The New Sudoku Players' Forum

[denis_berthier]

Code: Select all

+-------+-------+-------+
! . . . ! . . . ! 4 5 . !
! . . . ! 9 . 5 ! 3 . 6 !
! . . . ! 4 . 6 ! . . 7 !
+-------+-------+-------+
! . . . ! . . . ! 5 . 3 !
! . 9 3 ! 5 7 . ! . 6 4 !
! . . 4 ! 6 . . ! 9 7 . !
+-------+-------+-------+
! . 8 . ! 7 . . ! . . . !
! . 2 1 ! 3 . . ! . . . !
! 6 . . ! . . . ! . . 9 !
+-------+-------+-------+
......45....9.53.6...4.6..7......5.3.9357..64..46..97..8.7......213.....6.......9
28 clues

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Resolution state after Singles (and whips[1]):
   +----------------------+----------------------+----------------------+
   ! 12389  136    2689   ! 128    1238   7      ! 4      5      128    !
   ! 12478  147    278    ! 9      128    5      ! 3      128    6      !
   ! 12358  135    258    ! 4      1238   6      ! 128    9      7      !
   +----------------------+----------------------+----------------------+
   ! 1278   167    2678   ! 128    12489  12489  ! 5      128    3      !
   ! 128    9      3      ! 5      7      128    ! 128    6      4      !
   ! 1258   15     4      ! 6      128    3      ! 9      7      128    !
   +----------------------+----------------------+----------------------+
   ! 3459   8      59     ! 7      124569 1249   ! 126    1234   125    !
   ! 4579   2      1      ! 3      45689  489    ! 678    48     58     !
   ! 6      3457   57     ! 128    12458  1248   ! 1278   12348  9      !
   +----------------------+----------------------+----------------------+
177 candidates.

.

[Leren]

Code: Select all

Resolution state after basics including 2 Naked Triples
*--------------------------------------------------------------------------------*
| 12389   136     2689     |*128     1238    7        | 4       5      *128      |
| 12478   147     278      | 9      *128     5        | 3      *128     6        |
| 12358   135     258      | 4       1238   *6        |*128T    9       7        |
|--------------------------+--------------------------+--------------------------|
| 1278    167     2678     |*128     49      49       | 5      *128     3        |
| 128     9       3        | 5       7      *128T     |*128T    6       4        |
| 1258    15      4        | 6      *128     3        | 9       7      *128      |
|--------------------------+--------------------------+--------------------------|
| 3459    8       59       | 7       4569    1249     | 126     1234    125      |
| 4579    2       1        | 3       4569    489      | 678     48      58       |
| 6       3457    57       | 128     45      1248     | 7-128   12348   9        |
*--------------------------------------------------------------------------------*

Solved Trigadon (128) Boxes 2356 cells marked *

Remote Triples in play, the important one being r3c7, r5c7, r5c6 (cells marked T)

r9c7 = 128 =RT= r5c6 = 128 => No 128 in Box 8 => - 128 r9c7 => r9c7 = 7

Put r9c7 = 7 as an extra clue and the puzzle solves pretty easily.

Working out the Remote Triples by hand was certainly a nightmare.

Removing the 6 from r3c6 gives multiple solutions, so I had to locate the RT's and find a contradiction chain by hand - ouch !

Leren

[denis_berthier]

.
This puzzle is in B19 - an extremely rare case.
The way I found it is described here: http://forum.enjoysudoku.com/the-layered-structure-of-t-e-depth-d-t45647-4.html
(It's a scrambled version of the 1st puzzle there in B19)
It has no tridagon or degenerate-cyclic tridagon - in this case because the tridagsn is already solved and can bring nothing more.
But it has other impossible patterns, the most frequent ones, close to the tridagon.
.

[Leren]

Whatever you call the pattern it certainly behaves like a Type 1 Trigadon whose solution digit has been placed as a clue.

I used the fact that when a Trigadon Type 1 digit has been placed, any Remote Triples are still there. Together with the 128 ER Box 8 I was able to proceed to solve r9c7 as per a normal Trigadon with RTs.

Was this just a fluke ? Certainly if the Remote Triples were not there I don't think that I could have solved it without Forcing Chains.

Leren

[denis_berthier]

.
The results of Remote Triples based on Tridagons can generally be obtained in a standalone way with the few most frequent other impossible patterns close to the Tridagon.
.

[Leren]

Obtained from previous puzzle by - 6 r3c6 + 3 r1c5

....3.45....9.53.6...4....7......5.3.9357..64..46..97..8.7......213.....6.......9

Code: Select all

*---------------------------------------------------------*
| 1289  16   2689 |*128  3       7     | 4     5     *128 |
| 12478 147  278  | 9   *128     5     | 3    *128    6   |
| 12358 135  258  | 4    1268   *6-128 |*128   9      7   |
|-----------------+--------------------+------------------|
| 1278  167  2678 |*128  49      49    | 5    *128    3   |
| 128   9    3    | 5    7      *128   |*128   6      4   |
| 1258  15   4    | 6   *128     3     | 9     7     *128 |
|-----------------+--------------------+------------------|
| 3459  8    59   | 7    124569  12469 | 126   1234   125 |
| 4579  2    1    | 3    45689   4689  | 678   48     58  |
| 6     3457 57   | 128  12458   1248  | 1278  12348  9   |
*---------------------------------------------------------*

Type 1 Trigadon - Digits 128 in Boxes 6532 => -128 r3c6

Code: Select all

*---------------------------------------------------*
| 1289  16   2689 | 128 3    7    | 4     5     128 |
| 147   147  278  | 9   128  5    | 3     128   6   |
| 12358 135  258  | 4   128  6    | 128T  9     7   |
|-----------------+---------------+-----------------|
| 1278  167  2678 | 128 49   49   | 5     128   3   |
| 128   9    3    | 5   7    128T | 128T  6     4   |
| 1258  15   4    | 6   128  3    | 9     7     128 |
|-----------------+---------------+-----------------|
| 3459  8    59   | 7   4569 1249 | 126   1234  125 |
| 4579  2    1    | 3   4569 489  | 678   48    58  |
| 6     3457 57   | 128 45   1248 | 7-128 12348 9   |
*---------------------------------------------------*

Trigadon ER Chain. 8 in r9c7 => RT Contradiction in r5c6, r5c7 & r3c7. Puzzle solves with two Skyscrapers after that.

Leren

[denis_berthier]

.
I'm not surprised that you can slightly tweek the puzzle so as to get one with a plain tridagon. My original puzzle was obtained from a T&E(3) one with only small changes.
Your puzzle is in T&E(2) and B4B.
.

[eleven]

.
The results of Remote Triples based on Tridagons can generally be obtained in a standalone way with the few most frequent other impossible patterns close to the Tridagon.
.

Yes, but finding the RT elimination is much easier than to spot this pattern (which you would prove simplest with the RT again)

Code: Select all

+----------------------+----------------------+
| 128    1238   .      | .      .      128    |
| .      128    .      | .      128    .      |
| .      1238   .      | 128    .      .      |
+----------------------+----------------------+
| 128    .      .      | .      128    .      |
| .      .      128    | 128    .      .      |
| .      128    .      | .      .      128    |
+----------------------+----------------------+
| .      .      .      | .      .      .      |
| .      .      .      | .      .      .      |
| 128    .      .      | 128    .      .      |
+----------------------+----------------------+

[denis_berthier]

.
This is not the pattern one would have to find. One can use two much simpler patterns and then very short ORk-chains:

hidden-pairs-in-a-row: r4{n4 n9}{c5 c6} ==> r4c6≠8, r4c6≠2, r4c6≠1, r4c5≠8, r4c5≠2, r4c5≠1

The 2 simple patterns (one used twice):

Code: Select all

EL14c30s-OR2-relation for digits: 1, 2 and 8
   in cells (marked #): (r9c4 r9c7 r1c4 r1c9 r3c5 r3c7 r2c5 r2c8 r4c4 r4c8 r6c5 r6c9 r5c6 r5c7)
   with 2 guardians (in cells marked @) : n7r9c7 n3r3c5
   +----------------------+----------------------+----------------------+
   ! 12389  136    2689   ! 128#   1238   7      ! 4      5      128#   !
   ! 12478  147    278    ! 9      128#   5      ! 3      128#   6      !
   ! 12358  135    258    ! 4      1238#@ 6      ! 128#   9      7      !
   +----------------------+----------------------+----------------------+
   ! 1278   167    2678   ! 128#   49     49     ! 5      128#   3      !
   ! 128    9      3      ! 5      7      128#   ! 128#   6      4      !
   ! 1258   15     4      ! 6      128#   3      ! 9      7      128#   !
   +----------------------+----------------------+----------------------+
   ! 3459   8      59     ! 7      124569 1249   ! 126    1234   125    !
   ! 4579   2      1      ! 3      45689  489    ! 678    48     58     !
   ! 6      3457   57     ! 128#   12458  1248   ! 1278#@ 12348  9      !
   +----------------------+----------------------+----------------------+

EL14c13s-OR2-relation for digits: 1, 2 and 8
   in cells (marked #): (r9c4 r9c7 r3c7 r2c5 r2c8 r1c5 r1c4 r1c9 r4c4 r4c8 r6c5 r6c9 r5c6 r5c7)
   with 2 guardians (in cells marked @) : n7r9c7 n3r1c5
   +----------------------+----------------------+----------------------+
   ! 12389  136    2689   ! 128#   1238#@ 7      ! 4      5      128#   !
   ! 12478  147    278    ! 9      128#   5      ! 3      128#   6      !
   ! 12358  135    258    ! 4      1238   6      ! 128#   9      7      !
   +----------------------+----------------------+----------------------+
   ! 1278   167    2678   ! 128#   49     49     ! 5      128#   3      !
   ! 128    9      3      ! 5      7      128#   ! 128#   6      4      !
   ! 1258   15     4      ! 6      128#   3      ! 9      7      128#   !
   +----------------------+----------------------+----------------------+
   ! 3459   8      59     ! 7      124569 1249   ! 126    1234   125    !
   ! 4579   2      1      ! 3      45689  489    ! 678    48     58     !
   ! 6      3457   57     ! 128#   12458  1248   ! 1278#@ 12348  9      !
   +----------------------+----------------------+----------------------+

EL14c13-OR3-relation for digits: 1, 2 and 8
   in cells (marked #): (r3c7 r1c4 r1c5 r1c9 r2c1 r2c5 r2c8 r6c5 r6c9 r4c4 r4c8 r5c1 r5c6 r5c7)
   with 3 guardians (in cells marked @) : n3r1c5 n4r2c1 n7r2c1
   +-------------------------+-------------------------+-------------------------+
   ! 12389   136     2689    ! 128#    1238#@  7       ! 4       5       128#    !
   ! 12478#@ 147     278     ! 9       128#    5       ! 3       128#    6       !
   ! 12358   135     258     ! 4       1238    6       ! 128#    9       7       !
   +-------------------------+-------------------------+-------------------------+
   ! 1278    167     2678    ! 128#    49      49      ! 5       128#    3       !
   ! 128#    9       3       ! 5       7       128#    ! 128#    6       4       !
   ! 1258    15      4       ! 6       128#    3       ! 9       7       128#    !
   +-------------------------+-------------------------+-------------------------+
   ! 3459    8       59      ! 7       124569  1249    ! 126     1234    125     !
   ! 4579    2       1       ! 3       45689   489     ! 678     48      58      !
   ! 6       3457    57      ! 128     12458   1248    ! 1278    12348   9       !
   +-------------------------+-------------------------+-------------------------+

and then the short chains:

z-chain[3]: r1n9{c1 c3} - c3n6{r1 r4} - c3n2{r4 .} ==> r1c1≠2
z-chain[3]: r1n9{c1 c3} - c3n6{r1 r4} - c3n8{r4 .} ==> r1c1≠8
naked-quads-in-a-column: c5{r1 r3 r2 r6}{n8 n3 n2 n1} ==> r9c5≠8, r9c5≠2, r9c5≠1, r8c5≠8, r7c5≠2, r7c5≠1
biv-chain[4]: r8n6{c5 c7} - b9n7{r8c7 r9c7} - r9c3{n7 n5} - r9c5{n5 n4} ==> r8c5≠4
EL14c13s-OR2-whip[4]: OR2{{n3r1c5 | n7r9c7}} - r9c3{n7 n5} - r9c5{n5 n4} - r9c2{n4 .} ==> r1c2≠3
EL14c30s-OR2-whip[2]: OR2{{n7r9c7 | n3r3c5}} - c2n3{r3 .} ==> r9c2≠7
EL14c30s-OR2-whip[3]: r9c3{n5 n7} - OR2{{n7r9c7 | n3r3c5}} - c2n3{r3 .} ==> r9c2≠5
biv-chain[4]: c2n7{r4 r2} - c2n4{r2 r9} - r9c5{n4 n5} - r9c3{n5 n7} ==> r4c3≠7
z-chain[4]: c3n8{r3 r4} - r4n6{c3 c2} - c2n7{r4 r2} - r2n4{c2 .} ==> r2c1≠8
z-chain[4]: c3n2{r3 r4} - r4n6{c3 c2} - c2n7{r4 r2} - r2n4{c2 .} ==> r2c1≠2
EL14c30s-OR2-whip[4]: c3n7{r2 r9} - OR2{{n7r9c7 | n3r3c5}} - c2n3{r3 r9} - c2n4{r9 .} ==> r2c2≠7
singles ==> r4c2=7, r4c3=6, r1c2=6
whip[1]: b4n2{r6c1 .} ==> r3c1≠2
whip[1]: b4n8{r6c1 .} ==> r3c1≠8
biv-chain[4]: r9c5{n4 n5} - r9c3{n5 n7} - c1n7{r8 r2} - b1n4{r2c1 r2c2} ==> r9c2≠4
singles ==> r9c2=3, r7c8=3, r2c2=4
At least one candidate of a previous EL14c13-OR3-relation between candidates n3r1c5 n4r2c1 n7r2c1 has just been eliminated.
There remains an EL14c13-OR2-relation between candidates: n3r1c5 n7r2c1

z-chain[4]: c1n4{r7 r8} - r8c8{n4 n8} - r8c6{n8 n9} - r4c6{n9 .} ==> r7c6≠4
EL14c13s-OR2-whip[4]: r3n3{c1 c5} - OR2{{n3r1c5 | n7r9c7}} - c3n7{r9 r2} - r2c1{n7 .} ==> r3c1≠1
EL14c30s-OR2-whip[3]: r8n7{c1 c7} - OR2{{n7r9c7 | n3r3c5}} - r3c1{n3 .} ==> r8c1≠5
EL14c30s-OR2-whip[3]: r9c3{n5 n7} - OR2{{n7r9c7 | n3r3c5}} - r3c1{n3 .} ==> r3c3≠5
whip[1]: c3n5{r9 .} ==> r7c1≠5
EL14c30s-OR2-whip[4]: b1n3{r1c1 r3c1} - OR2{{n3r3c5 | n7r9c7}} - c3n7{r9 r2} - r2c1{n7 .} ==> r1c1≠1
EL14c13s-OR2-whip[3]: r8n7{c1 c7} - OR2{{n7r9c7 | n3r1c5}} - r1c1{n3 .} ==> r8c1≠9
whip[1]: r8n9{c6 .} ==> r7c5≠9, r7c6≠9
biv-chain[3]: r8c8{n8 n4} - r8c1{n4 n7} - b9n7{r8c7 r9c7} ==> r9c7≠8
biv-chain[3]: r8c1{n4 n7} - r9c3{n7 n5} - r9c5{n5 n4} ==> r8c6≠4
biv-chain[4]: r9c5{n4 n5} - b7n5{r9c3 r7c3} - r7n9{c3 c1} - r7n4{c1 c5} ==> r4c5≠4, r9c6≠4
singles ==> r4c5=9, r4c6=4, r8c6=9
whip[1]: r8n8{c9 .} ==> r9c8≠8
EL14c13-OR2-ctr-whip[4]: b1n1{r3c2 r2c1} - b4n1{r4c1 r6c2} - c5n1{r6 r1} - OR2{{n3r1c5 n7r2c1 | .}} ==> r3c7≠1
naked-pairs-in-a-row: r3{c3 c7}{n2 n8} ==> r3c5≠8, r3c5≠2
EL14c13s-OR2-whip[4]: r3c5{n1 n3} - OR2{{n3r1c5 | n7r9c7}} - c3n7{r9 r2} - r2c1{n7 .} ==> r3c2≠1
end in SFin[2]

Still not trivial but much easier to find than long chains - especially braids[19] if you don't use tridagons or close patterns in any way.
.

[eleven]

.This is not the pattern one would have to find. One can use two much simpler patterns and then very short ORk-chains:

It's the combination of your first 2 patterns, a "twin pattern" (the 3 must be here or there), as totuan has called them.

[Leren]

Checking though the 78 solutions that are available if the 6 is removed from 3rc6, the Trigadon is found if one adds r1c5 = 3, r3c1 = 3, r6c6 = 3, r7c5 = 6, or r9c5 = 4.

r7c5 = 6 is a bit ridiculous because the puzzle solves with singles but you can see the solved Trigadon, halfway through the singles markoff, but as we learnt last Sunday, that should count.

r9c5 = 4 is interesting in that it is well concealed and does not appear until a few moves have been made.

Leren

[denis_berthier]

.This is not the pattern one would have to find. One can use two much simpler patterns and then very short ORk-chains:

It's the combination of your first 2 patterns, a "twin pattern" (the 3 must be here or there), as totuan has called them.

... in the same way as people see a Quad when there are only 2 Pairs in the same line. Good for them if that makes them feel very smart.
.

[denis_berthier]

Checking though the 78 solutions that are available if the 6 is removed from 3rc6, the Trigadon is found if one adds r1c5 = 3, r3c1 = 3, r6c6 = 3, r7c5 = 6, or r9c5 = 4.
r7c5 = 6 is a bit ridiculous because the puzzle solves with singles but you can see the solved Trigadon, halfway through the singles markoff, but as we learnt last Sunday, that should count.

It counts only in a very restricted sense. It's useless.
In SudoRules, Tridagons are only detected after any pattern based on 2 or fewer CSP-variables and after Subsets[3]. When I say that every known puzzle in T&E(3) has a tridagon, I mean it still has one after these patterns have been applied - which is a stronger result than if I detected them earlier.

r9c5 = 4 is interesting in that it is well concealed and does not appear until a few moves have been made.

I've tried this case.
Indeed, the tridagon appears in the standard path, with 3 guardians:

Code: Select all

hidden-pairs-in-a-row: r7{n3 n4}{c1 c8} ==> r7c8≠2, r7c8≠1
Trid-OR3-relation for digits 1, 2 and 8 in blocks:
        b2, with cells (marked #): r1c4, r2c5, r3c6
        b3, with cells (marked #): r1c9, r2c8, r3c7
        b5, with cells (marked #): r4c4, r6c5, r5c6
        b6, with cells (marked #): r4c8, r6c9, r5c7
with 3 guardians (in cells marked @): n3r3c6 n6r3c6 n3r6c5
   +-------------------------+-------------------------+-------------------------+
   ! 9       136     268     ! 128#    12368   7       ! 4       5       128#    !
   ! 1278    4       278     ! 9       128#    5       ! 3       128#    6       !
   ! 12358   1356    2568    ! 4       12368   12368#@ ! 128#    9       7       !
   +-------------------------+-------------------------+-------------------------+
   ! 1278    167     2678    ! 128#    9       4       ! 5       128#    3       !
   ! 128     9       3       ! 5       7       128#    ! 128#    6       4       !
   ! 1258    15      4       ! 6       1238#@  1238    ! 9       7       128#    !
   +-------------------------+-------------------------+-------------------------+
   ! 34      8       9       ! 7       1256    126     ! 126     34      125     !
   ! 47      2       1       ! 3       568     9       ! 678     48      58      !
   ! 6       357     57      ! 128     4       128     ! 1278    1238    9       !
   +-------------------------+-------------------------+-------------------------+

SudoRules has a way of doing some cleaning before identifying the tridagon: solving with preferences. It may work or not; it may also destroy the tridagon. In the present case, it works with bivalue-chains.
I could probably have used a weaker preference set.

(solve-w-prefs "......45....9.53.6...4....7......5.3.9357..64..46..97..8.7......213.....6...4...9" BIVALUE-CHAINS)

Code: Select all

biv-chain[2]: r7n3{c8 c1} - r7n4{c1 c8} ==> r7c8≠1, r7c8≠2
biv-chain[3]: r8c8{n8 n4} - r8c1{n4 n7} - b9n7{r8c7 r9c7} ==> r9c7≠8
biv-chain[5]: r1n3{c5 c2} - b7n3{r9c2 r7c1} - b7n4{r7c1 r8c1} - r8n7{c1 c7} - r8n6{c7 c5} ==> r1c5≠6
whip[1]: b2n6{r3c6 .} ==> r3c2≠6, r3c3≠6
biv-chain[5]: r3n6{c6 c5} - r8n6{c5 c7} - r8n7{c7 c1} - c1n4{r8 r7} - c1n3{r7 r3} ==> r3c6≠3
hidden-single-in-a-column ==> r6c6=3

  +----------------------+----------------------+----------------------+
  ! 9      136    268    ! 128#   1238   7      ! 4      5      128#   !
  ! 1278   4      278    ! 9      128#   5      ! 3      128#   6      !
  ! 12358  135    258    ! 4      12368  1268#@ ! 128#   9      7      !
  +----------------------+----------------------+----------------------+
  ! 1278   167    2678   ! 128#   9      4      ! 5      128#   3      !
  ! 128    9      3      ! 5      7      128#   ! 128#   6      4      !
  ! 1258   15     4      ! 6      128#   3      ! 9      7      128#   !
  +----------------------+----------------------+----------------------+
  ! 34     8      9      ! 7      1256   126    ! 126    34     125    !
  ! 47     2      1      ! 3      568    9      ! 678    48     58     !
  ! 6      357    57     ! 128    4      128    ! 127    1238   9      !
  +----------------------+----------------------+----------------------+
tridagon for digits 1, 2 and 8 in blocks:
       b2, with cells (marked #): r3c6 (target cell, marked @), r2c5, r1c4
       b3, with cells (marked #): r3c7, r2c8, r1c9
       b5, with cells (marked #): r5c6, r6c5, r4c4
       b6, with cells (marked #): r5c7, r6c9, r4c8
==> r3c6≠1,2,8
naked-single ==> r3c6=6
end in W9

[denis_berthier]

.
If you're interested in this kind of puzzles, you can try the 35 ones I published here : http://forum.enjoysudoku.com/the-layered-structure-of-t-e-depth-d-t45647-4.html

All of them are in B19 - exceptional for a T&E(1) puzzle, beyond any possibility of computing a probability - and each of them is derived by a relatively simple process from some minimal puzzle in T&E(3). The puzzle at the start of this thread is a scrambled version of the first there.
.

[eleven]

It's the combination of your first 2 patterns, a "twin pattern" (the 3 must be here or there), as totuan has called them.

... in the same way as people see a Quad when there are only 2 Pairs in the same line. Good for them if that makes them feel very smart.
.

So you and your program did not see, that one of the patterns must be true without the 3, and you can place 7r9c7.