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[ArkieTech]

Code: Select all

 *-----------*
 |.76|...|.9.|
 |5..|1.2|...|
 |.2.|.7.|.31|
 |---+---+---|
 |...|32.|..7|
 |...|8.9|...|
 |3..|.61|...|
 |---+---+---|
 |84.|.3.|.6.|
 |...|6.4|..9|
 |.1.|...|47.|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 1       7       6      | 45     58     3      | 2      9      48     
 5       39      3-4    | 1      89     2      | 7     c48     6     
a49      2       8      | 49     7      6      | 5      3      1     
------------------------+----------------------+---------------------
b49      689    b14     | 3      2      5      | 689   b148    7     
 27      56      1257   | 8      4      9      | 36     125    235   
 3       589     245    | 7      6      1      | 89     2458   48     
------------------------+----------------------+---------------------
 8       4       259    | 259    3      7      | 1      6      25     
 27      35      2357   | 6      1      4      | 38     258    9     
 6       1       2359   | 259    59     8      | 4      7      235   


(4=9)r3c1 - (9=8)r4c138 - (8=4)r2c8 => -4 r2c3; stte

Phil

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 1     7     6     | 45    58    3     | 2     9     48    |
 | 5     39    34    | 1    a89    2     | 7     4-8   6     |
 |b49    2     8     |a49    7     6     | 5     3     1     |
 *-------------------+-------------------+-------------------|
 |c49    689  c14    | 3     2     5     | 689  c148   7     |
 | 27    56    1257  | 8     4     9     | 36    125   235   |
 | 3     589   245   | 7     6     1     | 89    2458  48    |
 *-------------------+-------------------+-------------------|
 | 8     4     259   | 259   3     7     | 1     6     25    |
 | 27    35    2357  | 6     1     4     | 38    258   9     |
 | 6     1     2359  | 259   59    8     | 4     7     235   |
 *-----------------------------------------------------------*


(8=49)b2p57 - (4=9)r3c1 - (9=148)r4c138 => -8 r2c8 ; stte

[Leren]

Code: Select all

*-----------------------------------------------------*
| 1    7    6     | 45   58   3     | 2    9    48    |
| 5    39  c34    | 1    89   2     | 7   b48   6     |
|d49   2    8     | 49   7    6     | 5    3    1     |
|-----------------+-----------------+-----------------|
| 9-4  689 a14    | 3    2    5     | 689 a148  7     |
| 27   56   1257  | 8    4    9     | 36   125  235   |
| 3    589  245   | 7    6    1     | 89   2458 48    |
|-----------------+-----------------+-----------------|
| 8    4    259   | 259  3    7     | 1    6    25    |
| 27   35   2357  | 6    1    4     | 38   258  9     |
| 6    1    2359  | 259  59   8     | 4    7    235   |
*-----------------------------------------------------*

(4=8) r4c38 - (8=4) r2c8 - r2c3 = (4) r3c1 => - 4 r4c1; stte

Leren

[bat999]

Code: Select all

.---------------------.------------.-----------------.
|  1    7      6      | 45   58  3 | 2     9     48  |
|  5    9-3   c34     | 1    89  2 | 7    c48    6   |
|  49   2      8      | 49   7   6 | 5     3     1   |
:---------------------+------------+-----------------:
| b49  a689   b14     | 3    2   5 | 689  b148   7   |
|  27  a56     1257   | 8    4   9 | 36    125   235 |
|  3   a589    245    | 7    6   1 | 89    2458  48  |
:---------------------+------------+-----------------:
|  8    4      259    | 259  3   7 | 1     6     25  |
|  27  a35     257-3  | 6    1   4 | 38    258   9   |
|  6    1      259-3  | 259  59  8 | 4     7     235 |
'---------------------'------------'-----------------'

(3=9)r4568c2 - (9=8)r4c138 - (8=3)r2c38 => -3 r2c2,r89c3; stte

[Ngisa]

Code: Select all

+-------------+----------+--------------+
| 1  7   6    | 45  58 3 | 2   9    48  |
| 5  c39  34   | 1   d89 2 | 7   4-8   6   |
| b49 2   8    | 49  7  6 | 5   3    1   |
+-------------+----------+--------------+
| a49 689 a14   | 3   2  5 | 689 a148  7   |
| 27 56  1257 | 8   4  9 | 36  125  235 |
| 3  589 245  | 7   6  1 | 89  2458 48  |
+-------------+----------+--------------+
| 8  4   259  | 259 3  7 | 1   6    25  |
| 27 35  2357 | 6   1  4 | 38  258  9   |
| 6  1   2359 | 259 59 8 | 4   7    235 |
+-------------+----------+--------------+


Almost like Steve
(8=9)r4c138 - r3c1 = r2c2 - (9=8)r2c5 => -8r2c8; stte

Clement

[Sudtyro2]

Code: Select all

 *-----------------------------------------------------------*
 | 1     7     6     | 45    58    3     | 2     9     48    |
 | 5     39  ab3-4   | 1     89    2     | 7    a48    6     |
 |e49    2     8     | 49    7     6     | 5     3     1     |
 |-------------------+-------------------+-------------------|
 |d49    689  b14    | 3     2     5     | 689  c148   7     |
 | 27    56    1257  | 8     4     9     | 36    125   235   |
 | 3     589   245   | 7     6     1     | 89    2458  48    |
 |-------------------+-------------------+-------------------|
 | 8     4     259   | 259   3     7     | 1     6     25    |
 | 27    35    2357  | 6     1     4     | 38    258   9     |
 | 6     1     2359  | 259   59    8     | 4     7     235   |
 *-----------------------------------------------------------*

Myth's [CoALS Rule] applied to the two overlapping ALS marked (a&b).
[(34=18)r2c38,r4c3] - (1|8=4)r4c8 - r4c1 = r3c1 => -4r2c3; stte
Note use of the identical 6-cell group seen in Phil's and Leren's solutions.

SteveC

[bat999]

...Myth's [CoALS Rule] applied to the two overlapping ALS...

Hi
Where is the documentation for that rule?

Also, is there anything wrong with this solution?
If not, is it just a different way of using that CoALS rule?

Code: Select all

.-----------------.------------.-----------------.
|  1   7     6    | 45   58  3 | 2     9     48  |
|  5   39    3-4  | 1    89  2 | 7    a48    6   |
| d49  2     8    | 49   7   6 | 5     3     1   |
:-----------------+------------+-----------------:
| c49  689  a14   | 3    2   5 | 689  b148   7   |
|  27  56    1257 | 8    4   9 | 36    125   235 |
|  3   589   245  | 7    6   1 | 89    2458  48  |
:-----------------+------------+-----------------:
|  8   4     259  | 259  3   7 | 1     6     25  |
|  27  35    2357 | 6    1   4 | 38    258   9   |
|  6   1     2359 | 259  59  8 | 4     7     235 |
'-----------------'------------'-----------------'

(4=18)r2c8,r4c3 - (1|8=4)r4c8 - r4c1 = r3c1 => -4 r2c3; stte

I'm testing is there a 4 in any of r2c8,r4c3.
If yes, then the trivial stream...
(4)r2c8,r4c3 - (4)r2c3
If no, then the second stream...
(4=18)r2c8,r4c3 - (1|8=4)r4c8 - r4c1 = r3c1 - (4)r2c3
=> -4 r2c3; stte

[Sudtyro2]

Where is the documentation for that rule?
Also, is there anything wrong with this solution?

Hi bat,
Myth's CoALS Rule is discussed in the following link:
http://forum.enjoysudoku.com/combined-overlapping-almost-locked-sets-rule-coals-t4863.html
I've used it in several previous posts. You can view those posts by using the Forum's search tool. The rule is not very popular, but it does give an easy way to quickly spot derived strong inferences between candidates that do not share a common group (row, col, or box). IOW, it indirectly shows that 3r2c3 = 4r4c8, which then leads to the AIC-based elimination.

That, BTW, is a problem with the first entry in your chain: (4=18)r2c8,r4c3.
That looks like an ALS, but the candidates in those two cells cannot directly "see" each other, which is a basic requirement for any ALS.

EDIT to add: However, your first node may very well fall into the "split node" category that was discussed at length in the May 29, 2016 puzzle. If so, then I think SteveG48 might formalize your logic as a full AIC by adding an extra lead node...
(3=4)r2c3 - (4=18)r2c8,r4c3 - (1|8=4)r4c8 - r4c1 = r3c1 => -4 r2c3; stte
I'm trying to better understand the split-node issue myself, and proper notation is a mystery. Maybe Steve would be available for comment?

SteveC

[Marty R.]

Code: Select all

+-------------+----------+--------------+
| 1  7   6    | 45  58 3 | 2   9    48  |
| 5  39  34   | 1   89 2 | 7   48   6   |
| 49 2   8    | 49  7  6 | 5   3    1   |
+-------------+----------+--------------+
| 49 689 14   | 3   2  5 | 689 148  7   |
| 27 56  1257 | 8   4  9 | 36  125  235 |
| 3  589 245  | 7   6  1 | 89  2458 48  |
+-------------+----------+--------------+
| 8  4   259  | 259 3  7 | 1   6    25  |
| 27 35  2357 | 6   1  4 | 38  258  9   |
| 6  1   2359 | 259 59 8 | 4   7    235 |
+-------------+----------+--------------+


Play this puzzle online at the Daily Sudoku site

(4=9)r3c1-(9=4)r4c1-(4=18)r2c38-(8=4)r2c8=> -4r2c3

[SteveG48]

Hi, Bat, Steve.

That's an interesting discussion above. I see no problem with Bat's solution as written (in fact, I like it a lot), though some folks might find it unpalatable. If so, Steve's variant may be more acceptable to some, but I have no problem with either. The idea of starting a chain with a split mode is one that I've considered a number of times. I don't remember if I've actually done it.

[bat999]

... some folks might find it unpalatable...
...starting a chain with a split mode...

I am not sure myself about starting the chain with a split node... (4=18)r2c8,r4c3.
Those cells r2c8,r4c3 aren't an ALS because they can't "see" each other.
But if there are no 4s in r2c8,r4c3 then there can only be 1 and 8 in r2c8,r4c3.
This "(4=18)r2c8,r4c3" says to me "If 4 is false in r2c8,r4c3 then 1 and 8 are true in r2c8,r4c3".
So they are behaving like an ALS.

I asked about the "ALS whose cells are not in a single house" here ---> http://forum.enjoysudoku.com/may-29-2016-t33129-15.html#p251249

[Sudtyro2]

Hi SteveG48,
Special thx for your prompt and clarifying remarks! Most helpful!!

Hi Bat,
Looks like you were on the right track all along! Nice work!

While the "split-node" issue looks better, now take a look at SteveG48's solution to today's (June 9) puzzle...
1r89c2 = r8c1 - (1=25)r45c1 - (2|5=134)r145c9 - (3=1)r1c3 => -1 r2c2 ; stte
Steve links (25)r45c1 to (2|5)r45c9, and that's in two separate rows! I'd say that's pretty awesome and means there's a lot more for us to learn!

SteveC