Box/Line Reduction Sudoku Technique
A pointing pair run backwards: what the row knows, it tells the box.
Also called: locked candidates type 2, line-to-box, claiming.
What box/line reduction is
Every remaining home for a digit on a row (or column) happens to fall inside one box. The row must contain that digit, so the digit must land in that box.
The rest of the box can then be cleared. The box already owes this digit to the row, so it cannot spend it on any of its other cells.
Pointing pairs push information from a box out to a line; box/line reduction pushes it from a line into a box. Learning both roughly doubles how often locked candidates fire.
How to spot one
- Take a row and a digit and mark every cell that could still hold it. If all the marks land in one box, the reduction is available.
- Rows that are mostly complete are the best hunting ground — with six digits placed, the survivors have few homes and cluster easily.
- Always check the column version too. The same grid state often yields one and not the other.
Worked example
| Digit 3 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Row 4 | 3 | 3 | |||||||
| Row 5 | × | × | × | ||||||
| Row 6 | × | × | × |
3 marks a cell where the digit can still go. × marks a candidate this technique removes. Blank cells are not part of the pattern.
- On row 4 the only cells that can still take a 3 are at columns 4 and 5 — both inside box 5.
- Row 4 must contain a 3, so box 5 must supply it. The 3 for box 5 is spoken for.
- Clear 3 from every other cell of box 5: the whole of rows 5 and 6 within columns 4 to 6.
What it eliminates
The digit, from every cell of the box that does not lie on the line that forced it.
When you need it
Alongside pointing pairs, from Medium grids upward. The two together resolve most mid-grid stalls before anything heavier is needed.
Difficulty here is set by how many clues are left in the grid: Easy starts from 46, Medium 40 and Hard 34, with Extreme and Insane stripped further still. Fewer clues is what makes the techniques below necessary — the fewer digits you start with, the deeper you have to reason.