c9 c4} - r7n9{c4 c5} - r7n1{c5 c8} - r7n8{c8 .} ==> r7c9≠2, r7c9≠7, r7c9≠6, r7c9≠5
   +-------------------+-------------------+-------------------+
   ! 14    23    23    ! 49    5     6     ! 47    178   1789  !
   ! 4567  567   567   ! 1     8     49    ! 2     3     569   !
   ! 1456  8     9     ! 2     3     7     ! 456   156   156   !
   +-------------------+-------------------+-------------------+
   ! 2     19    567   ! 45679 1679  1459  ! 8     567   3     !
   ! 3     567   4     ! 8     267   25    ! 1     9     567   !
   ! 567   19    8     ! 3     1679  159   ! 567   2     4     !
   +-------------------+-------------------+-------------------+
   ! 567   4     2567  ! 5679  12679 3     ! 567   15678 18    !
   ! 8     23567 23567 ! 567   1267  125   ! 9     4     12567 !
   ! 9     2567  1     ! 567   4     8     ! 3     567   2567  !
   +-------------------+-------------------+-------------------+

Code: Select all

OR5-anti-tridagon[12] (type diag) for digits 5, 6 and 7 in blocks:
        b4, with cells: r4c3, r5c2, r6c1
        b6, with cells: r4c8, r5c9, r6c7
        b7, with cells: r8c3, r9c2, r7c1
        b9, with cells: r8c9, r9c8, r7c7
with 5 guardians: n2r8c3 n3r8c3 n1r8c9 n2r8c9 n2r9c2

OR5-forcing-whip-elim[7] based on OR5-anti-tridagon[12] for n1r8c9, n2r8c3, n2r8c9, n2r9c2 and  n3r8c3:
   || n1r8c9 - partial-whip[1]: r7n1{c9 c5} -
   || n2r8c3 - partial-whip[1]: b8n2{r8c6 r7c5} -
   || n2r8c9 - partial-whip[1]: b8n2{r8c6 r7c5} -
   || n2r9c2 - partial-whip[1]: r7n2{c3 c5} -
   || n3r8c3 - partial-whip[2]: r1c3{n3 n2} - r7n2{c3 c5} -
 ==> r7c5≠9

This single anti-tridagon elimination allows an easy solution in W7:

Code: Select all

singles ==> r7c4=9, r1c4=4, r1c1=1, r1c7=7, r1c8=8, r1c9=9, r2c6=9, r7c9=8, r3c7=4, r2c1=4, r4c6=4
hidden-pairs-in-a-row: r4{n1 n9}{c2 c5} ==> r4c5≠7, r4c5≠6
whip[5]: c2n3{r8 r1} - c2n2{r1 r9} - r7n2{c3 c5} - r7n7{c5 c8} - r7n1{c8 .} ==> r8c2≠7
whip[7]: r7n2{c3 c5} - r7n1{c5 c8} - r7n7{c8 c1} - r6n7{c1 c5} - r5c5{n7 n6} - r4n6{c4 c8} - c7n6{r6 .} ==> r7c3≠6
whip[7]: b3n5{r3c9 r3c8} - r2c9{n5 n6} - r5c9{n6 n7} - r4c8{n7 n6} - c3n6{r4 r8} - c4n6{r8 r9} - b8n5{r9c4 .} ==> r8c9≠5
whip[7]: c7n6{r6 r7} - c8n6{r7 r3} - c1n6{r3 r6} - r6n7{c1 c5} - r5c5{n7 n2} - r7c5{n2 n1} - c8n1{r7 .} ==> r5c9≠6
t-whip[5]: r5c9{n7 n5} - b3n5{r3c9 r3c8} - b9n5{r7c8 r7c7} - c1n5{r7 r6} - r6n7{c1 .} ==> r5c5≠7
z-chain[5]: r5n6{c5 c2} - b7n6{r9c2 r7c1} - c1n7{r7 r6} - b5n7{r6c5 r4c4} - c4n6{r4 .} ==> r8c5≠6
t-whip[7]: r5c9{n7 n5} - b3n5{r3c9 r3c8} - b9n5{r7c8 r7c7} - c1n5{r7 r6} - c6n5{r6 r8} - b7n5{r8c2 r9c2} - r9n2{c2 .} ==> r9c9≠7
whip[6]: c2n3{r8 r1} - c2n2{r1 r9} - c9n2{r9 r8} - c9n7{r8 r5} - r5n5{c9 c6} - c6n2{r5 .} ==> r8c2≠5
t-whip[5]: r9n2{c9 c2} - r1c2{n2 n3} - r8c2{n3 n6} - r5n6{c2 c5} - b8n6{r7c5 .} ==> r9c9≠6
whip[6]: r5n6{c5 c2} - r9n6{c2 c8} - r7c7{n6 n5} - r7c1{n5 n7} - b4n7{r6c1 r4c3} - c8n7{r4 .} ==> r7c5≠6
whip[1]: b8n6{r9c4 .} ==> r4c4≠6
whip[5]: c7n5{r6 r7} - c8n5{r7 r3} - r3c1{n5 n6} - r7n6{c1 c8} - c8n1{r7 .} ==> r5c9≠5
naked-single ==> r5c9=7
finned-x-wing-in-rows: n7{r4 r8}{c3 c4} ==> r9c4≠7
biv-chain[3]: r5c2{n5 n6} - r4n6{c3 c8} - b6n5{r4c8 r6c7} ==> r6c1≠5
biv-chain[4]: r7n1{c8 c5} - c6n1{r8 r6} - r6n5{c6 c7} - b6n6{r6c7 r4c8} ==> r7c8≠6
biv-chain[5]: c8n7{r9 r7} - b9n1{r7c8 r8c9} - c6n1{r8 r6} - r6n5{c6 c7} - b6n6{r6c7 r4c8} ==> r9c8≠6
t-whip[4]: r3c1{n5 n6} - c8n6{r3 r4} - b4n6{r4c3 r5c2} - b4n5{r5c2 .} ==> r2c3≠5
biv-chain[3]: c2n7{r9 r2} - r2n5{c2 c9} - r9c9{n5 n2} ==> r9c2≠2
hidden-single-in-a-row ==> r9c9=2
whip[1]: c9n5{r3 .} ==> r3c8≠5
hidden-pairs-in-a-column: c2{n2 n3}{r1 r8} ==> r8c2≠6
biv-chain[4]: r9c8{n5 n7} - c2n7{r9 r2} - r2c3{n7 n6} - r4n6{c3 c8} ==> r4c8≠5
singles ==> r4c8=6, r3c8=1, r6c7=5, r6c6=1, r4c5=9, r4c2=1, r6c2=9, r7c7=6, r8c9=1, r7c5=1, r7c3=2, r1c3=3, r1c2=2, r8c2=3
whip[1]: b8n7{r8c5 .} ==> r8c3≠7
finned-x-wing-in-columns: n5{c3 c6}{r8 r4} ==> r4c4≠5
stte

[Cenoman]

My two cents...

Code: Select all

 +-------------------------+-------------------------+-------------------------+
 |  147    23      23      |  49      5       6      |  47    178     1789     |
 |  4567   567     567     |  1       8       49     |  2     3       5679     |
 |  1456   8       9       |  2       3       7      |  456   156     156      |
 +-------------------------+-------------------------+-------------------------+
 |  2      19      567#    |  45679   1679    1459   |  8     567#    3        |
 |  3      567#    4       |  8       267     25     |  1     9       567#     |
 |  567#   19      8       |  3       1679    159    |  567#  2       4        |
 +-------------------------+-------------------------+-------------------------+
 |  567#   4       2567    |  5679    12-679  3      |  567#  15678   125678   |
 |  8      23567   23567#  |  567     1267    125    |  9     4       12567#   |
 |  9      2567#   1       |  567     4       8      |  3     567#    2567     |
 +-------------------------+-------------------------+-------------------------+

1. TH(567)b4679 (#)
(2)r9c2|(23)r18c3 - (2=5679)r7c1347
(1|2)r8c9 - (12)r8c56 = (1|2)r7c5
=> -679 r7c5; lcls, 11 placements

Code: Select all

 +------------------------+---------------------+----------------------+
 |  1     23      23      |  4     5      6     |  7    8      9       |
 |  4     567     567     |  1     8      9     |  2    3      56      |
 |  56    8       9       |  2     3      7     |  4    156    156     |
 +------------------------+---------------------+----------------------+
 |  2     19      567     |  567   19     4     |  8    567    3       |
 |  3     567     4       |  8     267    25    |  1    9      567     |
 |  567   19      8       |  3     1679   15    |  56   2      4       |
 +------------------------+---------------------+----------------------+
 |  567   4       2567    |  9     12     3     |  56   1567   8       |
 |  8     23567   23567   |  567   1267   125   |  9    4      12567   |
 |  9     2567    1       |  567   4      8     |  3    567    2567    |
 +------------------------+---------------------+----------------------+

2. UR(19)r46c25 => -19 r6c5; 4 placements
3. UR(23)r18c23 using externals: (2)r7c3 == r9c2 => -2 r8c23

Code: Select all

 +----------------------+--------------------+----------------------+
 |  1     23     23     |  4     5      6    |  7    8      9       |
 |  4     567    567    |  1     8      9    |  2    3      56      |
 |  56    8      9      |  2     3      7    |  4    156    156     |
 +----------------------+--------------------+----------------------+
 |  2     1      567    |  567   9      4    |  8    567    3       |
 |  3     567    4      |  8     267    25   |  1    9      567     |
 |  567   9      8      |  3     67     1    |  56   2      4       |
 +----------------------+--------------------+----------------------+
 |  567   4      2567   |  9     12     3    |  56   1567   8       |
 |  8     3567   3567   |  567   1267   25   |  9    4      12567   |
 |  9     2567   1      |  567   4      8    |  3    567    2567    |
 +----------------------+--------------------+----------------------+

4. (6=5)r7c7 - r6c7 = r6c1-(5=6)r3c1 => -6 r7c1
5. Almost Kite:
[(6)r7c7 = r6c7 - r4c8 = r4c3] = (6-5)r4c4 = r5c6 - (5=2)r8c6 - r7c5 = (2)r7c3 => -6 r7c3
6. (5)r6c7=r7c7-(5=7)r9c8-r4c8=(7)r5c9 =>-5r5c9
7. Almost X-Chain (6):
[(6)r2c9 = r2c23 - r3c1 = r6c1 - r6c5 = r5c5] = (6-1)r8c5=(127)r589c9 => -6 r5c9; lcls, 1 placement
8. (6)r8c3 = r89c2 - r5c2 = r5c5 - (6=7)r6c5 - r6c1 = (7)r7c1 => -7 r8c3
9. (6)r9c4 = r9c2 - (6=5)r5c2 - r5c6 = (5)r8c6 => -5 r9c4

10. Kraken row (6)r6c157 =>-1r8c5
(6)r6c1-r3c1=(61)r38c9
(6-7)r6c5=(7)r8c5
(6)r6c7-(6=251)b9p169
=>-1r8c5; 13 placements

11. BUG+1 => +5 r2c2; ste

[Mauriès Robert]

1. TH(567)b4679 (#)

Hi Cenoman,
What does this writing mean?
Cordialy
Robert