XYZ-Wing
XYZ-Wing is like XY-Wing, but the pivot has all three candidates: XYZ.
Learn the techniqueALS (Almost Locked Sets)
ALS stands for Almost Locked Sets and links two groups of cells that are almost locked, that is, n cells with n+1 candidates, via a common digit.
See the technique in practice
Work through the examples step by step. Each step explains what you see on the puzzle and why the conclusion holds.
Example:
- Look at the highlighted cells in row 1, column 3 and row 1, column 7. Together they have one more candidate than number of cells—an almost locked set.
- The highlighted cells in row 4, column 7 and row 8, column 7 form a corresponding almost locked set.
- Digit 1 appears in both sets, and all cells with 1 in one see all cells with 1 in the other. Therefore, only one of the sets can use 1 as a solution.
- Whichever set it is, the other is forced to use digit 2 somewhere in its cells.
- Cells that see all 2-candidates in both sets therefore cannot contain 2 themselves. We remove it from the notes in row 9, column 7.
How to recognize the pattern
ALS stands for Almost Locked Sets. A locked set is n cells in the same unit with a total of n candidates, while an almost locked set has one candidate too many, that is, n cells with n+1 candidates. A single cell with two candidates is the smallest variant. The technique links two such sets via a common digit.
The link digit X must be restricted: all cells with X in one set must see all cells with X in the other, so only one of the sets can end up using X. The set that loses X becomes locked and must use all its remaining digits. If the sets additionally share another digit Z, Z is used in one of the sets regardless, and Z can be removed from all cells that see all Z-candidates in both sets.
Step-by-step procedure
- Look for two groups of cells where each group lies in one unit and has one more candidate than number of cells.
- Find a common digit X where all X-candidates in one group see all X-candidates in the other.
- Find another common digit Z that exists in both groups.
- Remove Z from all cells outside the groups that see all Z-candidates in both groups.
Common mistakes
- Counting candidates wrong. The number of different candidates in the group must be exactly one more than the number of cells, or the set is not almost locked.
- Using a link digit that is not restricted. If not all X-candidates in one set see all in the other, both sets can use X, and the logic breaks.
- Removing Z from cells that only see some of the Z-candidates. The removal requires line of sight to every single Z-candidate in both sets.
When do you need the technique?
The hardest puzzles require techniques that follow long logical chains through the entire puzzle. They are in practice proof by contradiction: assume something, follow the consequences and see what does not hold. Try your way through the examples below, step by step, using the same tools the solver uses on your own puzzle.
Try it on your own puzzle
Enter your puzzle in the Sudoku Solver and it will find the next step and explain the technique behind it.
Open Sudoku Solver