Is an ALS XY-wing considered a chain?

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Is an ALS XY-wing considered a chain?

Is an ALS XY-wing considered a chain?

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

ArkieTech

Posts: 3035
Joined: 29 May 2006
Location: NW Arkansas USA

Re: Is an ALS XY-wing considered a chain?

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
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Re: Is an ALS XY-wing considered a chain?

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

ArkieTech

Posts: 3035
Joined: 29 May 2006
Location: NW Arkansas USA

Re: Is an ALS XY-wing considered a chain?

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.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006