Pointing Pairs in Sudoku
Pointing pairs — sometimes called box-line intersection — are a key technique for medium and hard sudoku puzzles. They allow you to eliminate candidates from outside a box based on patterns inside it. Once you see how they work, you'll spot them quickly across the entire grid.
What Is a Pointing Pair?
A pointing pair occurs when all the remaining candidates for a particular digit within a 3×3 box are confined to a single row or single column.
When this happens, you know that digit must be placed somewhere in that row (or column) within the box. Therefore, it cannot appear in the same row (or column) outside the box — and you can eliminate it from those cells.
Why Does This Work?
The digit must go somewhere in the box. All valid locations for it are in the same row (or column). That row (or column) can only contain one instance of that digit. So if it goes into the box along that row, no other cell in that row can hold it. The "pair" points outward along the row or column, eliminating candidates.
Step-by-Step: Finding a Pointing Pair
- Choose a digit and a box that doesn't yet contain it.
- Mark all empty cells in the box where that digit is still a candidate (i.e., not blocked by the row, column, or existing placements).
- Check if all remaining candidate cells are in the same row or the same column.
- If yes — eliminate that digit from all other cells in that row (or column) that are outside the box.
Example: Pointing Pair in a Row
You're scanning for the digit 4 in the top-center box (rows 1–3, columns 4–6). Rows 1 and 3 of the box are already fully filled, leaving three empty cells in row 2: columns 4, 5, and 6. Column 6 already contains a 4 elsewhere on the grid (dark cell below), which eliminates column 6 as a candidate. Only columns 4 and 5 remain — both in row 2.
This is a pointing pair. The 4 must land somewhere in row 2 within this box, so it cannot appear in row 2 outside the box. Eliminate 4 from all cells in columns 1–3 and 7–9 that are in row 2. This might reduce another cell to a naked single, or create a hidden single in a different box along row 2.
Pointing Triple
When three cells (instead of two) in the same row or column within a box are the only candidates for a digit, it's called a pointing triple. The logic is identical — eliminate that digit from the rest of the row or column outside the box.
Difference From Box-Line Reduction
Pointing pairs look outward: the pattern is inside a box, and the eliminations happen outside the box along a row or column.
Box-line reduction is the reverse: the pattern is inside a row or column, and the eliminations happen inside a box. Both techniques use box-row or box-column intersections, just from opposite directions.
When to Look for Pointing Pairs
Pointing pairs are most useful after naked singles and hidden singles are exhausted. Set up pencil marks for the entire puzzle, then scan each box for each digit. When a digit's candidates in a box form a line, apply the elimination.
They appear most often in medium and hard puzzles where multiple digits are competing for the same rows and columns across several boxes.