Almost Locked Sets
N Cells with N+1 Candidates
An Almost Locked Set (ALS) is a group of N cells in a unit containing exactly N+1 candidates. They're "almost" locked because removing any one candidate would create a true locked set (Naked N-tuple).
- Definition: N cells with exactly N+1 different candidates
- Example: 3 cells containing {1,2,3,4} = ALS
- Key insight: Any candidate from the ALS that's eliminated "locks" the remaining N
- Difficulty: Expert — foundation for ALS-XZ, ALS-XY-Wing, etc.
The Concept
Recall that a Naked Pair is 2 cells with 2 candidates. A Naked Triple is 3 cells with 3 candidates. These are "locked" — the candidates are claimed.
An ALS has one extra candidate, making it "almost" locked. If any external factor removes one candidate from the set, it becomes fully locked.
ALS Examples
2-cell ALS (Almost Naked Pair):
Cells: [1,2,3] and [1,3]
Candidates: {1,2,3} = 3 candidates in 2 cells
3-cell ALS (Almost Naked Triple):
Cells: [4,5], [5,6], [4,6,7]
Candidates: {4,5,6,7} = 4 candidates in 3 cells
If 7 is eliminated from the 3rd cell:
→ Becomes Naked Triple {4,5,6} in 3 cells!ALS-Based Techniques
ALS become powerful when combined:
Two ALS connected by a restricted common candidate (X). Eliminate the other common candidate (Z) from cells seeing Z in both ALS.
Three ALS forming a wing pattern. Similar to Y-Wing but with ALS instead of single cells.
Longer chains of ALS connected through restricted commons.