Box/Line Reduction
Short answer: box/line reduction is when a shape's only spots along a whole row or column all fall inside a single box. The shape must go somewhere on that line, so it must go in that box here — which means it can be struck from the rest of that box. It is the line-to-box half of "locked candidates".
What box/line reduction looks like
Take a row or column and pick a shape it still needs. Mark every cell on that line where the shape could still go. If all of them fall inside one box, the shape is pinned into that box by the line — so the other cells of that box, the ones off the line, can't hold it.
It is the mirror of a pointing pair. There the box constrains the line; here the line constrains the box. Either way you remove a candidate rather than placing a shape.
How to use box/line reduction
- Choose a line and a shape. Pick a row or column and one shape it still needs.
- Mark where the shape can go on the line. Note every empty cell along that line where the shape is still possible.
- Check if they share a box. If all those cells fall inside a single 3×3 box, the shape is locked into that box by the line.
- Eliminate from the rest of the box. Strike that shape from the box cells that are not on the line. The shape must sit on the line inside the box, so it cannot be elsewhere in the box.
Box/line reduction is the line-to-box half of locked candidates; the box-to-line half is the pointing pair. If you are already pencilling candidates, it is worth checking both directions each time a line or box gets tight.
Box/line reduction vs pointing pairs
Same rule, opposite starting point. A pointing pair reads box → line: a shape stuck on one line inside a box, cleared from the line outside. Box/line reduction reads line → box: a shape stuck in one box along a line, cleared from the rest of the box. Scan the box first for pointing, the line first for reduction.
Frequently asked questions
What is box/line reduction in sudoku?
Box/line reduction happens when a shape's only possible cells along a row or column all lie inside one 3×3 box. The shape must be on that line, and the line only meets that box, so the shape can be eliminated from the box cells that are off the line.
How is it different from a pointing pair?
They are the two directions of locked candidates. A pointing pair starts with a box and clears a line; box/line reduction starts with a line and clears a box. The logic — a shape trapped in the overlap of a box and a line — is identical.
Does box/line reduction place a shape?
No. Like other candidate-elimination moves it removes possibilities. The cleared box often then reveals a hidden single or another placement.
Do I need pencil marks to use it?
Practically, yes — you need to see where each missing shape can still go along the line. With candidates noted, box/line reduction is quick to check whenever a row or column is nearly full.