Pointing Pairs
Pointing pairs are the first sudoku technique that makes two units talk to each other, and they clear candidates that no amount of single-unit scanning would ever touch. The idea is simple: if a digit is trapped in one line inside a box, it is banned from the rest of that line.
What the pattern is
Take a box and one digit still missing from it. Look at every cell of the box where that digit is still a candidate. If all of them lie in the same row, then whichever cell finally takes the digit, it lands in that row. The box must contain the digit somewhere, so the row's share of the digit is used up inside the box, and the digit can be deleted from that row's cells in the other two boxes.
Two such cells make a pointing pair, three make a pointing triple, and the logic is identical. The same applies to columns.
| Pointing pair | Box line reduction | |
|---|---|---|
| Digit confined to | one line inside a box | one box inside a line |
| You erase from | the rest of that row or column | the rest of that box |
| Direction | the box points outwards along the line | the line reduces the box |
| Cells cleared | up to six, in two other boxes | up to six, in the same box |
Both are called locked candidates, and they are worth learning as a pair because you scan for them in opposite directions.
When to look for it
- Once singles and pairs stop producing anything.
- On digits that appear only two or three times inside a box. Those are the ones that can be aligned.
- In boxes with three or four empty cells, where alignment happens naturally.
- Right after a placement in a box, which often squeezes a digit down onto one line.
How to apply it, step by step
- Pick a box and list the digits it still needs.
- For one digit, mark every cell of the box where it remains legal.
- If those cells all share one row, the digit is locked into that row inside the box.
- Erase the digit from the same row in the other two boxes.
- Repeat the check for columns, then for the next digit.
- Work through all nine boxes. Each successful elimination can create a hidden single somewhere on the cleared line.
A worked example
Watch the 1s in box 6.
Box 6 needs a 1, and the only cells left for it are D7 and D8, both in row D. So the 1 of row D lives inside box 6, and D4 and D5 in box 5 lose their 1.
The two cells do not have to be next to each other, and they may hold plenty of other candidates. All that matters is that no third cell of the box can take a 1.
Common mistakes
- Erasing inside the box. The pattern says nothing about the other cells of the box. Only the line outside it loses the candidate.
- Missing a third cell. If the digit is also legal somewhere else in the box, off that row, there is no pointing pair. Check the whole box, not just the row.
- Forgetting columns. Half of all pointing pairs are vertical, and solvers who only scan rows find half as many.
- Reversing the direction. Confining a digit to one box inside a row is a different pattern with a different conclusion.
Where you meet it
Pointing pairs start to matter around medium classic Sudoku and are essential from Hard upwards, in classic and Killer alike. They are also the mental habit behind most advanced patterns: find where a digit cannot go, and the grid tells you the rest.