June 3, 2026 · 5 min read

Box/Line Reduction (Claiming)

Box/line reduction — also called claiming or "locked candidates, type 2" — is the reverse of a pointing pair. When a digit's only possible cells in a row or column all fall inside a single 3×3 box, that digit is claimed by the line and can be eliminated from the rest of that box. It's an essential intermediate technique for unlocking hard Sudoku.

The name captures the logic: the line "claims" the digit. You don't know which cell of the line will hold it, but you know it sits inside one particular box — so the other cells of that box can't.

How box/line reduction works

• the unit in focus
• the pattern
• a placement
• an elimination

Look at the highlighted row. The digit 1 can only go in two of its cells (amber), and both of those cells happen to lie inside the same box. The row must contain a 1, so the 1 is somewhere in those two cells — which means it's definitely inside that box, on that row. Therefore no other cell in the box can be a 1, and the candidate is removed from the cell above (red), elsewhere in the same box.

The elimination lands inside the box, not along the line — that's the difference from a pointing pair, where the elimination runs out along the line.

Spotting the pattern

Work line by line. For a row or column, pick a digit it still needs and find every cell on that line that can hold it. If all of those cells sit within one box, you have a box/line reduction. Then clear that digit from the box's other cells — the ones not on the original line.

It helps to scan with pencil marks in place: you're hunting for a digit that appears as a candidate two or three times on a line, with all those appearances clustered in one box.

Telling it apart from pointing

This is the most common mix-up at the intermediate level, so it's worth a clear rule. Ask: which unit confines the digit?

• If a box confines the digit to one line, it's a pointing pair, and you eliminate along the line.
• If a line confines the digit to one box, it's box/line reduction, and you eliminate inside the box.

Both rely on the same overlap between a box and a line; they just read it from opposite ends.

Where it leads

Box/line reduction clears candidates inside a box, which frequently produces a hidden single or tidies a box down to a naked pair. Combined with pointing pairs, it resolves a large share of hard puzzles before you ever need advanced patterns like the X-Wing. To see how all eight techniques fit together, head back to the Sudoku strategies guide.