The New Sudoku Players' Forum

[champagne]

........1.....234...5.1..62....3.....5.1..4..21.6....5..3....5..7.24....89.56.... ED=10.9/1.2/1.2
I am curious to see what solving experts will do with this one from mith's file

Edit ; skfr ratings

[denis_berthier]

.
I haven't found anything special.
The fact that the SER is low (for a puzzle in T&E(3)) has no impact on Tridagon classifications. It's relatively hard.
It's easier to solve if one also uses another very frequent impossible 3-digit pattern (EL14c1).
Without it, there's a solution in W10 + Trid-OR3W10. With it, we need only W8 + (Trid+EL14c1)-OR5W8.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 479    2348   24789  ! 34789  789    6      ! 5      789    1      !
   ! 1679   68     16789  ! 789    5      2      ! 3      4      789    !
   ! 479    348    5      ! 34789  1      4789   ! 789    6      2      !
   +----------------------+----------------------+----------------------+
   ! 4679   468    46789  ! 4789   3      5      ! 126789 12789  6789   !
   ! 3      5      6789   ! 1      2      789    ! 4      789    6789   !
   ! 2      1      4789   ! 6      789    4789   ! 789    3      5      !
   +----------------------+----------------------+----------------------+
   ! 146    246    3      ! 789    789    1789   ! 126789 5      46789  !
   ! 5      7      16     ! 2      4      1389   ! 1689   189    3689   !
   ! 8      9      124    ! 5      6      137    ! 127    127    347    !
   +----------------------+----------------------+----------------------+
176 candidates.

hidden-pairs-in-a-row: r4{n1 n2}{c7 c8} ==> r4c8≠9, r4c8≠8, r4c8≠7, r4c7≠9, r4c7≠8, r4c7≠7, r4c7≠6
whip[1]: c7n6{r8 .} ==> r7c9≠6, r8c9≠6

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Trid-OR3-relation for digits 7, 8 and 9 in blocks:
        b2, with cells (marked #): r1c5, r2c4, r3c6
        b3, with cells (marked #): r1c8, r2c9, r3c7
        b5, with cells (marked #): r6c5, r4c4, r5c6
        b6, with cells (marked #): r6c7, r4c9, r5c8
with 3 guardians (in cells marked @): n4r3c6 n4r4c4 n6r4c9
   +----------------------+----------------------+----------------------+
   ! 479    2348   24789  ! 34789  789#   6      ! 5      789#   1      !
   ! 1679   68     16789  ! 789#   5      2      ! 3      4      789#   !
   ! 479    348    5      ! 34789  1      4789#@ ! 789#   6      2      !
   +----------------------+----------------------+----------------------+
   ! 4679   468    46789  ! 4789#@ 3      5      ! 12     12     6789#@ !
   ! 3      5      6789   ! 1      2      789#   ! 4      789#   6789   !
   ! 2      1      4789   ! 6      789#   4789   ! 789#   3      5      !
   +----------------------+----------------------+----------------------+
   ! 146    246    3      ! 789    789    1789   ! 126789 5      4789   !
   ! 5      7      16     ! 2      4      1389   ! 1689   189    389    !
   ! 8      9      124    ! 5      6      137    ! 127    127    347    !
   +----------------------+----------------------+----------------------+

Trid-OR3-relation between candidates n4r3c6, n4r4c4 and n6r4c9
+ same valence for candidates n4r4c4 and n4r3c6 via c-chain[2]: n4r4c4,n4r6c6,n4r3c6
==> Trid-OR3-relation can be split into two Trid-OR2-relations with respective lists of guardians:
n4r3c6 n6r4c9 and n4r4c4 n6r4c9 .

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EL14c1s-OR5-relation for digits: 7, 8 and 9
   in cells (marked #): (r7c7 r7c5 r7c4 r4c4 r6c7 r6c5 r5c8 r5c6 r3c7 r3c6 r1c8 r1c5 r2c9 r2c4)
   with 5 guardians (in cells marked @) : n1r7c7 n2r7c7 n6r7c7 n4r4c4 n4r3c6 
   +----------------------------+----------------------------+----------------------------+
   ! 479      2348     24789    ! 34789    789#     6        ! 5        789#     1        !
   ! 1679     68       16789    ! 789#     5        2        ! 3        4        789#     !
   ! 479      348      5        ! 34789    1        4789#@   ! 789#     6        2        !
   +----------------------------+----------------------------+----------------------------+
   ! 4679     468      46789    ! 4789#@   3        5        ! 12       12       6789     !
   ! 3        5        6789     ! 1        2        789#     ! 4        789#     6789     !
   ! 2        1        4789     ! 6        789#     4789     ! 789#     3        5        !
   +----------------------------+----------------------------+----------------------------+
   ! 146      246      3        ! 789#     789#     1789     ! 126789#@ 5        4789     !
   ! 5        7        16       ! 2        4        1389     ! 1689     189      389      !
   ! 8        9        124      ! 5        6        137      ! 127      127      347      !
   +----------------------------+----------------------------+----------------------------+

EL14c1s-OR5-relation between candidates n1r7c7, n2r7c7, n6r7c7, n4r4c4 and n4r3c6
+ same valence for candidates n4r4c4 and n4r3c6 via c-chain[2]: n4r4c4,n4r6c6,n4r3c6
==> EL14c1s-OR5-relation can be split into two EL14c1s-OR4-relations with respective lists of guardians:
n1r7c7 n2r7c7 n6r7c7 n4r3c6 and n1r7c7 n2r7c7 n6r7c7 n4r4c4 .

z-chain[3]: c9n4{r7 r9} - r9n3{c9 c6} - r9n7{c6 .} ==> r7c9≠7
EL14c1s-OR4-whip[5]: r7n2{c7 c2} - r7n6{c2 c1} - OR4{{n6r7c7 n1r7c7 n2r7c7 | n4r4c4}} - b4n4{r4c1 r6c3} - b7n4{r9c3 .} ==> r7c7≠7
whip[1]: b9n7{r9c9 .} ==> r9c6≠7
EL14c1s-OR4-whip[5]: r7n2{c7 c2} - r7n6{c2 c1} - OR4{{n6r7c7 n1r7c7 n2r7c7 | n4r4c4}} - b4n4{r4c1 r6c3} - b7n4{r9c3 .} ==> r7c7≠8
Trid-OR2-whip[5]: OR2{{n4r3c6 | n6r4c9}} - r5n6{c9 c3} - r8n6{c3 c7} - c7n8{r8 r6} - r5n8{c8 .} ==> r3c6≠8
EL14c1s-OR4-whip[5]: r7n2{c7 c2} - r7n6{c2 c1} - OR4{{n6r7c7 n1r7c7 n2r7c7 | n4r4c4}} - b4n4{r4c1 r6c3} - b7n4{r9c3 .} ==> r7c7≠9
Trid-OR2-whip[5]: OR2{{n4r3c6 | n6r4c9}} - r5n6{c9 c3} - r8n6{c3 c7} - c7n9{r8 r6} - r5n9{c8 .} ==> r3c6≠9
whip[6]: c4n3{r1 r3} - b2n4{r3c4 r3c6} - r3c2{n4 n8} - r2c2{n8 n6} - r4c2{n6 n4} - c4n4{r4 .} ==> r1c4≠7
whip[6]: c4n3{r1 r3} - b2n4{r3c4 r3c6} - r3c2{n4 n8} - r2c2{n8 n6} - r4c2{n6 n4} - c4n4{r4 .} ==> r1c4≠8
whip[6]: c4n3{r1 r3} - b2n4{r3c4 r3c6} - r3c2{n4 n8} - r2c2{n8 n6} - r4c2{n6 n4} - c4n4{r4 .} ==> r1c4≠9
Trid-OR2-whip[6]: r8c3{n6 n1} - c1n1{r7 r2} - c1n6{r2 r4} - OR2{{n6r4c9 | n4r4c4}} - r4c2{n4 n8} - r2c2{n8 .} ==> r7c2≠6
Trid-OR2-ctr-whip[7]: r9n4{c9 c3} - r6n4{c3 c6} - r3c6{n4 n7} - b3n7{r3c7 r1c8} - r5n7{c8 c3} - r5n6{c3 c9} - OR2{{n6r4c9 n4r3c6 | .}} ==> r9c9≠7
biv-chain[3]: r9n7{c7 c8} - c8n2{r9 r4} - b6n1{r4c8 r4c7} ==> r9c7≠1
whip[5]: r8c3{n1 n6} - r7n6{c1 c7} - b9n1{r7c7 r9c8} - r9n7{c8 c7} - b9n2{r9c7 .} ==> r8c6≠1
biv-chain[5]: c6n1{r7 r9} - r9n3{c6 c9} - r9n4{c9 c3} - r6n4{c3 c6} - r3c6{n4 n7} ==> r7c6≠7
Trid-OR2-whip[7]: c6n1{r7 r9} - r9n3{c6 c9} - r9n4{c9 c3} - r6n4{c3 c6} - OR2{{n4r3c6 | n6r4c9}} - c1n6{r4 r2} - c2n6{r2 .} ==> r7c1≠1
hidden-single-in-a-column ==> r2c1=1
Trid-OR2-whip[6]: OR2{{n4r4c4 | n6r4c9}} - b4n6{r4c1 r5c3} - b4n9{r5c3 r6c3} - r2n9{c3 c9} - c7n9{r3 r8} - r8n6{c7 .} ==> r4c4≠9
Trid-OR2-whip[3]: r6n4{c3 c6} - OR2{{n4r3c6 | n6r4c9}} - r4n9{c9 .} ==> r6c3≠9
Trid-OR2-whip[8]: OR2{{n4r4c4 | n6r4c9}} - b4n6{r4c1 r5c3} - b4n8{r5c3 r6c3} - r4c2{n8 n4} - c2n6{r4 r2} - r2n8{c2 c9} - c7n8{r3 r8} - r8n6{c7 .} ==> r4c4≠8
z-chain[3]: r4c4{n7 n4} - c6n4{r6 r3} - c6n7{r3 .} ==> r6c5≠7
Trid-OR2-whip[3]: r6n4{c3 c6} - OR2{{n4r3c6 | n6r4c9}} - r4n8{c9 .} ==> r6c3≠8
whip[7]: r2c2{n8 n6} - r4c2{n6 n4} - r4c4{n4 n7} - c6n7{r5 r3} - c1n7{r3 r1} - r1c8{n7 n9} - r1c5{n9 .} ==> r1c2≠8
whip[6]: r6n4{c3 c6} - c4n4{r4 r3} - r3n3{c4 c2} - r3n8{c2 c7} - r1n8{c8 c5} - r6n8{c5 .} ==> r1c3≠4
whip[8]: r3n3{c2 c4} - r3n8{c4 c7} - r3n9{c7 c1} - r1c1{n9 n7} - r1c8{n7 n9} - r1c5{n9 n8} - r6n8{c5 c6} - c6n4{r6 .} ==> r3c2≠4
whip[8]: r6n4{c3 c6} - r3n4{c6 c4} - b1n4{r3c1 r1c2} - c2n3{r1 r3} - r3n8{c2 c7} - r6n8{c7 c5} - r1n8{c5 c3} - r1n2{c3 .} ==> r4c1≠4
Trid-OR2-ctr-whip[5]: r4c4{n4 n7} - c6n7{r5 r3} - r3c1{n7 n9} - r4c1{n9 n6} - OR2{{n4r3c6 n6r4c9 | .}} ==> r3c4≠4
t-whip[4]: c4n4{r4 r1} - r1n3{c4 c2} - c2n2{r1 r7} - c2n4{r7 .} ==> r4c3≠4
whip[8]: c3n2{r1 r9} - r9c7{n2 n7} - r6n7{c7 c6} - c6n4{r6 r3} - r3c1{n4 n9} - r3c7{n9 n8} - r6n8{c7 c5} - r1n8{c5 .} ==> r1c3≠7
whip[8]: r8n6{c7 c3} - c3n1{r8 r9} - r9c6{n1 n3} - r8c6{n3 n8} - b5n8{r6c6 r6c5} - c7n8{r6 r3} - r1n8{c8 c3} - c3n2{r1 .} ==> r8c7≠9
whip[6]: c7n9{r3 r6} - r6c5{n9 n8} - c7n8{r6 r8} - c7n6{r8 r7} - r7n1{c7 c6} - c6n8{r7 .} ==> r3c7≠7
whip[7]: r6c5{n9 n8} - r6c7{n8 n7} - c7n9{r6 r3} - c7n8{r3 r8} - c7n6{r8 r7} - r7n1{c7 c6} - c6n8{r7 .} ==> r6c6≠9
t-whip[7]: b5n8{r6c6 r6c5} - r6n9{c5 c7} - r3c7{n9 n8} - r1n8{c8 c3} - r1n2{c3 c2} - r7n2{c2 c7} - r7n1{c7 .} ==> r7c6≠8
t-whip[5]: c7n9{r3 r6} - r6c5{n9 n8} - c6n8{r6 r8} - r8n3{c6 c9} - r8n9{c9 .} ==> r1c8≠9
z-chain[3]: r1n9{c3 c5} - r6n9{c5 c7} - b3n9{r3c7 .} ==> r2c3≠9
biv-chain[4]: c5n7{r7 r1} - b3n7{r1c8 r2c9} - b3n9{r2c9 r3c7} - r6n9{c7 c5} ==> r7c5≠9
finned-x-wing-in-columns: n9{c7 c5}{r6 r3} ==> r3c4≠9
z-chain[3]: r3n7{c6 c1} - r3n9{c1 c7} - r2n9{c9 .} ==> r2c4≠7
t-whip[2]: r2n7{c9 c3} - c1n7{r3 .} ==> r4c9≠7
z-chain[3]: r4n7{c3 c4} - b5n4{r4c4 r6c6} - r6c3{n4 .} ==> r5c3≠7
z-chain[4]: r1c8{n7 n8} - r1c5{n8 n9} - r2n9{c4 c9} - r2n7{c9 .} ==> r1c1≠7
finned-x-wing-in-columns: n7{c1 c6}{r3 r4} ==> r4c4≠7
singles ==> r4c4=4, r1c4=3, r3c2=3, r3c6=4, r6c3=4, r9c9=4, r8c9=3, r9c6=3, r7c6=1
x-wing-in-columns: n9{c6 c8}{r5 r8} ==> r5c9≠9, r5c3≠9
whip[1]: b4n9{r4c3 .} ==> r4c9≠9
naked-pairs-in-a-row: r4{c2 c9}{n6 n8} ==> r4c3≠8, r4c3≠6, r4c1≠6
singles ==> r7c1=6, r7c7=2, r4c7=1, r4c8=2, r7c2=4, r1c2=2, r9c7=7, r9c8=1, r9c3=2, r8c3=1, r6c6=7, r1c1=4, r8c7=6
finned-x-wing-in-rows: n8{r6 r3}{c7 c5} ==> r1c5≠8
whip[1]: b2n8{r3c4 .} ==> r7c4≠8
finned-x-wing-in-rows: n8{r7 r6}{c5 c9} ==> r5c9≠8, r4c9≠8
stte

[totuan]

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 *-------------------------------------------------------------------------------*
 | 479     2348    24789   |  34789 *#789     6       |  5     *#789     1       |
 | 1679    68     *789+16  |*#789     5       2       |  3       4     *#789     |
 | 479     348     5       |  34789   1     *#789+4   |*#789     6       2       |
 |-------------------------+--------------------------+--------------------------|
 | 4679    468     46789   |*#789+4   3       5       |  12      12     #789+6   |
 | 3       5       6789    |  1       2     *#789     |  4      #789    *789+6   |
 | 2       1      *789+4   |  6     *#789     789-4   |*#789     3       5       |
 |-------------------------+--------------------------+--------------------------|
 | 146     246     3       |  789     789     1789    |  126789  5       4789    |
 | 5       7       16      |  2       4       1389    |  1689    189     389     |
 | 8       9       124     |  5       6       137     |  127     127     347     |
 *-------------------------------------------------------------------------------*

My path for this one:
Tridagon(789) #-marked cells => (4)r3c6,r4c4=(6)r4c9
Impossible pattern(789) *-marked cells => (16)r2c3=(4)r6c3=(6)r5c9
01: Combination Tridagon & Impossible pattern – present as diagram: => r6c6<>4, some singles

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(4)r3c6,r4c4,r6c3*
 ||
(16)r28c3-(6)r5c3=r5c9--(6)r4c9==(4)r3c6,r4c4*
 ||                    |
(6)r5c9----------------

Impossible pattern (789) – proved:

Hidden Text: Show

Code: Select all

A=(7|8|9)
 *-----------------------------------------------------------*
 | .     .     .     | .     789   .     | .     789   .     |
 | .     .     789   | 789   .     .     | .     .     789   |
 | .     .     .     | .     .     789   | 789   .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | 789   .     .     | .     .     .     |
 | .     .     .     | .     .     789   | .     789   789   |
 | .     .     789A  | .     789   .     | 789   .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | .     .     .     | .     .     .     |
 | .     .     .     | .     .     .     | .     .     .     |
 | .     .     .     | .     .     .     | .     .     .     |
 *-----------------------------------------------------------*
Let A=7 => r6c57<>7 => r5c89=7 => r5c6<>7 => r4c4=7 => r2c9=7 => r5c8=8
 *-----------------------------------------------------------*
 | .     .     .     | .    g789   .     | .    f89    .     |
 | .     .     89    | 89    .     .     | .     .     7     |
 | .     .     .     | .     .    d789   |c89    .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | 7     .     .     | .     .     .     |
 | .     .     .     | .     .    e89    | .     7     89    |
 | .     .     7     | .    a89    .     |b89    .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | .     .     .     | .     .     .     |
 | .     .     .     | .     .     .     | .     .     .     |
 | .     .     .     | .     .     .     | .     .     .     |
 *-----------------------------------------------------------*
Oddagon(89) abcde => r3c6=7 => Oddagon(89) abcfg => impossible.
The same for A=(8|9)

Code: Select all

 *-----------------------------------------------------------*
 | 479   24    2789  | 3    #789   6     | 5    #789   1     |
 | 1     68   #789+6 |#789   5     2     | 3     4    #789   |
 | 79    3     5     |#789   1     4     |#789   6     2     |
 |-------------------+-------------------+-------------------|
 | 679   68    789-6 | 4     3     5     | 12    12   #789+6 |
 | 3     5    #789+6 | 1     2    #789   | 4    #789  *6789  |
 | 2     1     4     | 6    #789  #789   |#789   3     5     |
 |-------------------+-------------------+-------------------|
 | 46    24    3     |#789  #789   1     | 26    5    #89    |
 | 5     7     1-6   | 2     4     89    | 1689  189   3     |
 | 8     9     12    | 5     6     3     | 127   127   4     |
 *-----------------------------------------------------------*

Impossible pattern(789) #-marked cells => (6)r25c3=(6)r4c9
02: (6)r25c3==(6)r4c9-r5c9=r5c3 => r48c3<>6, some singles then ER-6.6

Impossible pattern (789) – proved:

Hidden Text: Show

Code: Select all

A=(7|8|9)
 *-----------------------------------------------------------*
 | .     .     .     | .     789   .     | .     789   .     |
 | .     .     789   | 789   .     .     | .     .     789   |
 | .     .     .     | 789   .     .     | 789   .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | .     .     .     | .     .     789   |
 | .     .     789A  | .     .     789   | .     789   .     |
 | .     .     .     | .     789   789   | 789   .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | 789   789   .     | .     .     789   |
 | .     .     .     | .     .     .     | .     .     .     |
 | .     .     .     | .     .     .     | .     .     .     |
 *-----------------------------------------------------------*
Let A=7 => r5c68<>7 => r6c56=7 => r4c9=7 => r2c4=7 => r7c5=7 => r6c6=7
 *-----------------------------------------------------------*
 | .     .     .     | .    b89    .     | .    a89+7  .     |
 | .     .     89    | 7     .     .     | .     .    j89    |
 | .     .     .     |g89    .     .     |f89+7  .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     | .     .     .     | .     .     7     |
 | .     .     7     | .     .     89    | .    e89    .     |
 | .     .     .     | .    c89    7     |d89    .     .     |
 |-------------------+-------------------+-------------------|
 | .     .     .     |h89    7     .     | .     .    i89    |
 | .     .     .     | .     .     .     | .     .     .     |
 | .     .     .     | .     .     .     | .     .     .     |
 *-----------------------------------------------------------*
Oddagon(89) abcde => r1c8=7 => oddagon(89) fghij => impossible
The same for A=(8|9)

Thanks for the puzzle!
totuan

[champagne]

Code: Select all

 *-------------------------------------------------------------------------------*
 | 479     2348    24789   |  34789 *#789     6       |  5     *#789     1       |
 | 1679    68     *789+16  |*#789     5       2       |  3       4     *#789     |
 | 479     348     5       |  34789   1     *#789+4   |*#789     6       2       |
 |-------------------------+--------------------------+--------------------------|
 | 4679    468     46789   |*#789+4   3       5       |  12      12     #789+6   |
 | 3       5       6789    |  1       2     *#789     |  4      #789    *789+6   |
 | 2       1      *789+4   |  6     *#789     789-4   |*#789     3       5       |
 |-------------------------+--------------------------+--------------------------|
 | 146     246     3       |  789     789     1789    |  126789  5       4789    |
 | 5       7       16      |  2       4       1389    |  1689    189     389     |
 | 8       9       124     |  5       6       137     |  127     127     347     |
 *-------------------------------------------------------------------------------*

My path for this one:
Tridagon(789) #-marked cells => (4)r3c6,r4c4=(6)r4c9
Impossible pattern(789) *-marked cells => (16)r2c3=(4)r6c3=(6)r5c9
01: Combination Tridagon & Impossible pattern – present as diagram: => r6c6<>4, some singles
[code](4)r3c6,r4c4,r6c3*

totuan

Hi totuan,

Thanks for the entire solution, but, you have already here reached the oddity of this puzzle (for me)
Having established r3c6=4, the solution grid does not have the tridagon pattern, what is not common at all.
This appears like a cannibalization of the pattern or a threat of tridagon in the PM.

[Cenoman]

Hidden Text: Show

Code: Select all

 *-------------------------------------------------------------------------------*
 | 479     2348    24789   |  34789 *#789     6       |  5     *#789     1       |
 | 1679    68     *789+16  |*#789     5       2       |  3       4     *#789     |
 | 479     348     5       |  34789   1     *#789+4   |*#789     6       2       |
 |-------------------------+--------------------------+--------------------------|
 | 4679    468     46789   |*#789+4   3       5       |  12      12     #789+6   |
 | 3       5       6789    |  1       2     *#789     |  4      #789    *789+6   |
 | 2       1      *789+4   |  6     *#789     789-4   |*#789     3       5       |
 |-------------------------+--------------------------+--------------------------|
 | 146     246     3       |  789     789     1789    |  126789  5       4789    |
 | 5       7       16      |  2       4       1389    |  1689    189     389     |
 | 8       9       124     |  5       6       137     |  127     127     347     |
 *-------------------------------------------------------------------------------*

My path for this one:
Tridagon(789) #-marked cells => (4)r3c6,r4c4=(6)r4c9
Impossible pattern(789) *-marked cells => (16)r2c3=(4)r6c3=(6)r5c9
01: Combination Tridagon & Impossible pattern – present as diagram: => r6c6<>4, some singles

Code: Select all

(4)r3c6,r4c4,r6c3*
 ||
(16)r28c3-(6)r5c3=r5c9--(6)r4c9==(4)r3c6,r4c4*
 ||                    |
(6)r5c9----------------

.....

Very nice initial move !!

Thanks for the entire solution, but, you have already here reached the oddity of this puzzle (for me)
Having established r3c6=4, the solution grid does not have the tridagon pattern, what is not common at all.
This appears like a cannibalization of the pattern or a threat of tridagon in the PM.

Hi Champagne, maybe you have interpreted the +4 @r3c6 in totuan's PM as a placement, which it isn't. The '+' symbol is just a tag for the guardian role of 4r3c6.

[champagne]

Thanks for the entire solution, but, you have already here reached the oddity of this puzzle (for me)
Having established r3c6=4, the solution grid does not have the tridagon pattern, what is not common at all.
This appears like a cannibalization of the pattern or a threat of tridagon in the PM.

Hi Champagne, maybe you have interpreted the +4 @r3c6 in totuan's PM as a placement, which it isn't. The '+' symbol is just a tag for the guardian role of 4r3c6.

Hi Cenoman

Maybe I read to fast but the fact is that the solution for this puzzle has no tridagon pattern.

428 396 571
167 852 349
935 714 862

789 435 126
356 129 487
214 687 935

643 971 258
571 248 693
892 563 714

And the pattern 789 is killed by 4r3c6

This is quite unusual in mith's file

EDIT Asssuming that a tridagon pattern in the solution is the following

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -x--
..x --.

where the last digit on the pattern in the last box is anywhere but not in the last cell

[totuan]

(4)r3c6,r4c4,r6c3*

Hi totuan,
Thanks for the entire solution, but, you have already here reached the oddity of this puzzle (for me)
Having established r3c6=4, the solution grid does not have the tridagon pattern, what is not common at all.
This appears like a cannibalization of the pattern or a threat of tridagon in the PM.

Hi champagne,
Yes, my mistake... a bit
it should be:

Code: Select all

(4)r6c3*
 ||
(16)r28c3-(6)r5c3=r5c9--(6)r4c9==(4)r3c6,r4c4*
 ||                    |
(6)r5c9----------------


totuan

[denis_berthier]

the fact is that the solution for this puzzle has no tridagon pattern.

The tridagon pattern is defined by the presence of precise candidates in a resolution state. NO complete grid can have a tridagon pattern.
.

[denis_berthier]

you have already here reached the oddity of this puzzle (for me)
Having established r3c6=4, the solution grid does not have the tridagon pattern, what is not common at all.
This appears like a cannibalization of the pattern or a threat of tridagon in the PM.

What you're observing here is the tridagon pattern degenerating. But this happens after the ORk-relation based on it has been established.
That's a very common behaviour in mith's collection.
In particular, this happens to every tridagon with a single guardian; but of course in this case, there's no further tridagon elimination.
In the general case, the tridagon is detected with a certain number of guardians; some eliminations are made; at some point, the original tridagon degenerates but the OR relation is still there (possibly with a reduced number of guardians) and further eliminations remain possible.
I have given many detailed examples of this behaviour.
.

[denis_berthier]

.
In order to avoid any confusion with other patterns, here's the solution in W10 + Trid-OR3-W10 using only tridagons, starting from the same RS after whips[1]:

hidden-pairs-in-a-row: r4{n1 n2}{c7 c8} ==> r4c8≠9, r4c8≠8, r4c8≠7, r4c7≠9, r4c7≠8, r4c7≠7, r4c7≠6
whip[1]: c7n6{r8 .} ==> r7c9≠6, r8c9≠6

Code: Select all

Trid-OR3-relation for digits 7, 8 and 9 in blocks:
        b2, with cells (marked #): r1c5, r2c4, r3c6
        b3, with cells (marked #): r1c8, r2c9, r3c7
        b5, with cells (marked #): r6c5, r4c4, r5c6
        b6, with cells (marked #): r6c7, r4c9, r5c8
with 3 guardians (in cells marked @): n4r3c6 n4r4c4 n6r4c9
   +----------------------+----------------------+----------------------+
   ! 479    2348   24789  ! 34789  789#   6      ! 5      789#   1      !
   ! 1679   68     16789  ! 789#   5      2      ! 3      4      789#   !
   ! 479    348    5      ! 34789  1      4789#@ ! 789#   6      2      !
   +----------------------+----------------------+----------------------+
   ! 4679   468    46789  ! 4789#@ 3      5      ! 12     12     6789#@ !
   ! 3      5      6789   ! 1      2      789#   ! 4      789#   6789   !
   ! 2      1      4789   ! 6      789#   4789   ! 789#   3      5      !
   +----------------------+----------------------+----------------------+
   ! 146    246    3      ! 789    789    1789   ! 126789 5      4789   !
   ! 5      7      16     ! 2      4      1389   ! 1689   189    389    !
   ! 8      9      124    ! 5      6      137    ! 127    127    347    !
   +----------------------+----------------------+----------------------+

Trid-OR3-relation between candidates n4r3c6, n4r4c4 and n6r4c9
+ same valence for candidates n4r4c4 and n4r3c6 via c-chain[2]: n4r4c4,n4r6c6,n4r3c6
==> Trid-OR3-relation can be split into two Trid-OR2-relations with respective lists of guardians:
    n4r3c6 n6r4c9  and n4r4c4 n6r4c9 .

z-chain[3]: c9n4{r7 r9} - r9n3{c9 c6} - r9n7{c6 .} ==> r7c9≠7
whip[6]: c4n3{r1 r3} - b2n4{r3c4 r3c6} - r3c2{n4 n8} - r2c2{n8 n6} - r4c2{n6 n4} - c4n4{r4 .} ==> r1c4≠7
whip[6]: c4n3{r1 r3} - b2n4{r3c4 r3c6} - r3c2{n4 n8} - r2c2{n8 n6} - r4c2{n6 n4} - c4n4{r4 .} ==> r1c4≠8
whip[6]: c4n3{r1 r3} - b2n4{r3c4 r3c6} - r3c2{n4 n8} - r2c2{n8 n6} - r4c2{n6 n4} - c4n4{r4 .} ==> r1c4≠9
Trid-OR2-whip[6]: r8c3{n6 n1} - c1n1{r7 r2} - c1n6{r2 r4} - OR2{{n6r4c9 | n4r4c4}} - r4c2{n4 n8} - r2c2{n8 .} ==> r7c2≠6
Trid-OR2-whip[7]: r7n6{c1 c7} - r7n2{c7 c2} - b7n4{r7c2 r9c3} - r6n4{c3 c6} - OR2{{n4r3c6 | n6r4c9}} - c1n6{r4 r2} - c2n6{r2 .} ==> r7c1≠1
hidden-single-in-a-column ==> r2c1=1
biv-chain[3]: r7n1{c6 c7} - b9n6{r7c7 r8c7} - r8c3{n6 n1} ==> r8c6≠1
Trid-OR2-whip[9]: c7n6{r8 r7} - c1n6{r7 r4} - c9n6{r4 r5} - OR2{{n6r4c9 | n4r4c4}} - r4c2{n4 n8} - c9n8{r4 r2} - b1n8{r2c3 r1c3} - r1n2{c3 c2} - r7n2{c2 .} ==> r8c7≠8
Trid-OR2-whip[9]: OR2{{n6r4c9 | n4r4c4}} - r6n4{c6 c3} - r9n4{c3 c9} - r7c9{n4 n9} - b8n9{r7c4 r8c6} - r8n8{c6 c8} - c7n8{r7 r3} - c7n9{r3 r6} - b5n9{r6c5 .} ==> r4c9≠8

;;; Note that, at this point, the tridagon pattern has already degenerated (one candidate missing).
;;; But the OR2 relation is still true and can still be used:

Trid-OR2-whip[3]: r5n6{c3 c9} - OR2{{n6r4c9 | n4r4c4}} - r4n8{c4 .} ==> r5c3≠8
whip[10]: r6n4{c6 c3} - r9n4{c3 c9} - c9n3{r9 r8} - r8n8{c9 c8} - c7n8{r7 r3} - b6n8{r6c7 r5c9} - r7c9{n8 n9} - c7n9{r7 r6} - c5n9{r6 r1} - c8n9{r1 .} ==> r6c6≠8
Trid-OR2-whip[10]: OR2{{n6r4c9 | n4r4c4}} - r6n4{c6 c3} - r9n4{c3 c9} - r7c9{n4 n8} - b8n8{r7c4 r8c6} - b5n8{r5c6 r6c5} - c7n8{r6 r3} - b2n8{r3c6 r2c4} - r2n9{c4 c3} - b4n9{r4c3 .} ==> r4c9≠9
Trid-OR2-whip[3]: r5n6{c3 c9} - OR2{{n6r4c9 | n4r4c4}} - r4n9{c4 .} ==> r5c3≠9
whip[7]: r8n6{c7 c3} - r7c1{n6 n4} - r7c9{n4 n8} - b8n8{r7c4 r8c6} - r5n8{c6 c8} - b6n9{r5c8 r5c9} - r5n6{c9 .} ==> r8c7≠9
naked-pairs-in-a-row: r8{c3 c7}{n1 n6} ==> r8c8≠1
hidden-pairs-in-a-column: c8{n1 n2}{r4 r9} ==> r9c8≠7
whip[7]: r6n4{c6 c3} - r9n4{c3 c9} - c9n3{r9 r8} - r8c6{n3 n8} - r5c6{n8 n7} - r9n7{c6 c7} - r6n7{c7 .} ==> r6c6≠9
whip[7]: c8n7{r1 r5} - c9n7{r4 r9} - r9n3{c9 c6} - c6n1{r9 r7} - c6n7{r7 r6} - r6n4{c6 c3} - r9n4{c3 .} ==> r3c7≠7
whip[7]: r3c7{n9 n8} - r6c7{n8 n7} - c8n7{r5 r1} - c5n7{r1 r7} - r7c4{n7 n8} - c6n8{r7 r5} - b6n8{r5c8 .} ==> r7c7≠9
t-whip[2]: c7n9{r3 r6} - r5n9{c9 .} ==> r3c6≠9
z-chain[3]: c7n9{r6 r3} - r2n9{c9 c4} - r4n9{c4 .} ==> r6c3≠9
whip[1]: b4n9{r4c3 .} ==> r4c4≠9
whip[5]: r6c6{n7 n4} - r3c6{n4 n8} - r3c7{n8 n9} - r6n9{c7 c5} - r5c6{n9 .} ==> r9c6≠7
whip[1]: r9n7{c9 .} ==> r7c7≠7
whip[5]: r6c6{n7 n4} - r3c6{n4 n8} - r3c7{n8 n9} - r6n9{c7 c5} - r5c6{n9 .} ==> r7c6≠7
whip[5]: c6n4{r3 r6} - c6n7{r6 r5} - b5n9{r5c6 r6c5} - r1c5{n9 n7} - c8n7{r1 .} ==> r3c6≠8
naked-pairs-in-a-column: c6{r3 r6}{n4 n7} ==> r5c6≠7
z-chain[3]: r5n7{c9 c3} - r5n6{c3 c9} - r4c9{n6 .} ==> r6c7≠7
hidden-single-in-a-column ==> r9c7=7
naked-pairs-in-a-column: c7{r3 r6}{n8 n9} ==> r7c7≠8
Trid-OR2-whip[5]: r4n8{c3 c4} - OR2{{n4r4c4 | n6r4c9}} - c2n6{r4 r2} - r2n8{c2 c9} - c7n8{r3 .} ==> r6c3≠8

The end in W6 is trivial (for this kind of puzzles):
whip[1]: b4n8{r4c3 .} ==> r4c4≠8
naked-pairs-in-a-block: b5{r4c4 r6c6}{n4 n7} ==> r6c5≠7
whip[6]: c2n6{r2 r4} - r4c9{n6 n7} - c8n7{r5 r1} - r1n8{c8 c5} - r6n8{c5 c7} - r3n8{c7 .} ==> r2c2≠8
naked-single ==> r2c2=6
whip[6]: r4c2{n8 n4} - r4c4{n4 n7} - c6n7{r6 r3} - c1n7{r3 r1} - r1c8{n7 n9} - r1c5{n9 .} ==> r1c2≠8
t-whip[6]: c2n8{r4 r3} - r3c7{n8 n9} - r6n9{c7 c5} - b2n9{r1c5 r2c4} - r2c3{n9 n7} - r6c3{n7 .} ==> r4c2≠4
naked-single ==> r4c2=8
finned-x-wing-in-rows: n8{r6 r3}{c7 c5} ==> r1c5≠8
whip[1]: b2n8{r3c4 .} ==> r7c4≠8
biv-chain[3]: c8n7{r5 r1} - r1c5{n7 n9} - r6n9{c5 c7} ==> r5c8≠9
finned-x-wing-in-rows: n9{r5 r7}{c9 c6} ==> r8c6≠9
whip[1]: r8n9{c9 .} ==> r7c9≠9
biv-chain[3]: b3n7{r2c9 r1c8} - r5c8{n7 n8} - c7n8{r6 r3} ==> r2c9≠8
biv-chain[3]: r2c9{n7 n9} - r3c7{n9 n8} - b2n8{r3c4 r2c4} ==> r2c4≠7
finned-x-wing-in-rows: n7{r2 r5}{c3 c9} ==> r4c9≠7
singles ==> r4c9=6, r5c3=6, r8c3=1, r8c7=6, r7c1=6
biv-chain[3]: c3n8{r1 r2} - r2c4{n8 n9} - r1c5{n9 n7} ==> r1c3≠7
z-chain[3]: r3c2{n4 n3} - c4n3{r3 r1} - r1n4{c4 .} ==> r3c1≠4
biv-chain[4]: r4c4{n4 n7} - c6n7{r6 r3} - r3c1{n7 n9} - b4n9{r4c1 r4c3} ==> r4c3≠4
biv-chain[4]: c1n4{r1 r4} - r4c4{n4 n7} - c6n7{r6 r3} - r3c1{n7 n9} ==> r1c1≠9
biv-chain[4]: r1n8{c3 c8} - r3c7{n8 n9} - c1n9{r3 r4} - b4n4{r4c1 r6c3} ==> r1c3≠4
biv-chain[4]: r1n3{c4 c2} - b1n2{r1c2 r1c3} - b1n8{r1c3 r2c3} - b2n8{r2c4 r3c4} ==> r3c4≠3
singles ==> r1c4=3, r3c2=3
biv-chain[4]: c5n7{r7 r1} - r1c1{n7 n4} - c2n4{r1 r7} - r7c9{n4 n8} ==> r7c5≠8
stte

[champagne]

but the fact is that the solution for this puzzle has no tridagon pattern.

428 396 571
167 852 349
935 714 862

789 435 126
356 129 487
214 687 935

643 971 258
571 248 693
892 563 714

EDIT Asssuming that a tridagon pattern in the solution is the following

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -x--
..x --.

where the last digit on the pattern in the last box is anywhere but not in the last cell

Nothing to add to this,
this is by far the most common final status in mith's file

[denis_berthier]

EDIT Asssuming that a tridagon pattern in the solution is the following

Code: Select all

..x x..
.x. .x.
x.. ..x

x.. x--
.x. -x--
..x --.

where the last digit on the pattern in the last box is anywhere but not in the last cell

Nothing to add to this,
this is by far the most common final status in mith's file

For a puzzle with a tridagon having this solution pattern, this corresponds to a tridagon with a single guardian - which is VERY far from being the most common case, as proven by my precise statistical results.
.