Pointing pairs and claiming in sudoku
The two box–line interactions: when a box pins a digit to one line, and when a line pins a digit to one box. Cheap, constant, and the reason most Medium puzzles fall.
Pointing and claiming are the two techniques that pay for themselves more than any others. They cost almost nothing to check, they turn up constantly, and between them they are what carries an ordinary puzzle from the scanning stage into the pencil-mark stage without any real work.
They are also the two people most often confuse, because they are built from the same observation looked at from opposite ends. Both are about a box and a line — a row or column — overlapping in three cells. The only question is which of the two units does the confining.
The overlap that both techniques live in
Every box shares exactly three cells with each of three rows, and exactly three cells with each of three columns. Take the top-left box. Its top row of three cells is also the leftmost third of row 1. Those three cells belong to two units at once, and everything below follows from that double membership.
Whenever a digit is forced into that shared strip, it has been forced into both units simultaneously. That is the whole engine. The two techniques differ only in which unit supplied the force.
Pointing: the box pins the digit to a line
Look inside a single box and pick a digit — say 4. Ask where a 4 could still go in this box. If every remaining possibility sits in the same row, then wherever the 4 lands, it lands in that row.
The box has to contain a 4 somewhere. All the candidate cells are in row 5, say. So row 5 gets its 4 from inside this box. That means no cell in row 5 outside this box can be a 4, and you cross it out of all six of them.
The name comes from the picture: the two or three candidate cells inside the box point along the line, and the elimination happens outside the box, further down that line.
The same works with columns. If the box’s remaining 4s all sit in one column, erase 4 from the rest of that column outside the box.
Two candidates or three
Most of the time the pattern is a pointing pair — two candidate cells. Three cells in the same line works identically and is called a pointing triple. Nothing about the argument changes; the digit is still confined to the line. People miss triples because they are looking for a pair by name.
Claiming: the line pins the digit to a box
Now start from a line instead. Look along row 5 and ask where a 4 can go. If every remaining possibility in the entire row falls inside one box, then the row will get its 4 from that box.
The row must contain a 4. All its candidate cells are in the middle-left box. So that box gets its 4 from those cells, and no other cell in that box can be a 4 — including the six cells that are in the box but not in row 5. Cross the 4 out of those six.
That is claiming, sometimes called box-line reduction. The row has claimed the digit on behalf of the box.
Telling them apart when you are actually playing
One sentence covers it. Ask which unit you were looking at when you noticed the digit had nowhere else to go.
- You were scanning a box and saw the digit confined to one line → pointing → erase along the rest of that line, outside the box.
- You were scanning a line and saw the digit confined to one box → claiming → erase in the rest of that box, off that line.
The elimination always happens in the unit you were not looking at. If you find yourself erasing candidates inside the unit you were just scanning, you have mixed them up.
How to find them without a full candidate grid
This is the appealing part: both techniques work at the scanning stage, before you have written a single pencil mark. A digit is confined by the digits already on the board — you can see it directly.
- Pick a digit with plenty of copies already placed, five or more. Crowded digits are the ones that get confined.
- Take a band of three boxes stacked horizontally. Find a box in that band where the digit is not yet placed.
- Cross off the rows of that box that are already blocked, either by a copy of the digit in that row elsewhere, or by cells already filled.
- If exactly one row of the box survives, that is a pointing pattern. Erase the digit from the rest of that row.
- Repeat vertically, for the three boxes stacked in a column.
- For claiming, do the mirror: run along a row, mark the cells where the digit could still go, and check whether they all fall inside one box.
A single band-and-digit pass takes seconds, and it very often knocks out the one candidate that was propping up a stalled position.
What they are worth
These are the techniques that define the middle of the difficulty range. In Sudoku - Calm Number Puzzle, pointing and claiming both sit in the Medium band, alongside naked pairs — a puzzle whose hardest required step is one of these is graded Medium and nothing tougher. That is a fair reflection of how they feel: not automatic like a single, but not a hunt either.
They also explain why so many players find an apparently hard grid collapses once they finally write out candidates. The candidates make the confinement visible, and confinement is the most common thing going on in a stuck grid.
Frequently asked questions
Is box-line reduction the same as claiming?
Yes. Box-line reduction, claiming and line-box interaction are three names for the same technique: a digit whose only places in a row or column all lie inside one box, which lets you erase it from the rest of that box. Pointing is the reverse direction.
Can I use pointing pairs before writing pencil marks?
Yes, and that is where they are most valuable. You only need to know where a digit can still go inside one box, which the already-placed digits tell you directly. Many players never write candidates at all until pointing and claiming stop producing anything.
Does a pointing pair place a digit?
Not by itself. It removes the digit from cells further along the line. Very often one of those removals leaves a cell or a unit with only one possibility left, and that is the placement — but the technique itself is purely an elimination.
What if the digit is confined to a line in the box and also to that box in the line?
Then both eliminations are valid and you should make both. It happens fairly often. Applying only the one you spotted first leaves free progress on the table.
Try it on a real puzzle
Sudoku - Calm Number Puzzle grades every puzzle by the hardest technique it actually needs, verifies a single solution before you ever see the grid, and its hints name the technique instead of just filling in a digit. Free, offline, no ads and no account.