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Extreme Used in extreme puzzles.

Almost Locked Sets (ALS-XZ)

Two almost locked sets

An Almost Locked Set (ALS) is a few cells of one row, column or box holding one digit more than there are cells: two cells with three digits between them, or one cell with two. Take away any one of its digits, and the others fill its cells: it is locked.

Take two such sets, apart, and a digit X of both whose places in one all see its places in the other. X can be in one of the two at most, so the other is locked without it, and holds all its other digits.

So Z, another digit of both sets, is in one of them for sure: a cell that sees all of Z's places in the two sets cannot be Z. Remove it there.

What to look for

Look for two small groups of cells, each with one candidate too many, sharing two digits: one whose places see each other from set to set, and the one to remove.

Example

6291525783257892789178432942678267891278967857815256425923913636997368245252413683615566816789342679143462167867897898953674584567328248569121369575736484583494816357372 112233445566778899
ALS-XZ: R5C5, R6C6 (box 5) hold {7,8,9} and R4C8, R4C9, R6C7, R6C9 (box 6) hold {3,6,7,8,9}: two sets, each with one digit more than it has cells. 7 cannot be in both, as every 7 of one sees every 7 of the other. So one of them is without 7 and holds all its other digits, 9 among them: 9 is in one of the two sets. Remove 9 from R6C5.
  • The cells the technique relies on
  • Cells where it removes candidates, struck out in red
  • The two sets, one in each colour
  • Strong link (solid line) and weak link (dashed)

Practise it

In the app, Learn › Almost Locked Sets (ALS-XZ) sets exercises on real positions, then a full puzzle that needs this technique and nothing harder.

Practise in your browser