Pointing in Sudoku: using boxes to eliminate candidates

Pointing is an intermediate Sudoku technique based on the relationship between boxes, rows and columns.

The idea is simple: if, inside a 3×3 box, all possible positions of a certain number are on the same row or the same column, then that number must be placed in that box along that line. As a result, it can be eliminated from the other cells of the same row or column outside the box.

This technique does not necessarily place a number immediately, but it allows you to eliminate candidates and simplify the grid.

In this guide, we will see what Pointing is, how to recognize it and how to apply it without confusing it with Claiming.

The Pointing technique occurs when, inside a box, a number can appear only in cells that belong to the same row or the same column.

This means that, in that box, the number must necessarily be on that row or column. Even if you do not yet know which cell inside the box it will occupy, you know that outside the box, along the same line, that number can no longer appear.

For example, in a box, number 4 can go only in two cells, both on the same row. Then the 4 of that box must be in that row. As a result, in the other cells of the same row but outside the box, candidate 4 can be eliminated.

The most common case is the relationship between a box and a row.

Imagine a 3×3 box. Number 7 is a candidate only in two cells of the box, and both cells are on the same row.

Since in classic Sudoku every box must contain number 7 exactly once, the 7 must be in one of those two cells. This means that, on the same row, 7 cannot be placed outside that box.

You can therefore eliminate candidate 7 from the other cells of the row outside the box.

This reasoning is very useful because it connects local information, inside the box, to a wider elimination along the row.

Pointing can also work on columns.

In this case, inside a box, all candidates for a certain number are in the same column. This means that the number for that box must be in that column.

As a result, you can eliminate that candidate from the other cells of the column outside the box.

For example, if in a box number 2 can go only in two cells of the same column, the 2 of that box will certainly be in one of those cells. The other cells of the column, outside the box, can no longer contain 2.

The principle is identical to the row case: only the direction of the alignment changes.

The keyword for Pointing is “alignment”.

It is not enough for a number to appear two or three times as a candidate in a box. To apply the technique, all of its possible positions in the box must be on the same row or the same column.

If the candidates are distributed in non-aligned positions, Pointing does not apply.

For example, if number 5 appears in three cells of the same box but one is top-left, one is in the center and one is bottom-right, you do not have a useful alignment. If instead all three are in the same row of the box, then you can use Pointing.

With Pointing, eliminations happen outside the box.

If the number is aligned on a row inside the box, you eliminate that candidate from the other cells of the same row outside the box.

If the number is aligned on a column inside the box, you eliminate that candidate from the other cells of the same column outside the box.

You should not eliminate candidates inside the box, because that is exactly where the number still has to be placed. The useful information is that the number of the box will be on that line, so it cannot appear elsewhere on the same line.

Imagine the top-left box of the grid. In this box, number 9 is missing.

After checking the candidates, you discover that 9 can go only in two cells of the box. Both are in the first row.

This means that the 9 of the top-left box will certainly be in the first row. As a result, in the first row, outside that box, no other cell can contain candidate 9.

You can therefore eliminate 9 from the cells of the first row that are in the other boxes.

If one of those cells is left with only one candidate, you have created a new immediate move.

Pointing and Claiming are similar techniques because both work with the relationship between boxes and lines. The difference is the starting point.

In Pointing, you start from the box. You notice that the candidates of a number inside the box are all on the same row or column. Then you eliminate that number outside the box along that line.

In Claiming, instead, you start from a row or a column. You notice that, in that line, a number can go only inside a certain box. Then you eliminate that number from the other cells of the box.

To remember it: Pointing goes from the box toward the line. Claiming goes from the line toward the box.

Pointing is an intermediate technique that uses the alignment of candidates inside a box.

If in a box all candidates for a number are on the same row or column, that number can be eliminated from the other cells of the same row or column outside the box.

It is a very useful technique in medium Sudoku because it lets you eliminate candidates and unlock new moves without guessing.