ALS Chain
Links built from almost-locked sets – N cells sharing N+1 candidates.
Also known as: Almost Locked Sets, ALS-XZ, ALS-XY-Wing
Quick Summary
An Almost Locked Set (ALS) is a set of N cells in a house sharing N+1 candidates. When connected through restricted common candidates, they form extraordinarily powerful elimination chains.
Understanding the ALS Chain Technique
An Almost Locked Set (ALS) is an N-cell group in a house that contains N+1 candidates. A single bivalue cell is the simplest ALS (1 cell, 2 candidates); two cells sharing three candidates is another (2 cells, 3 candidates). Because N cells can only hold N numbers, exactly one candidate is the 'odd one out'. If you eliminate even one candidate from an ALS, the remaining N candidates become a locked Naked Subset! By linking almost-locked sets together via restricted common candidates, solvers can make eliminations that no fish, wing, or simple bivalue chain can ever reach.
Visual Examples
Green cells highlight the ALS Chain pattern, amber cells denote where candidates are affected, and struck-through pencil marks show the eliminations. Use the buttons or arrow keys to browse examples.
Almost-locked sets do the work here. A set holding just one more candidate than it has cells must place all but one of those digits, so ruling a digit out of the set pins the rest inside it.
Suppose R1C2 is not 8.
- Then R2C1 is 3, since R1C2, R1C3, R2C1 and R2C3 hold only five candidates between them and cannot lack both 8 and 3.
- So R2C8 is not 3, since row 2 holds just one 3.
- So R1C7 is 7, since R1C7, R1C8 and R2C8 hold only four candidates between them and cannot lack both 3 and 7.
Either R1C2 is 8 or R1C7 is 7, so any candidate both of them rule out can go.
How to Spot & Solve a ALS Chain (Step-by-Step Guide)
The complete visual scanning and logical deduction process to execute this technique:
- 1Identify two 'almost-locked sets' in different houses (groups of cells that have just one more candidate than cells, such as 2 cells with 3 candidates).
- 2Find a shared candidate digit that connects the two sets, where all instances in the first set see all instances in the second set.
- 3Because that connecting digit cannot be true in both sets at once, at least one set will not contain it.
- 4Whichever set loses the connecting digit instantly locks down its remaining candidates like a naked subset.
- 5Find a second candidate number shared between both sets.
- 6Eliminate that second candidate from any cell in the grid that has line of sight to all occurrences of that digit in both sets.
Common Traps & Mistakes to Avoid
- Failing to verify that the connecting candidate is truly restricted (all instances in set A must see all instances in set B).
- Eliminating the candidate from cells that only see the digits in one of the two sets.
- Miscounting the candidate total: an ALS of size N must have exactly N+1 candidates.
Frequently Asked Questions
What is an ALS-XZ rule?
ALS-XZ is the fundamental two-ALS rule. One restricted candidate connects the two sets, and a second common candidate is eliminated from intersecting external cells.
Why are ALS techniques considered so advanced?
Because nodes in an ALS chain are entire sets of cells rather than individual digits or bivalue cells, allowing eliminations across complex multi-digit relationships.
Related Solving Techniques
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