The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |8..|.1.|.2.|
 |5..|..6|.9.|
 |4..|3..|...|
 |---+---+---|
 |.7.|4..|13.|
 |...|.6.|...|
 |.13|..5|.8.|
 |---+---+---|
 |...|..2|..1|
 |.2.|7..|..9|
 |.5.|.9.|..7|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*-----------------------------------------------------------------------*
| 8      6      7       | 59A    1      49      |a45     2      3       |
| 5      3      1       | 28     248    6       | 7      9      48      |
| 4      9      2       | 3      58A    7       |a56     1     b568bB   |
|-----------------------+-----------------------+-----------------------|
| 269    7      5       | 4      28a    89a     | 1      3      26a     |
| 29     48     48      | 1      6      3       | 59     7      25      |
| 269    1      3       | 2-9    7      5       |a469    8      246     |
|-----------------------+-----------------------+-----------------------|
| 7      48     9       | 568    3458   2       | 38     456    1       |
| 1      2      468     | 7      3458   48      | 38     456    9       |
| 3      5      468     | 68     9      1       | 2      46     7       |
*-----------------------------------------------------------------------*

3 Petal Death Blossom: Stem Cell r3c9 {568} :

(9=5) r136c7     - (5) r3c9;

(9=6) r4c569     - (6) r3c9;

(9=8) r1c4, r3c5 - (8) r3c9; => - 9 r6c4; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 8     6     7     |a59    1     4-9   |a45    2     3     |
 | 5     3     1     | 28    248   6     | 7     9     48    |
 | 4     9     2     | 3     58    7     | 56    1     568   |
 *-------------------+-------------------+-------------------|
 | 269   7     5     | 4   bc28  bc89    | 1     3    b26    |
 | 29    48    48    | 1     6     3     | 59    7     25    |
 | 269   1     3     |c29    7     5     |S469   8     246   |
 *-------------------+-------------------+-------------------|
 | 7     48    9     | 568   3458  2     | 38    456   1     |
 | 1     2     468   | 7     3458  48    | 38    456   9     |
 | 3     5     468   | 68    9     1     | 2     46    7     |
 *-----------------------------------------------------------*


3 petal death blossom => -9 r1c6 ; stte

Stem: [469]r6c7

Petal a, [459]r1c47; 4r6c7 - (4=59)r1c47 - 9r1c6
Petal b, [2689]r4c569; 6r6c7 - (6=289)r4c569 - 9r1c6
Petal c, [289]b5p237; 9r6c7 - (9=289)b5p237 - 9r1c6

Now the question. The last chain, 9r6c7 - (9=289)b5p237 - 9r1c6, is clearly not a proper AIC since the middle term
has a 9 on both sides of the equal sign. Properly, it should be written 9r6c7 - r6c4 = r4c6 - r1c6, but then it wouldn't
be a death blossom. Petal c is already a locked set. Eliminating the 9 at r6c4 determines which candidates are
where. So is it a proper death blossom?

[Leren]

SteveG48 wrote : So is it a proper death blossom?

I think that whether or not a move has a name is just a matter of style over substance (has the elimination been proved ?).

Death Blossoms are a subset of Kraken cells, where all of the forcing chains are ALS's.

Perhaps you could call your move an "Almost Death Blossom" and be elevated to the Sudoku Hall of Fame for discovering this "new" move .

BTW I don't nominate 2 petal Death Blossoms any more, because they are always ALS XY wings with the middle ALS a bi-value cell, and I've never come across a 4 petal Death blossom. Can anyone provide an example ?

Leren

[SteveG48]

SteveG48 wrote : So is it a proper death blossom?

I think that whether or not a move has a name is just a matter of style over substance (has the elimination been proved ?).

True, and in this case the elimination is obvious. Beyond style, however, I'm interested in the technical issue here. A proper AIC needs for each term to be true, and one term in my third chain isn't true. On the other hand, the logic is fine. So how do you handle this situation technically? I've seen a number of situations in which a set that is already locked is "improved" by a further elimination that pins down the location of the candidates in the set. How should this be handled using Eureka?

[Leren]

Well one way is to simply recognize that your 3 cell locked set is also an XY chain.

So you could write your third leg as 9 r6c7 - (9=2) r6c4 - (2=8) r4c5 - (8=9) r4c6 - 9 r1c6.

So all of the intermediate terms are ALSs and it's standard Eureka - just a thought.

Leren

PS You could simplify a bit and write your third leg as 9 r6c7 - (9=2) r6c4 - (2=9) r4c56 - 9 r1c6.

Leren

[JC Van Hay]

Code: Select all

+--------------+------------------+------------------+
| 8    6   7   | (59)  1     49   | (45)   2    3    |
| 5    3   1   | 28    248   6    | 7      9    48   |
| 4    9   2   | 3     58    7    | 56     1    568  |
+--------------+------------------+------------------+
| 269  7   5   | 4     (28)  (89) | 1      3    (26) |
| 29   48  48  | 1     6     3    | 59     7    25   |
| 269  1   3   | 2-9   7     5    | (469)  8    246  |
+--------------+------------------+------------------+
| 7    48  9   | 568   3458  2    | 38     456  1    |
| 1    2   468 | 7     3458  48   | 38     456  9    |
| 3    5   468 | 68    9     1    | 2      46   7    |
+--------------+------------------+------------------+


[XYWing(459)r1c47.r6c7=6r6c7-(6=289)r4c569]-9r6c4; stte

[pjb]

Code: Select all

 8       6       7      | 59     1      49     | 45     2      3     
 5       3       1      | 28     248    6      | 7      9      48     
 4       9       2      | 3      58     7      | 56     1      568   
------------------------+----------------------+---------------------
 269     7       5      | 4      28     89     | 1      3      26     
 29      48      48     | 1      6      3      | 59     7      25     
 269     1       3      | 29     7      5      | 469    8      246   
------------------------+----------------------+---------------------
 7       48      9      | 568    3458   2      | 38     456    1     
 1       2       468    | 7      3458   48     | 38     456    9     
 3       5       468    | 68     9      1      | 2      46     7     


(2-6)r6c1 = (6-9)r4c1
(2-9)r6c4 = r4c6 - r4c1
(2-4)r6c9 = r2c9 - r1c7 = (4-9)r1c6 = r4c6 - r4c1 => -9 r4c1; stte

Phil

[Sudtyro2]

Code: Select all

 *-----------------------------------------------------------*
 | 8     6     7     | 59    1     49d   | 5-4   2     3     |
 | 5     3     1     | 28    248   6     | 7     9     48    |
 | 4     9     2     | 3     58    7     | 56    1     568   |
 |-------------------+-------------------+-------------------|
 | 269b  7     5     | 4     28c   89c   | 1     3    *26    |
 |*29    48    48    | 1     6     3     | 59    7    *25a   |
 | 269   1     3     | 29    7     5     | 469   8     246   |
 |-------------------+-------------------+-------------------|
 | 7     48    9     | 568   3458  2     | 38    456   1     |
 | 1     2     468   | 7     3458  48    | 38    456   9     |
 | 3     5     468   | 68    9     1     | 2     46    7     |
 *-----------------------------------------------------------*

The CoALS Rule applied to overlapping ALS(*) states that (52=69).
One can then form the short chain segment, (52=69) - (6|9=2)r4c1, which establishes a derived strong link between 5r5c9 and 2r4c1.
It seems OK to then use that link to process a Kraken 2c9 as follows:

Code: Select all

2r5c9 - [5r5c9=2r4c1] - (2=89)r4c56 - (9=4)r1c6 - 4r1c7; stte
 ||                   /                         /
2r4c9 ---------------                          /
 ||                                           /
(2-4)r6c9 = 4r2c9 ---------------------------

The only question might be that 2r5c9 is also one of the three 2s in the overlapping ALS. Is this type of linking allowed?

SteveC

[bat999]

Code: Select all

.--------------.------------------.-----------------.
| 8    6   7   | a59    1      49 | b45   2     3   |
| 5    3   1   |  28    248    6  |  7    9     48  |
| 4    9   2   |  3     58     7  |  56   1     568 |
:--------------+------------------+-----------------:
| 269  7   5   |  4    a28    a89 |  1    3    b26  |
| 29   48  48  |  1     6      3  |  59   7     25  |
| 269  1   3   |  2-9   7      5  | c469  8     246 |
:--------------+------------------+-----------------:
| 7    48  9   |  568   3458   2  |  38   456   1   |
| 1    2   468 |  7     3458   48 |  38   456   9   |
| 3    5   468 |  68    9      1  |  2    46    7   |
'--------------'------------------'-----------------'

(9=25)r1c4,r4c56 - (2|5=46)r1c7,r4c9 - (4|6=9)r6c7 => -9 r6c4;stte

[Sudtyro2]

(9=25)r1c4,r4c56 - (2|5=46)r1c7,r4c9 - (4|6=9)r6c7 => -9 r6c4;stte

Bat, I like your chain and can follow the logic. It looks like you're sort of propagating "split nodes," but how do you find such an animal?

SteveC

[bat999]

... propagating "split nodes," but how do you find such an animal?

Hi
I had originally considered 'kraken' cell r6c7...
(4)r6c7 - (4=9)r1c47 - (9)r6c4 [where r1c4 is 9]
(6)r6c7 - (6=9)r4c569 - (9)r6c4 [where r4c6 is 9]
(9)r6c4 - (9)r6c4
=> -9 r6c4


Then I worked backwards to investigate what happens if neither of r1c4 or r4c6 is 9.
The result seems to be a 'split node', but I didn't set out to propagate one deliberately.

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 8     6     7     | 59    1     49d   | 5-4   2     3     |
 | 5     3     1     | 28    248   6     | 7     9     48    |
 | 4     9     2     | 3     58    7     | 56    1     568   |
 |-------------------+-------------------+-------------------|
 | 269b  7     5     | 4     28c   89c   | 1     3    *26    |
 |*29    48    48    | 1     6     3     | 59    7    *25a   |
 | 269   1     3     | 29    7     5     | 469   8     246   |
 |-------------------+-------------------+-------------------|
 | 7     48    9     | 568   3458  2     | 38    456   1     |
 | 1     2     468   | 7     3458  48    | 38    456   9     |
 | 3     5     468   | 68    9     1     | 2     46    7     |
 *-----------------------------------------------------------*

The CoALS Rule applied to overlapping ALS(*) states that (52=69).
One can then form the short chain segment, (52=69) - (6|9=2)r4c1, which establishes a derived strong link between 5r5c9 and 2r4c1.
It seems OK to then use that link to process a Kraken 2c9 as follows:

Code: Select all

2r5c9 - [5r5c9=2r4c1] - (2=89)r4c56 - (9=4)r1c6 - 4r1c7; stte
 ||                   /                         /
2r4c9 ---------------                          /
 ||                                           /
(2-4)r6c9 = 4r2c9 ---------------------------

The only question might be that 2r5c9 is also one of the three 2s in the overlapping ALS. Is this type of linking allowed?

SteveC

Steve, I don't see any problem with your solution. I'm not sure that I understand the question.

[Sudtyro2]

Steve, I don't see any problem with your solution. I'm not sure that I understand the question.

Thx, Steve, for the feedback. My concern in the first chain above was the initial linking into the CoALS structure via 2r5c9 - (52=69), where 2r5c9 is actually one of three 2s (bold) in the overlapping ALS. The 52 premise says that the single 5-digit and the three 2-digits are logically AND'd. That's what made me a little nervous about the initial weak link. However, it sounds like it's a non-issue.

SteveC

[SteveG48]

Steve, I don't see any problem with your solution. I'm not sure that I understand the question.

Thx, Steve, for the feedback. My concern in the first chain above was the initial linking into the CoALS structure via 2r5c9 - (52=69), where 2r5c9 is actually one of three 2s (bold) in the overlapping ALS. The 52 premise says that the single 5-digit and the three 2-digits are logically AND'd. That's what made me a little nervous about the initial weak link. However, it sounds like it's a non-issue.

SteveC

I see. Actually, I wouldn't worry about the overlapping ALS and simply treat it as a split node:

2r5c9 - (2=69)r4c9,r5c1 - (6|9=2)r4c1 .......