- Code: Select all
*-----------*
|...|.8.|...|
|..2|4.3|5..|
|.9.|...|.2.|
|---+---+---|
|3..|...|..7|
|.2.|7.6|.1.|
|..8|...|4..|
|---+---+---|
|.6.|.1.|.9.|
|..4|...|8..|
|...|.6.|...|
*-----------*
Play/Print this puzzle online
*-----------*
|...|.8.|...|
|..2|4.3|5..|
|.9.|...|.2.|
|---+---+---|
|3..|...|..7|
|.2.|7.6|.1.|
|..8|...|4..|
|---+---+---|
|.6.|.1.|.9.|
|..4|...|8..|
|...|.6.|...|
*-----------*
*-----------------------------------------------------------------------*
| 14567 13457 13567 | 12569 8 12579 | 13679 367 1369 |
| 167 b17 2 | 4 79 3 | 5 8 169 |
| 8 9 13567 | 156 57 157 | 1367 2 4 |
*-------------------------+----------------------+----------------------|
| 3 ac145 156-9 | 1259 2459 8 | 269 56 7 |
|ac459 2 ac59 | 7 345-9 6 | 3-9 1 8 |
| 1567-9 ac157 8 | 12359 2359 1259 | 4 356 23569 |
*-------------------------+----------------------+----------------------|
| 257 6 357 | 8 1 4 | 237 9 235 |
| 12579 1357 4 | 2359 23579 2579 | 8 3567 12356 |
| 12579 8 13579 | 2359 6 2579 | 1237 4 1235 |
*-----------------------------------------------------------------------*
SteveG48 wrote:(9=1457)b4p2468 - (1=7)r2c2 - (7=1459)b4p2468 => -9 r4c3,r5c57,r6c1 ; stte
SCLT wrote:Are all SDC patterns just doubly-linked ALSes?
123456 456 # | . . . | . . .
123456 456 # | . . . | . . .
@# # # | . . . | . . .
-------------+-------+-------
123 . . | . . . | . . .
123 . . | . . . | . . .
@ . . | . . . | . . .
-------------+-------+-------
@ . . | . . . | . . .
@ . . | . . . | . . .
@ . . | . . . | . . .
@ =/= 123
# =/= 456
999_Springs wrote:SteveG48 wrote:(9=1457)b4p2468 - (1=7)r2c2 - (7=1459)b4p2468 => -9 r4c3,r5c57,r6c1 ; stte
that's in fact a sue-de-coq pattern, so in addition to this, you can also get rid of 1,7 from the rest of column 2, and 5 from the rest of block 4. good job spotting that, i haven't seen one of those in years
999_Springs wrote:in answer to your question, i haven't seen a sue-de-coq in a real puzzle that wasn't just a pair of doubly linked als's (not that i know of), but i'm pretty sure this hypothetical pattern counts as a sue-de-coq but i don't see how to get it as doubly linked als's
- Code: Select all
123456 456 # | . . . | . . .
123456 456 # | . . . | . . .
@# # # | . . . | . . .
-------------+-------+-------
123 . . | . . . | . . .
123 . . | . . . | . . .
@ . . | . . . | . . .
-------------+-------+-------
@ . . | . . . | . . .
@ . . | . . . | . . .
@ . . | . . . | . . .
@ =/= 123
# =/= 456
SCLT wrote:Are all SDC patterns just doubly-linked ALSes?
Cenoman wrote:Sue de Coq: one AALS doubly linked to two ALS's, therefore possibly three different sectors for the pattern.
Doubly linked ALS's: two different sectors at most.
If a Sue de Coq spreading over three sectors exists, the conjecture would be demonstrated False.
12345 123 @ | 12 @ @ | @ @ @
345 . . | . . . | . . .
# . . | . . . | . . .
------------+--------+-------
45 . . | . . . | . . .
# . . | . . . | . . .
# . . | . . . | . . .
------------+--------+-------
# . . | . . . | . . .
# . . | . . . | . . .
# . . | . . . | . . .
@ =/= 12
# =/= 45
Cenoman wrote:The reciprocal conjecture "Can all doubly-linked ALS's be split into a SDC pattern ?" could also be raised.
7 126 8 | 459 4569 4569 | 3 1456 1259
469 36 3469 | 2 34569 1 | 4679 45678 5789
5 1236 123469 | 78 3469 78 | 12469 146 129
------------------------+----------------------+---------------------
189 4 1579 | 3579 59 3579 | 178 2 6
3 1267 12679 | 479 8 24679 | 147 1457 157
268 2567 2567 | 1 2456 24567 | 478 9 3
------------------------+----------------------+---------------------
12 9 12357 | 6 125 2358 | 127 1378 4
1246 8 12346 | 349 7 2349 | 5 136 129
1246 123567 1234567 | 34589 12459 234589 | 12679 13678 12789
als a = r2c12357
als b = r7c157
restricted common 5,7
eliminations -5r1469c5 -7r4569c7 -46r2c8 -9r2c9 -1r7c38 -2r7c36
Cenoman wrote:SCLT wrote:Are all SDC patterns just doubly-linked ALSes?
According to the definitions of each pattern, the answer is No.
ALS: subset of n unsolved cells in a sector (row, column, box) with n+1 digits, AALS: subset of n unsolved cells in a sector with n+2 digits
Sue de Coq: one AALS doubly linked to two ALS's, therefore possibly three different sectors for the pattern.
Doubly linked ALS's: two different sectors at most.
If a Sue de Coq spreading over three sectors exists, the conjecture would be demonstrated False. I have not in mind such a counter example.
Cenoman wrote:Sue de Coq: one AALS doubly linked to two ALS's, therefore possibly three different sectors for the pattern.
SteveG48 wrote:When we say one AALS doubly linked to two ALS's, we mean that the AALS has double links to each of the ALS's. That is, two candidated in the AALS "see" two candidates in one of the ALS's and two candidates in the AALS "see" two candidates in the other ALS. Is that correct? Given that, my understanding of the SDC has an additional requirement that the 2 candidates in one of those double links both need to be different from both candidates in the other double link. Is that also correct?
SpAce wrote: I think SDC cores can be AAALS as well as AALS).
999_Springs wrote:you mean something like this hypothetical pattern?
12345 123 @ | 12 @ @ | @ @ @
345 . . | . . . | . . .
# . . | . . . | . . .
------------+--------+-------
45 . . | . . . | . . .
# . . | . . . | . . .
# . . | . . . | . . .
------------+--------+-------
# . . | . . . | . . .
# . . | . . . | . . .
# . . | . . . | . . .
@ =/= 12
# =/= 45
123456 125 @ | 12 @ @ | @ @ @ r1c1 could be 156, 256, 356 or 456 only
345 56 & | . . . | . . .
# & & | . . . | . . .
-------------+--------+-------
34 . . | . . . | . . .
# . . | . . . | . . .
# . . | . . . | . . .
-------------+--------+-------
# . . | . . . | . . .
# . . | . . . | . . .
# . . | . . . | . . .
@ =/= 12
# =/= 34
& =/= 56
Cenoman wrote:SteveG48 wrote:When we say one AALS doubly linked to two ALS's, we mean that the AALS has double links to each of the ALS's. That is, two candidated in the AALS "see" two candidates in one of the ALS's and two candidates in the AALS "see" two candidates in the other ALS. Is that correct? Given that, my understanding of the SDC has an additional requirement that the 2 candidates in one of those double links both need to be different from both candidates in the other double link. Is that also correct?
To me, yes that is also correct.
Steve's requirement is the application of the general rule for chaining ALS's, AALS's, AAALS's...
General rule: each of these "not locked sets" must have at least as many restricted commons as freedom degrees, and all its RCs must be distinct.
SpAce wrote: I think SDC cores can be AAALS as well as AALS).
What makes SDC eliminate any candidate in sight of its digit groups is its freedom degree equal to 0. If you select an AAALS as a core, you must have one more restricted common to keep this character (In total an AAALS triply linked with an ALS and doubly linked with another ALS)