An Almost Locked Set (ALS) is a group of N unsolved cells in one house containing N+1 candidate digits in total.
A Locked Set has N cells / N digits. An ALS is one candidate away from becoming locked.
By itself, an ALS usually makes no elimination. Its power appears when another structure forces one candidate out of it, because the remaining N digits become locked into the N cells.
That simple observation turns ALS into a general language for many expert Sudoku techniques.
The definition
Inside one row, column, or box:
N cells + exactly N+1 candidates = an Almost Locked Set.
Examples:
- one bivalue cell
{2,7}is a size-1 ALS; - two cells whose union is
{2,5,7}form a size-2 ALS; - three cells whose union is
{1,3,6,9}form a size-3 ALS.
Why a bivalue cell is an ALS
One cell containing two candidates has:
N = 1 cell
N+1 = 2 candidatesSo every bivalue cell is the smallest possible ALS.
This is why ALS theory connects naturally to familiar Wings and Chains: those patterns already use small almost-locked candidate structures.
What happens when one candidate is removed?
Suppose two cells form ALS {2,5,7}.
If candidate 7 is proven absent from the ALS, the two cells are left with {2,5}.
Now two cells contain two digits: a Naked Pair / Locked Set.
The ALS has “collapsed” into a locked structure.
This gives ALS a Strong-like inference:
if candidate X is absent from the ALS, the remaining candidate structure becomes locked.
Restricted Common Candidate (RCC)
Two ALS can interact through a Restricted Common Candidate.
A digit X is an RCC between ALS A and ALS B when all possible X occurrences across the two ALS are mutually restricted in a house relationship such that X cannot be true in both ALS at once.
So:
- if X is true in ALS A, X is excluded from ALS B;
- ALS B then becomes locked on its remaining digits;
- and vice versa.
RCCs are the links that make ALS-XZ and ALS Chains work.
An ALS is not automatically a technique
Finding N cells / N+1 candidates does not by itself justify an elimination.
This is a common beginner-to-expert transition mistake.
You must also find:
- another ALS or chain node;
- a valid RCC or other link;
- a common candidate that becomes forced/restricted;
- and a target that sees all possible forced occurrences.
Think of an ALS as potential energy, not a completed move.
Worked ALS identification
ALS and Naked Subsets
The relationship is direct:
- Naked Pair: 2 cells / 2 digits;
- size-2 ALS: 2 cells / 3 digits.
When one ALS candidate is removed, the ALS becomes the corresponding Naked Subset.
This makes ALS easier to learn if you already understand subsets as counting/reservation logic.
ALS and Wings
Many named Wings can be represented through ALS relationships.
A bivalue cell is an ALS. A trivalue pair of cells can be another ALS. Link them through a restricted candidate and familiar Wing eliminations appear.
Named patterns remain useful because they are visually fast. ALS explains why a broader range of candidate layouts follow the same logic.
ALS and Chains
An ALS can also act as a compound chain node.
Entering the ALS through one candidate removal can lock the remaining candidates and create an outgoing elimination. In Strong/Weak language, the almost-locked property supplies the internal forcing relationship between those states.
This is why Grouped AIC discussions often lead naturally into ALS nodes.
How to find ALS without drowning in combinations
Almost every candidate-rich grid contains many ALS. Searching all of them manually is inefficient.
Start with:
- bivalue cells;
- two cells with a three-digit union;
- small groups inside constrained houses;
- ALS that share candidates with nearby ALS;
- candidate relationships that are restricted by an intersection.
Do not catalog every ALS. Search for useful connectivity.
ALS overlap
Two ALS may sometimes share cells or candidate positions depending on the exact technique and rule set being used.
Overlap can create subtle invalid assumptions if the same candidate occurrence is effectively counted twice.
For the first ALS techniques, prefer clearly separate sets and validate every RCC explicitly. More complex overlap rules belong in later expert expansion.
Common mistakes
N cells with N candidates
That is a Locked Set, not Almost Locked.
Cells from multiple houses
One ALS itself must live inside a single house.
Calling an ALS an elimination
The ALS needs a relationship to another structure.
Declaring an RCC because both sets contain X
Common is not enough. X must be restricted between the ALSs.
Searching huge ALS first
Small sets are easier to validate and often produce the same useful logic.
FAQ
What does ALS stand for in Sudoku?
Almost Locked Set.
What is the formula for an ALS?
N cells in one house containing exactly N+1 distinct candidates.
Is every bivalue cell an ALS?
Yes. One cell with two candidates is a size-1 ALS.
What is an RCC?
A Restricted Common Candidate is a digit shared by two ALS whose possible occurrences are restricted so the digit cannot be true in both ALS at once.
Does an ALS itself eliminate anything?
Usually no. It becomes useful when linked to another ALS or chain structure.
What to learn next
ALS-XZ is the best first complete ALS technique. It uses two ALS, at least one RCC, and a shared elimination digit to turn the definition into a practical deduction.