Pointing Pairs, Triples and Locked Candidates: One Family of Clean Eliminations

The Unified Logic of Locked Candidates

All three techniques—Pointing Pairs, Pointing Triples, and Locked Candidates (also called Box-Line Reduction)—operate on a single, powerful rule: if all possible positions for a specific candidate digit within a 3x3 box are aligned in the same row or column, then that digit must be placed somewhere within that alignment inside the box. Consequently, it cannot appear anywhere else in that row or column outside the box. The only difference is the number of cells involved (two or three) and the direction of the logical 'look.' This rule is absolute and leads to guaranteed, error-free eliminations. It's a foundational stepping stone before moving to more complex interactions like Naked Pairs or Hidden Pairs.

Pointing Pairs: The Basic Lock

Pointing Pairs occur when a candidate digit appears in only two cells within a 3x3 box, and both of those cells lie in the same row or column. This alignment 'points' the digit's placement along that line, but confined to the box. You can then eliminate that candidate from all other cells in that row or column that are outside the containing box. For example, if the digit 7 is a candidate only in the top-left and top-middle cells of a box (both in the box's top row), you can remove 7 from any other cell in that top row across the entire puzzle, but only in the two adjacent boxes. This is often the first locked candidate technique solvers encounter, as the pattern of just two cells is easy to spot during pencil marking.

• Scan each box for digits that appear as candidates in only two cells. Check if those two cells share a row or column.
• After elimination, re-check the affected row/column, as new Naked Pairs or singles may appear.

Pointing Triples: The Extended Lock

A Pointing Triple follows the exact same logic but with three cells. If a candidate digit appears in exactly three cells within a box, and all three are aligned in the same row or column, that digit is locked to that alignment. You then eliminate it from the rest of that row or column outside the box. A concrete example: imagine in a box, the digit 3 is a candidate only in three cells that form a vertical stack in the box's left column. This means the 3 for this box must be placed in one of those three cells. Therefore, the digit 3 can be safely eliminated from every other cell in that left column in the two boxes above and below. While less common than pairs, triples are a natural extension and are identified using the same scanning method.

Locked Candidates (Box/Line Reduction): The Reverse View

This technique, often called Box-Line Reduction, is the umbrella term for the family. In its most common form (the 'claiming' direction), you look from the perspective of a row or column instead of a box. If all instances of a candidate digit within a row or column are confined to a single 3x3 box, then that digit must be placed within that box's intersection with the line. You can therefore eliminate that candidate from all other cells within that box. For instance, if in a row, the candidate 5 appears only in three cells that all lie within the same box, then the 5 for that row must be inside that box. You can remove 5 from all other cells in that box. This is the logical mirror of a Pointing Pair/Triple; it's the same confinement principle applied from the opposite angle.

Practice Walkthrough: Spotting the Family

Let's walk through a practical scenario. Suppose you are pencil-marking a puzzle and in a center box, you note that candidate 8 appears only in two cells, both in the box's middle row. Immediately, you have a Pointing Pairs for digit 8. Eliminate 8 from the rest of that middle row in the left and right neighbor boxes. Later, while scanning rows, you see that in a different row, candidate 2 appears only in three cells, all of which are in the same bottom-center box. This is a Locked Candidates (Claiming) pattern. Eliminate candidate 2 from all other cells in that bottom-center box. Both moves use the same rule: confinement leads to external elimination. Practicing this dual perspective—scanning boxes for pointers and lines for claimers—will make these techniques second nature.