Box-line reduction works the opposite direction from a pointing pair. Instead of a box restricting a line, a row or column restricts a box. Look at where a digit's candidates sit within one row: if every one of them falls inside the same box, that digit must go inside that box somewhere along the row. It cannot appear anywhere else in the box, including the other two rows, or columns, that pass through it.
This technique is also called claiming (line-to-box), because the row or column is claiming the digit's spot inside the box for itself. The name changes depending on the book you read, but the elimination is always the same: candidates for a digit that lie outside the row or column but inside the shared box get crossed out.
It pairs naturally with pointing pairs. Learn to spot one and the other becomes easier, since both come from asking the same question about a digit's candidates, just starting from a different unit.
The two techniques are so closely related that some solving guides teach them as a single skill called locked candidates, with pointing pairs and box-line reduction as its two directions. Whichever name you use, the payoff is the same: fewer candidates cluttering the board and a cleaner path to the next single.
Worked example
The same real puzzle position, one row up. Step through to see row 8 claim a digit out of its box.
How to find a box-line reduction
Pick a row or column with several empty cells and work through the digits 1 to 9. For each digit, mark which empty cells in that line still have it as a candidate. If all of them sit inside the same box, even though the row or column runs through three boxes total, you have found the pattern.
- Two or three cells both work. As with pointing pairs, the number of candidate cells does not matter as long as they all sit in one box.
- Check the whole line, not just part of it. A digit's candidates need to be confined to one box across the entire row or column, not just the section you happened to look at first.
Box-line reduction or pointing pair?
Both patterns connect a box to a row or column, just from opposite starting points. A pointing pair starts inside a box and clears a line. Box-line reduction starts along a line and clears the rest of a box. If a row looks stuck, check whether one of its digits is confined to a single box before moving on to pairs or triples.
A useful habit is to check both directions for every box you pass through while scanning: does a digit inside this box point out to a line, and does any line running through this box claim a digit for it. Doing both takes only a little longer than doing one, and between them they catch most of the eliminations a Hard puzzle needs before naked or hidden pairs come into play.
Common mistakes
- Eliminating from the row or column itself. The elimination happens inside the box, in the cells that are not part of the row or column you started from. The candidate cells in the line keep their marks.
- Stopping after checking two boxes. A row passes through three boxes. Confirm the digit truly has no candidates in the other two boxes along that row before you conclude it is confined to one.
- Applying it with only one candidate cell. One candidate cell is not a pattern to eliminate with, it is close to a naked single already. Box-line reduction needs at least two candidate cells confined to the same box.
Check it before reaching for an X-Wing
Hard puzzles on this site carry 28 to 32 givens, few enough that naked and hidden singles stall repeatedly. Box-line reduction, alongside pointing pairs and naked triples, is one of the moves built into that difficulty band. Extreme Hard puzzles (23 to 27 givens) lean on it even more, often chaining several of these eliminations before a cell opens up.
If a row or column feels stuck, check each digit's candidates against the three boxes it runs through before assuming you need a harder technique like an X-wing. Box-line reduction is simpler and comes up far more often.
Hard boards carry 28 to 32 givens. When a line looks stuck, check whether a digit is claimed by a single box.
Frequently asked questions
It is when a digit's candidates within one row or column all fall inside a single box. That digit can then be removed from the rest of the box, outside the row or column.
Because the row or column is claiming that digit's spot inside the box for itself, ruling it out everywhere else in the box.
A pointing pair starts inside a box and eliminates along a row or column. Box-line reduction starts along a row or column and eliminates inside a box. Same idea, opposite direction.
Not usually. It removes candidates from a box, which often sets up a naked or hidden single elsewhere on a later move.
Yes, at minimum. If a digit already has only one candidate cell in the row or column, that is a hidden single, not box-line reduction; just place it.
Hard puzzles, at 28 to 32 givens, use it regularly once singles run out. Extreme Hard puzzles at 23 to 27 givens rely on it even more.
A little. You are scanning a full row or column of up to nine cells instead of a single 3x3 box, so it takes a few more seconds. The payoff, an elimination inside a box, is the same size either way.