Almost Locked Sets (ALS-XZ)

Extreme

Two sets of N cells with N+1 candidates each, linked by a Restricted Common Candidate; their other common candidate is eliminated from all cells seeing both ALS.

How It Works

An ALS is N cells with N+1 candidates. Two ALSs are linked by a Restricted Common Candidate (RCC) — a digit that can only go in one of the two ALSs. This means any other candidate shared by both ALSs can be eliminated from cells seeing both.

Extremely powerful; generalizes Naked Pairs, XY-Wings, and many other techniques.

Example

258
258
1479863
467298571
39
58
37
6418
35
2579
2579
2579
843192
143
57
8
25
679
2369
35
174
35
968
35
29354
852643217
79
35
256834
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

ALS-A: R1C1,R1C2 → {2,5,8}. ALS-B: R4C1,R4C2,R4C3 → {2,5,7,9}. RCC=2 → Eliminate 5 from cells seeing all 5s in both ALS.

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Hard24 givens