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.
