Pointing Pair

The principle

Every box must contain each digit from 1 to 9. Suppose that, in one box, all the cells where a digit is still possible line up on the same row. The digit must be in one of them, so it is on that row and inside the box. But a row holds that digit only once: the box has already used it up.

In the cells of that row that lie outside the box, the digit is therefore impossible, and you can remove it from their candidates. It works the same way for a column. The name “pair” comes from the most common case, two cells in line, but three cells in line work exactly the same.

How to spot it

This technique needs candidate notes. Go through the boxes one by one and, for each digit, check in which cells of the box it still appears in the notes. If all those cells lie on the same row, or the same column, you have a Pointing Pair.

Now extend that line in your mind on both sides of the box. In every empty cell of the line outside the box, erase the digit from the notes. Do not touch the cells of the box itself: they stay as they are.

After the elimination, check whether a neighboring cell is left with a single candidate, or whether a digit now has only one place in a zone. That is often how the Pointing Pair unlocks a grid without placing a digit itself.

A worked example

In one box, a digit has only two possible cells left, both on the same row of the box. The digit will therefore be in one of the two, and nowhere else on the row.

Extend the row: the two other boxes it crosses each contain three cells of that row. In those six cells the digit is forbidden, so you erase it from their notes. Sometimes one of those boxes is then left with a single possible cell for that digit: that is a Hidden Single, and the grid moves again.

Common mistakes

The most common trap is to mix up the direction of the elimination. The Pointing Pair removes the digit outside the box, along the row. Erasing the digit inside the box, or on the wrong row, ruins the whole grid. The reverse technique, the Claiming Pair, works the other way round: it starts from a row and eliminates inside a box.

Another mistake is to conclude there is an alignment when a cell of the box still carries the digit off the row. All the possible cells of the box must line up, not just two of them. Finally, incomplete or wrong notes create false alignments. Check the notes of the box before relying on what they show.

When to use it

The Pointing Pair is expected at the Hard level, where singles are no longer enough. When a puzzle stalls, it is one of the first eliminations to try, because it is quick to spot once the candidates are noted.

The technique that logically comes next in the catalog is the Claiming Pair, its mirror image: same idea, but starting from a row or a column and working toward a box.

Frequently asked questions