The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . 3 1 |
| . . 8 | 1 . . | 4 . . |
| . 7 . | . 2 . | . 6 . |
+-------+-------+-------+
| . 6 . | . 3 . | . 7 . |
| . . 5 | 4 . . | 8 . . |
| . . . | . . . | 9 . . |
+-------+-------+-------+
| . 3 . | . 7 8 | . . . |
| 2 . 4 | 5 . . | . . . |
| 1 . . | . . . | . . . |
+-------+-------+-------+
.......31..81..4...7..2..6..6..3..7...54..8........9...3..78...2.45.....1........

[Ajò Dimonios]

Code: Select all

+---------+-----------+-------------+
| 6  4  2 | 89 58 59  | 7  3    1   |
| 3  5  8 | 1  6  7   | 4  29   29  |
| 9  7  1 | 3  2  4   | 5  6    8   |
+---------+-----------+-------------+
| 48 6  9 | 28 3  125 | 12 7    45  |
| 7  12 5 | 4  9  6   | 8  12   3   |
| 48 12 3 | 7  58 12  | 9  45   6   |
+---------+-----------+-------------+
| 5  3  6 | 29 7  8   | 12 1249 249 |
| 2  89 4 | 5  1  3   | 6  89   7   |
| 1  89 7 | 6  4  29  | 3  2589 259 |
+---------+-----------+-------------+


(5=4)r4c9-r6c8=(4-1)r7c8=1r5c8-r4c7=(1-5)r4c6=5r4c9=>+5r4c9=>Stte

Paolo

[rjamil]

1) JF (Row wise): 2 @ r2569c2689; and

Code: Select all

 +-------------+---------------+-----------------+
 | 6     4   2 | 89    58  59  | 7   3     1     |
 | 3     5   8 | 1     6   7   | 4   29    29    |
 | 9     7   1 | 3     2   4   | 5   6     8     |
 +-------------+---------------+-----------------+
 | (48)  6   9 | (28)  3   125 | 12  7     5-4   |
 | 7     12  5 | 4     9   6   | 8   12    3     |
 | 48    12  3 | 7     58  12  | 9   45    6     |
 +-------------+---------------+-----------------+
 | 5     3   6 | (29)  7   8   | 12  1249  (49)  |
 | 2     89  4 | 5     1   3   | 6   89    7     |
 | 1     89  7 | 6     4   29  | 3   2589  259   |
 +-------------+---------------+-----------------+

2) ALS move: 2489 @ r4c14 r7c49 => -4 @ r4c9; stte

R. Jamil
Added 1st step as per below given my clarification.

[Cenoman]

Code: Select all

 +-----------------+------------------+--------------------+
 |  6    4    2    |  89   58   59    |  7    3      1     |
 |  3    5    8    |  1    6    7     |  4    29     29    |
 |  9    7    1    |  3    2    4     |  5    6      8     |
 +-----------------+------------------+--------------------+
 |  48   6    9    |  28   3   e125   |  12   7     d45    |
 |  7    12   5    |  4    9    6     |  8    12     3     |
 |  48   12   3    |  7    58  e12    |  9   c45     6     |
 +-----------------+------------------+--------------------+
 |  5    3    6    |  29   7    8     |  12   1249   249   |
 |  2    89*  4    |  5    1    3     |  6    89*    7     |
 |  1    89*  7    |  6    4    9-2   |  3  ab25-89* 259   |
 +-----------------+------------------+--------------------+

UR(89)r89c28 using internals
(2)r9c8 == (5)r9c8* - r6c8 = r4c9 - (5=12)r46c6 => -89 r9c8*, -2 r9c6; ste

[SteveG48]

Code: Select all

 *--------------------------------------------------------------*
 | 6     4     2     |  89    58    59    |   7     3     1     |
 | 3     5     8     |  1     6     7     |   4     29    29    |
 | 9     7     1     |  3     2     4     |   5     6     8     |
 *-------------------+--------------------+---------------------|
 | 48    6     9     |  8-2   3   ab125   |abd12    7    b45    |
 | 7     12    5     |  4     9     6     |   8     12    3     |
 | 48    12    3     |  7     58    12    |   9     45    6     |
 *-------------------+--------------------+---------------------|
 | 5     3     6     |ab29    7     8     |  c12    1249 c249   |
 | 2     89    4     |  5     1     3     |   6     89    7     |
 | 1     89    7     |  6     4     29    |   3     2589  259   |
 *--------------------------------------------------------------*


2r4c67,r7c4 = (1549)r4c679,r8c4 - (4|9=21)r7c79 - (1=2)r4c7 => -2 r4c4 ; stte

[SteveG48]

Code: Select all

 +-------------+---------------+-----------------+
 | 6     4   2 | 89    58  59  | 7   3     1     |
 | 3     5   8 | 1     6   7   | 4   29    29    |
 | 9     7   1 | 3     2   4   | 5   6     8     |
 +-------------+---------------+-----------------+
 | (48)  6   9 | (28)  3   125 | 12  7     5-4   |
 | 7     12  5 | 4     9   6   | 8   12    3     |
 | 48    12  3 | 7     58  12  | 9   45    6     |
 +-------------+---------------+-----------------+
 | 5     3   6 | (29)  7   8   | 12  1249  (249) |
 | 2     89  4 | 5     1   3   | 6   89    7     |
 | 1     89  7 | 6     4   29  | 3   2589  259   |
 +-------------+---------------+-----------------+

ALS move: 2489 @ r4c14 r7c49 => -4 @ r4c9; stte

R. Jamil

I don't follow R. Jamil. Why can't cells r4c14 r7c49 be 8292 respectively? How does that give the elimination?

[pjb]

Code: Select all

 6       4       2      | 89     58     59     | 7      3      1     
 3       5       8      | 1      6      7      | 4      29     29     
 9       7       1      | 3      2      4      | 5      6      8     
------------------------+----------------------+---------------------
 48      6       9      |c28     3      125    | 12     7      45     
 7       12      5      | 4      9      6      | 8      12     3     
 48      12      3      | 7     d58     12     | 9     e45     6     
------------------------+----------------------+---------------------
 5       3       6      |b29     7      8      |a12    f249-1  249   
 2       89      4      | 5      1      3      | 6      89     7     
 1       89      7      | 6      4      29     | 3      2589   259   


(1=2)r7c7 - r7c4 = (2-8)r4c4 = (8-5)r6c5 = (5-4)r6c8 = r7c8 => -1 r7c8; stte

(use type 1 UR to remove 89 from r9c8, then simpler solution: (2)r7c4 = (2-8)r4c4 = (8-5)r6c5 = (5)r6c8 - (5=2)r9c8 => -2 r7c789, r9c6)

Phil

[Leren]

Code: Select all

*--------------------------------------*
| 6  4  2 | 89 58  59  | 7   3     1   |
| 3  5  8 | 1  6   7   | 4   29    29  |
| 9  7  1 | 3  2   4   | 5   6     8   |
|---------+------------+---------------|
| 48 6  9 | 28 3  e125 |d12  7    f5-4 |
| 7  12 5 | 4  9   6   | 8  c12    3   |
| 48 12 3 | 7  58  12  | 9  a4-5   6   |
|---------+------------+---------------|
| 5  3  6 | 29 7   8   | 12 b1249  249 |
| 2  89 4 | 5  1   3   | 6   89    7   |
| 1  89 7 | 6  4   29  | 3   2589  259 |
*--------------------------------------*

(4) r6c8 = (4-1) r7c8 = r5c8 - r4c7 = (1-5) r4c6 = (5) r4c9 => - 4 r4c9, - 5 r6c8; stte

Leren

[rjamil]

Code: Select all

 +-------------+---------------+-----------------+
 | 6     4   2 | 89    58  59  | 7   3     1     |
 | 3     5   8 | 1     6   7   | 4   29    29    |
 | 9     7   1 | 3     2   4   | 5   6     8     |
 +-------------+---------------+-----------------+
 | (48)  6   9 | (28)  3   125 | 12  7     5-4   |
 | 7     12  5 | 4     9   6   | 8   12    3     |
 | 48    12  3 | 7     58  12  | 9   45    6     |
 +-------------+---------------+-----------------+
 | 5     3   6 | (29)  7   8   | 12  1249  (249) |
 | 2     89  4 | 5     1   3   | 6   89    7     |
 | 1     89  7 | 6     4   29  | 3   2589  259   |
 +-------------+---------------+-----------------+

ALS move: 2489 @ r4c14 r7c49 => -4 @ r4c9; stte

R. Jamil

I don't follow R. Jamil. Why can't cells r4c14 r7c49 be 8292 respectively? How does that give the elimination?

Hi SteveG48,

I was also surprised not to see that move in HoDoku and YZF_Sudoku solvers. Actually, I skipped some moves before ALS move for which I will need time to investigate.

R. Jamil

[SpAce]

I was also surprised not to see that move in HoDoku and YZF_Sudoku solvers.

That should have been a hint

Actually, I skipped some moves before ALS move for which I will need time to investigate.

Your solution works if you apply an X-Wing with 2s first. That eliminates 2r7c9 which blocks your move otherwise.

Another possibility is to append a bit more logic to your move to prove the same elimination for the 2r7c9 case:

Code: Select all

[(48=2)r4c14 - (2=94)r7c49] = (2)r7c9 - r7c7 = r4c7 - (2=84)r4c41 => -4 r4c9; stte

In other words, either [your move] is true or else 2r7c9 is true which leads to 4r4c1 being true. In both cases 4r4c9 dies.

Or more simply as an ALS-W-Wing:

Code: Select all

(48=2)r4c14 - r4c7 = r7c7 - (2=94)r7c49 => -4 r4c9; stte

Or as I would write it:

Code: Select all

(482)r4c147 = (294)r7c749 => -4 r4c9; stte

[rjamil]

Hi SteveG48 and SpAce,

First of all, thank you both for pointing the error and correction advise (respectively).

Actually, my solver detected Jellyfish (Row wise) 2 @ r2569c2689 (instead of column wise X-Wing) first, which exclude 2 from r7c9, result 49 @ r7c9 remain.
Similarly, next move detected W-Wing 29 @ r2c8 r9c6 ERI 2 @ b6r4c8 and ERI 2 @ b5r4c6 => -9 @ r9c8 unnecessarily.
I wrongly skipped both the above mentioned moves and tried to apply ALS move directly before them. Reason for not detecting the error at first place is due to all four cells still contain four digits.

R. Jamil

[SpAce]

Hi rjamil,

Reason for not detecting the error at first place is due to all four cells still contain four digits.

Yes, they do. However, you should also check that only one of them (the elimination digit) can be true twice in the pattern. That ensures that it's true at least once, which guarantees the elimination (if both possibilities see it). In your original pattern digit 2 can also be true twice (in r4c4 and r7c9), which means there's no guarantee that 4 is true at all.

more formal explanation: Show

In terms of set logic, all candidates of the working pattern (without 2r7c9) can be covered with five sets, which is just one more than the number of base sets (the four cells). 5 covers vs 4 base sets makes it a Rank 1 pattern:

Code: Select all

4x5 (Rank 1): {4N14 7N49 \ 8r4 9r7 2c4 [4r4 4c9]} => -4 r4c9

It works because Rank 1 guarantees that any two cover sets have at least one true base candidate. Thus it's not possible that both 4r4 and 4c9 (which cover the elimination) are without a true base candidate, which validates the elimination. In general, a Rank 1 pattern guarantees that any external candidate that is covered at least twice can be eliminated.

However, if 2r7c9 is in play it needs an additional cover set (because it's not covered by the existing 2c4), which would make the logic Rank 2 (4x6). That only guarantees that any three cover sets must have at least one true base candidate. In that case both 4r4 and 4c9 could be without one, and the elimination is not guaranteed. In general, a Rank 2 pattern guarantees an external elimination only if it's covered at least three times. (The extended version I wrote does exactly that.)