Pointing Pairs in Sudoku
Sometimes a 3x3 box doesn't solve a digit on its own — but it points to where that digit can't live in the surrounding row or column. That single shove often unlocks the rest of the grid.
What is a Pointing Pair?
A Pointing Pair (sometimes called a Pointing Pair/Triple or box-line reduction in one direction) happens when a digit, inside a single 3x3 box, can only appear in cells that all share the same row or the same column. The digit is "pointing" out of the box along that line.
When that happens, the digit must end up in one of those box cells — which means it cannot appear anywhere else in the same row or column outside the box. You can erase that digit from every cell of the line that lies outside the box.
Why it works (the logic)
Every 3x3 box must contain digit X exactly once. Suppose inside the top-left box, digit X can only be a candidate in two cells, both sitting in row 2. Whichever of those two cells eventually holds X, it will be in row 2.
That gives you a guarantee: digit X is going to land in row 2 (specifically, somewhere inside the top-left box). So in row 2, the cells that lie outside the top-left box can no longer be X — that slot is already promised to one of the box cells.
The technique doesn't solve any cell directly. It simply removes candidates. But those removals often expose a Hidden Single or a Naked Single elsewhere in the row or column — and those removals are what makes the technique worth running.
Example 1: Pointing along a row
Look at the middle row band below. Digits 5 and 8 are placed in the middle-left box, and digits 1 and 9 in the middle-right box. Suppose, after pencil-marking the middle box, you find that digit 3 can only be placed in two cells — both sitting in row 4.
Action: Erase 3 from every other cell of row 4 that sits outside the center box — that is, the three cells in the middle-left box portion of row 4, and the three cells in the middle-right box portion. Six potential eliminations from one observation.
Example 2: Pointing along a column
The same logic works on columns. Suppose in the top-middle box, digit 4 can only fit in two cells, both in column 5.
Action: Erase 4 from every other cell of column 5 outside the top-middle box — six cells in the middle and bottom bands. Often this is enough to crack a Hidden Single in column 5 immediately.
How to spot Pointing Pairs
The fastest way is to scan by digit, by box:
- Pick a 3x3 box and a digit that isn't placed in it yet.
- Identify every cell in the box where that digit could go (using pencil marks or eliminations from existing digits in the surrounding rows and columns).
- If all those candidate cells share the same row, the digit is pointing along that row. If they share the same column, it's pointing along that column.
- Erase the digit from the rest of that row or column outside the box.
Once you finish a box, repeat for each remaining digit and each remaining box. With practice this becomes a fast left-to-right sweep.
Pointing Pairs vs. Box-Line Reduction (the cousin)
These are two halves of the same idea, often grouped together as locked candidates:
- Pointing Pair — the digit is locked inside a box to one line; you eliminate that digit from the line outside the box.
- Box-Line Reduction (Claiming) — the digit is locked inside a row or column to one box; you eliminate that digit from the box outside the line.
The mental gear shift is which structure (box or line) constrains which. Both deliver candidate eliminations rather than direct solutions, but those eliminations propagate quickly into Naked and Hidden Singles.
Common beginner mistakes
- Eliminating inside the box. The candidates inside the box are still valid — the digit must go in one of them. You only erase from the rest of the row or column outside the box.
- Missing pencil marks. Without accurate candidates, you can't spot which cells of the box a digit could fit in. Pencil-mark first, hunt second.
- Stopping at 2 cells. A Pointing Triple (three candidate cells, same row or column) gives the same elimination. Don't assume only pairs work.
- Forgetting to re-scan after eliminations. Each successful Pointing Pair changes the candidate landscape. A second pass often reveals new Pointing Pairs you couldn't see before.
Try it on a real puzzle (with our Hint)
SudokuHint's Hint engine actively detects Pointing Pairs and explains them with a two-level reveal. Open a Medium or Hard puzzle on SudokuHint, progress until Naked Singles and Hidden Singles stall, and tap the 💡 Hint button. When the engine identifies a Pointing Pair, you'll see exactly which box points where — and which digits to erase along the line.
Article draft v1 · pending native-speaker review