TECHNIQUE · INTERMEDIATE
Box/Line Reduction — a line points into a box
When all candidate cells for a digit on one row or column fall inside the same box, that digit will land inside that box on that line. Every other cell in the box can be cleared of the digit.
The logic
The digit appears once on the row. If its candidates on that row lie entirely within one box, the row's placement will fall in that box on that row. Cells in the same box but on other rows cannot carry the digit.
How to find it
Scan each row and column for digits whose candidates are confined to a single box. The box can then be cleared of the digit outside the original line.
- Choose a row or column with many remaining candidates.
- Check whether a digit's candidates on that line fall inside a single box.
- Eliminate the digit from the rest of that box (cells outside the line).
Pair with Pointing Pairs
Pointing Pairs go box → line; Box/Line Reduction goes line → box. Applying both directions removes candidates from both perspectives on the same region.
Practice order
- Pick a lineChoose a row or column with many candidates.
- Check box confinementFind a digit whose candidates on the line live in one box.
- Clear the boxRemove the digit from that box outside the original line.
- RepeatApply the same logic to other digits and lines.
Walk through Box/Line Reduction
Step 1 of 4
Row 1 already shows 1–6 in columns 4–9, so 7, 8, and 9 must fill columns 1, 2, 3 — all inside the top-left box.