sudokUI › Sudoku techniques › ALS-XY-Wing
ALS-XY-Wing in sudoku
XY-Wing made of sets · how it fits
Three non-overlapping almost locked sets: every hinge X sees every X in one wing, every hinge Y sees every Y in the other, and both wings hold another digit Z.
Why it works
The hinge can lack only one digit, so it holds X or Y, removing that digit from the matching wing, which becomes a locked set containing Z. So Z is removed from any cell outside all three sets seeing every Z in both wings.
How to spot it
Picture an XY-Wing whose cells have grown into sets: find a hinge linked to two wings by different digits, then look for a shared Z.
Worked example
ALS-XY-Wing: hinge r6c3 links r8c3, r8c8 (via 4) and r4c9, r6c8 (via 6); digit 7 can be removed from cells seeing every 7 of both outer sets. So 7 is removed from r4c8.
Practise it on a real puzzle. sudokUI generates a puzzle that needs ALS-XY-Wing and takes you straight to the position where it applies. Hints draw the pattern on the board and explain the step.
In a puzzle's rating
Each time the solver needs ALS-XY-Wing, the puzzle's difficulty rating grows by 320. Its class is Unfair. It is needed in 1 in 50 puzzles that sudokUI generates. How the rating works.