The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |.6.|..9|...|
 |..7|...|..2|
 |.5.|7.4|..1|
 |---+---+---|
 |6..|..2|5.3|
 |...|.6.|...|
 |4.2|1..|..6|
 |---+---+---|
 |8..|5.1|.2.|
 |5..|...|8..|
 |...|6..|.9.|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 13-2  6     134    |a23    5     9      | 34    7     8      |
|c39    348   7      |a38    1     6      | 349   5     2      |
|c239   5     38     | 7     38-2  4      | 369   36    1      |
|--------------------+--------------------+--------------------|
| 6     1789  189    | 489   4789  2      | 5     14    3      |
|c137   1378  5      |a348   6     378    | 2    b14    9      |
| 4     39    2      | 1     39    5      | 7     8     6      |
|--------------------+--------------------+--------------------|
| 8     3479  3469   | 5     3479  1      | 36    2     47     |
| 5     12347 13469  | 2349  23479 37     | 8     36    47     |
|c37    2347  34     | 6     23478 378    | 1     9     5      |
*--------------------------------------------------------------*

ALS XY Wing: (2=4) r125c4 - (4=1) r5c8 - (1=2) r2359c1 => - 2 r1c1, r3c5; stte

Leren

[bat999]

...ALS XY Wing

Hi Leren
It's starting to make sense now.
You're asking, what happens if r5c4 is 4 or not 4?
If it's 4, the two 37s in column 1 produce a 2 at r3c1.
If it's not 4, the two 38s in column 4 produce a 2 at r1c4.

Those 2s knock out the 2s from r1c1 and r3c5.

[SteveG48]

Code: Select all

 *-----------------------------------------------------------------------------*
 |b123     6      a134     | 2-3     5       9       |a34      7       8       |
 | 39      348     7       |e38      1       6       | 349     5       2       |
 | 239     5       38      | 7       238     4       | 369     36      1       |
 *-------------------------+-------------------------+-------------------------|
 | 6       1789    189     | 489     4789    2       | 5       14      3       |
 |c137     1378    5       |e348     6       378     | 2      d14      9       |
 | 4       39      2       | 1       39      5       | 7       8       6       |
 *-------------------------+-------------------------+-------------------------|
 | 8       3479    3469    | 5       3479    1       | 36      2       47      |
 | 5       123479  13469   | 2349    23479   37      | 8       36      47      |
 | 37      2347    34      | 6       23478   378     | 1       9       5       |
 *-----------------------------------------------------------------------------*


(3=1)r1c37 - r1c1 = r5c1 - (1=4)r5c8 - (4=3)r25c4 => -3 r1c4 ; stte

[SteveG48]

...ALS XY Wing

Hi Leren
It's starting to make sense now.
You're asking, what happens if r5c4 is 4 or not 4?
If it's 4, the two 37s in column 1 produce a 2 at r3c1.
If it's not 4, the two 38s in column 4 produce a 2 at r1c4.

Those 2s knock out the 2s from r1c1 and r3c5.

Bat, what you say is true, but I think it's easier, and clearly shown by Leren's notation, to think of it as "if r1c4 is not a 2, then r3c1 is a 2 (and vice versa). Therefore, one of them knocks out the 2's at r1c1 and r3c5. In technical terms, Leren is establishing a strong link between the 2's at r1c4 and r3c1.

[Leren]

Hi Bat, as Steve said your POV is OK in this case but is unlikely to apply to ALS chains with more complex interactions.

Have a look at ArkieTech's solution to the November 4th puzzle - a chain of 5 ALSs. If you can follow that then you should be well on your way to understanding ALS chains.

Leren

[bat999]

... and clearly shown by Leren's notation, to think of it as...

Yes I see.
First I have to think about the 2 at r1c4.
If r1c4 is 3 instead of 2 then r2c4 is 8 which only leaves only the 4 for r5c4.
Next follow the 4 to see the two 37s in column 1 that produce a 2 at r3c1.
Got it.