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ALS-XZ

When two almost locked sets share a restricted common digit.

Explanation

An Almost Locked Set (ALS) is a group of N cells holding N+1 candidates. If two ALSs are connected by a restricted common digit X (all X cells of both sets see each other), one of them must consume X, which locks the other common digit Z into the sets. Any cell that sees every Z in both sets loses Z.

ALS-XZ example Sudoku board 8 6 3 1 5 1 6 2 9 4 9 2 8 7 2 5 8 4 9 2 2 7 6 3 2 7 4 2
An example board where ALS-XZ applies

Practice tip

Hunt for small ALSs first: a bivalue cell already is one. Then look for a partner set sharing two candidates with it.

Example steps

  1. Find two almost locked sets (N cells with N+1 candidates).
  2. Check the restricted common digit X: its cells must all see each other.
  3. Remove the other common digit Z from cells seeing every Z in both sets.

Try this technique on a real puzzle.

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