How it works
Box-line reduction looks at the constraint from the opposite direction of pointing pairs. Instead of a box restricting a row, a row restricts a box.
If a digit has two or three candidate cells in a row, and all of them sit inside the same 3x3 box, the digit must land in that box on that row. That means the digit cannot go in the other cells of the same box outside the row.
The elimination clears the digit from up to six other cells in the box, which often produces a single elsewhere.
When to look for it
Alongside pointing pairs. Scan each row and column and check if a digit's candidates are confined to a single box.
Tips for spotting the pattern
- Scan each row and column, checking for box-confined candidates of each digit.
- Pair this with pointing pairs; together they cover every box-row and box-column overlap.
- Box-line reductions are often invisible without complete pencil marks.
Common mistakes
- Confusing direction. The elimination removes the digit from inside the box, not outside.
- Stopping at finds. Apply the eliminations and re-scan for singles immediately.
- Missing the pattern when only two candidate cells share a row but they sit in different boxes.