## ALS-XZ/vwxyz-Wing Example

Advanced methods and approaches for solving Sudoku puzzles

### ALS-XZ/vwxyz-Wing Example

I normally have a hard time finding ALS-XZ, but this time I found one which is also a pattern technique called a vwxyz-wing. Ib terms of the ALS-XZ Rule the two ALS's are 1, 2, 3, 8, 9 in row 8 with cells marked with ', and 2,3 in r9c5. The restricted common digit X is 2 and the common digit Z is 3. The digit 3 in r8c4 sees all the 3's in the both ALS's cells and can be eliminated. In terms of the rhe vwxyz-wing V is 2 and Z is 3. If r9c5 is 2 then r8c2589 is a locked set and 3 cannot be in r8c4. If r9c5 is 3 then again 3 cannot be in r8c4.

vwxyz-Wing Example
Code: Select all
` |-----------------+-----------------+-----------------| |  389   7    4   |   1  2359  29   | 3589 2389   6   | |   1    5   389  | 2389   7    6   |  389   4   239  | |  389   2    6   |  389  359   4   |   1    7   359  | |-----------------+-----------------+-----------------| |  579   6   79   |  259   8   129  | 3579  129   4   | | 5789   4   789  |   6   129   3   |  579  129  259  | |   2    3    1   |  59    4    7   |   59   6    8   | |-----------------+-----------------+-----------------| |  34   18    5   |  349   6   19   |   2   389   7   | | 347   18'  237  | 2-349 1239' 5   |   6   389' 39'  | |   6    9   23   |   7   23*   8   |   4    5    1   | |-----------------+-----------------+-----------------| `

This is Sudoku9981 Extreme Puzzle Book 25 #4. I used a 5 color wing to get to this point in the puzzle.
Bud

Posts: 56
Joined: 24 August 2008

I normally have a hard time finding ALS-XZ

Just as every naked set has an equivalent hidden set that makes the same deduction, it is also the case that every ALS will have an equivalent AHS that makes the same deduction. A relatively large ALS implies a relatively small AHS which may be easier to see, especially if you use coloring.
Code: Select all
` |-----------------+-----------------+-----------------|  |  389   7    4   |   1  2359  29   | 3589 2389   6   |  |   1    5   389  | 2389   7    6   |  389   4   239  |  |  389   2    6   |  389  359   4   |   1    7   359  |  |-----------------+-----------------+-----------------|  |  579   6   79   |  259   8   129  | 3579  129   4   |  | 5789   4   789  |   6   129   3   |  579  129  259  |  |   2    3    1   |  59    4    7   |   59   6    8   |  |-----------------+-----------------+-----------------|  |  34   18    5   |  349   6   19   |   2   389   7   |  |34a7b  18'  237B |2-34A9 1239' 5   |   6   389' 39'  |  |   6    9   23   |   7   23*   8   |   4    5    1   |  |-----------------+-----------------+-----------------|`

The AIC representation for your ALS deduction is

(3&1&8&9=2)r8c2589 - (2=3)r9c5 => r8c4 <> 3

From the hidden point of view, not only are there fewer digits in this case, but you have your coloring to aid you. It is simple from coloring to note that 4's and 7's are locked in r8c134. One other digit that is almost locked in those cells is 2. Thus we have...

(4&7&2)r8c134 = (2)r8c5 - (2=3)r9c5 => r8c4 <> 3

In this case one can break the hidden triple down into a greater amount of smaller hidden sets like...

(4&7)r8c14 = (7-2)r8c3 = (2)r8c45 - (2=3)r9c5 => r8c4 <> 3

...or using the locked sevens AH-pair instead of the locked fours AH-pair...

(4)r8c4 = (4&7-7&2)r8c13 = (2)r8c45 - (2=3)r9c5 => r8c4 <> 3

...or even three almost hidden singles...

(4)r8c4 = (4-7)r8c1 = (7-2)r8c3 = (2)r8c45 - (2=3)r9c5 => r8c4 <> 3
Myth Jellies

Posts: 593
Joined: 19 September 2005

### ALS-XZ/vwxyz-Wing Example

Hi Myth,
Thanks for your tip, but it will take me awhile to digest it.
Bud

Posts: 56
Joined: 24 August 2008