Box/Line Reduction

Box/Line Reduction (also called Claiming or Locked Candidates Type 2) is the mirror image of pointing pairs. Both use the overlap between a box and a line — but this one works the other way round, clearing a candidate from a box rather than from a line.

What is Box/Line Reduction?

Look at a single row or column. Suppose a digit — say 4 — can only go in the cells of that line that fall inside one box. Then the 4 for that line must live in that box, on that line. So the 4 can be removed from every other cell of the box — the ones not on the line.

The line "claims" the digit for that box, squeezing it out of the box's remaining cells.

Step by step

1. Fill in your pencil marks. No candidates, no reduction.
2. Pick a row or column and a digit. Find where that digit can still go along the line.
3. Check if they share a box. If all of them fall inside a single box, the line has claimed that digit for the box.
4. Clear the box. Delete that digit from the box's other cells — the ones off the line.
5. Re-scan. The box often collapses to a single straight after.

The two intersection techniques together

Pointing pairs and box/line reduction are the same idea seen from two directions. Pointing pairs: a digit locked to a line inside a box clears the rest of the line. Box/line reduction: a digit locked to a box inside a line clears the rest of the box. Once both are second nature you'll rarely stall at intermediate level — and you're ready for the first true advanced pattern, the X-Wing.

Common mistakes

• Mixing up the direction. Box/line reduction clears the box; pointing pairs clear the line. Ask which one is doing the trapping.
• Checking only rows. Columns claim boxes too — scan both directions.
• Forgetting to re-scan the box. The reduction usually leaves a single behind; don't walk away without checking.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.