## Easy ALS-XY-Wing Example

Advanced methods and approaches for solving Sudoku puzzles

### Easy ALS-XY-Wing Example

When I first began studying the ALS-XY-Wing, I realized that finding a complex example such as that in Sudopedia called Ruud's Nightmare would be a daunting task, so I decided to concentrate on finding the simpler patterns. This is an example of the simplest pattern I have ever found. It is what I would call an almost XY- Wing pattern. In this example r4c2 is the pivot cell with restricted common digits 27. The 24 cell in r4c8 is also part of the pattern. If a 47 cell were present in box 4, this would be an XY- Wing, but r6c13 contains the ALS set 467, which is just as good. Here r4c2=2 => r8c2=4 and r6c7<>4. Also, r4c2=7 => r6c3 =6 => r6c1 = 4 and 46c7<>4. Therefore r6c7=8 and basic moves identify 18 additional cells in the puzzle.

Easy ALS-XY-Wing Example
Code: Select all
` |-----------------+-------------------+-----------------| |   5    8   14   |  29    19     6   |   7    3   24   | |   3    6   14   | 278   178   12578 | 2458   9   248  | |  27   27    9   |  38     4    358  |  58    6    1   | |-----------------+-------------------+-----------------| |   1   27    8   | 467     5     9   |   3   24   67   | | 2467   9    5   | 34678  378  3478  | 1248 1248  67   | | 467    3   67   |   1     2    478  | -48    5    9   | |-----------------+-------------------+-----------------| |   9    5   23   | 2348    6   12348 | 1248   7   248  | | 678    4  267   |   5    178  1278  |   9   128   3   | |  78    1  237   | 234789 3789 23478 |   6   248   5   | |-----------------+-------------------+-----------------| `

This is Sudoku9981 Expert puzzle, Book 21 #8. I used only basic moves to reach this point in the puzzle.
Bud

Posts: 56
Joined: 24 August 2008

Bud,

r4c28 form an ALS 247
r6c13 form an ALS 467

both ALSs have a restricted common "7"
Both have a non restricted common "4" ...

That is an ALS-xz rule ... you can obviously divide it into 3 ALSs & call it an ALS -xy rule if spotting that way is easier.

tarek

tarek

Posts: 2966
Joined: 05 January 2006

### Easy ALS-XY-Wing Example

Hi Tarek,
Thanks for your reply. Now that you pointed it out, I realize that grouping the two cells in row 4 together makes this an ALS-XZ example. My problem is that I can find the ALS=Wing patterns much more easily because of their resemblance to the XY=Wing.
Bud

Posts: 56
Joined: 24 August 2008

Or, you could use a generalized M-Wing (gM-Wing) and bypass either ALS interpretation.

Code: Select all
` +--------------------------------------------------------------------------------+ |  5       8       14      |  29      19      6       |  7       3       24      | |  3       6       14      |  278     178     12578   |  2458    9       248     | |  27      27      9       |  38      4       358     |  58      6       1       | |--------------------------+--------------------------+--------------------------| |  1      b27      8       |  467     5       9       |  3      a24      67      | | c2467    9       5       |  34678   378     3478    |  1248    1248    67      | | d467     3       67      |  1       2       478     | -48      5       9       | |--------------------------+--------------------------+--------------------------| |  9       5       23      |  2348    6       12348   |  1248    7       248     | |  678     4       267     |  5       178     1278    |  9       128     3       | |  78      1       237     |  234789  3789    23478   |  6       248     5       | +--------------------------------------------------------------------------------+`

gM-Wing: here
daj95376
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