Box-line reduction: let the line claim the box

Box-line reduction is the reverse of pointing pairs. All candidates for one digit in a row or column fall inside a single box.

Key idea

Because the line must place the digit inside that box, the digit can be removed from the rest of the box outside the line.

See the move, step by step

Use row 2 to claim digit 7 inside box 1.

Step 1 of 4

Row 2 still needs a 7. Compare every legal 7 position along the row with the box boundaries.

Row and box being checked

Step 2 of 4

The only 7s in row 2 are R2C2 and R2C3, and both lie in box 1.

Claimed row and boxOnly 7 positions in row 2

Step 3 of 4

R1C1 and R3C1 share box 1 but not row 2. Neither can contain 7.

Claiming candidatesCandidates to remove

Step 4 of 4

The 7 remains claimed by row 2 while the other box cells retain only their remaining candidates.

Claiming pairUpdated box cells

Check rows and columns whose candidates cluster inside one box. Then remove that digit from the box cells outside the line.