Box-Line Reduction

Difficulty level: hard

Box-line reduction is the converse of the pointing pair. Here the line constrains the box: scan a row or column, and note where a missing number can still go. If all of those cells fall inside a single 3×3 box, the number is trapped there.

Because the row (or column) must place the number inside that box, the box's other cells — the ones outside the line — can drop the candidate entirely.

Used together, pointing pairs and box-line reduction let the boxes and lines continually squeeze each other, which is the rhythm of most hard-rated puzzles.

Worked example

Row 1 can only place its 6 in the highlighted cells — all inside the top-right box. The 6 can be erased from the box's other six cells.
6 (highlighted) (highlighted) (highlighted)
6

How to apply it

  1. Pick a row or column and a number missing from it.
  2. Mark the cells of that line which can still take the number.
  3. If they all sit in one box, erase the number from the box's other cells.
  4. Re-scan the box for new singles.

Practice it

The fastest way to internalize the box-line reduction is to use it. Play a free hard puzzle — the in-game hint system points out exactly this pattern when it appears, or browse the full technique library.