The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|95.|.7.|
 |..7|..3|1..|
 |.4.|..1|..8|
 |---+---+---|
 |.53|..9|8..|
 |17.|...|.94|
 |..8|7..|51.|
 |---+---+---|
 |8..|1..|.4.|
 |..2|5..|3..|
 |.1.|.86|...|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 3    a26    1      | 9     5     8      | 4     7     26     |
|b269   8     7      | 246   24    3      | 1     25    2569   |
| 569-2 4     59     | 26    7     1      | 69    3     8      |
|--------------------+--------------------+--------------------|
|b24    5     3      | 24    1     9      | 8     6     7      |
| 1     7     6      | 8     3     5      | 2     9     4      |
|b249   29    8      | 7     6     24     | 5     1     3      |
|--------------------+--------------------+--------------------|
| 8     3     59     | 1     29    27     | 679   4     569    |
| 679   69    2      | 5     49    47     | 3     8     1      |
| 579   1     4      | 3     8     6      | 79    25    259    |
*--------------------------------------------------------------*

ALS XZ Rule: X = 6, Z = 2: (2=6) r1c2 - (6=2) r246c1 => - 2 r3c1; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 3     26    1     | 9     5     8     | 4     7     26    |
 | 269   8     7     | 246   24    3     | 1     25    2569  |
 | 2569  4    b59    |c26    7     1     |c69    3     8     |
 *-------------------+-------------------+-------------------|
 |e24    5     3     |d24    1     9     | 8     6     7     |
 | 1     7     6     | 8     3     5     | 2     9     4     |
 | 249  f29    8     | 7     6     24    | 5     1     3     |
 *-------------------+-------------------+-------------------|
 | 8     3    a59    | 1     29    27    | 679   4     569   |
 | 679   6-9   2     | 5     49    47    | 3     8     1     |
 | 579   1     4     | 3     8     6     | 79    25    259   |
 *-----------------------------------------------------------*


(9)r7c3 = r3c3 - (9=26)r3c47 - (2)r4c4 = r4c1 - (2=9)r5c2 => -9 r8c2 ; stte

[pjb]

Code: Select all

3     C26     1      | 9      5      8      |  4      7     B26     
269    8      7      | 246   c24     3      |  1      25     2569   
2569   4      59     |b26     7      1      |Aa69     3      8     
---------------------+----------------------+----------------------
24     5      3      | 24     1      9      |  8      6      7     
1      7      6      | 8      3      5      |  2      9      4     
249    29     8      | 7      6      24     |  5      1      3     
---------------------+----------------------+----------------------
8      3      59     | 1      29     27     |  679    4      569   
679  eD69     2      | 5     d49     47     |  3      8      1     
579    1      4      | 3      8      6      |  79     25     259   


(6)r3c7 - (6=2)r3c4 - (2=4)r2c5 - (4=9)r8c5 - r8c2
(6)r3c7 - (6=2)r1c9 - (2=6)r1c2 - (2=9)r8c2
therefore r3c7 <> 6; stte

Phil

[daj95376]

Code: Select all

3     C26     1      | 9      5      8      |  4      7     B26     
269    8      7      | 246   c24     3      |  1      25     2569   
2569   4      59     |b26     7      1      |Aa69     3      8     
---------------------+----------------------+----------------------
24     5      3      | 24     1      9      |  8      6      7     
1      7      6      | 8      3      5      |  2      9      4     
249    29     8      | 7      6      24     |  5      1      3     
---------------------+----------------------+----------------------
8      3      59     | 1      29     27     |  679    4      569   
679  eD69     2      | 5     d49     47     |  3      8      1     
579    1      4      | 3      8      6      |  79     25     259   


(6)r3c7 - (6=2)r3c4 - (2=4)r2c5 - (4=9)r8c5 - r8c2
(6)r3c7 - (6=2)r1c9 - (2=6)r1c2 - (6=9)r8c2
therefore r3c7 <> 6; stte

An unusual way to present an XY-Chain.

(6=2)r3c4 - (2=4)r2c5 - (4=9)r8c5 - (9=6)r8c2 - (6=2)r1c2 - (2=6)r1c9 => -6 r3c7

[daj95376]

Code: Select all

*--------------------------------------------------------------*
| 3    a26    1      | 9     5     8      | 4     7     26     |
|b269   8     7      | 246   24    3      | 1     25    2569   |
| 569-2 4     59     | 26    7     1      | 69    3     8      |
|--------------------+--------------------+--------------------|
|b24    5     3      | 24    1     9      | 8     6     7      |
| 1     7     6      | 8     3     5      | 2     9     4      |
|b249   29    8      | 7     6     24     | 5     1     3      |
|--------------------+--------------------+--------------------|
| 8     3     59     | 1     29    27     | 679   4     569    |
| 679   69    2      | 5     49    47     | 3     8     1      |
| 579   1     4      | 3     8     6      | 79    25    259    |
*--------------------------------------------------------------*

ALS XZ Rule: X = 6, Z = 2: (2=6) r1c2 - (6=2) r246c1 => - 2 r3c1; stte

A boxed perspective of your cells:

Code: Select all

 (24=9)r46c1 - (9=26)r1c2,r2c1  =>  -2 r3c1


[7b53]

Code: Select all

3     C26     1      | 9      5      8      |  4      7     B26     
269    8      7      | 246   c24     3      |  1      25     2569   
2569   4      59     |b26     7      1      |Aa69     3      8     
---------------------+----------------------+----------------------
24     5      3      | 24     1      9      |  8      6      7     
1      7      6      | 8      3      5      |  2      9      4     
249    29     8      | 7      6      24     |  5      1      3     
---------------------+----------------------+----------------------
8      3      59     | 1      29     27     |  679    4      569   
679  eD69     2      | 5     d49     47     |  3      8      1     
579    1      4      | 3      8      6      |  79     25     259   


(6)r3c7 - (6=2)r3c4 - (2=4)r2c5 - (4=9)r8c5 - r8c2
(6)r3c7 - (6=2)r1c9 - (2=6)r1c2 - (6=9)r8c2
therefore r3c7 <> 6; stte

seems like Phil is also listing other strong-links..
(6)r3c4 = (6)r1c9
(2)r2c5 = (2)r1c2
(4)r8c5 = (6)r8c2

[ArkieTech]

Code: Select all

 *-----------------------------------------------------------*
 | 3     26    1     | 9     5     8     | 4     7     26    |
 | 269   8     7     | 246   4-2   3     | 1     25    2569  |
 | 2569  4    a59    |a26    7     1     |a69    3     8     |
 |-------------------+-------------------+-------------------|
 | 24    5     3     | 24    1     9     | 8     6     7     |
 | 1     7     6     | 8     3     5     | 2     9     4     |
 | 249   29    8     | 7     6     24    | 5     1     3     |
 |-------------------+-------------------+-------------------|
 | 8     3    b59    | 1    b29    27    | 679   4     569   |
 | 679   69    2     | 5     49    47    | 3     8     1     |
 | 579   1     4     | 3     8     6     | 79    25    259   |
 *-----------------------------------------------------------*
(2=5)r3c347-(5=2)r7c35 => -2r2c5; ste

[Marty R.]

Code: Select all

+------------+-----------+-------------+
| 3    26 1  | 9   5  8  | 4   7  26   |
| 269  8  7  | 246 24 3  | 1   25 2569 |
| 2569 4  59 | 26  7  1  | 69  3  8    |
+------------+-----------+-------------+
| 24   5  3  | 24  1  9  | 8   6  7    |
| 1    7  6  | 8   3  5  | 2   9  4    |
| 249  29 8  | 7   6  24 | 5   1  3    |
+------------+-----------+-------------+
| 8    3  59 | 1   29 27 | 679 4  569  |
| 679  69 2  | 5   49 47 | 3   8  1    |
| 579  1  4  | 3   8  6  | 79  25 259  |
+------------+-----------+-------------+


Play this puzzle online at the Daily Sudoku site

Same elimination as Dan, using an XY-Chain.

(2=9)r7c5-r7c3=r3c3-(9=6)r3c7-(6=2)r3c4=>r2c5<>2

[Marty R.]

Phil,

Is there a name for your solution?

[Luke]

Phil,

Is there a name for your solution?

Bifurcation?

[pjb]

Marty,

This is just one technique I picked up playing with Sudoku Explainer. It is called "contradiction forcing chains" or something like that. It uses the approach that if you find a chain starting with A = true which implies B = true, and find a second chain again starting with A = true but which implies B = false; then the original assumption that that A = true must be false. The team of gurus that created "skfr" know infinitely more about the various chains in SE that I.

Phil

[Marty R.]

Thank you.

[DonM]

Marty,

This is just one technique I picked up playing with Sudoku Explainer. It is called "contradiction forcing chains" or something like that. It uses the approach that if you find a chain starting with A = true which implies B = true, and find a second chain again starting with A = true but which implies B = false; then the original assumption that that A = true must be false. The team of gurus that created "skfr" know infinitely more about the various chains in SE that I.

Phil

Or as Luke said, Bifurcation.

The techniques used by Sudoku Explainer were pretty much considered out-of-date circa 2006-7. IMO, it's only present-day value is its ability to assign a broadly useful 'difficulty' score to a puzzle.

[daj95376]

Marty,

This is just one technique I picked up playing with Sudoku Explainer. It is called "contradiction forcing chains" or something like that. It uses the approach that if you find a chain starting with A = true which implies B = true, and find a second chain again starting with A = true but which implies B = false; then the original assumption that that A = true must be false. The team of gurus that created "skfr" know infinitely more about the various chains in SE that I.

Phil

Or as Luke said, Bifurcation.

The techniques used by Sudoku Explainer were pretty much considered out-of-date circa 2006-7. IMO, it's only present-day value is its ability to assign a broadly useful 'difficulty' score to a puzzle.

_

_

Bifurcation

A limited form of Trial & Error where only constraints with 2 remaining candidates are considered.

When there are only 2 candidates left for a constraint, one of them must be true and the other must be false. In bifurcation, both branches of the fork are tried by placing the candidate in its cell and solving the puzzle from that point forward. When a contradiction is found, the remaining candidate can be placed.

Bifurcation has a bad reputation in the Sudoku community because it relies on backtracking and looks similar to guessing. Many advanced solving techniques were introduced to reduce the need for bifurcation.

All I see in Phil's forcing chain is a candidate with two chains/streams leading to contradicting conclusions on another candidate.

Code: Select all

(6)r3c7 - (6=2)r3c4 - (2=4)r2c5 - (4=9)r8c5 - r8c2
(6)r3c7 - (6=2)r1c9 - (2=6)r1c2 - (6=9)r8c2
therefore r3c7 <> 6; stte


If he had just one chain/stream for 6r3c7 leading to a contradiction, then I would consider it bifurcation -- with the implication that 9r3c7 must be true. For example:

Code: Select all

(6*)r3c7 - (6=2)r3c4 - (2=4)r2c5 - (4=9)r8c5 - (9=6)r8c2 - (6=2)r1c2 - (*62)r1c9; contradiction


_