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[coloin]

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+---+---+---+
|89.|.67|.45|
|5.7|4.8|.96|
|.46|...|...|
+---+---+---+
|.7.|.4.|...|
|4..|.75|6..|
|65.|8.9|4..|
+---+---+---+
|.8.|...|.61|
|76.|...|832|
|...|.8.|9.4|
+---+---+---+  WheresMyHammer 


Just wondering how this solves... as the tridagon isnt in the solution grid ...

[Mauriès Robert]

Hi coloin,
Here's my solution, which relies on the presence of two guardians in the Tridagon, and then on the uniqueness of the puzzle solution. It's achieved using anti-tracks, which are memory chains (-> indicating that the next candidate depends on the previous candidates).

TD= Tridagon 123p357B1,123p159B2,123p159B4,123p348B5
(-7r7c4)->7r9c4->[6r9c6 & 5r9c8->45r78c3]->9r7c1->TD->... => r7c4=7 + 5 placements
(-5r9c3)->[5r8c3->4r7c3->9r7c1 & 5r9c4->6r9c6]->TD->... => r9c3=5
UR(59r38c45) => r8c3=9 + 9 placements
(-1r4c46)->1r3c6->1r12c7->1r4c3->8r4c9->3r3c9->2r3c1->3r1c3->2r6c3->2r2c5->... r1c4 vide => -1r5c4 => -23r4c46, -1r4c37
(-3r2c5)->2r2c5->3r6c5->2r5c4->2r1c7->3r4c7->2r4c3->8r5c3->3r5c2->1r2c2->... => r2c7 empty => r2c5=3, stte.

Robert

[eleven]

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+------------------------+--------------------------+-------------------------+
| 8       9       123    |  123     6       7       | 123     4       5       |
| 5       123     7      |  4       123     8       | 123     9       6       |
| 123     4       6      | #59     #59      123     | 1237    1278    378     |
+------------------------+--------------------------+-------------------------+
| 1239    7       12389  |  1236    4       1236    | 1235    1258    389     |
| 4       123     12389  |  123     7       5       | 6       128     389     |
| 6       5       123    |  8       123     9       | 4       127     37      |
+------------------------+--------------------------+-------------------------+
| 239     8       23459  |  23579   2359    234     | 57      6       1       |
| 7       6       459-1  | #59+1    #59+1   4-1     | 8       3       2       |
| 123     123     1235   |  23567-1 8       236-1   | 9       57      4       |
+------------------------+--------------------------+-------------------------+

UR 59r38c45 => -1r8c36,r9c46

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+-----------------------+-----------------------+----------------------+
|  8      9     *123    | *123    6      7      | 123    4      5      |
|  5     *123    7      |  4     *123    8      | 123    9      6      |
| *123    4      6      |  59     59    *123    | 1237   1278   378    |
+-----------------------+-----------------------+----------------------+
| *123+9  7      12389  |  1236   4     *123+6  | 1235   1258   389    |
|  4     *123    12389  | *123    7      5      | 6      128    389    |
|  6      5     *123    |  8     *123    9      | 4      127    37     |
+-----------------------+-----------------------+----------------------+
|  23-9   8      4      |  23579  2359   23     | 57     6      1      |
|  7      6     b59     |  159    159    4      | 8      3      2      |
| a123   a123   a1235   |  23567  8     a236    | 9      57     4      |
+-----------------------+-----------------------+----------------------+

Tridagon 123b1245: 9r4c1 == 6r4c6 - (6=1235)r9c1263 -(5=9)r8c3 => -9r7c1

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+-------------------+-------------------+-------------------+
| 8     9     123   | 123   6     7     |*123   4     5     |
| 5     123   7     | 4     23    8     |*123   9     6     |
| 123   4     6     | 9     5    *123   | 7     28-1  38    |
+-------------------+-------------------+-------------------+
| 9     7     128   | 126   4    *126   |*123   5     38    |
| 4     123   1238  | 123   7     5     | 6     128   9     |
| 6     5     123   | 8     23    9     | 4     12    7     |
+-------------------+-------------------+-------------------+
| 23    8     4     | 7     9     23    | 5     6     1     |
| 7     6     9     | 5     1     4     | 8     3     2     |
| 123   123   5     | 236   8     236   | 9     7     4     |
+-------------------+-------------------+-------------------+

Skyscraper 1c67 => -1r3c8

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+-------------------+-------------------+--------------------+
| 8     9    *123   | *123   6     7    | #123   4     5     |
| 5     123   7     |  4    *23    8    |  123   9     6     |
| 123   4     6     |  9     5    #123  |  7     28   a38    |
+-------------------+-------------------+--------------------+
| 9     7     128   |  126   4     126  |  2-3   5   cb38    |
| 4     123  #1238  |  123   7     5    |  6    c128   9     |
| 6     5    *123   |  8    *23    9    |  4     12    7     |
+-------------------+-------------------+--------------------+
| 23    8     4     |  7     9     23   |  5     6     1     |
| 7     6     9     |  5     1     4    |  8     3     2     |
| 123   123   5     |  236   8     236  |  9     7     4     |
+-------------------+-------------------+--------------------+

Oddagon 3 (*), guardians r1c7,r3c6,r5c3
3r3c6 - r3c9 = 3r4c9
(3-8)r5c3 = 83b6p53
=> -3r3c7

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+----------------+----------------+----------------+
| 8    9    13-2 | 123  6    7    | 13   4    5    |
| 5   *123  7    | 4   *23   8    | 13   9    6    |
| 13   4    6    | 9    5    13   | 7    2    8    |
+----------------+----------------+----------------+
| 9    7    8    | 16   4    16   | 2    5    3    |
| 4    13-2 123  | 23   7    5    | 6    8    9    |
| 6    5   *23   | 8   *23   9    | 4    1    7    |
+----------------+----------------+----------------+
| 23   8    4    | 7    9    23   | 5    6    1    |
| 7    6    9    | 5    1    4    | 8    3    2    |
| 123  13   5    | 36   8    236  | 9    7    4    |
+----------------+----------------+----------------+

Skyscraper 2r26 => -2r1c3,r5c2, stte

[denis_berthier]

.
The fact that the tridagon is present or not in the solution grid is irrelevant to the way it can be solved - or to the difficulty of solving.

1) Using only the tridagon pattern, a solution with chains of length ≤ 11:

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Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 8      9      123    ! 123    6      7      ! 123    4      5      !
   ! 5      123    7      ! 4      123    8      ! 123    9      6      !
   ! 123    4      6      ! 12359  12359  123    ! 1237   1278   378    !
   +----------------------+----------------------+----------------------+
   ! 1239   7      12389  ! 1236   4      1236   ! 1235   1258   389    !
   ! 4      123    12389  ! 123    7      5      ! 6      128    389    !
   ! 6      5      123    ! 8      123    9      ! 4      127    37     !
   +----------------------+----------------------+----------------------+
   ! 239    8      23459  ! 23579  2359   234    ! 57     6      1      !
   ! 7      6      1459   ! 159    159    14     ! 8      3      2      !
   ! 123    123    1235   ! 123567 8      1236   ! 9      57     4      !
   +----------------------+----------------------+----------------------+
157 candidates.

hidden-pairs-in-a-row: r3{n5 n9}{c4 c5} ==> r3c5≠3, r3c5≠2, r3c5≠1, r3c4≠3, r3c4≠2, r3c4≠1

RESOLUTION STATE RS1

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Trid-OR2-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 2 guardians (in cells marked @): n9r4c1 n6r4c6
   +----------------------+----------------------+----------------------+
   ! 8      9      123#   ! 123#   6      7      ! 123    4      5      !
   ! 5      123#   7      ! 4      123#   8      ! 123    9      6      !
   ! 123#   4      6      ! 59     59     123#   ! 1237   1278   378    !
   +----------------------+----------------------+----------------------+
   ! 1239#@ 7      12389  ! 1236   4      1236#@ ! 1235   1258   389    !
   ! 4      123#   12389  ! 123#   7      5      ! 6      128    389    !
   ! 6      5      123#   ! 8      123#   9      ! 4      127    37     !
   +----------------------+----------------------+----------------------+
   ! 239    8      23459  ! 23579  2359   234    ! 57     6      1      !
   ! 7      6      1459   ! 159    159    14     ! 8      3      2      !
   ! 123    123    1235   ! 123567 8      1236   ! 9      57     4      !
   +----------------------+----------------------+----------------------+

t-whip[5]: r8n9{c5 c3} - c3n4{r8 r7} - c3n5{r7 r9} - r9c8{n5 n7} - r7n7{c7 .} ==> r7c4≠9
Trid-OR2-whip[5]: c4n7{r7 r9} - r9n6{c4 c6} - OR2{{n6r4c6 | n9r4c1}} - r7c1{n9 n3} - b8n3{r7c4 .} ==> r7c4≠2
Trid-OR2-whip[5]: c4n7{r7 r9} - r9n6{c4 c6} - OR2{{n6r4c6 | n9r4c1}} - r7c1{n9 n2} - b8n2{r7c5 .} ==> r7c4≠3
naked-pairs-in-a-row: r7{c4 c7}{n5 n7} ==> r7c5≠5, r7c3≠5
Trid-OR2-whip[5]: r8n1{c6 c3} - c3n4{r8 r7} - b7n9{r7c3 r7c1} - OR2{{n9r4c1 | n6r4c6}} - r9n6{c6 .} ==> r9c4≠1
Trid-OR2-whip[5]: r8n5{c5 c3} - c3n4{r8 r7} - b7n9{r7c3 r7c1} - OR2{{n9r4c1 | n6r4c6}} - r9n6{c6 .} ==> r9c4≠5
Trid-OR2-whip[6]: r8n5{c5 c3} - c3n4{r8 r7} - b7n9{r7c3 r7c1} - OR2{{n9r4c1 | n6r4c6}} - r9n6{c6 c4} - c4n7{r9 .} ==> r7c4≠5
singles ==> r7c4=7, r7c7=5, r9c8=7, r6c9=7, r3c7=7, r9c3=5
hidden-pairs-in-a-column: c4{n5 n9}{r3 r8} ==> r8c4≠1
z-chain[3]: b6n3{r4c9 r5c9} - r3c9{n3 n8} - r4n8{c9 .} ==> r4c3≠3
Trid-OR2-whip[3]: OR2{{n6r4c6 | n9r4c1}} - c9n9{r4 r5} - b6n3{r5c9 .} ==> r4c6≠3
Trid-OR2-whip[6]: b6n3{r4c9 r5c9} - c9n9{r5 r4} - OR2{{n9r4c1 | n6r4c6}} - c4n6{r4 r9} - c4n3{r9 r1} - r3n3{c6 .} ==> r4c1≠3
whip[7]: c3n4{r7 r8} - b7n9{r8c3 r7c1} - c1n3{r7 r3} - c2n3{r2 r5} - c9n3{r5 r4} - r4n8{c9 c3} - r4n9{c3 .} ==> r7c3≠3
whip[11]: b5n3{r5c4 r6c5} - c3n3{r6 r5} - c3n8{r5 r4} - b4n9{r4c3 r4c1} - r4c9{n9 n3} - r3n3{c9 c1} - r7c1{n3 n2} - c5n2{r7 r2} - b1n2{r2c2 r1c3} - c7n2{r1 r4} - r6n2{c8 .} ==> r1c4≠3
biv-chain[3]: b2n3{r3c6 r2c5} - r6n3{c5 c3} - r1n3{c3 c7} ==> r3c9≠3
singles ==> r3c9=8, r5c8=8, r4c3=8
whip[1]: c9n3{r5 .} ==> r4c7≠3
finned-x-wing-in-rows: n3{r3 r7}{c1 c6} ==> r9c6≠3
z-chain[3]: r5n2{c3 c4} - r1n2{c4 c7} - b6n2{r4c7 .} ==> r6c3≠2
biv-chain[3]: b6n1{r4c7 r6c8} - r6c3{n1 n3} - r1n3{c3 c7} ==> r1c7≠1
finned-x-wing-in-rows: n1{r1 r5}{c4 c3} ==> r6c3≠1
w2-tte

2) Using the tridagon pattern + 3 different instantiations of the EL13c290 impossible pattern, a pattern very close to the tridagon and among the most frequent ones in T&E(3) puzzles, a solution with chains of lengths ≤ 6
Starting from previous resolution state RS1:

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Trid-OR2-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 2 guardians (in cells marked @): n9r4c1 n6r4c6
   +----------------------+----------------------+----------------------+
   ! 8      9      123#   ! 123#   6      7      ! 123    4      5      !
   ! 5      123#   7      ! 4      123#   8      ! 123    9      6      !
   ! 123#   4      6      ! 59     59     123#   ! 1237   1278   378    !
   +----------------------+----------------------+----------------------+
   ! 1239#@ 7      12389  ! 1236   4      1236#@ ! 1235   1258   389    !
   ! 4      123#   12389  ! 123#   7      5      ! 6      128    389    !
   ! 6      5      123#   ! 8      123#   9      ! 4      127    37     !
   +----------------------+----------------------+----------------------+
   ! 239    8      23459  ! 23579  2359   234    ! 57     6      1      !
   ! 7      6      1459   ! 159    159    14     ! 8      3      2      !
   ! 123    123    1235   ! 123567 8      1236   ! 9      57     4      !
   +----------------------+----------------------+----------------------+

EL13c290s-OR2-relation for digits: 1, 2 and 3
   in cells (marked #): (r9c3 r9c2 r9c6 r5c2 r5c4 r6c3 r6c5 r2c2 r2c5 r1c3 r1c4 r3c1 r3c6)
   with 2 guardians (in cells marked @) : n5r9c3 n6r9c6 
   +----------------------+----------------------+----------------------+
   ! 8      9      123#   ! 123#   6      7      ! 123    4      5      !
   ! 5      123#   7      ! 4      123#   8      ! 123    9      6      !
   ! 123#   4      6      ! 59     59     123#   ! 1237   1278   378    !
   +----------------------+----------------------+----------------------+
   ! 1239   7      12389  ! 1236   4      1236   ! 1235   1258   389    !
   ! 4      123#   12389  ! 123#   7      5      ! 6      128    389    !
   ! 6      5      123#   ! 8      123#   9      ! 4      127    37     !
   +----------------------+----------------------+----------------------+
   ! 239    8      23459  ! 23579  2359   234    ! 57     6      1      !
   ! 7      6      1459   ! 159    159    14     ! 8      3      2      !
   ! 123    123#   1235#@ ! 123567 8      1236#@ ! 9      57     4      !
   +----------------------+----------------------+----------------------+

EL13c290-OR2-relation for digits: 1, 2 and 3
   in cells (marked #): (r3c6 r2c7 r2c2 r2c5 r1c7 r1c3 r1c4 r5c2 r5c4 r6c3 r6c5 r4c7 r4c6)
   with 2 guardians (in cells marked @) : n5r4c7 n6r4c6 
   +----------------------+----------------------+----------------------+
   ! 8      9      123#   ! 123#   6      7      ! 123#   4      5      !
   ! 5      123#   7      ! 4      123#   8      ! 123#   9      6      !
   ! 123    4      6      ! 59     59     123#   ! 1237   1278   378    !
   +----------------------+----------------------+----------------------+
   ! 1239   7      12389  ! 1236   4      1236#@ ! 1235#@ 1258   389    !
   ! 4      123#   12389  ! 123#   7      5      ! 6      128    389    !
   ! 6      5      123#   ! 8      123#   9      ! 4      127    37     !
   +----------------------+----------------------+----------------------+
   ! 239    8      23459  ! 23579  2359   234    ! 57     6      1      !
   ! 7      6      1459   ! 159    159    14     ! 8      3      2      !
   ! 123    123    1235   ! 123567 8      1236   ! 9      57     4      !
   +----------------------+----------------------+----------------------+

EL13c290-OR2-relation for digits: 1, 2 and 3
   in cells (marked #): (r3c1 r2c7 r2c5 r2c2 r1c7 r1c4 r1c3 r6c5 r6c3 r5c4 r5c2 r4c7 r4c1)
   with 2 guardians (in cells marked @) : n5r4c7 n9r4c1 
   +----------------------+----------------------+----------------------+
   ! 8      9      123#   ! 123#   6      7      ! 123#   4      5      !
   ! 5      123#   7      ! 4      123#   8      ! 123#   9      6      !
   ! 123#   4      6      ! 59     59     123    ! 1237   1278   378    !
   +----------------------+----------------------+----------------------+
   ! 1239#@ 7      12389  ! 1236   4      1236   ! 1235#@ 1258   389    !
   ! 4      123#   12389  ! 123#   7      5      ! 6      128    389    !
   ! 6      5      123#   ! 8      123#   9      ! 4      127    37     !
   +----------------------+----------------------+----------------------+
   ! 239    8      23459  ! 23579  2359   234    ! 57     6      1      !
   ! 7      6      1459   ! 159    159    14     ! 8      3      2      !
   ! 123    123    1235   ! 123567 8      1236   ! 9      57     4      !
   +----------------------+----------------------+----------------------+

EL13c290-OR2-whip[3]: c4n6{r9 r4} - OR2{{n6r4c6 | n5r4c7}} - b9n5{r7c7 .} ==> r9c4≠5
EL13c290-OR2-whip[4]: r9n6{c4 c6} - OR2{{n6r4c6 | n5r4c7}} - r7c7{n5 n7} - c4n7{r7 .} ==> r9c4≠3
EL13c290-OR2-whip[4]: r9n6{c4 c6} - OR2{{n6r4c6 | n5r4c7}} - r7c7{n5 n7} - c4n7{r7 .} ==> r9c4≠2
EL13c290-OR2-whip[4]: r9n6{c4 c6} - OR2{{n6r4c6 | n5r4c7}} - r7c7{n5 n7} - c4n7{r7 .} ==> r9c4≠1
t-whip[5]: r8n9{c5 c3} - c3n4{r8 r7} - c3n5{r7 r9} - r9c8{n5 n7} - r7n7{c7 .} ==> r7c4≠9
EL13c290-OR2-whip[5]: c3n4{r7 r8} - b7n9{r8c3 r7c1} - OR2{{n9r4c1 | n5r4c7}} - b9n5{r7c7 r9c8} - c3n5{r9 .} ==> r7c3≠2
EL13c290-OR2-whip[5]: c3n4{r7 r8} - b7n9{r8c3 r7c1} - OR2{{n9r4c1 | n5r4c7}} - b9n5{r7c7 r9c8} - c3n5{r9 .} ==> r7c3≠3
Trid-OR2-whip[5]: c4n7{r7 r9} - r9n6{c4 c6} - OR2{{n6r4c6 | n9r4c1}} - r7c1{n9 n3} - b8n3{r7c4 .} ==> r7c4≠2
Trid-OR2-whip[5]: c4n7{r7 r9} - r9n6{c4 c6} - OR2{{n6r4c6 | n9r4c1}} - r7c1{n9 n2} - b8n2{r7c5 .} ==> r7c4≠3
naked-pairs-in-a-row: r7{c4 c7}{n5 n7} ==> r7c5≠5, r7c3≠5
Trid-OR2-ctr-whip[5]: c6n6{r4 r9} - b8n3{r9c6 r7c5} - b8n2{r7c5 r7c6} - r7c1{n2 n9} - OR2{{n9r4c1 n6r4c6 | .}} ==> r4c6≠3
Trid-OR2-ctr-whip[5]: c6n6{r4 r9} - b8n2{r9c6 r7c5} - b8n3{r7c5 r7c6} - r7c1{n3 n9} - OR2{{n9r4c1 n6r4c6 | .}} ==> r4c6≠2
EL13c290s-OR2-whip[3]: c8n5{r4 r9} - OR2{{n5r9c3 | n6r9c6}} - r4c6{n6 .} ==> r4c8≠1
EL13c290-OR2-whip[5]: c3n5{r8 r9} - c8n5{r9 r4} - OR2{{n5r4c7 | n9r4c1}} - b7n9{r7c1 r7c3} - c3n4{r7 .} ==> r8c3≠1
whip[1]: r8n1{c6 .} ==> r9c6≠1
EL13c290-OR2-whip[5]: OR2{{n9r4c1 | n5r4c7}} - r7n5{c7 c4} - b8n7{r7c4 r9c4} - r9n6{c4 c6} - r4c6{n6 .} ==> r4c1≠1
Trid-OR2-whip[6]: r9n5{c3 c8} - r9n7{c8 c4} - r9n6{c4 c6} - OR2{{n6r4c6 | n9r4c1}} - r7c1{n9 n3} - b8n3{r7c5 .} ==> r9c3≠2
Trid-OR2-whip[6]: r9n5{c3 c8} - r9n7{c8 c4} - r9n6{c4 c6} - OR2{{n6r4c6 | n9r4c1}} - r7c1{n9 n2} - b8n2{r7c5 .} ==> r9c3≠3
biv-chain[4]: c7n7{r3 r7} - b9n5{r7c7 r9c8} - r9c3{n5 n1} - c1n1{r9 r3} ==> r3c7≠1
t-whip[5]: r9c8{n7 n5} - r9c3{n5 n1} - b4n1{r4c3 r5c2} - b1n1{r2c2 r3c1} - c8n1{r3 .} ==> r6c8≠7
hidden-single-in-a-block ==> r6c9=7
t-whip[2]: r6n3{c3 c5} - c4n3{r5 .} ==> r1c3≠3
whip[1]: c3n3{r6 .} ==> r4c1≠3, r5c2≠3
z-chain[3]: b6n3{r4c9 r5c9} - r5n9{c9 c3} - c3n8{r5 .} ==> r4c3≠3
EL13c290-OR2-ctr-whip[3]: c9n9{r5 r4} - b6n3{r4c9 r4c7} - OR2{{n5r4c7 n9r4c1 | .}} ==> r5c9≠8
z-chain[4]: r1n3{c7 c4} - r5n3{c4 c3} - r5n8{c3 c8} - r3n8{c8 .} ==> r3c9≠3
naked-single ==> r3c9=8
whip[1]: c9n3{r5 .} ==> r4c7≠3
biv-chain[3]: r4n8{c3 c8} - c8n5{r4 r9} - r9c3{n5 n1} ==> r4c3≠1
z-chain[3]: b4n1{r5c3 r6c3} - c3n3{r6 r5} - r5n8{c3 .} ==> r5c8≠1
z-chain[3]: r5n1{c3 c4} - r1n1{c4 c7} - b6n1{r4c7 .} ==> r6c3≠1
whip[1]: b4n1{r5c3 .} ==> r5c4≠1
biv-chain[4]: r4n8{c3 c8} - c8n5{r4 r9} - r9c3{n5 n1} - r1c3{n1 n2} ==> r4c3≠2
t-whip[4]: r1n3{c7 c4} - b5n3{r5c4 r6c5} - r6c3{n3 n2} - r1c3{n2 .} ==> r1c7≠1
biv-chain[2]: r6n1{c5 c8} - b3n1{r3c8 r2c7} ==> r2c5≠1
biv-chain[3]: r1c7{n3 n2} - r1c3{n2 n1} - r2n1{c2 c7} ==> r2c7≠3
biv-chain[3]: c5n1{r8 r6} - c8n1{r6 r3} - b2n1{r3c6 r1c4} ==> r8c4≠1
naked-pairs-in-a-column: c4{r3 r8}{n5 n9} ==> r7c4≠5
singles ==> r7c4=7, r7c7=5, r9c8=7, r9c4=6, r4c6=6, r3c7=7, r1c7=3, r4c8=5, r5c8=8, r4c3=8, r9c3=5

At least one candidate of a previous EL13c290-OR2-relation between candidates n5r4c7 n9r4c1 has just been eliminated.
There remains an EL13c290-OR1-relation between candidates: n9r4c1

EL13c290-ORk-relation with only one candidate => r4c1=9
w2-tte

.

[champagne]

.
The fact that the tridagon is present or not in the solution grid is irrelevant to the way it can be solved - or to the difficulty of solving.

This is partially true, but;
If the "loki pattern" is in the solution grid, you can have "relatively hard moves" clearing all guardians but one
This is not true if the "loki pattern" is not in the solution grid

[denis_berthier]

If the "loki pattern" is in the solution grid, you can have "relatively hard moves" clearing all guardians but one
This is not true if the "loki pattern" is not in the solution grid

This is devoid of any meaning and it relies on no statistics of effective resolution.

[champagne]

If the "loki pattern" is in the solution grid, you can have "relatively hard moves" clearing all guardians but one
This is not true if the "loki pattern" is not in the solution grid

This is devoid of any meaning and it relies on no statistics of effective resolution.

The proof is so trivial that I thought dishonest to give it

[denis_berthier]

If the "loki pattern" is in the solution grid, you can have "relatively hard moves" clearing all guardians but one
This is not true if the "loki pattern" is not in the solution grid

This is devoid of any meaning and it relies on no statistics of effective resolution.

The proof is so trivial that I thought dishonest to give it

What I think dishonest is making claims that rely on nothing.

[champagne]

denis_berthier wrote:
.There has never been any "tridagon search hype" - because there has never been any tridagon search at all.
What there has been is a search for T&E(3) puzzles. .

and now

The fact that the tridagon is present or not in the solution grid is irrelevant to the way it can be solved - or to the difficulty of solving.

This is devoid of any meaning and it relies on no statistics of effective resolution.

What I think dishonest is making claims that rely on nothing.

I'll have to comment on these niece pieces.
Not the first time to read strong sentences

We have plenty examples of puzzles in mith's file where the start PM does not show the "loki" pattern.
In the last example that I posted, applying pairs was enough to get it.

is it enough to write

The fact that the tridagon is present or not in the solution grid is irrelevant to the way it can be solved - or to the difficulty of solving.

Surely not and the charge of the stats proving the contrary when the simple logic is there is the burden of the one claiming that.

The proof that the door is open is very simple.

1) if the "loki" pattern is not in the solution grid:
then, any rules clearing a candidate of the solution grid would be a bug, and we have a minimum of 2 candidates not in the "loki" pattern

2) if the "loki" pattern is in the solution grid.

The SE set of rules solves the grid. Following the path, you'll find eliminations clearing the guardians not in the "loki" pattern.
The path can be very hard, but also relatively easy. What is sure is that this set of rules can be oriented to clean all guardians in excess.

=====================

As usual in the sudoku field, most of the puzzles will ask for relatively simple rules, but not all.
In my first tests, it seems that a huge majority of puzzles in mith's collection reach the "simple guardian" using locked sets and fishes.
I'll have in some days a test done in several steps (adding rules) to run on the entire file of mith,
This will give a precise answer to claims done without any number

[champagne]

one example coming in my last test

Code: Select all

.12......3.4......67....51..9.81..56......7.1.6..7.98.....68.7......1..5...59.16. 
812957634354126897679384512297813456538649721461275983125468379986731245743592168


skfr after easy moves

Code: Select all

589   1     2    |34679 3458 345679 |3468 349  34789
3     58    4    |1     258  25679  |268  29   2789 
6     7     89   |2349  2348 2349   |5    1    23489
----------------------------------------------------
247   9     37   |8     1    234    |234  5    6     
2458  23458 358  |69    2345 69     |7    234  1     
1245  6     135  |234   7    2345   |9    8    234   
----------------------------------------------------
12459 2345  1359 |234   6    8      |234  7    2349 
24789 2348  6    |2347  234  1      |2348 2349 5     
2478  2348  378  |5     9    2347   |1    6    2348 

3 guardians

after moves rating 8.3

Code: Select all

58    1     2   |69  3458 679 |3468 349  34789
3     58    4   |1   258  679 |268  29   2789 
6     7     9   |234 2348 234 |5    1    2348 
----------------------------------------------
247   9     37  |8   1    234 |234  5    6     
2458  23458 358 |69  234  69  |7    234  1     
124   6     13  |234 7    5   |9    8    234   
----------------------------------------------
12459 2345  135 |234 6    8   |234  7    2349 
2489  2348  6   |7   234  1   |2348 2349 5     
2478  2348  378 |5   9    234 |1    6    2348 


now 2 guardians

after hard moves (10.)

Code: Select all

58   1     2   |69  3458 7   |346 349 348 
3    58    4   |1   258  69  |268 29  7   
6    7     9   |234 2348 234 |5   1   2348
------------------------------------------
247  9     37  |8   1    234 |234 5   6   
2458 23458 358 |69  234  69  |7   234 1   
124  6     13  |234 7    5   |9   8   234 
------------------------------------------
1245 2345  135 |234 6    8   |234 7   9   
9    2348  6   |7   234  1   |28  234 5   
2478 2348  378 |5   9    234 |1   6   2348



The "loki" pattern is on the path just before the hardest steps

EDIT I don't know what an expert can do with the three guardians, but surely a better end can be done with the 2 guardians

[denis_berthier]

is it enough to write

The fact that the tridagon is present or not in the solution grid is irrelevant to the way it can be solved - or to the difficulty of solving.

Surely not and the charge of the stats proving the contrary when the simple logic is there is the burden of the one claiming that.

The proof that the door is open is very simple.

1) if the "loki" pattern is not in the solution grid:
then, any rules clearing a candidate of the solution grid would be a bug, and we have a minimum of 2 candidates not in the "loki" pattern

2) if the "loki" pattern is in the solution grid.

The SE set of rules solves the grid. Following the path, you'll find eliminations clearing the guardians not in the "loki" pattern.
The path can be very hard, but also relatively easy. What is sure is that this set of rules can be oriented to clean all guardians in excess.

All this is pure nonsense, because the solver doesn't know the solution and therefore doesn't know if the pattern is in it or not.
.

[champagne]

is it enough to write

The fact that the tridagon is present or not in the solution grid is irrelevant to the way it can be solved - or to the difficulty of solving.

Surely not and the charge of the stats proving the contrary when the simple logic is there is the burden of the one claiming that.

The proof that the door is open is very simple.

1) if the "loki" pattern is not in the solution grid:
then, any rules clearing a candidate of the solution grid would be a bug, and we have a minimum of 2 candidates not in the "loki" pattern

2) if the "loki" pattern is in the solution grid.

The SE set of rules solves the grid. Following the path, you'll find eliminations clearing the guardians not in the "loki" pattern.
The path can be very hard, but also relatively easy. What is sure is that this set of rules can be oriented to clean all guardians in excess.

All this is pure nonsense, because the solver doesn't know the solution and therefore doesn't know if the pattern is in it or not.
.

and this does not prevent the player to try the best path!!!

EDIT BTW, many players and likely all bots know what is the solution. The game is to find a nice path

[denis_berthier]

.
OK. Nonsense confirmed.
.

[champagne]

.
OK. Nonsense confirmed.
.

no comment

[ghfick]

Hi champagne,

I tried this puzzle with YZF_Sudoku. I get:

Hidden Single: 1 in r2 => r2c4=1
Hidden Single: 6 in r8 => r8c3=6
Hidden Pair: 69 in r5c4,r5c6 => r5c4<>234,r5c6<>2345
Uniqueness External Test 2/4: 15 in r67c13 => r6c1<>5
Uniqueness Test 7: 69 in r15c46; 2*biCell + 1*conjugate pairs(6c4) => r1c6 <> 9
Almost Locked Set XZ-Rule: A=r7c2479 {23459},B=b1p59 {589}, X=5, Z=9 => r3c9<>9 r7c3<>9
Hidden Single: 9 in c3 => r3c3=9
Naked Triple: in r3c4,r6c4,r7c4 => r1c4<>34,r8c4<>234,
Naked Single: r8c4=7
Naked Triple: in r3c6,r4c6,r9c6 => r1c6<>34,r2c6<>2,r6c6<>234,
Naked Single: r6c6=5
Uniqueness External Test 2/4: 79 in r12c69 => r1c9<>9
Uniqueness Test 1: 69 in r15c46 => r1c6 <> 69
Naked Single: r1c6=7
Hidden Single: 7 in r2 => r2c9=7
Hidden Single: 9 in c9 => r7c9=9
Hidden Single: 9 in r8 => r8c1=9
Empty Rectangle : 8 in b1 connected by r8 => r1c7 <> 8
Triplet Oddagon Type 1: 234r58c58,r4c67,r6c49,r7c47,r9c69 => r9c9<>234
...then, nothing more than Skyscrapers

The snag (for me) is the ALS XZ-Rule (there are several of these available at that stage) to reveal the TH with 1 guardian. Some might dislike the Uniqueness steps but they are fairly easy to spot.

Gordon