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ALS-XZ (Almost Locked Sets)
Learn the ALS-XZ rule: two almost-locked sets sharing a restricted common digit and a second digit Z let you eliminate Z wherever it sees both sets.
An Almost Locked Set (ALS) is a group of N cells in a unit holding exactly N+1 candidates — one digit short of being a locked set. Place any one of its digits and the rest lock into singles. ALSs are everywhere on a hard board once you look for them.
The ALS-XZ rule pairs two of them. They must share two digits, X and Z, where X is "restricted common" — every X in one set sees every X in the other, so X can be true in only one of the two ALSs. Whichever set misses out on X becomes locked, and a locked set must use up all its digits, including Z.
So one of the two ALSs is guaranteed to contain Z. Any cell outside both that can see every Z candidate in both sets therefore cannot be Z, and you remove it. ALS-XZ is a gateway into the wider world of almost-locked-set chains, reaching eliminations that single-digit fish and basic wings miss. The example highlights the two sets and the Z it clears.
Practise the ALS-XZ
The best way to learn a technique is to use it. Play a puzzle at the level where it first appears, or drop a tricky board into the solver to watch it in action.
Frequently asked questions
What is an Almost Locked Set?
A set of N cells within one unit whose candidates total N+1 digits. It is one placement away from being "locked" — fix any one digit and the others resolve.
What does "restricted common" mean in ALS-XZ?
A digit X shared by both ALSs such that every cell holding X in one set sees every cell holding X in the other. That forces X into at most one of the two sets.
What can I eliminate with ALS-XZ?
The second shared digit Z, from any cell outside both sets that sees all of the Z candidates in both ALSs, because one of the two sets is guaranteed to supply Z.
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