ALS-XY-Wing
Three Almost Locked Sets are joined by two different restricted common candidates, forcing an outside candidate from both outer sets.
What it is
An ALS contains one more distinct candidate than cells. ALS-XY-Wing uses three disjoint ALS: outer set A shares restricted candidate X with the middle set C, while C shares different restricted candidate Y with outer set B. If the common digit Z were absent from A, A would force X; C would then force Y; and B would have to contain Z. The opposite direction also leads to Z in A. Therefore Z is unavoidable in one of the two outer sets, so Z is impossible in any outside cell that sees every Z position in both.
How to spot it
First find small ALS with two to four cells. Keep only links where each occurrence of the shared digit in one set sees every occurrence in the other: that digit is a restricted common candidate. Build two such links through one middle ALS, using different digits X and Y. Finally check an outside candidate Z that sees all Z positions in both outer ALS.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 8/1, 8/3, 8/7, 9/3, 9/7, 9/8
- Digits
- 8, 3, 2
- Eliminations
- 8/8
Press a marked square to point it out on the board above.
Why it matters
The pattern is more advanced than ALS-XZ because it has two logical bridges rather than one, yet it remains a finite proof. Sudoku Luna highlights all three sets, labels the two bridges and removes Z only after every required sight line has been verified.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
How is ALS-XY-Wing different from ALS-XZ?
ALS-XZ connects two almost locked sets through one restricted common candidate. ALS-XY-Wing adds a middle ALS and a second restricted bridge, so the argument carries from one outer set through the middle to the other.
What must an outside Z candidate see?
It must see every possible Z cell in both outer ALS. Seeing only some of them is not enough, because an unseen Z could still be the forced occurrence.
Do the three ALS have to be the same size?
No. Each set only needs exactly one more distinct candidate than cells. The clearest examples use small two-cell ALS, but three- and four-cell sets are valid too.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
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