Almost Locked Sets (ALS-XZ)

Expert

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

346
256
8
35
14
9
1257
24
67
1
259
349
35
67
59
248
89
456
7
4569
2
14
8
159
3
69
25
59
1873
29
64
347
8
34
692
37
15
2367
69
369
154
2379
28
789
56
3
56
781492
842935671
917426853
Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Practice with a Real Puzzle

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

Hard24 givens