The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|..7|.4.|
 |..1|5..|7..|
 |.4.|.3.|..2|
 |---+---+---|
 |.7.|...|.6.|
 |..2|.5.|..3|
 |8..|...|5..|
 |---+---+---|
 |.3.|..6|4..|
 |9..|2..|..6|
 |..8|.7.|.9.|
 *-----------*


Play/Print this puzzle online

[eleven]

Code: Select all

 *--------------------------------------------------------------------------------*
 |  2356    25689   3569   |  1689     12689   7        |  13689   4       1589   |
 |  236     2689    1      |  5        24689   2489     |  7       38      89     |
 |  567     4       5679   |  1689     3       189      |  1689    158     2      |
 |-------------------------+----------------------------+-------------------------|
 |  1345    7       3459   |  13489    12489   123489   |  1289    6       1489   |
 |  146    b169     2      |  146789   5       1489     |  189     178     3      |
 |  8      b169     3469   |  134679   12469   12349    |  5       127     1479   |
 |-------------------------+----------------------------+-------------------------|
 | c1257    3     ca57     |  189      189     6        |  4       12578   1578   |
 |  9     ba15      4-57   |  2        148     13458    |  138     13578   6      |
 |  1246-5 c1256    8      |  134      7       1345     |  123     9       15     |
 *--------------------------------------------------------------------------------*

Sue de Coc ?
57r7c3,r8c2 = (1,96)r8c2,r56bc2 - (1|6=257)r7c13,r9c2 => -57r8c3,-5r9c1, stte

[SpAce]

Code: Select all

.---------------------------.-----------------------.--------------------.
|  2356       25689   3569  | 1689    12689  7      | 13689  4      1589 |
|  236        2689    1     | 5       24689  2489   | 7      38     89   |
|  567        4       5679  | 1689    3      189    | 1689   158    2    |
:---------------------------+-----------------------+--------------------:
|  1345       7       3459  | 13489   12489  123489 | 1289   6      1489 |
|  146       b169     2     | 146789  5      1489   | 189    178    3    |
|  8         b169     3469  | 134679  12469  12349  | 5      127    1479 |
:---------------------------+-----------------------+--------------------:
|  1257       3      c57    | 189     189    6      | 4      12578  1578 |
|  9         b15     c57(4) | 2       148    13458  | 138    13578  6    |
| a125(6)-4  b1256    8     | 134     7      1345   | 123    9      15   |
'---------------------------'-----------------------'--------------------'

(6)r9c1 = (6195)r9568c2 - (5=74)r78c3 => -4 r9c1; stte

[SpAce]

57r7c3,r8c2 = (1,96)r8c2,r56bc2 - (1|6=257)r7c13,r9c2 => -57r8c3,-5r9c1, stte

Very nice!

Sue de Coc ?

My first instinct is no, at least not with your chain because it's not a loop and its eliminations aren't typical of SDC. Hodoku doesn't see any SDCs here either, and it's much better at spotting them than me. I agree that it's quite close, but I doubt it's any standard form of SDC.

Did you see the (1256)r89c2 as the core AALS? To have an SDC with that you'd need two ALSs, one in the column and one in the box, so that their digits together cover the AALS digits. We have one in the column (169)r56c2 covering (16), but I can't find a suitable one in the box covering (25). The (1257)r7c13 is an AALS, and (1257)b7p135 overlaps with the core.

Added. To have an SDC that produces the critical eliminations (-57 r8c3) I think you'd need something like this:

Code: Select all

.-------------------------.
|  2356      568-29  3569 |
|  236       68-29   1    |
|  567       4       5679 |
:-------------------------+
|  1345      67-2    3459 |
|  146      a129     278  |
|  68       a129     3469 |
:-------------------------+
| b567       3      b567  |
|  9        b15      4-57 |
|  1248-56  b1257    8-6  |
'-------------------------'

Sue de Coq: ANS(129)r56c2 -12- AANS(1257)r89c2 -57- ANS(567)r7c13

<-> Doubly-Linked ALS-XZ: A=(129)r56c2; B=(12567)b7p1358; X={1,2} (btw, why don't we simply call that ALS-XX or something?)

<-> (2=9'1)r56c2 - (1=567'2)r89c2,r7c13 - loop => -57 r8c3, -56 r9c1, -6 r9c13, -29 r12c2, -2 r4c2

(other ways to see and write a corresponding DL-ALS-XZ and a loop exist, of course)

[Cenoman]

Code: Select all

 +--------------------------+----------------------------+-------------------------+
 |  2356    a25689   3569   |  1689     12689   7        |  13689   4       1589   |
 |  23      a2689    1      |  5        24689   2489     |  7       38      89     |
 |  567      4       5679   |  1689     3       189      |  1689    158     2      |
 +--------------------------+----------------------------+-------------------------+
 |  1345     7       3459   |  13489    12489   123489   |  1289    6       1489   |
 |  146     c169     2      |  146789   5       1489     |  189     178     3      |
 |  8       c169     3469   |  134679   12469   12349    |  5       127     1479   |
 +--------------------------+----------------------------+-------------------------+
 |  1257     3      B57     |  189      189     6        |  4       12578   1578   |
 |  9       A15     B457    |  2        148     13458    |  138     13578   6      |
 |zb1256-4 yb1256    8      |  134      7       1345     |  123     9       15     |
 +-------------------------+----------------------------+-------------------------+

Kraken column (5)r189c2
(5-82)r12c2 = (26)r9c12
(5)r8c2 - (57=4)r78c3
(5-6)r9c2 = (6)r9c1
=> -4 r9c1; ste

[eleven]

Did you see the (1256)r89c2 as the core AALS?

There are 6 cells with 6 digits in 2 units, 16 "crossing", so in the column we have 1-526 or or 6-125 or 16-25.
The question was, how to formulate it.

[SpAce]

Did you see the (1256)r89c2 as the core AALS?

There are 6 cells with 6 digits in 2 units, 16 "crossing", so in the column we have 1-526 or or 6-125 or 16-25.
The question was, how to formulate it.

Yeah, it's actually much closer than I thought (what was I thinking). However, the 1s are still a problem because all of them don't see each other, but all you have to do is to eliminate (1)r7c1 (pretty difficult, actually) and you have a standard Sue de Coq with those cells:

Code: Select all

.------------------------.-----------------------.--------------------.
|  2356     258-69  3569 | 1689    12689  7      | 13689  4      1589 |
|  236      28-69   1    | 5       24689  2489   | 7      38     89   |
|  567      4       5679 | 1689    3      189    | 1689   158    2    |
:------------------------+-----------------------+--------------------:
|  1345     7       3459 | 13489   12489  123489 | 1289   6      1489 |
|  146     a169     2    | 146789  5      1489   | 189    178    3    |
|  8       a169     3469 | 134679  12469  12349  | 5      127    1479 |
:------------------------+-----------------------+--------------------:
| b257      3      b57   | 189     189    6      | 4      12578  1578 |
|  9       b15      4-57 | 2       148    13458  | 138    13578  6    |
|  146-25  b1256    8    | 134     7      1345   | 123    9      15   |
'------------------------'-----------------------'--------------------'

Sue de Coq: (169)r56c2 -16- (1256)r89c2 -25- (257)r7c13

(1=9'6)r56c2 - (6=257'1)r89c2,r7c13 - loop => -69 r12c2, -25 r9c1, -57 r8c3

...or another one if you add r8c3 to the pattern:

Code: Select all

.------------------------.-----------------------.--------------------.
|  2356     258-69  3569 | 1689    12689  7      | 13689  4      1589 |
|  236      28-69   1    | 5       24689  2489   | 7      38     89   |
|  567      4       5679 | 1689    3      189    | 1689   158    2    |
:------------------------+-----------------------+--------------------:
|  1345     7       3459 | 13489   12489  123489 | 1289   6      1489 |
|  146     a169     2    | 146789  5      1489   | 189    178    3    |
|  8       a169     3469 | 134679  12469  12349  | 5      127    1479 |
:------------------------+-----------------------+--------------------:
| b257      3      b57   | 189     189    6      | 4      12578  1578 |
|  9       b15     b457  | 2       148    13458  | 138    13578  6    |
|  16-245  b1256    8    | 134     7      1345   | 123    9      15   |
'------------------------'-----------------------'--------------------'

Sue de Coq: (169)r56c2 -16- (1256)r89c2 -25- (2457)b7p136

(1=9'6)r56c2 - (6=2457'1)b7p58136 - loop => -69 r12c2, -245 r9c1

I still don't see any SDC without that preliminary elimination. On the other hand, your chain works great, so no need for one anyway.

PS. Sue de Coq and any DDS should follow this rule:

A subset of N cells sharing only N different digits is disjoint, if all occurrences of the same digit share one common sector.

Even though your pattern has "6 cells with 6 digits in 2 units", it fails that test because of the extra 1. I'm pretty sure a true SDC or DDS should always be a Rank 0 pattern, no matter how it's presented (loop, MSLS, etc). Maybe yours could be presented as an MSLS, though, as that allows Rank 1 patterns too?

Edit: "On the hand" -> "On the other hand". Lol.

[eleven]

Yes, that's probably the easiest view (which i used to find doubly linked ALS's too - with n-1 digits for n cells):
All digits must be in the 6 cells, unless one of the digits is there twice. This only could be 1 in r7c1 and r56c2, but then 5r8c2 and 7r7c3.

[SpAce]

Yes, that's probably the easiest view (which i used to find doubly linked ALS's too - with n-1 digits for n cells):
All digits must be in the 6 cells, unless one of the digits is there twice. This only could be 1 in r7c1 and r56c2, but then 5r8c2 and 7r7c3.

Yep. If you want to formulate that in Eureka, I guess you could use the almost-SdC:

Code: Select all

.-----------------------------.-----------------------.--------------------.
|   2356       25689     3569 | 1689    12689  7      | 13689  4      1589 |
|   236        2689      1    | 5       24689  2489   | 7      38     89   |
|   567        4         5679 | 1689    3      189    | 1689   158    2    |
:-----------------------------+-----------------------+--------------------:
|   1345       7         3459 | 13489   12489  123489 | 1289   6      1489 |
|   146       a169       2    | 146789  5      1489   | 189    178    3    |
|   8         a169       3469 | 134679  12469  12349  | 5      127    1479 |
:-----------------------------+-----------------------+--------------------:
| ba2(57)#1    3      ba(57)  | 189     189    6      | 4      12578  1578 |
|   9        ba1(5)      4-57 | 2       148    13458  | 138    13578  6    |
|   1246-5    a12(5)6    8    | 134     7      1345   | 123    9      15   |
'-----------------------------'-----------------------'--------------------'

Almost Sue de Coq: (257#1)r7c13 -25- (1256)r89c2 -16- (169)r56c2

SdC = (157)b7p153 => -57 r8c3, -5 r9c1; stte

(kinda cool that way, though it's probably harder to understand than your original)

[Cenoman]

Sue de Coc ?
57r7c3,r8c2 = (1,96)r8c2,r56bc2 - (1|6=257)r7c13,r9c2 => -57r8c3,-5r9c1, stte

Sorry to enter late in the debate. I agree with everything already said above.

eleven's chain translated into a matrix:

Code: Select all

(57)b3p35    (1)r8c2
             (1)r56c2  (69)r56c2
(257)b3p138  (1)b3p18  (6)r9c2
=>-5 r9c1, -57 r8c3


It is clear that this matrix cannot be shifted to a symmetric pigeonhole matrix, due to missing weak links in columns 1 and 2 (between 1r56c2 & 1b3p18) It is not the matrix of a rank-0 logic.

Trying to write a Sue-de-Coq, one gets e.g. (169)r56c2 -16- (1256)r89c2 -(125)- (1257)r7c13, but this ALS-AALS-AALS chain is not an extended SDC, because 1 is a restricted common on both side of AALS r89c2, without sharing a single sector.

Even though your pattern has "6 cells with 6 digits in 2 units", it fails that test because of the extra 1

Agreed.

My overall conclusion: eleven's solution is very nice, anyhow !

Added Feb. 17, 2019 9:15 pm
If I had to name such a solution, I woould call it a Kraken-AALS, or an almost-almost NT:
(257)b3p138
(1)b3p18 - (1=57)b3p35
(6)r9c2 - (69=1)r56c2 - (1=57)b3p35
=>-5 r9c1, -57 r8c3; ste

[Leren]

Code: Select all

*----------------------------------------------------------------*
| 2356    25689  3569 | 1689   12689  7      | 13689 4      1589 |
| 236     2689   1    | 5      24689  2489   | 7     38     89   |
| 567     4      5679 | 1689   3      189    | 1689  158    2    |
|---------------------+----------------------+-------------------|
| 1345    7      3459 | 13489  12489  123489 | 1289  6      1489 |
| 146    b169    2    | 146789 5      1489   | 189   178    3    |
| 8      b169    3469 | 134679 12469  12349  | 5     127    1479 |
|---------------------+----------------------+-------------------|
| 1257    3     a57   | 189    189    6      | 4     12578  1578 |
| 9      a15    a457  | 2      18-4   1358-4 | 138   13578  6    |
| 1256-4 c1256   8    |c134    7     c1345   |c123   9     c15   |
*----------------------------------------------------------------*

ALS XY Wing: (4=1) r7c3, r8c23 - (1=6) r56c2 - (6=4) r9c24679 => - 4 r8c56, r9c1; stte

Leren