An ALS is N cells in a single house with exactly N+1 distinct candidates. It is "almost locked" -- remove one candidate and it becomes a naked subset. The simplest ALS is a bivalue cell (1 cell, 2 candidates). All cells must share a house.

The RCC is a digit appearing in both ALS A and ALS B where every instance of that digit in A sees every instance of that digit in B. Because the two ALSs cannot both use the RCC at the same time, at least one ALS must lose the RCC and become a locked set.

That locked-set pressure is what creates eliminations. If the two ALSs also share another digit Z, then Z must appear in at least one of the ALSs. Any outside cell that sees all possible Z locations in both ALSs cannot contain Z.

ALS-XZ uses two ALSs. They share a restricted common candidate X and a second common candidate Z. Since X cannot occupy both ALSs, at least one ALS is forced to resolve without X. When that happens, Z is locked into that ALS unless it is already forced in the other one.

Therefore, Z must appear somewhere in the two ALSs. Eliminate Z from any cell that sees every Z candidate in both ALSs. Level 10 (Master).

The app also lists Almost Locked Sets as a technique because recognizing ALSs is useful on its own. An ALS is not an elimination until it interacts with another ALS, a stem cell, or a block-line intersection. The practical skill is learning to spot small groups of cells whose candidate union is only one digit larger than the number of cells.

Most ALS-based techniques start by cataloging these sets, then checking whether their shared candidates have the visibility needed for an RCC.

An ALS Chain connects several ALSs through RCCs. Each neighboring pair has a restricted common candidate, and the chain alternates which ALS is forced to become locked as each RCC is considered.

The elimination target appears in both the first and last ALSs. If an outside cell sees all possible target locations at both ends of the chain, it can be eliminated. Level 11 (Extreme). ALS-XZ is the shortest useful version of this idea.

Sue de Coq exploits the intersection of a block with a row or column. That intersection contains two or three cells that belong to both houses. The candidates in those intersection cells must be supplied by the line side, the block side, or the intersection itself.

The technique looks for two helper sets: one in the rest of the row or column, and one in the rest of the block. Their candidates are disjoint, and together they account for the candidates that can occupy the intersection. Once the accounting is complete, matching candidates can be removed from other cells in the same line or block.

Level 9 (Master).

Death Blossom starts with a stem cell that has N candidates. For each stem candidate, there is a matching petal ALS. If the stem takes one candidate, its paired petal loses that candidate and becomes locked.

No matter which value the stem eventually takes, one of the petals is forced into its locked state. If the same elimination digit appears across all petals, then that digit must be supplied by at least one petal. Any outside cell that sees every possible instance of that digit across the petals can eliminate it.

Level 11 (Extreme).

Catalog ALSs in each house. Look for pairs sharing candidates with valid RCCs. For Sue de Coq, focus on block-line intersections. For Death Blossom, start from stem cells with few candidates.

Almost Locked Sets: Level 9, Master

Sue de Coq: Level 9, Master

ALS-XZ: Level 10, Master

ALS Chain: Level 11, Extreme

Death Blossom: Level 11, Extreme

ALS techniques build on two concepts: the Almost Locked Set (N cells, N+1 candidates) and the Restricted Common Candidate. Almost Locked Sets provide the building blocks; ALS-XZ, ALS Chains, Sue de Coq, and Death Blossom use those blocks in different configurations. Together they form one of the most powerful families for tackling the hardest puzzles.