The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |3..|..2|...|
 |.1.|..4|7.5|
 |9.4|.7.|3..|
 |---+---+---|
 |.25|9..|...|
 |.3.|...|.4.|
 |...|..3|15.|
 |---+---+---|
 |..1|.5.|8.7|
 |7.8|3..|.2.|
 |...|2..|..4|
 *-----------*


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[pjb]

Code: Select all

 3       578     67     | 568    9      2      | 4      68     1     
a68      1       2      | 8-6    3      4      | 7      9      5     
 9       58      4      | 1568   7      1568   | 3      68     2     
------------------------+----------------------+---------------------
 148     2       5      | 9      14     18     | 6      7      3     
 18      3       79     | 1578   6      158    | 2      4      89     
b468     78      679    |c478    2      3      | 1      5      89     
------------------------+----------------------+---------------------
 2       49      1      |d46     5      69     | 8      3      7     
 7       49      8      | 3      14     19     | 5      2      6     
 5       6       3      | 2      8      7      | 9      1      4     


(6)r2c1 = (6-4)r6c1 = r6c4 - (4=6)r7c4 => -6 r2c4; stte

Phil

[SteveG48]

Code: Select all

 *------------------------------------------------------------*
 | 3     578   67    |  568   9     2     | 4     68    1     |
 | 68c   1     2     |  68b   3     4     | 7     9     5     |
 | 9     58    4     |  1568  7     1568  | 3     68    2     |
 *-------------------+--------------------+-------------------|
 |B148c  2     5     |  9   bC1-4d  18    | 6     7     3     |
 |B18c   3     79    |  1578  6     158   | 2     4     89    |
 | 468  B78    679   |aA478a  2     3     | 1     5     89    |
 *-------------------+--------------------+-------------------|
 | 2     49    1     |  46    5     69    | 8     3     7     |
 | 7     49    8     |  3     14    19    | 5     2     6     |
 | 5     6     3     |  2     8     7     | 9     1     4     |
 *------------------------------------------------------------*

Kraken cell [478]r6c4 => -4 r4c5 ; stte

(4)r6c4                             - (4)r4c5
  ||
(7)r6c4 - (7=184)r4c1,r5c1,r6c2     - (4)r4c5
  ||
(8)r6c4 - (8=6)r2c4 - (6=184)r245c1 - (4)r4c5



Or a variant:

Code: Select all

 *------------------------------------------------------------*
 |  3     578   67    | 568   9     2     | 4     68    1     |
 | b68    1     2     |c68    3     4     | 7     9     5     |
 |  9     58    4     | 1568  7     1568  | 3     68    2     |
 *--------------------+-------------------+-------------------|
 |ab148   2     5     | 9     1-4   18    | 6     7     3     |
 | b18    3     79    | 1578  6     158   | 2     4     89    |
 |  68-4 b78    679   |c478   2     3     | 1     5     89    |
 *--------------------+-------------------+-------------------|
 |  2     49    1     | 46    5     69    | 8     3     7     |
 |  7     49    8     | 3     14    19    | 5     2     6     |
 |  5     6     3     | 2     8     7     | 9     1     4     |
 *------------------------------------------------------------*


(4)r4c1 = (186)r245c1     - (67=84)r26c4 => -4 r4c5,r6c1 ; stte
        = (187)r45c1,r6c2 -/



[Leren]

Code: Select all

*--------------------------------------------------------------*
| 3     578  a7-6    | 568   9     2      | 4     68    1      |
|b68    1     2      |c68    3     4      | 7     9     5      |
| 9     58    4      | 1568  7     1568   | 3     68    2      |
|--------------------+--------------------+--------------------|
| 148   2     5      | 9     14    18     | 6     7     3      |
| 18    3     79     | 1578  6     158    | 2     4     89     |
| 468   78   f69-7   |e478   2     3      | 1     5     89     |
|--------------------+--------------------+--------------------|
| 2     49    1      |d46    5     69     | 8     3     7      |
| 7     49    8      | 3     14    19     | 5     2     6      |
| 5     6     3      | 2     8     7      | 9     1     4      |
*--------------------------------------------------------------*

(7=6) r1c3 - (6=8) r2c1 - (8=6) r2c4 - (6=4) r7c4 - (4) r6c4 = (4-6) r6c1 = (6) r6c3 => - 6 r1c3, - 7 r6c3; stte

Leren

[Marty R.]

Code: Select all

+-------------+--------------+---------+
| 3   578 67  | 568  9  2    | 4 68 1  |
| 68  1   2   | 68   3  4    | 7 9  5  |
| 9   58  4   | 1568 7  1568 | 3 68 2  |
+-------------+--------------+---------+
| 148 2   5   | 9    14 18   | 6 7  3  |
| 18  3   79  | 1578 6  158  | 2 4  89 |
| 468 78  679 | 478  2  3    | 1 5  89 |
+-------------+--------------+---------+
| 2   49  1   | 46   5  69   | 8 3  7  |
| 7   49  8   | 3    14 19   | 5 2  6  |
| 5   6   3   | 2    8  7    | 9 1  4  |
+-------------+--------------+---------+


Play this puzzle online at the Daily Sudoku site

9r8c6=(9-6)r8c6)=(6-4)r7c4=4r6c4-(4=1)r4c5=>r4c6,r8c5<>1

[Ngisa]

Code: Select all

+--------------+--------------+---------+
| 3   578  7-6  | f568  9  2    | 4 i68 1  |
| a68  1    2   | f68   3  4    | 7 9  5  |
| 9   58   4   | f1568 7  g1568 | 3 h68 2  |
+--------------+--------------+---------+
| b148 2    5   | 9    c14 18   | 6 7  3  |
| b18  3    79  | 1578 6  158  | 2 4  89 |
| 468 4789 679 | 478  2  3    | 1 5  89 |
+--------------+--------------+---------+
| 2   49   1   | e46   5  69   | 8 3  7  |
| 7   49   8   | 3    d14 19   | 5 2  6  |
| 5   6    3   | 2    8  7    | 9 1  4  |
+--------------+--------------+---------+


(6=8)r2c1-(8=14)r45c1-(4=1)r4c5-(1=4)r8c5-(4=6)r7c4-r123c4=r3c6-(6=8)r3c8-(8=6)r1c8 => -6r1c3; stte

[Marty R.]

Code: Select all

+--------------+--------------+---------+
| 3   578  7-6  | f568  9  2    | 4 i68 1  |
| a68  1    2   | f68   3  4    | 7 9  5  |
| 9   58   4   | f1568 7  g1568 | 3 h68 2  |
+--------------+--------------+---------+
| b148 2    5   | 9    c14 18   | 6 7  3  |
| b18  3    79  | 1578 6  158  | 2 4  89 |
| 468 4789 679 | 478  2  3    | 1 5  89 |
+--------------+--------------+---------+
| 2   49   1   | e46   5  69   | 8 3  7  |
| 7   49   8   | 3    d14 19   | 5 2  6  |
| 5   6    3   | 2    8  7    | 9 1  4  |
+--------------+--------------+---------+


(6=8)r2c1-(8=14)r45c1-(4=1)r4c5-(1=4)r8c5-(4=6)r7c4-r123c4=r3c6-(6=8)r3c8-(8=6)r1c8 => -6r1c3; stte

Ngisa,

I don't understand. If r2c1 is not a 6, then r1c8 IS a 6. if r2c1 is not a 6, then r1c3 MUST be a 6, thus a 6 in r1c8 is an invalidity. My conclusion would be that r2c1 must be=6, since the original premise led to a contradiction.

[Ngisa]

Code: Select all

+--------------+--------------+---------+
| 3   578  7-6  | f568  9  2    | 4 i68 1  |
| a68  1    2   | f68   3  4    | 7 9  5  |
| 9   58   4   | f1568 7  g1568 | 3 h68 2  |
+--------------+--------------+---------+
| b148 2    5   | 9    c14 18   | 6 7  3  |
| b18  3    79  | 1578 6  158  | 2 4  89 |
| 468 4789 679 | 478  2  3    | 1 5  89 |
+--------------+--------------+---------+
| 2   49   1   | e46   5  69   | 8 3  7  |
| 7   49   8   | 3    d14 19   | 5 2  6  |
| 5   6    3   | 2    8  7    | 9 1  4  |
+--------------+--------------+---------+


(6=8)r2c1-(8=14)r45c1-(4=1)r4c5-(1=4)r8c5-(4=6)r7c4-r123c4=r3c6-(6=8)r3c8-(8=6)r1c8 => -6r1c3; stte

Ngisa,

I don't understand. If r2c1 is not a 6, then r1c8 IS a 6. if r2c1 is not a 6, then r1c3 MUST be a 6, thus a 6 in r1c8 is an invalidity. My conclusion would be that r2c1 must be=6, since the original premise led to a contradiction.

I think I have the same conclusion, removing 6 in r1c3 sets r2c1=6. Is there any flaw in my chain? Can you elaborate more?

[Marty R.]

Code: Select all

+--------------+--------------+---------+
| 3   578  7-6  | f568  9  2    | 4 i68 1  |
| a68  1    2   | f68   3  4    | 7 9  5  |
| 9   58   4   | f1568 7  g1568 | 3 h68 2  |
+--------------+--------------+---------+
| b148 2    5   | 9    c14 18   | 6 7  3  |
| b18  3    79  | 1578 6  158  | 2 4  89 |
| 468 4789 679 | 478  2  3    | 1 5  89 |
+--------------+--------------+---------+
| 2   49   1   | e46   5  69   | 8 3  7  |
| 7   49   8   | 3    d14 19   | 5 2  6  |
| 5   6    3   | 2    8  7    | 9 1  4  |
+--------------+--------------+---------+


(6=8)r2c1-(8=14)r45c1-(4=1)r4c5-(1=4)r8c5-(4=6)r7c4-r123c4=r3c6-(6=8)r3c8-(8=6)r1c8 => -6r1c3; stte

Ngisa,

I don't understand. If r2c1 is not a 6, then r1c8 IS a 6. if r2c1 is not a 6, then r1c3 MUST be a 6, thus a 6 in r1c8 is an invalidity. My conclusion would be that r2c1 must be=6, since the original premise led to a contradiction.

I think I have the same conclusion, removing 6 in r1c3 sets r2c1=6. Is there any flaw in my chain? Can you elaborate more?

Ngisa,

Keep in mind that most of the folks who play these puzzles are more advanced players than me. As to flaws in your chain, it looks OK to me, but in your 2nd term the cells are listed as r45c1. The 4 is presumably in r4 since the next term is in r4. That might just be a personal preference, not a rule but I prefer to show the last cell of the result of the ALS. As to elaborating more, I don't know how much more I can doexcept that the 1st premise leads to an invalidity so it must be false.

I would really like to hear from one of the regulars: Are you listening, Phil, Steve, Leren and Dan?

[David P Bird]

Marty, Ngisa
The chain is perfectly valid as can be seen by checking that no two strongly linked arguments can both be false and that no two weakly linked arguments can both be true.

Reading the chain forwards if (6)r2c1 is false then (6)r8c1 must be true
Reading the chain backwards if (6)r8c1 is false then (6)r2c1 must be true
This proves that at least one of these two argument must be true, but doesn't prevent both of them being true.
As (6)r1c3 sees both these candidates it can't be true

That's the way AICs work (which needs every to link work in both directions).

If a chain produces a wrong conclusion it's because one of the links isn't sound. So looking around for contradictions that would arise if an elimination is made is one way to prove that there's a flaw somewhere. However looking for contradictions when an eliminated candidate is true won't ever do that; at best all it can achieve is to show another route to the same conclusion.

DPB

[Marty R.]

David,

Thank you.

Marty