Sudoku techniques · Extreme
ALS-XY-Wing in Sudoku
ALS-XY-Wing is the wing pattern rewritten in Almost Locked Sets. Two wing sets connect to a hinge set through two different restricted common candidates. Between them they force a third shared candidate into one of the wings, so that candidate can be removed from any outside cell seeing all its homes in both wings.
Why it works
Two almost-locked wing sets joined through a hinge by two different restricted common candidates force a third shared candidate into one of the wings, so that candidate can be removed from any outside cell that sees every cell with that candidate across both wings.
How to spot it
Read it as a Y-Wing in which each of the three cells has been replaced by a set.
- Hinge plus two wings, connected by two distinct restricted common candidates.
- The eliminated candidate must be shared by both wings and not by the hinge's connection.
- At this level the app is doing the searching; the lesson is about recognising the shape when a hint draws it.
Builds on
Worked example
These are the app's own lesson boards. Step through them the same way a hint does.
PatternAnswerContextBlockerElimination
125
125
59
139
15
379
59
46
49
67
Step 1 of 3
- 1
Look at the two wing sets . Each lies within a single row, column, or box and holds exactly one more candidate than it has cells. Such a set is called an Almost Locked Set (ALS): remove one of its candidates and it locks, placing every remaining candidate inside itself.
- 2
The hinge set is also an ALS, and it links the two wings. With the first wing it shares candidate 1 as a restricted common candidate (RCC): every cell holding 1 in one set sees every cell holding 1 in the other, so the digit 1 can serve at most one of the two sets. With the second wing it shares candidate 7 the same way.
- 3
Could a cell that sees every 9 in both wings still be 9? No: it would strip 9 from both wings and lock them. The first wing would then use 1 and the second 7, and through the restricted links the hinge would lose both 1 and 7, leaving it fewer candidates than cells. So 9 must be placed inside one of the two wings, and every outside cell that sees all the 9 candidates of both wings loses 9. Here X is 1, Y is 7 and Z is 9.