Almost Locked Sets (ALS-XZ)
Two nearly locked candidate groups share a restricted digit, allowing a second shared digit to be eliminated outside both sets.
What it is
An Almost Locked Set, or ALS, is a group of cells in one unit with exactly one more candidate digit than cells. In ALS-XZ, two disjoint ALS share a restricted common candidate X and another candidate Z. X appears once in each ALS and those two X cells see each other, so they cannot both be true. That restriction forces the two sets to cover Z in a way that removes Z from any outside cell seeing every Z position in both sets.
How to spot it
Look for two to four cells in a row, column or box whose combined candidates are exactly one more than the number of cells. Compare disjoint sets for two shared digits. One shared digit must occur once in each set and its two cells must see each other; that is the restricted common candidate. Then inspect external cells that see every occurrence of the other shared digit.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 2/8, 3/8, 4/1, 4/2, 4/3, 4/8, 5/8, 8/8
- Digits
- 6, 3
- Eliminations
- 5/8
Press a marked square to point it out on the board above.
Why it matters
ALS-XZ is a compact way to expose hidden structure in dense candidate regions. It is advanced because the sets are not obvious by shape, but the finished proof is still local and solution-independent: two sets, one restricted bridge and a fully specified target set.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
What makes a set almost locked?
If N cells contain exactly N+1 distinct candidates between them, the set is almost locked. One candidate must appear outside the set, but the group is still constrained enough to combine with another ALS.
What is the restricted common candidate?
It is a digit shared by both ALS that appears in exactly one cell of each set, and those two cells see each other. They cannot both take it, which creates the ALS-XZ deduction.
Why are only some outside Z candidates removed?
An outside candidate must see every Z occurrence in both ALS. If it misses even one, that unseen occurrence could still satisfy the logic, so the candidate remains possible.
Put it to use
Where you will meet it
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