Pointing pairs are the workhorse of hard sudoku. They are the first technique that uses the box rule to constrain a row or column, rather than the other way around. Once you can spot them, most hard puzzles open up.
How it works
A pointing pair (or pointing triple) starts inside a single 3x3 box. Pick a digit that has not been placed yet in that box. List every cell in the box where the digit could legally go. If all those candidate cells happen to sit on the same row, the digit must land somewhere on that row inside this box.
That is the key step. The digit is restricted to the box and within the box restricted to one row. So the digit goes in that row, and it cannot go anywhere else on that row outside the box. Erase the digit from those outside cells.
The same logic works for columns. If a digit's candidate cells in a box all sit on a single column, the digit gets eliminated from the rest of that column outside the box.
When to look for it
Right after pencil marks are complete. Pointing pairs need accurate candidate sets to be visible. Scan each box one digit at a time and ask: do the remaining candidate cells for this digit share a row or a column?
Pointing pairs are the single most useful technique for hard sudoku. If you are stuck on a hard or expert puzzle, this is the first technique to try.
Step-by-step example
- Take a box that still has four or five empty cells. Pencil-mark every candidate.
- For each unplaced digit in the box, find the cells that still hold it as a candidate.
- If those cells all share one row, you have a pointing pair (two cells) or pointing triple (three).
- Erase the digit from every cell in that row outside the box.
- Re-scan affected cells for naked and hidden singles. Pointing pairs usually create at least one placement nearby.
Pointing pair vs box-line reduction
Pointing pairs and box-line reduction are reciprocal patterns. A pointing pair uses the box to constrain a row or column. A box-line reduction uses a row or column to constrain a box. Same rectangle, different direction. Learn both and you cover every box-line overlap.
Tips for spotting it
- Scan one box at a time, one digit at a time.
- If a digit has only two or three candidate cells in a box, check whether they share a row or column.
- If pointing pairs are not producing eliminations, the puzzle may need a naked pair first.
- After applying, re-mark the affected row or column. New singles often appear.
Common mistakes
- Eliminating inside the box. The eliminations apply to the rest of the row or column outside the box.
- Confusing a hidden single with a pointing pair. If the digit has only one candidate cell in the box, it is a hidden single, not a pointing pair.
- Letting one stray candidate sit on a different row inside the box. The pattern requires all box candidates for the digit to be aligned.
- Skipping this technique and reaching for X-wing first. Pointing pairs are simpler and usually clear the same cells.
Practise it
Hard sudoku is the natural playground for pointing pairs. Mark every candidate first, then walk through each box scanning one digit at a time. After a few sessions, you will spot the alignment in under a second. Combine with box-line reduction to cover both directions of the same idea.