Is an ALS XY-wing considered a chain?

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Is an ALS XY-wing considered a chain?

Postby ArkieTech » Wed Apr 16, 2014 4:00 pm

Is an ALS XY-wing considered a chain?

I have long considered a chain to be 4SIS (containing four strong links) and above.
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Re: Is an ALS XY-wing considered a chain?

Postby daj95376 » Wed Apr 16, 2014 5:06 pm

ArkieTech wrote:Is an ALS XY-wing considered a chain?

I have long considered a chain to be 4SIS (containing four strong links) and above.


Sudopedia Mirror wrote:The ALS-XZ rule is an ALS-XY-Chain of length two, while the ALS-XY-Wing is an ALS-XY-Chain of length three.


Code: Select all
 +-----------------------+
 | 5 8 . | 7 . . | . . 2 |
 | . . . | . . . | . . . |
 | . . . | . . . | 1 . . |
 |-------+-------+-------|
 | . . 9 | . . . | 6 3 . |
 | . . . | . . . | . . 4 |
 | 7 . 1 | . 4 5 | . . 8 |
 |-------+-------+-------|
 | . . 5 | 2 . 3 | . . . |
 | . . 6 | . . 4 | . 7 . |
 | 1 2 . | . 6 . | 3 . . |
 +-----------------------+   # Sudopedia example for ALS-XZ

 +--------------------------------------------------------------------------------+
 |  5       8       3       |  7       19      169     |  4       69      2       |
 |  2469    1       247     |  345689  23589   2689    |  57      5689    35679   |
 |  2469    4679    247     |  345689  23589   2689    |  1       5689    35679   |
 |--------------------------+--------------------------+--------------------------|
 |  248    b45      9       |  18      1278    1278    |  6       3       157     |
 |  2368   b356     28      |  13689   123789  126789  |  57      15      4       |
 |  7      b36      1       |  36      4       5       |  9       2       8       |
 |--------------------------+--------------------------+--------------------------|
 | a49      479     5       |  2       179     3       |  8       1469    169     |
 |  389    a39      6       |  1589    1589    4       |  2       7       159     |
 |  1       2       478     |  589     6       789     |  3       459     59      |
 +--------------------------------------------------------------------------------+
 # 122 eliminations remain

                            ALS XY-Chain equivalent
                         =============================

 ALS-XZ w/ X=9 and Z=4:  (4=9)r7c1      - (9=4)r4568c2  =>  r4c1,r7c2<>4

 -or-

 ALS-XZ w/ X=3 and Z=4:  (4=3)r7c1,r8c2 - (3=4)r456c2   =>  r4c1,r7c2<>4


Viewing the five cells in their simplest format for the eliminations.

Code: Select all
 (4=9)r7c1 - (9=3)r8c2 - (36=5)r56c2 - (5=4)r4c2  =>  r4c1,r7c2<>4
daj95376
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Re: Is an ALS XY-wing considered a chain?

Postby ArkieTech » Wed Apr 16, 2014 7:22 pm

daj95376 wrote:
ArkieTech wrote:Is an ALS XY-wing considered a chain?

I have long considered a chain to be 4SIS (containing four strong links) and above.


Sudopedia Mirror wrote:The ALS-XZ rule is an ALS-XY-Chain of length two, while the ALS-XY-Wing is an ALS-XY-Chain of length three.


Code: Select all
 +-----------------------+
 | 5 8 . | 7 . . | . . 2 |
 | . . . | . . . | . . . |
 | . . . | . . . | 1 . . |
 |-------+-------+-------|
 | . . 9 | . . . | 6 3 . |
 | . . . | . . . | . . 4 |
 | 7 . 1 | . 4 5 | . . 8 |
 |-------+-------+-------|
 | . . 5 | 2 . 3 | . . . |
 | . . 6 | . . 4 | . 7 . |
 | 1 2 . | . 6 . | 3 . . |
 +-----------------------+   # Sudopedia example for ALS-XZ

 +--------------------------------------------------------------------------------+
 |  5       8       3       |  7       19      169     |  4       69      2       |
 |  2469    1       247     |  345689  23589   2689    |  57      5689    35679   |
 |  2469    4679    247     |  345689  23589   2689    |  1       5689    35679   |
 |--------------------------+--------------------------+--------------------------|
 |  248    b45      9       |  18      1278    1278    |  6       3       157     |
 |  2368   b356     28      |  13689   123789  126789  |  57      15      4       |
 |  7      b36      1       |  36      4       5       |  9       2       8       |
 |--------------------------+--------------------------+--------------------------|
 | a49      479     5       |  2       179     3       |  8       1469    169     |
 |  389    a39      6       |  1589    1589    4       |  2       7       159     |
 |  1       2       478     |  589     6       789     |  3       459     59      |
 +--------------------------------------------------------------------------------+
 # 122 eliminations remain

                            ALS XY-Chain equivalent
                         =============================

 ALS-XZ w/ X=9 and Z=4:  (4=9)r7c1      - (9=4)r4568c2  =>  r4c1,r7c2<>4

 -or-

 ALS-XZ w/ X=3 and Z=4:  (4=3)r7c1,r8c2 - (3=4)r456c2   =>  r4c1,r7c2<>4


Viewing the five cells in their simplest format for the eliminations.

Code: Select all
 (4=9)r7c1 - (9=3)r8c2 - (36=5)r56c2 - (5=4)r4c2  =>  r4c1,r7c2<>4


Then all wings must be chains of length 2 or length 3? :?
dan
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Re: Is an ALS XY-wing considered a chain?

Postby daj95376 » Wed Apr 16, 2014 10:04 pm

ArkieTech wrote:Then all wings must be chains of length 2 or length 3? :?

Length = 3 is my understanding.

However, there was a time, before everyone started using ALS, that people would treat 2-3 bivalues cells as a conjugate(?) vertex cell for a wing pattern. Now, everyone uses ALS XY-Wing.
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