ALS-XZ: connect two almost locked sets

ALS-XZ uses two ALSs that share a restricted common candidate X: every X in one ALS sees every X in the other.

Key idea

The two sets cannot both use X freely, so another shared candidate Z must occur in at least one set. A cell seeing every Z occurrence can lose Z.

See the move, step by step

Connect two two-cell ALSs through candidate 6 and eliminate candidate 7.

Step 1 of 4

Each highlighted pair has two cells and three distinct candidates.

Rows and shared box

Step 2 of 4

Candidate 6 is restricted common because all 6s across the sets see each other. Candidate 7 is the second shared digit.

ALS regionsTwo linked ALSs

Step 3 of 4

R3C6 sees the 7 at R1C6 through column 6 and the 7 at R3C8 through row 3, so its 7 is impossible.

ALS-XZ patternCandidate to remove

Step 4 of 4

Remove only candidate 7 from R3C6. The ALSs remain useful structures for later deductions.

Linked ALSsUpdated target

Prove the restricted common candidate first: every X in ALS A must see every X in ALS B. Then require the target to see every relevant Z.