Pointing Pairs

Two cells in a box aiming like a weapon.

Pointing Pairs — sometimes called box-line reduction — connects a 3×3 box to the row or column that crosses it. It occurs when a digit appears as a candidate in exactly two cells within a box, and both cells sit in the same row or column. Because Sudoku requires the digit to appear somewhere in that box, and both legal cells fall on the same line, the digit is guaranteed to end up on that row or column regardless of which cell it fills. That guarantee lets you eliminate the digit as a candidate from every other cell on that same row or column outside the box — cells the box has no other claim on.

Pointing pairs don't fill in any cell by themselves; their value is purely in the eliminations they force on neighboring regions, which frequently sets up an obvious single or hidden single elsewhere on the board.

How It Works

  1. Choose a digit and find a 3×3 box where it appears as a candidate in exactly two cells.
  2. Check whether both cells share the same row (or column).
  3. If yes: the digit is locked into that row (or column) within the box. It cannot appear in any other cell in that row (or column) outside the box.
  4. Eliminate the digit from all other candidates in that row (or column).

Pointing pairs work because of a box-line relationship: whatever arrangement the box chooses, that digit stays within the locked line.

Example

Below board presents an example of a pointing pair on digit 6, confined to a single row within a box.

digit 6 confined to this row within the box
eliminated outside the box

Within this box, 6 can only go in two cells — and both happen to sit in row 2. Wherever the box eventually places its 6, it will be in row 2. That means no other cell in row 2, outside this box, can be 6. The candidate is eliminated there.

On Evil Boards

Pointing pairs do not fill any cell directly — they eliminate. The elimination may feel small — removing a candidate here, a candidate there — but each removal tightens the vise on the grid. Expect to apply many of them, carefully and in sequence, before producing a naked single or a hidden single. If the candidates don't line up on one row or column, check that box for obvious pairs or hidden pairs instead.