When a line has already spent a box's digit

The short version

Claiming is pointing read backwards. In a row or column, all remaining homes for a digit fall inside one box. That line must place the digit somewhere in that box, so the box's copy is already supplied — and the box cannot take the digit anywhere outside the line.

Same fact, opposite direction. Pointing shoots out of a box; claiming shoots into one.

The shape

Pick a row. Pick a digit. Mark where the digit can still go in that row.

If every mark falls inside the same box, the box is claimed. The row will place its digit there, which means that box already has its copy, which means the rest of the box — the cells outside the row — cannot hold the digit.

Columns work identically: every home for the digit in that column inside one box, and the box's other cells lose it.

Why it works

Each box contains exactly one of each digit, and each row contains exactly one of each digit. Both constraints are absolute.

If a row's only homes for a digit lie in box B, then the digit lands in box B. Box B now has its digit. Since a box can hold only one, the other cells of box B are out.

Notice that the argument never establishes which cell inside the row takes the digit — only that whichever it is, it is inside the box. That is enough, because the conclusion is about the box's remaining cells, not about the row.

A real board

The claim: in row 3, 7 has exactly two homes, R3C1 and R3C3, and both are inside the top-left box.

• Row 3's empty cells that can still take a 7 are those two.
• Both sit in the top-left box, so row 3 will place its 7 inside that box.
• The box therefore already has its 7, and R1C1 cannot be 7. It gets deleted.

This is exactly the pointing pattern from the other end: the same three cells, the same confinement, the opposite conclusion. In one reading the box constrains the row; in the other the row constrains the box.

How to scan for one

Claiming is found line by line, which makes it slower than pointing and easier to skip. Do it anyway — it catches eliminations pointing cannot see.

1. Take a row, take a digit. Rows first, then columns. Same nine-digit sweep.
2. Ask where the digit can go in this line. Count the legal cells. If there are more than three, claiming is unlikely to help and you can move on.
3. Check the box. If all of those cells sit in one box, delete the digit from the box's other cells.
4. Repeat for columns. A digit can be claimed in a row and still be free in a column, and vice versa. The two passes are not redundant.
5. Watch the interaction. A claiming elimination inside a box often creates a new pointing pair in a different digit, which creates another elimination. This ping-pong is how medium puzzles collapse.

The productive case is a line with two or three homes clustered at one end. If a row's candidate positions for a digit are spread across two boxes, nothing follows.

Claiming vs pointing

The two halves of box-line reduction, and the distinction that matters:

Both patterns can exist for the same digit at the same time, in different boxes. Neither is more powerful; they simply see different consequences of the same constraint.

The classic error is applying pointing logic to a claiming shape. You spot that a row's homes are all in one box, and then delete from the row — which is not justified, and will eventually contradict the board.

Pointing, the outward direction.

The traps

Homes spread across a box boundary. Three cells in a row, two in one box and one in the next. No claim. The condition is all homes inside one box, and "almost all" is worth nothing.

Forgetting the column pass. Claiming is most often taught as a row technique. Columns claim just as often, and solvers who only scan rows leave half the eliminations on the table.

Treating it as a placement. Like pointing, claiming removes candidates. It does not tell you where the digit goes in the line, and it never places a number directly.

Where to use it

Claiming and pointing together are the highest value-per-second moves in intermediate sudoku. They need no candidate grid — only a count of where one digit can go in one line — and they resolve puzzles that look genuinely stuck.

If both directions come up empty across all nine digits, that is a reliable signal that the board has moved past cheap techniques and it is time to write candidates down. The next step from there is usually a naked pair or a hidden pair, both of which need the grid.