Sudoku technique
Claiming Pair
On a row or column, a digit can only land inside one box. It “claims” that box: every other candidate for that digit inside the box gets eliminated. The mirror image of the pointing pair, same weight.
A puzzle that requires it
Level Hard — the puzzle is shown twice: right below, and again in the demo that follows.
| 2 | 6 | 3 | 9 | |||||
| 8 | 9 | 7 | 2 | 3 | ||||
| 9 | 3 | |||||||
| 3 | 2 | 6 | 5 | |||||
| 2 | 5 | 8 | 1 | |||||
| 1 | 9 | |||||||
| 7 | 9 | 1 | 2 | 4 | ||||
| 8 | 3 | 4 | 7 |
Demonstration
State of the grid right when the technique applies, after 4 earlier deductions.
Demo — watch first, you'll play right after.
- Technique's pattern
- Candidates removed
- Solved earlier
- Given (clue)
| 4 | 4 | 2 | 6 | 3 | 9 | |||
| 8 | 9 | 7 | 2 | 3 | ||||
| 4 | 9 | 3 | 2 | |||||
| 3 | 2 | 8 | 6 | 5 | ||||
| 8 | ||||||||
| 2 | 5 | 8 | 1 | |||||
| 1 | 9 | |||||||
| 7 | 9 | 1 | 2 | 4 | ||||
| 8 | 3 | 4 | 9 | 7 |
Paire revendiquée
Sur cette ligne, le 4 ne peut tomber que dans un seul carré. Il est donc exclu du reste de ce carré.
Candidates removed:
- the 4 from cell L1C1
- the 4 from cell L1C2
- the 4 from cell L3C1
The Claiming Pair, also known as Box/Line Reduction, is the mirror image of the Pointing Pair. When, on a row or column, a digit can only sit inside one box, it “claims” that box: you erase it from every other cell of the box. Like the Pointing Pair, it places no digit, it removes candidates.
The principle
Every row must contain each digit from 1 to 9. Suppose that, on one row, all the cells where a digit is still possible lie in the same box. The row’s digit must be in one of them, so it is in that box. The box receives its digit from this row.
In the other cells of the box, those on the two other rows, that digit is therefore impossible: the box holds it only once, and the row has already supplied it. You can remove it from their candidates. The reasoning is identical for a column, and for two or three cells in line.
How to spot it
You need candidate notes. Take a row, then a digit, and check in which empty cells of the row it still appears in the notes. If all those cells belong to the same box, you have a Claiming Pair. Repeat the same check for every column.
Then look at that box, and only at it. In the cells that are not on your row, erase the digit from the notes. The cells of the row stay as they are, and the rest of the row is not affected by the elimination.
Next, examine the cells you touched: one of them may be left with a single candidate, or a digit may now have only one place in the box. That is the usual follow-up to this technique.
A worked example
On one row, a digit is only possible in two cells, both in the left-hand box. The other cells of the row have already ruled it out, because of digits placed in their columns or boxes. The row’s digit is therefore in the left-hand box.
Look at that box: its other cells are on the two other rows. The digit is forbidden there, since the box already receives it from the row. Erase it from their notes. If one of those cells had only two candidates, this one included, it is now left with a single one.
Common mistakes
The most common confusion is with the Pointing Pair. Both techniques rely on the same meeting between a row and a box, but they do not work in the same direction. The Pointing Pair starts from the box: the digit is lined up there, so you erase it along the row, outside the box. The Claiming Pair starts from the row: the digit only fits in one box, so you erase it inside the box, off the row.
To avoid mistakes, first ask yourself where you spotted the constraint. In a box, you erase along the row. On a row, you erase inside the box. Another mistake is to erase the digit in the cells of the row that are inside the box. They are exactly the ones that keep it.
When to use it
The Claiming Pair is expected at the Hard level, together with the Pointing Pair, which it complements. It is slower to spot, because you must sweep row by row and column by column, but it unlocks puzzles where the Pointing Pair finds nothing.
Try it systematically after the Pointing Pair. When neither gives anything more, the Naked and Hidden Pairs take over.
- Hard sudoku
- Technique: the Pointing Pair
- Technique: the Naked Pair
- How to solve a sudoku
- Learn the techniques
Frequently asked questions
What is the difference between a Claiming Pair and a Pointing Pair?
The direction of the deduction. In a Pointing Pair, you start from a box where the digit is lined up, and erase it from the rest of the row. In a Claiming Pair, you start from a row (or column) where the digit only has room in one box, and erase it from the other cells of that box. Box to line on one side, line to box on the other.
Why do we say the digit “claims” the box?
Because the row can only place its digit in that box. It appropriates it: the box’s digit is the row’s digit, so no cell of the box on another row can carry it.
Can a Claiming Pair involve three cells?
Yes. The name comes from the most frequent case, but three cells in line inside the same box give exactly the same deduction.
Does a Claiming Pair place a digit?
No, it only removes candidates. Those eliminations then make a Naked or Hidden Single appear.
Practice
Every technique helps remove candidates ; once a cell has only one left, you place it.
Three puzzles where Claiming Pair is the key move, served right before the step, with a coach.
Puzzle 1
Hard
The technique is used once in this puzzle
Puzzle 2
Hard
The technique is used once in this puzzle
Puzzle 3
Hard
The technique is used twice in this puzzle
Puzzles change every day.