Box-line reduction (locked candidates)
When a digit's only possible cells inside a row or column all sit in the same 3×3 box, that digit can be eliminated from the rest of that box.
A box-line reduction (also called locked candidates, type 2, or claiming) is the inverse of the pointing pair. It happens when a digit's only legal cells within a row or column all sit inside the same 3×3 box. Because the digit must end up somewhere on that line, and every available cell sits within the same box, the digit is locked to the box within the line. That means it can be eliminated from every other cell of the box outside the line.
How to spot one
Pick a row or column. Pick a digit that hasn't been placed in it. Look at the digit's pencil-marked cells along the line. If they all sit inside the same 3×3 box, the digit's elimination radiates into the rest of that box.
Worked example: in row 7, the digit 4 can only go in cells (7, 1), (7, 2), and (7, 3) — all inside box 7. The 4 must land somewhere in row 7, which means it must land somewhere in box 7. So every other cell of box 7 outside row 7 — cells (8, 1), (8, 2), (8, 3), (9, 1), (9, 2), (9, 3) — can have 4 ruled out.
Why "claiming"
The line claims the digit on behalf of the box. Where the pointing pair has the box pushing eliminations outward into the line, box-line reduction has the line pushing eliminations inward into the box. Same locked-candidates logic, opposite direction. Together the two techniques cover both directions of the box-and-line interaction.
When you'll see it
Box-line reduction is common on medium-and-up puzzles and often surfaces after a few placements have shrunk a row or column's candidate footprint. It's particularly useful for cracking open a stuck box: once the elimination fires, the box's remaining empty cells often collapse into hidden singles.
For a longer walk-through of both pointing pairs and box-line reductions and the relationship between them, see Pointing pairs and the snake.
See also
- Pointing pair (locked candidates)— When a digit's only possible cells inside a 3×3 box all share a row or a column, that digit can be eliminated from the rest of that row or column outside the box.
- Hidden single— A digit with only one possible cell within a unit (row, column, or 3×3 box) — even if that cell could legally hold other digits. The unit-first sibling of the naked single.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Pointing pairs and the snake
The pointing-pair pattern is one of the most useful mid-level moves in Sudoku — and one of the easiest to miss. Here's the perceptual habit that surfaces them.