The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |347|...|12.|
 |...|...|9..|
 |...|43.|..7|
 |---+---+---|
 |7..|...|.5.|
 |..4|6.1|3..|
 |.5.|...|..2|
 |---+---+---|
 |4..|.28|...|
 |..3|...|...|
 |.15|...|293|
 *-----------*


Play/Print this puzzle online

[Cenoman]

Code: Select all

 +-----------------------+---------------------+-----------------------+
 |  3      4     7       |  589    689   569   |  1      2     a568    |
 |  56     68    268     |  1258   168   7     |  9      3      4      |
 |  1569   689   12689   |  4      3     256   |  568    68     7      |
 +-----------------------+---------------------+-----------------------+
 |  7      3     1689    |  289    489   249   |  68     5      1689   |
 |  29     289   4       |  6      5     1     |  3      7      9-8    |
 |  169    5     1689    |  89     7     3     |  468    1468   2      |
 +-----------------------+---------------------+-----------------------+
 |  4      679   69      |  3      2     8     |  567   b16    b156    |
 |  26     267   3       |  159    19    59    |  4678   468  ab68     |
 |  8      1     5       |  7      46    46    |  2      9      3      |
 +-----------------------+---------------------+-----------------------+

(8=5)r18c9 - (5=8)b9p236 => -8 r5c9; stte

Cenoman

[pjb]

Code: Select all

 3       4       7      | 589    689    569    | 1      2      568   
 56      68      268    | 1258   168    7      | 9      3      4     
 1569    689     12689  | 4      3      256    | 568    68     7     
------------------------+----------------------+---------------------
 7       3       1689   | 289    489    249    | 68     5     d1689   
 29      289     4      | 6      5      1      | 3      7     e9-8     
 169     5       1689   | 89     7      3      | 468    1468   2     
------------------------+----------------------+---------------------
 4       679     69     | 3      2      8      | 567   b16    c156   
 26      267     3      | 159    19     59     | 4678   468   a68     
 8       1       5      | 7      46     46     | 2      9      3     


(8=6)r8c9 - (6=1)r7c8 - r7c9 = (1-9)r4c9 = r5c9 => -8 r5c9; stte

Phil

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 3      4      7      | 589    689    569    | 1      2     a568    |
 | 56     68     268    | 1258   168    7      | 9      3      4      |
 | 1569   689    12689  | 4      3      256    | 568    68     7      |
 *----------------------+----------------------+----------------------|
 | 7      3      1689   | 289    489    249    | 68     5      1689   |
 |b29     289    4      | 6      5      1      | 3      7     a89     |
 | 169    5      1689   | 89     7      3      | 468    1468   2      |
 *----------------------+----------------------+----------------------|
 | 4      679    69     | 3      2      8      | 567   a16    a156    |
 |b26     267    3      | 159    19     59     | 4678   468    68     |
 | 8      1      5      | 7      46     46     | 2      9      3      |
 *--------------------------------------------------------------------*


I don't know how the group feels about these, but:

(6=1589)r147c9,r7c8 - (9=26)r58c1 => -6 r8c9 ; stte

[Leren]

Code: Select all

*---------------------------------------------------------*
| 3     4     7     | 589   689   569 | 1     2     568   |
| 56    68    268   | 1258  168   7   | 9     3     4     |
| 1569  689   12689 | 4     3     256 | 568   68    7     |
|-------------------+-----------------+-------------------|
| 7     3     1689  | 289   489   249 | 68    5    e16-89 |
| 29    289   4     | 6     5     1   | 3     7    a89    |
| 169   5     1689  | 89    7     3   | 468   1468  2     |
|-------------------+-----------------+-------------------|
| 4     679   69    | 3     2     8   | 567  c16   d156   |
| 26    267   3     | 159   19    59  | 4678  468  b68    |
| 8     1     5     | 7     46    46  | 2     9     3     |
*---------------------------------------------------------*

(9=8) r5c9 - (8=6) r8c9 - (6=1) r7c8 - r7c9 = (1) r4c9 => - 89 r4c9; stte

Leren

[Cenoman]

I don't know how the group feels about these, but:

(6=1589)r147c9,r7c8 - (9=26)r58c1 => -6 r8c9 ; stte

Side remark: typo (6=1589)r157c9,r7c8

The elimination is correct. But the presentation is ambiguous. I wonder if in your mind (6=1589)r157c9,r7c8 is equivalent to an ALS ?
To me, it is not, since (15689)r157c9 is an AALS with a freedom degree of 2. The assembly (6=1589)r157c9,r7c8 is equivalent to
(6=1)r7c8-(1=5689)r157c9 and it has still a freedom degree of 2, as there exist only one restricted common. Therefore the whole chain
(6=1589)r157c9,r7c8 - (9=26)r58c1 has a freedom degree of 2. Any candidate in sight of 2+1 elements in the chain can be eliminated ("element in the chain" means here all instances of a digit in any ALS, AALS of the chain) In the past, this was known as "rule I" on French forums, with I = freedom degree. There must be something similar on this site...
This is the case for 6r8c9 which is in sight of 6r8c1, 6r7c8 and 6r1c9.
Personally, I'd rather present it as a kraken AALS:
AALS (5689)r15c9: any three digits from this can't be false (otherwise one cell is void) e.g. 5, 6, 9
They form a derived kraken column:
(5)r1c9 - (5=16)r7c89
(6)r1c9
(9)r5c9 - (9=26)r58c1
=> -6 r8c9; stte

EDIT: or with your own breakdown,
Kraken AALS (15689)r157c9:
(1)r7c9 - (1=6)r7c8
(6)r17c9
(9)r5c9 - (9=26)r58c1
=> -6 r8c9; stte

Cenoman

[Ngisa]

Code: Select all

+------------------------+----------------------+-------------------------+
| 3        4       7     | 589      689     569 |  1        2        568  |
| 56       68      268   | 1258     168     7   |  9        3        4    |
| 1569     89      12689 | 4        3       256 |  568      68       7    |
+------------------------+----------------------+-------------------------+
| 7        3       1689  | 289      489     249 | b68       5        1689 |
| 29       289     4     | 6        5       1   |  3        7       a9-8  |
| 169      5       1689  | 89       7       3   | b468     b1468     2    |
+------------------------+----------------------+-------------------------+
| 4        679     69    | 3        2       8   |  567     c16       156  |
| 26       267     3     | 159      19      59  |  4678     468     d68   |
| 8        1       5     | 7        46      46  |  2        9        3    |
+------------------------+----------------------+-------------------------+


8 r5c9 - (8=1)r46c7, r6c8 - (1=6)r7c8 - (6=8)r8c9 => - 8 r5c9; stte

Clement

[bat999]

Code: Select all

.------------------.----------------.---------------------.
| 3     4    7     | 589   689  569 | 1      2     b568   |
| 56    68   268   | 1258  168  7   | 9      3      4     |
| 1569  689  12689 | 4     3    256 | 568    68     7     |
:------------------+----------------+---------------------:
| 7     3    1689  | 289   489  249 | 68     5      169-8 |
| 29    289  4     | 6     5    1   | 3      7      9-8   |
| 169   5    1689  | 89    7    3   | 468    1468   2     |
:------------------+----------------+---------------------:
| 4     679  69    | 3     2    8   | 567   a16    a156   |
| 26    267  3     | 159   19   59  | 4678   468   a68    |
| 8     1    5     | 7     46   46  | 2      9      3     |
'------------------'----------------'---------------------'

(8=56)r7c89,r8c9 - (5|6=8)r1c9 => -8 r45c9; stte

[eleven]

(6=1589)r157c9,r7c8 - (9=26)r58c1 => -6 r8c9 ; stte

Looks ok and clear to me.
If there is no 6 in the 4 cells, the (158)9 falls into place.
If there is no 9 there, there must be a 6, which is the only of 4 digits (1568) in 4 cells, which could be doubled (apart from the fact, that "not 6 => 9" is logically equivalent to "not 9 => 6").

Of course (in this case) alternatively one could include r8c9 and write:
(6=1)r7c8-(1=9)r1578c9-(9=6)r58c1
or simply
(6=1)r7c8-r7c9=(1-9)r4c9=r5c9-(9=6)r58c1

Yet another variant of Cenoman's and Bat's:

Code: Select all

 *---------------------------------------------------------------------*
 |  3      4     7       |  589    689   569   |  1      2      568    |
 |  56     68    268     |  1258   168   7     |  9      3      4      |
 |  1569   689   12689   |  4      3     256   |  568    68     7      |
 |-----------------------+---------------------+-----------------------|
 |  7      3     1689    |  289    489   249   | a68     5      169-8  |
 |  29     289   4       |  6      5     1     |  3      7      9-8    |
 |  169    5     1689    |  89     7     3     | a468   a1468   2      |
 |-----------------------+---------------------+-----------------------|
 |  4      679   69      |  3      2     8     |  567   b16     156    |
 |  26     267   3       |  159    19    59    |  4678   468   b68     |
 |  8      1     5       |  7      46    46    |  2      9      3      |
 *---------------------------------------------------------------------*

(8=1)b6p167-(1=8)b9p26 => -8r45c9, stte

[Marty R.]

Code: Select all

+----------------+--------------+----------------+
| 3    4   7     | 589  689 569 | 1    2    568  |
| 56   68  268   | 1258 168 7   | 9    3    4    |
| 1569 689 12689 | 4    3   256 | 568  68   7    |
+----------------+--------------+----------------+
| 7    3   1689  | 289  489 249 | 68   5    1689 |
| 29   289 4     | 6    5   1   | 3    7    89   |
| 169  5   1689  | 89   7   3   | 468  1468 2    |
+----------------+--------------+----------------+
| 4    679 69    | 3    2   8   | 567  16   156  |
| 26   267 3     | 159  19  59  | 4678 468  68   |
| 8    1   5     | 7    46  46  | 2    9    3    |
+----------------+--------------+----------------+


Play this puzzle online at the Daily Sudoku site

7r8c7=r8c2-(7=6915)r7c2389-(5=689)r185c9-(9=2)r5c1-(2=697)r8c1,r7c32=> -7r7c7,r8c2

[SteveG48]

I don't know how the group feels about these, but:

(6=1589)r147c9,r7c8 - (9=26)r58c1 => -6 r8c9 ; stte

Side remark: typo (6=1589)r157c9,r7c8

The elimination is correct. But the presentation is ambiguous. I wonder if in your mind (6=1589)r157c9,r7c8 is equivalent to an ALS ?
To me, it is not, since (15689)r157c9 is an AALS with a freedom degree of 2. The assembly (6=1589)r157c9,r7c8 is equivalent to
(6=1)r7c8-(1=5689)r157c9 and it has still a freedom degree of 2, as there exist only one restricted common. Therefore the whole chain
(6=1589)r157c9,r7c8 - (9=26)r58c1 has a freedom degree of 2. Any candidate in sight of 2+1 elements in the chain can be eliminated ("element in the chain" means here all instances of a digit in any ALS, AALS of the chain) In the past, this was known as "rule I" on French forums, with I = freedom degree. There must be something similar on this site...
This is the case for 6r8c9 which is in sight of 6r8c1, 6r7c8 and 6r1c9.
Personally, I'd rather present it as a kraken AALS:
AALS (5689)r15c9: any three digits from this can't be false (otherwise one cell is void) e.g. 5, 6, 9
They form a derived kraken column:
(5)r1c9 - (5=16)r7c89
(6)r1c9
(9)r5c9 - (9=26)r58c1
=> -6 r8c9; stte

EDIT: or with your own breakdown,
Kraken AALS (15689)r157c9:
(1)r7c9 - (1=6)r7c8
(6)r17c9
(9)r5c9 - (9=26)r58c1
=> -6 r8c9; stte

Cenoman

Hi, Cenoman. Thanks for the typo correction and for taking the time to discuss this. I was hoping that there would be some discussion.

I'm not enough into theory to know what to call the construct that I wrote. I just know that the Boolean expression (6=1589)r157c9,r7c8 appears to be correct.
If 6 is not true in that set of four cells, then 1, 5, 8, and 9 must all be true, so I'm not sure why you would call the AIC ambiguous. On the other hand, I don't like the fact that the set (whatever it should be called) is not contained in one house.
On the third hand, I have recently seen some AIC presentations on the forum in which the sets were not contained in one house. I didn't care for them in situations where they were being used simply to shorten the chain, but no one seemed to be moved to comment on it.

Thanks to Eleven as well. Good discussion.

[eleven]

Basically i am happy, if everything is logically correct. But i would not enjoy something like
8r8c9=8r18c9,r7c89 => -8r5c9

[JC Van Hay]

I don't know how the group feels about these, but:

(6=1589)r157c9,r7c8 - (9=26)r58c1 => -6 r8c9 ; stte

In this case, I would prefer the following clearer notation :

Code: Select all

+------------------+----------------+-------------------+
| 3     4    7     | 589   689  569 | 1     2     (568) |
| 56    68   268   | 1258  168  7   | 9     3     4     |
| 1569  689  12689 | 4     3    256 | 568   68    7     |
+------------------+----------------+-------------------+
| 7     3    1689  | 289   489  249 | 68    5     1689  |
| (29)  289  4     | 6     5    1   | 3     7     (89)  |
| 169   5    1689  | 89    7    3   | 468   1468  2     |
+------------------+----------------+-------------------+
| 4     679  69    | 3     2    8   | 567   (16)  (156) |
| (26)  267  3     | 159   19   59  | 4678  468   8-6   |
| 8     1    5     | 7     46   46  | 2     9     3     |
+------------------+----------------+-------------------+
6r7c8 1r7c8
6r7c9 1r7c9 5r7c9
6r1c9       5r1c9 8r1c9
                  8r5c9 9r5c9 -> derived constraint : {6r7c8, 6r7c9, 6r1c9, 9r5c9}
                        9r5c1 2r5c1
                              2r8c1 6r8c1 -> derived constraint : {6r7c8, 6r7c9, 6r1c9, 6r8c1} => -{6r8c9}; stte

[bat999]

... the set (whatever it should be called) is not contained in one house...

When I enquired about this there didn't seem to be an answer.
The best that I could come up with was...
"A subset that is almost locked"
or
"An ALS whose cells are not all in the same house".

But these days I consider the Sudoku grid to be the Universal set and any selection of cells to be a subset.
I think of an ALS as a special case.
It is "A subset that is almost locked and whose cells are all in the same house".

...Basically i am happy, if everything is logically correct...

Me too.