ALS-XZ Sudoku Technique: Almost Locked Sets Explained for 2026

ALS-XZ is a set-based inference. An almost locked set (ALS) is a group of N cells inside a unit (row, column, or box) that together contain N+1 different candidate digits. That “extra” degree of freedom is what makes the set almost locked: if you knew which digit was “out,” the rest would collapse like a naked subset.

ALS-XZ links two ALS regions through two special digits:

• X is a restricted common: whichever ALS holds X, the other ALS cannot—because every possible placement of X in one set sees every possible placement of X in the other.
• Z is the elimination digit: it must leave at least one ALS regardless of how the shared logic resolves, so anything outside that sees all Z options across the combined pattern loses Z.

If you like mental imagery, think “two floppy locked sets pinned together by X, so Z cannot escape into certain witnesses.”

Pattern

Operational checklist:

1. Pick ALS1 with cell count n and n+1 total candidates.
2. Pick ALS2 with cell count m and m+1 total candidates.
3. Identify X such that X cannot be true in both sets simultaneously (restricted common across all pairings of X locations).
4. Identify Z present in the union of candidates such that, under the mutual constraint imposed by X, Z must be eliminated from shared peers of the pattern’s Z occurrences.

The elimination targets are any cells outside the ALS cells that see every place Z can land inside the combined ALS union consistent with the pattern.

This is not a memorized shape like a fish; it is a contract on candidate domains.

Logic

ALS-XZ shines when:

• A box or line has a dense candidate cloud—triple bivalue stacks, almost-naked subsets, and almost unique rectangles.
• Single-digit patterns stall: no X-Wing, but multi-digit residue keeps aligning across two houses.
• You already use XY-Wing and W-Wing, but the puzzle demands one extra digit of slack inside a local cluster.

Reach for ALS-XZ after uniform checks fail; it is powerful but easy to mis-draw if your candidate map is incomplete.

Example

Consider two boxes that overlap a shared band (rows or columns). In box 7, three cells form an ALS with candidates {2,5,8}—three cells, four total symbols if you include the “almost” digit. In box 8, two cells form an ALS with candidates {2,6,8}.

• Digit 2 is restricted common: every 2 candidate in the first ALS sees every 2 candidate in the second ALS along the band (no compatible pairing).
• Digit 8 appears in both ALS as Z.

Any cell outside those ALS cells that sees all current 8 positions spanning the two sets cannot keep 8: the X restriction forces the pair of ALS to trade responsibilities so 8 cannot only live on a cell your witness misses.

ALS1 (n cells, n+1 digits)   X bridges   ALS2 (m cells, m+1 digits)
            \                           /
             \   restricted common X    /
              -------------------------
                     Z peers outside -> lose Z

Translate this story to your sheet by listing ALS candidates explicitly—ALS-XZ errors are usually counting errors, not imagination errors.

Next step: Sudoku Face Off keeps ALS work practical: consistent pencil marks make the N vs N+1 headcount honest before you commit to an elimination.

Pitfalls

• Miscounting the ALS: N cells must carry exactly N+1 distinct digits across the union; hidden singles you forgot to pencil in will break the arithmetic.
• False restricted common: X must fail every cross-placement; one surviving pair undoes the entire inference.
• Over-extending Z: you may only eliminate where all Z endpoints in the pattern are visible; partial visibility means no cut.

Pair this page with forcing chains when ALS finds a relation you can feel but cannot yet phrase as a single strong link.

Return to the essential advanced techniques overview for fish and wings, or jump to extreme Sudoku for study order.