Proven Sudoku
Techniques / Almost locked sets
Almost Locked Set
Also called ALS, Almost Locked Subset.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A small group of squares holding exactly one number more than there are squares. One number will be left over. Which one it is depends on what happens around it, and that is what makes these useful.
The exact rule, for stronger players
The rule, stated exactly: A set of n cells within a single house whose candidates number exactly n+1. Placing any one of its digits outside the set would reduce it to a locked set.
What it removes: An ALS licenses nothing on its own. It is a building block: eliminations come from linking two or more ALSs, or an ALS and another node, through a restricted common candidate.
Why it works: n cells hold n digits. With n+1 candidates available, exactly one digit is surplus. Removing that surplus digit from the set forces the remaining n digits into the n cells, which is a naked subset.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Naked Subset (general form)Find some squares in one row, column or box.
Related almost-locked sets
- ALS ChainA row of almost full groups linked one to the next.
- ALS-XY-WingThree almost full groups arranged like a wing.
- ALS-XZTwo of those almost full groups share numbers.
- Death BlossomOne square is the stem.
- Subset ExclusionThe same idea for any size of group.
How often does it come up?
Our rough estimate: ALSs are everywhere. Any bivalue cell is an ALS of size one, which is why ALS theory subsumes so much of Tier 5.