The New Sudoku Players' Forum

[denis_berthier]

.

Code: Select all

+-------+-------+-------+
! 1 . 3 ! . . 6 ! . 8 . !
! 4 . . ! . 8 . ! 1 . . !
! . 8 . ! 1 . . ! . 6 . !
+-------+-------+-------+
! . 4 . ! . 9 5 ! . . 3 !
! . . 7 ! . . . ! . . . !
! . . . ! 3 . . ! . . . !
+-------+-------+-------+
! 3 . . ! 5 . 4 ! . 9 7 !
! 8 . . ! . 6 3 ! . 1 . !
! . . 5 ! . . . ! . . . !
+-------+-------+-------+
1.3..6.8.4...8.1...8.1...6..4..95..3..7.........3.....3..5.4.978...63.1...5......

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 1    27   3    ! 4    5    6    ! 27   8    9    !
   ! 4    2567 269  ! 27   8    279  ! 1    3    25   !
   ! 57   8    29   ! 1    3    279  ! 257  6    4    !
   +----------------+----------------+----------------+
   ! 2    4    1    ! 8    9    5    ! 6    7    3    !
   ! 59   3    7    ! 6    24   1    ! 49   25   8    !
   ! 6    59   8    ! 3    247  27   ! 49   25   1    !
   +----------------+----------------+----------------+
   ! 3    126  26   ! 5    12   4    ! 8    9    7    !
   ! 8    79   4    ! 79   6    3    ! 25   1    25   !
   ! 79   1279 5    ! 279  127  8    ! 3    4    6    !
   +----------------+----------------+----------------+
74 candidates

.

[pjb]

Code: Select all

 1       27      3      | 4      5      6      | 27     8      9     
 4       2567    269    | 27     8      279    | 1      3      25     
 57      8       29     | 1      3      279    | 257    6      4     
------------------------+----------------------+---------------------
 2       4       1      | 8      9      5      | 6      7      3     
 59      3       7      | 6     b24     1      | 49     25     8     
 6      c59      8      | 3     c247   c27     | 49    c25     1     
------------------------+----------------------+---------------------
 3       126     26     | 5     a12     4      | 8      9      7     
 8       7-9     4      |a79     6      3      | 25     1      25     
 79      12      5      | 279   a127    8      | 3   

If the object is to solve with a deadly pattern, I'll pass for now
(9=2)r79c5, r8c4 - (2=4)r5c5 - (4=9)r6c2568 => -9 r8c2; stte

Phil

[Cenoman]

Code: Select all

 +--------------------+--------------------+------------------+
 |  1    27     3     |  4     5     6     |  27    8    9    |
 |  4    56+27  69+2  |  27    8     79+2  |  1     3    25   |
 |  57   8      29    |  1     3     29+7  |  57+2  6    4    |
 +--------------------+--------------------+------------------+
 |  2    4      1     |  8     9     5     |  6     7    3    |
 |  59   3      7     |  6     24    1     |  49    25   8    |
 |  6    59     8     |  3     4+2-7 27    |  49    25   1    |
 +--------------------+--------------------+------------------+
 |  3    16+2   26    |  5     12    4     |  8     9    7    |
 |  8    79     4     |  79    6     3     |  25    1    25   |
 |  79   12     5     |  29+7  17+2  8     |  3     4    6    |
 +--------------------+--------------------+------------------+

BUG+10

Code: Select all

(26)r27c2|(7)r2c2  - - - - -
 ||                          \
(2)r2c236|r3c7 - (2=5)r2c9    \
 ||                  \         \
(7)r3c6 - (7=5)r3c1 - - - - - - (5)r2c2 = r6c2 - (5=27)r6c68 *
 ||                  /         /
(7)r9c4 - - - - (7=25)r2c49   /
 ||                          /
(2)r9c5 - r9c4 = r2c4 - (2=5)r2c9
 ||
(2)r6c5 *

=> -7 r6c5; ste

Hidden Text: Show

"Normal" solution for such a puzzle:
(2=5)r2c9 - r2c2 = r6c2 - (5=2)r6c8 - r6c6 = (2)r23c6 => -2 r2c4; ste (W-Wing with transport)

[eleven]

There is a big DP (and at least 7 smaller ones):

Code: Select all

+-------------------+-------------------+-------------------+
| 1     27     3    | 4     5     6     | 27    8     9     |
| 4    #57+26 #29+6 | 27    8    #79+2  | 1     3    #25    |
|#57    8     #29   | 1     3    #79+2  |#25+7  6     4     |
+-------------------+-------------------+-------------------+
| 2     4      1    | 8     9     5     | 6     7     3     |
|#59    3      7    | 6    #24    1     |#49   #25    8     |
| 6    #59     8    | 3    #24+7  27    |#49   #25    1     |
+-------------------+-------------------+-------------------+
| 3     126    26   | 5     12    4     | 8     9     7     |
| 8    #79     4    |#79    6     3     |#25    1    #25    |
|#79    1279   5    |#79+2  127   8     | 3     4     6     |
+-------------------+-------------------+-------------------+

All 8 extra candidates can lead to 2r9c4:
2r9c4
2r2c2 - (2=792)r289
(6-5)r2c2 = 59r35c1 - (9=42)r5c75 - r79c5 = r9c4
2r23c6 - r2c4 = 2r9c4
7r3c7 - (7=59)r35c1 - (9=42)r5c75 - r79c5 = r9c4
(7-4)r6c5 = 495r5c571 - (5=729)b1p729 - (7|9=2)r3c6 - r2c4 = 2r9c4
6r2c3 ... well ...that's much harder than Cenoman's "normal" solution ...

(however note, that 7r6c5->..->2r9c4 - (2=17)r79c5 => -7r6c5 already solves the puzzle)
[Edit:] thanx to Cenoman: i missed to include the pair 29r23c3, with an annoying additional guardian 6r2c3

[added:]How to find such a DP:
You know this one:

Code: Select all

 12 12 .
 -------
 12 12 .

Now you can extend it these ways:

Code: Select all

 . 12 . | 12 . .         .  .  .
 12 . . | 12 . .         13 13 .
 ---------------   or    -------
 12 12 .|                12 12 .
                          .  .  .
                         .  .  .
                         -------
                         23 23  .

Thus you can get such a pattern

[rjamil]

Code: Select all

 +------------------+---------------+------------------+
 | 1     279    3   | 4    5    6   | 279     8    29  |
 | 4     25679  269 | 279  8    279 | 1       3    259 |
 | 2579  8      29  | 1    3    279 | 2579    6    4   |
 +------------------+---------------+------------------+
 | 26    4      1   | 8    9    5   | 267     27   3   |
 | 259   3      7   | 6    24   1   | 2459    25   8   |
 | 2569  2569   8   | 3    247  27  | 245679  257  1   |
 +------------------+---------------+------------------+
 | 3     126    26  | 5    12   4   | 8       9    7   |
 | 8     279    4   | 279  6    3   | 25      1    25  |
 | 279   1279   5   | 279  127  8   | 3       4    6   |
 +------------------+---------------+------------------+

1) Single-digit POM: 2 in r1c279 r2c23469 r3c1367 r4c178 r5c1578 r6c125678 r7c235 r8c2479 r9c1245
Digit 2 not in 44 Templates => -2 @ r4c7 r5c7 r6c7 r8c2 r8c4 r9c1;
Single-digit POM: 5 in r1c5 r2c29 r3c17 r4c6 r5c178 r6c1278 r7c4 r8c79 r9c3
Digit 5 not in 3 Templates => -5 @ r5c7 r6c7;
Single-digit POM: 6 in r1c6 r2c23 r3c8 r4c17 r5c4 r6c127 r7c23 r8c5 r9c9
Digit 6 not in 4 Templates => -6 @ r6c2;
Single-digit POM: 7 in r1c27 r2c246 r3c167 r4c78 r5c3 r6c5678 r7c9 r8c24 r9c1245
Digit 7 not in 5 Templates => -7 @ r4c7 r6c7 r6c8;
Digit 7 in all 5 Templates => 7 @ r4c8;
Single-digit POM: 9 in r1c279 r2c23469 r3c1367 r4c5 r5c17 r6c127 r7c8 r8c24 r9c124
Digit 9 not in 10 Templates => -9 @ r1c2 r1c7 r2c2 r2c4 r2c9 r3c1 r3c7;
Digit 9 in all 10 Templates => 9 @ r1c9;

2) 7 @ r4c8; 2 @ r4c1 6 @ r6c1; 6 @ r4c7 9 @ r1c9;

Code: Select all

 +---------------+---------------+-------------+
 | 1   27    3   | 4    5    6   | 27   8   9  |
 | 4   2567  269 | 27   8    279 | 1    3   25 |
 | 57  8     29  | 1    3    279 | 257  6   4  |
 +---------------+---------------+-------------+
 | 2   4     1   | 8    9    5   | 6    7   3  |
 | 59  3     7   | 6    24   1   | 49   25  8  |
 | 6   59    8   | 3    247  27  | 49   25  1  |
 +---------------+---------------+-------------+
 | 3   126   26  | 5    12   4   | 8    9   7  |
 | 8   79    4   | 79   6    3   | 25   1   25 |
 | 79  1279  5   | 279  127  8   | 3    4   6  |
 +---------------+---------------+-------------+

3) Double-digit POM: 2 in r1c27 r2c23469 r3c367 r4c1 r5c58 r6c568 r7c235 r8c79 r9c245
and POM: 5 in r1c5 r2c29 r3c17 r4c6 r5c18 r6c28 r7c4 r8c79 r9c3
Digit 2 not in 5 Templates => -2 @ r2c4 r6c6 r7c5 r9c2 r9c5;
Double-digit POM: 2 in r1c27 r2c2369 r3c367 r4c1 r5c58 r6c58 r7c23 r8c79 r9c4
and POM: 7 in r1c27 r2c246 r3c167 r4c8 r5c3 r6c56 r7c9 r8c24 r9c1245
Digit 2 not in 6 Templates => -2 @ r3c3;
Double-digit POM: 7 in r1c27 r2c246 r3c167 r4c8 r5c3 r6c56 r7c9 r8c24 r9c1245
and POM: 2 in r1c27 r2c2369 r3c67 r4c1 r5c58 r6c58 r7c23 r8c79 r9c4
Digit 7 not in 4 Templates => -7 @ r9c4;
Double-digit POM: 9 in r1c9 r2c36 r3c36 r4c5 r5c17 r6c27 r7c8 r8c24 r9c124
and POM: 2 in r1c27 r2c2369 r3c67 r4c1 r5c58 r6c58 r7c23 r8c79 r9c4
Digit 9 not in 4 Templates => -9 @ r8c2 r9c4; stte

R. Jamil

[denis_berthier]

Hi rjamil,

I hadn't tried with templates, but I find a solution involving only templates[1]:

candidate in no template[1] for digit 2 ==> r9c2≠2
candidate in no template[1] for digit 2 ==> r7c5≠2
singles ==> r7c5=1, r9c2=1
candidate in no template[1] for digit 2 ==> r3c3≠2
singles ==> r3c3=9, r2c6=9
candidate common to all the templates[1] for digit 7 ==> r1c7=7
singles ==> r1c2=2, r2c3=6, r7c3=2, r7c2=6
candidate in no template[1] for digit 7 ==> r9c4≠7
candidate common to all the templates[1] for digit 2 ==> r5c8=2
stte
.

[denis_berthier]

.
Thanks for your answers.
As you have guessed, my purpose was to find a large DP - here in 10 cells. It's also funny to see that almost only DPs are used in the solution.
10 cells is the largest useful DP I've found until now.

whip[2]: r9c1{n9 n7} - r8c2{n7 .} ==> r9c2≠9
whip[2]: r9c1{n7 n9} - r8c2{n9 .} ==> r9c2≠7

Code: Select all

DP4-2-1s-OR4-relation for digits: 26
   in cells (marked #): (r7c3 r7c2 r2c3 r2c2)
   with 4 guardians (in cells marked @) : n1r7c2 n9r2c3 n5r2c2 n7r2c2
   +----------------------+----------------------+----------------------+
   ! 1      27     3      ! 4      5      6      ! 27     8      9      !
   ! 4      2567#@ 269#@  ! 27     8      279    ! 1      3      25     !
   ! 57     8      29     ! 1      3      279    ! 257    6      4      !
   +----------------------+----------------------+----------------------+
   ! 2      4      1      ! 8      9      5      ! 6      7      3      !
   ! 59     3      7      ! 6      24     1      ! 49     25     8      !
   ! 6      59     8      ! 3      247    27     ! 49     25     1      !
   +----------------------+----------------------+----------------------+
   ! 3      126#@  26#    ! 5      12     4      ! 8      9      7      !
   ! 8      79     4      ! 79     6      3      ! 25     1      25     !
   ! 79     12     5      ! 279    127    8      ! 3      4      6      !
   +----------------------+----------------------+----------------------+

DP4-2-1-OR2-relation for digits: 12
   in cells (marked #): (r9c5 r9c2 r7c5 r7c2)
   with 2 guardians (in cells marked @) : n7r9c5 n6r7c2
   +-------------------+-------------------+-------------------+
   ! 1     27    3     ! 4     5     6     ! 27    8     9     !
   ! 4     2567  269   ! 27    8     279   ! 1     3     25    !
   ! 57    8     29    ! 1     3     279   ! 257   6     4     !
   +-------------------+-------------------+-------------------+
   ! 2     4     1     ! 8     9     5     ! 6     7     3     !
   ! 59    3     7     ! 6     24    1     ! 49    25    8     !
   ! 6     59    8     ! 3     247   27    ! 49    25    1     !
   +-------------------+-------------------+-------------------+
   ! 3     126#@ 26    ! 5     12#   4     ! 8     9     7     !
   ! 8     79    4     ! 79    6     3     ! 25    1     25    !
   ! 79    12#   5     ! 279   127#@ 8     ! 3     4     6     !
   +-------------------+-------------------+-------------------+

DP4-2-1-OR2-whip[2]: OR2{{n6r7c2 | n7r9c5}} - r9n1{c5 .} ==> r7c2≠1
singles ==> r9c2=1, r7c5=1

Code: Select all

   +----------------+----------------+----------------+
   ! 1    27   3    ! 4    5    6    ! 27   8    9    !
   ! 4    2567 269  ! 27   8    279  ! 1    3    25   !
   ! 57   8    29   ! 1    3    279  ! 257  6    4    !
   +----------------+----------------+----------------+
   ! 2    4    1    ! 8    9    5    ! 6    7    3    !
   ! 59   3    7    ! 6    24   1    ! 49   25   8    !
   ! 6    59   8    ! 3    247  27   ! 49   25   1    !
   +----------------+----------------+----------------+
   ! 3    26   26   ! 5    1    4    ! 8    9    7    !
   ! 8    79   4    ! 79   6    3    ! 25   1    25   !
   ! 79   1    5    ! 279  27   8    ! 3    4    6    !
   +----------------+----------------+----------------+
At least one candidate of a previous DP4-2-1s-OR4-relation between candidates n1r7c2 n9r2c3 n5r2c2 n7r2c2 has just been eliminated.
There remains a DP4-2-1s-OR3-relation between candidates: n9r2c3 n5r2c2 n7r2c2

DP4-2-1s-OR3-whip[2]: OR3{{n7r2c2 n5r2c2 | n9r2c3}} - r2n6{c3 .} ==> r2c2≠2

Code: Select all

DP10-4-12-OR5-relation for digits: 2679
   in cells (marked #): (r7c3 r7c2 r1c7 r1c2 r2c6 r2c3 r2c2 r3c6 r3c7 r3c3)
   with 5 guardians (in cells marked @) : n2r2c6 n2r2c3 n5r2c2 n2r3c6 n5r3c7
   +-------------------+-------------------+-------------------+
   ! 1     27#   3     ! 4     5     6     ! 27#   8     9     !
   ! 4     567#@ 269#@ ! 27    8     279#@ ! 1     3     25    !
   ! 57    8     29#   ! 1     3     279#@ ! 257#@ 6     4     !
   +-------------------+-------------------+-------------------+
   ! 2     4     1     ! 8     9     5     ! 6     7     3     !
   ! 59    3     7     ! 6     24    1     ! 49    25    8     !
   ! 6     59    8     ! 3     247   27    ! 49    25    1     !
   +-------------------+-------------------+-------------------+
   ! 3     26#   26#   ! 5     1     4     ! 8     9     7     !
   ! 8     79    4     ! 79    6     3     ! 25    1     25    !
   ! 79    1     5     ! 279   27    8     ! 3     4     6     !
   +-------------------+-------------------+-------------------+

whip[3]: r1c2{n2 n7} - r8n7{c2 c4} - r2c4{n7 .} ==> r2c3≠2

Code: Select all

  +-------------+-------------+-------------+
   ! 1   27  3   ! 4   5   6   ! 27  8   9   !
   ! 4   567 69  ! 27  8   279 ! 1   3   25  !
   ! 57  8   29  ! 1   3   279 ! 257 6   4   !
   +-------------+-------------+-------------+
   ! 2   4   1   ! 8   9   5   ! 6   7   3   !
   ! 59  3   7   ! 6   24  1   ! 49  25  8   !
   ! 6   59  8   ! 3   247 27  ! 49  25  1   !
   +-------------+-------------+-------------+
   ! 3   26  26  ! 5   1   4   ! 8   9   7   !
   ! 8   79  4   ! 79  6   3   ! 25  1   25  !
   ! 79  1   5   ! 279 27  8   ! 3   4   6   !
   +-------------+-------------+-------------+
At least one candidate of a previous DP10-4-12-OR5-relation between candidates n2r2c6 n2r2c3 n5r2c2 n2r3c6 n5r3c7 has just been eliminated.
There remains a DP10-4-12-OR4-relation between candidates: n2r2c6 n5r2c2 n2r3c6 n5r3c7

DP4-2-1-OR2-whip[3]: OR2{{n6r7c2 | n7r9c5}} - c1n7{r9 r3} - b1n5{r3c1 .} ==> r2c2≠6
singles ==> r2c3=6, r7c3=2, r3c3=9, r7c2=6, r2c6=9, r1c2=2, r1c7=7

Code: Select all

   +-------------+-------------+-------------+
   ! 1   2   3   ! 4   5   6   ! 7   8   9   !
   ! 4   57  6   ! 27  8   9   ! 1   3   25  !
   ! 57  8   9   ! 1   3   27  ! 25  6   4   !
   +-------------+-------------+-------------+
   ! 2   4   1   ! 8   9   5   ! 6   7   3   !
   ! 59  3   7   ! 6   24  1   ! 49  25  8   !
   ! 6   59  8   ! 3   247 27  ! 49  25  1   !
   +-------------+-------------+-------------+
   ! 3   6   2   ! 5   1   4   ! 8   9   7   !
   ! 8   79  4   ! 79  6   3   ! 25  1   25  !
   ! 79  1   5   ! 279 27  8   ! 3   4   6   !
   +-------------+-------------+-------------+
At least one candidate of a previous DP10-4-12-OR4-relation between candidates n2r2c6 n5r2c2 n2r3c6 n5r3c7 has just been eliminated.
There remains a DP10-4-12-OR3-relation between candidates: n5r2c2 n2r3c6 n5r3c7

finned-x-wing-in-rows: n7{r2 r8}{c2 c4} ==> r9c4≠7
DP10-4-12-OR3-whip[2]: OR3{{n5r3c7 n2r3c6 | n5r2c2}} - r2c9{n5 .} ==> r3c7≠2
stte
.

[Cenoman]

10 cells is the largest useful DP I've found until now.

Here , an example of BUG+23

[denis_berthier]

10 cells is the largest useful DP I've found until now.

Here , an example of BUG+23

BUG+23 means "23 guardians"?

Here, I mean 10 cells (and only 5 guardians).

[eleven]

There is a bit confusion about, what a "deadly pattern" is.
Personally i distinguish between the uniqueness dependent DP's (deadly patterns) with 2 solutions, MUG's with at least 2 solutions and BUG's with 0 solutions,
and the non-uniqueness "impossible patterns" with 0 solutions.
(Note, that the uniqueness argument is used to prove a BUG pattern impossible in a unique puzzle, but the whole pattern does not have a solution.
[Added: To be more precise: otherwise it would be composed of smaller, independant DP's)

So in a pattern with a BUG there might be an isolated, so far unused DP, but i can't see one in Denis' last grid.

[rjamil]

Hi denis_berthier,

Hi rjamil,

I hadn't tried with templates, but I find a solution involving only templates[1]:

candidate in no template[1] for digit 2 ==> r9c2≠2
candidate in no template[1] for digit 2 ==> r7c5≠2
singles ==> r7c5=1, r9c2=1
candidate in no template[1] for digit 2 ==> r3c3≠2
singles ==> r3c3=9, r2c6=9
candidate common to all the templates[1] for digit 7 ==> r1c7=7
singles ==> r1c2=2, r2c3=6, r7c3=2, r7c2=6
candidate in no template[1] for digit 7 ==> r9c4≠7
candidate common to all the templates[1] for digit 2 ==> r5c8=2
stte

I see lot of ways to implement the POM move. I prefer cell counting instead of template counting, without keep tracking intermediate template steps, as mentioned by dobrichev here.

R. Jamil

[Cenoman]

BUG+23 means "23 guardians"?

I wasn't the author of the solution presented in the link. Obviously, that was meant by SpAce.
My own use is the same, though I'm aware that, it not in line with the Sudopedia definition of BUG n, n being the number of cells having guardians (so, BUG 17 for the linked example), but to me, this number of tri(or more)-value cells is useless to solve the puzzle, and furthermore doesn't indicates the size of the pattern, as already bivalued cells are part of the pattern (in the linked example: 23 guardians in 17 cells, out of a 29-cell pattern)
Of course, SpAce's solution for that puzzle was a joke. I've not clarified, but solving it with smaller DPs seems very likely.

Personally i distinguish between the uniqueness dependent DP's (deadly patterns) with 2 solutions, MUG's with at least 2 solutions and BUG's with 0 solutions,
and the non-uniqueness "impossible patterns" with 0 solutions.

Full agreement.
But I remember seeing in the Puzzles section, a BUG with two solutions (in a puzzle having itself two solutions) Not an error, but an example ad'hoc.

As I've never met one, I wonder whether a minimal MUG exists ? To me, MUGs are composed of two or more DP's

[eleven]

A BUG (with guardians) with 2 solutions would be a DP too. From the definition (each candidate occurs exactly 2 times in all of its 3 units) a UR pattern also would be a BUG. But with all other cells resolved it is not possible in a unique vanilla puzzle, because the non solved cells would have to be occupied by the DP candidates, i.e. it would have 2 solutions.

[denis_berthier]

.
To be clear about my statement "10 cells is the largest useful DP I've found until now":

- the only DPs I consider are Blue's list of 408 minimal DPs in 12 or fewer cells; indeed I've restricted all my calculations to 11 cells;
- the collections I've tried are [cbg-000] (21,375 puzzles) plus the first few thousand puzzles in mith's T&E(3) collection; as the results are mainly negative (apart from a few funny examples), I don't plan to invest much more time in DPs;
- I don't consider cases with more than 8 guardians;
- I consider a DP "useful" when it appears in a resolution path, it leads to at least one elimination and it effectively reduces the rating.

In all the patterns I've studied (oddagons, Impossible, DP...) that don't belong to my standard menagerie (whips, braids, g-whips, ORk-chains...), a reduced rating is my standard method for detecting the potentially interesting puzzles. SudoRules has functions for comparing ratings and extracting the interesting cases.
.

[eleven]

I have not realized, that from the 10-cell-DP only 3 single digits with a guardian each remained (2 other guardians eliminated).
Of course still one of the guardians must be true (you just have to remember them), though the pattern is almost completely destroyed and there is no DP anymore in the grid (or only well hidden with the ungiven solved cells).