Almost Locked Sets in Sudoku Explained

What makes a set almost locked

A locked set has the same number of candidates as cells. Two cells containing only A and B form a locked pair, because those two symbols must occupy those two cells. An Almost Locked Set, often shortened to ALS, has one extra candidate. Two cells with candidates drawn from A, B, and C form an ALS. Three cells using only A, B, C, and D form another. Remove the right candidate and the group becomes locked. This tension makes the set useful, even though none of its cells may be solved. The cells do not need to be adjacent, but they must belong to the same unit so the candidates compete for a fixed number of places. Thinking in terms of the combined candidate set, rather than reading each cell separately, is the first skill to practice.

How two ALS groups interact

The most common ALS deduction uses two separate sets that share candidates. Suppose set one and set two both contain candidate X, and every X in the first set sees every X in the second. X is then a restricted common candidate, because both sets cannot use X at the same time. If the sets also share another candidate Z, any outside Z that sees all Z positions in both sets can be removed. The reasoning is that one of the two sets must lock without X, forcing its remaining candidates, including Z, to stay inside that set. The external Z cannot survive either way. A useful way to test the logic is to imagine one set taking X. That prevents the other set from taking X, so the other set becomes locked into its remaining candidates. If Z is among them, Z must stay inside that set. Reversing the choice produces the matching conclusion from the first set.

How to search without drowning in combinations

Do not inspect every possible group of cells. Start with compact units and small candidate counts. Look for two cells in one row, column, or box that contain exactly three distinct candidates. Then search a nearby unit for another small ALS sharing one or two of those candidates. Mark restricted common candidates first, since they require all occurrences in one set to see all occurrences in the other. Only after that should you test possible eliminations. In Shapedoku, clean notes are essential because ALS logic depends on the exact candidate union, not just on one attractive pair. Begin with size-two ALS groups, since they are much easier to verify than larger groups. Highlight the cells, write the combined candidates once, and count them. If two cells contain four different candidates, they are not an ALS. Careful counting prevents attractive but invalid eliminations.

• Two cells with three total candidates form a size-two ALS.
• Three cells with four total candidates form a size-three ALS.
• All cells in one ALS must lie within a single row, column, or box.
• A restricted common candidate cannot be used by both interacting sets.
• Eliminate only a shared candidate seen by every relevant occurrence in both sets.