Pointing Pairs and Triples

A box and a row (or a box and a column) overlap in three cells. When a digit's candidates in one of them all fall inside that overlap, the other one loses that digit outside it. It comes in two directions, and both are the same idea.

• Pointing. Inside a box, a digit can only go in cells that share a row. The box's copy of that digit will be in that row, so the rest of the row can't have it. The two or three cells "point" along the row.
• Box-line reduction (also called claiming). Along a row, a digit can only go in cells that sit in one box. The row's copy of that digit will be in that box, so the rest of the box can't have it.

Both are called a pointing pair or pointing triple, depending on whether two or three cells are involved. Everything here works the same with columns in place of rows.

An example: a pair

Look at the second row. Where can its 2 go? Of the row's empty cells, only the last two, in the eighth and ninth columns, have 2 as a candidate. Both of those are in the top-right box.

So the row's 2 is in the top-right box, in the second row. That box can only have one 2, so no other cell of the box can be 2. Two cells in the third row lose it:

• the seventh-column cell goes from 1, 2 to just 1, which is now a naked single,
• the eighth-column cell goes from 1, 2, 4, 8 to 1, 4, 8.

An example: a triple

Same idea, three cells. In the top row, the only empty cell outside the top-left box can hold just 6 or 9, so the row's 2 has to be in one of its first three cells. All three are in the top-left box. The box's 2 is therefore in the top row, and every cell of the box in the second and third rows loses its 2: five eliminations from one observation.

How to look for them

• Go box by box, digit by digit. For one digit, look at where it can go inside a box. If all those cells are in one row or one column, follow that line out of the box and strike the digit.
• Then go line by line. For each row and column, check whether a digit's cells all sit inside one box. If so, clear the rest of the box.
• Look where a digit is nearly placed. A digit already on the board six or seven times has few candidates left, and they tend to line up.

Where it fits

Pointing is a Hard technique here, alongside hidden pairs and hidden triples. It works on every variant that has boxes or regions. On the irregular and triangle boards the overlap between a region and a line can be longer than three cells, and the app's hints call that case "Locked candidates"; the reasoning is the same.