Pointing Pair - Leveraging Block and Line Intersections

Consider a block where all candidates for a specific digit (say, 5) fall on the same row. Since 5 must go somewhere in this block, and all its possible positions are on the same row, 5 is locked into this row within this block. Therefore, 5 can be eliminated from all cells on the same row that belong to other blocks. This is a Pointing Pair. When the candidates occupy 2 cells it is called a Pair; when they occupy 3 cells, a Triple.

Pointing Pairs are often confused with Box/Line Reduction. A Pointing Pair eliminates in the direction from block to row/column. Box/Line Reduction works in the reverse direction, from row/column to block. If all candidates for a digit in a row fall within the same block, that digit can be eliminated from other cells in that block (those not on the same row). The direction is reversed, but the logical basis is the same: constraint intersection.

To find Pointing Pairs, check the candidate positions for each digit within each block. If candidates are limited to 2-3 cells and they all align on the same row or column, a Pointing Pair is established. In practice, blocks with 4-5 empty cells are the best targets. Too many empty cells cause candidates to scatter, while too few mean candidates are already constrained.

At Hard difficulty, Naked Singles and Hidden Singles alone will always reach a dead end. Pointing Pairs and Naked Pairs are the primary techniques for breaking through this wall. Pointing Pairs in particular are relatively easy to spot when pencil marks are accurately maintained, making them the most cost-effective technique for conquering Hard-level puzzles.