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Sudoku techniques

Box-line reduction

If a digit on a row or column can only go inside one box, it can't go anywhere else in that box.

The idea

This is pointing turned around. Take a row (or column) and a digit it still needs. If all the cells on the line that can hold the digit are inside one box, the line will put its copy of the digit in that box.

The box can hold the digit only once, so the other cells of the box, off the line, can't be that digit.

How to spot it

  • Look along each row and column for a digit whose notes sit in one box only.
  • Then clear that digit from the rest of the box.
  • Some books call it claiming or line-box reduction; it is the same move.

Worked example

Box-line reduction on a real puzzle

From our hard puzzle #9 (30 clues), after 23 earlier steps of our solver. Gold cells make the pattern; red notes are the ones it rules out.

Before. On column 4, the 5 can only go in the top-middle box (the marked cells). So no other cell in the top-middle box can be 5.
After. Remove 5 from row 3, column 5; row 3, column 6.

Play this puzzle

How often our puzzles need it

Our solver works like a careful player: it always uses the easiest technique that still makes progress. Counting the puzzles where it had to use box-line reduction at least once:

  • 280 of our 1000 hard puzzles
  • 462 of our 1000 expert puzzles
  • 364 of our 1000 master puzzles

The easiest level that can need it is hard Sudoku.