Claiming in Sudoku: using rows and columns to narrow a box

Claiming is an intermediate Sudoku technique that works with the relationship between rows, columns and boxes.

It is very similar to Pointing, but the reasoning starts from the opposite direction: not from the box toward the line, but from the line toward the box. In Claiming, you observe a row or column and notice that a certain number can be placed only inside a specific box. At that point, that number is “claimed” by that row or column inside the box, and it can be eliminated from the other cells of the box.

This technique is useful for reducing candidates and creating new solving opportunities.

In this guide, we will see what Claiming is, how to recognize it and how to distinguish it from Pointing.

Claiming occurs when, in a row or column, a number can be placed only in cells that belong to the same box.

Since that number must appear in the row or column, and its only possible positions are inside that box, the number will necessarily be in that box along that line.

As a result, the same number can be eliminated from the other cells of the box that do not belong to that row or column.

It is as if the row or column “claims” that number inside the box.

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

Imagine a row where number 6 can go only in two cells. Both of these cells are in the same 3×3 box.

Since the row must contain a 6, the 6 must be in one of those two cells. And since those two cells belong to the same box, the 6 of the box must be on that row.

As a result, in the other cells of the same box, but outside that row, candidate 6 can be eliminated.

Claiming can also start from a column.

If in a column a number can be placed only in cells that belong to the same box, then that number must be in that box along that column.

At this point, you can eliminate that candidate from the other cells of the box that are not in the same column.

For example, in a column, number 8 can go only in two cells, both in the central box. This means that the 8 of the central box will be in the considered column. The other cells of the central box can no longer contain 8.

The reasoning is identical to the row case, but applied vertically.

A row claims a number in a box when all possible positions of that number in the row are concentrated in the same box.

The row needs that number because every row must contain all numbers from 1 to 9. If the only available cells for that number are inside a single box, then that number must be at the intersection between that row and that box.

This information allows you to eliminate the candidate from the other cells of the box.

The important point is that the reasoning starts from the row, not from the box. You are asking: “Where can this number go in this row?”.

A column claims a number in a box when all possible positions of that number in the column belong to the same box.

Here too, the number must appear in the column. If it can appear only inside one specific box, then that number must be at the intersection between that column and that box.

As a result, the candidate can be eliminated from the other cells of the box, meaning the cells that do not belong to the column.

This situation can be less obvious than the row case, but it is just as useful. To recognize it, it is important to read the candidates vertically with care.

Imagine the second row of the grid. In this row, number 5 can go only in two cells. Both cells are in the top-middle box.

This means that the 5 of the second row must be in the top-middle box.

As a result, inside that box, 5 cannot appear in cells that do not belong to the second row. You can therefore eliminate candidate 5 from those cells.

After the elimination, one of the cells in the box might be left with only one candidate, or a new Hidden Single might appear.

This is the value of Claiming: it reduces possibilities and prepares new moves.

Claiming and Pointing are very close techniques, but they start from different directions.

In Pointing, you observe a box and notice that the candidates of a number are all in the same row or column. Then you eliminate the candidate outside the box, along that line.

In Claiming, you observe a row or column and notice that the candidates of a number are all inside the same box. Then you eliminate the candidate from the other cells of the box.

To remember it easily: Pointing starts from the box and points outward. Claiming starts from the line and narrows the box.

Claiming is an intermediate technique that uses rows and columns to eliminate candidates inside a box.

If in a row or column a number can go only inside a certain box, then that number must be at the intersection between that line and that box. You can therefore eliminate it from the other cells of the box.

It is a very useful technique in medium Sudoku and becomes even more effective when used together with Pointing.