Box Line Reduction
Box Line Reduction is a technique where, when a number’s candidates within a row or column are all concentrated in one block, you can eliminate that number from other cells in that block. It is the counterpart to Pointing Pair, which works in the opposite direction.
Overview of Box Line Reduction
Box Line Reduction occurs when a specific number’s candidate cells within a row (or column) all fall within the same 3×3 block. While Pointing Pair eliminates in the ‘block → row/column’ direction, Box Line Reduction eliminates in the ‘row/column → block’ direction — it’s the reverse reasoning.
How to Use Box Line Reduction
In a row (or column), check where a specific number’s candidates are located.
Check if all candidates fall within the same block.
If they do, eliminate that number from cells in that block that aren’t in the same row (or column).
Example
Suppose in the bottom row, ‘7’ can only go in two cells that are both in the bottom-left block. Since ‘7’ must be in the bottom-left block along this row, you can remove ‘7’ from other rows within the bottom-left block. For example, a cell whose candidates were ‘2, 7’ is now left with only ‘2’, confirming its value.
Tips for Finding Box Line Reduction
Check each row and column to see if any number’s candidates are all concentrated in one block. Learning this alongside Pointing Pair is recommended. Both focus on ‘block and row/column intersections,’ so you can check for both simultaneously.