ALS-XZ (Almost Locked Sets)

An almost locked set, or ALS, is a group of N cells in one row, column or box that hold N + 1 candidates between them. A single cell with two candidates is the smallest ALS. If one of its digits is taken away, the set becomes locked: its cells are filled by exactly the remaining digits. ALS-XZ uses two such sets, A and B, that share a restricted digit X: every X of A sees every X of B, so X can be in at most one of the sets. The set without X is then locked. If the two sets also share another digit Z, that digit must end up in A or in B, so every cell that sees all the Z candidates of both sets can lose Z. A Y-Wing is the smallest case of this idea. ALS-XZ is a Master technique in Bare Sudoku.

When to use it

Late in hard puzzles, when the board has many cells with two or three candidates and the chains find nothing. ALS techniques look at groups of cells instead of single candidates, so they find eliminations that chains of single cells miss.

How to spot it

Look for small groups first: a two-candidate cell, two cells of one unit with three candidates between them, or three cells with four. Take two such sets that do not share a cell. Find a digit X that both hold and check that every X in one set sees every X in the other. Then take any other digit Z that both sets hold, and remove Z from the cells that see every Z in both sets.

Example

ALS-XZ
	c1	c2	c3	c4	c5	c6	c7	c8	c9
r1	4	236	5678	5689	1	3568	259	359	3579
r2	9	136	156	7	456	2	145	1345	8
r3	258	123	1578	4589	458	358	12459	6	3579
r4	6	9	2	58	7	4	3	58	1
r5	7	8	4	3	569	1	569	2	59
r6	1	5	3	2	689	68	689	7	4
r7	58	7	15689	4568	2	568	14589	134589	359
r8	3	46	568	1	4568	9	7	458	2
r9	258	124	1589	458	3	7	14589	14589	6

Bold digits are given, blue digits were placed while solving, small digits are candidates. Highlighted cells form the pattern, crossed-out candidates are removed, and a circled candidate is the digit to place.

Set A is r7c1 (5 8), r7c6 (5 6 8): together these cells hold 5, 6, 8, one digit more than cells, so A is an almost locked set. Set B is r4c4 (5 8), r6c6 (6 8), holding 5, 6, 8.
Both sets hold 6, and every 6 of A sees every 6 of B, so at most one of the sets can contain 6.
The set that does not get 6 is locked: its cells take exactly its other digits, and 5 is one of them. So 5 ends up in A or in B.
A cell that sees every 5 of both sets cannot be 5. Remove 5 from r7c4.

Common mistakes

Using a digit X that is not restricted. If some X of A does not see some X of B, both sets could hold X, and nothing follows.
Letting the two sets share a cell. A and B must not overlap.
Removing Z from a cell that sees only some of the Z candidates. The cell must see every Z in A and every Z in B.

In Bare Sudoku

Needed from level: Master
In the game, the hint says: ALS-XZ

Play this puzzle · Play Sudoku · Sudoku solver

Practice puzzles

In these puzzles, ALS-XZ is the hardest technique you need. Each link opens the puzzle in the game; the solver link shows every step.

Frequently asked questions

What is an almost locked set?

A group of N cells in one row, column or box with N + 1 candidates between them. Taking away any one of those digits locks the set, so that its cells are filled by exactly the remaining digits.

What do X and Z stand for in ALS-XZ?

X is the restricted common digit: both sets hold it, but it can be in at most one of them. Z is the digit that gets removed: it is in both sets and must end up in one of them.

Is a Y-Wing an ALS-XZ?

Yes. A [Y-Wing](y-wing) is an ALS-XZ whose sets are the pivot with one wing and the other wing on its own. ALS-XZ applies the same idea to larger groups of cells.

What if the two sets share two restricted digits?

Then both sets are locked at once and more can be removed: each of the two digits leaves the cells that see all of its candidates in both sets, and every other digit of each set leaves the cells that see all of that digit within the set. This is called a doubly linked ALS-XZ.

Made by Alparslan Selçuk Develioğlu · Updated 2026-10-04