Proven Sudoku
Techniques / Almost locked sets
ALS-XZ
Also called ALS-XZ Rule, Doubly Linked ALS, ALS xz.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Two of those almost full groups share numbers. One shared number cannot appear in both. That forces the other shared number into one group or the other, so squares seeing all its homes lose it.
The exact rule, for stronger players
The rule, stated exactly: Two almost locked sets A and B sharing a restricted common candidate x, meaning every x in A sees every x in B. Then for any other digit z present in both, z is eliminated from cells outside A and B that see every z in both. If a second restricted common candidate exists the link is doubly linked and further eliminations follow inside each set.
What it removes: Remove z from cells seeing every z in A and every z in B. When doubly linked, also remove non-restricted digits from the other set.
Why it works: x cannot be in both sets, so at least one of A and B is locked. A locked set consumes all its digits, so z is confined to that set. Since either could be the locked one, z lies inside A or B, excluding it from anything seeing all its positions in both.
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
- Almost Locked SetA small group of squares holding exactly one number more than there are squares.
- Locked Candidates (general form)Sometimes all the spots for a digit inside one group also sit inside a second group.
Related almost-locked sets
- Death BlossomOne square is the stem.
- Subset ExclusionThe same idea for any size of group.
- Sue de CoqLook where a row or column crosses a box.
- Sue de Coq (extended)The same counting trick with more squares involved.
- Aligned Pair ExclusionLook at two squares together and list every pair of digits they could hold.
How often does it come up?
Our rough estimate: common on hard grids, and it subsumes most of the named wing family.