Intermediate

Box/Line Reduction

When a digit on a line is confined to one box, it can be eliminated from the rest of that box.

Box/line reduction is the complement of the pointing pair. If, along a row or column, a digit can only appear within the cells of a single box, then that digit must come from that box-on-line intersection — so it can be removed from the box’s other cells.

Together with pointing pairs, it clears the way for singles in tightly constrained regions.

How to spot it

Take a line (row or column) and a digit. If every candidate cell for that digit on the line falls inside one box, the digit is confined there: erase it from the rest of that box.

  • Pick a digit on a row or column.
  • Check its candidates on that line all sit in one box.
  • Remove the digit from the box’s cells outside the line.
Row 4 pins its 8 inside one box — so 8 leaves the rest of the box.

Worked example

  1. On row 4, digit 8 can only appear in three cells.
  2. All three lie inside the middle-left box.
  3. So 8 for row 4 must be in that box.
  4. Remove 8 from the other six cells of the middle-left box.
  5. This frequently resolves a naked single elsewhere in the box.

Try it yourself

5
2
8
7
7
4
9
1
6
5
1
3
9
2
2
1
2
4
3
6
7
2
6
7
3
4

Tap a cell, then a number, to practise.

Frequently asked questions

When is box/line reduction useful?
It shines on medium-to-hard puzzles where singles have stalled but the digit distribution is still lopsided across a box and a line.
Is it the same as locked candidates?
Yes. Pointing and box/line reduction are together called locked candidates (types 1 and 2).

Related techniques

Practice: Box/Line Reduction

Put the Box/Line Reduction to work on a live board — free puzzles with notes, hints and four difficulty levels.

Try it on a live board

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