Box-Line Reduction in Sudoku: Claiming Explained

Box-Line Reduction is the Claiming direction of Locked Candidates.

Start with a row or column.

If every remaining position for digit X in that line lies inside the same 3×3 box, then the line must place X inside that box.

So X can be removed from the rest of the box.

The technique is also widely called:

Claiming;
Claiming Candidates;
Locked Candidates Type 2.

Quick rule

If all candidate Xs in one row lie inside one box:

remove X from the rest of that box.

The same applies to a column.

Direction: line → box.

A simple example

Suppose row 7 still needs digit 3.

Candidate 3 appears only in:

r7c1
r7c3

Both cells lie inside the same 3×3 box.

Row 7 must eventually place its 3 in one of those two cells.

That means the box will receive its 3 from row 7.

Therefore no other cell in the box outside row 7 can contain 3.

The row has claimed the box's 3.

Step-by-step board example

The column version

Suppose column 5 has all candidate 8s inside the center box.

Column 5 must place 8 somewhere in that box.

So candidate 8 can be removed from other cells in the box outside column 5.

Why Claiming works

The line requires one copy of the digit.

If every possible location for that copy lies inside one box, then one of those intersection cells must be true.

The box may contain the digit only once.

So the rest of the box cannot contain that same digit.

Nothing about the proof requires knowing which source cell is correct.

Again, Intermediate Sudoku is using a regional certainty to make an elimination.

Why “Box-Line Reduction” and “Claiming” mean the same thing

The two names describe different views of the move.

Claiming

The source line claims the box's copy of the digit.

Box-Line Reduction

The candidate positions in the box are reduced because of information from the line.

VeyraPlay keeps Box-Line Reduction as the public title because it is common search terminology, while teaching Claiming as the shorter solving name.

How to find Claiming efficiently

Claiming is easiest with a digit filter.

1. Choose one digit

Keep your attention on a single candidate value.

2. Inspect constrained rows

Look for a row where all remaining positions for the digit sit in one box.

3. Inspect constrained columns

Repeat vertically.

4. Check the rest of the box

The pattern is only productive if the same candidate can actually be removed elsewhere in the box.

5. Re-scan the box

Claiming often simplifies a box enough to expose a Single or subset.

Claiming vs Pointing

Use the source-unit test.

Pointing

You proved the restriction by inspecting the box.

box → line

Claiming

You proved the restriction by inspecting the line.

line → box

The geometry can look almost identical after the pattern is highlighted, so identifying the source is the safest way to distinguish the names.

Claiming vs Hidden Single

Suppose row 4 needs digit 9.

Hidden Single

9 has exactly one possible cell in the row.

→ Place 9.

Claiming

9 has multiple possible cells in the row, but all are inside one box.

→ Remove 9 from the rest of that box.

The digit is not solved, but its box membership is solved.

A useful downstream pattern

Claiming can create a subset.

For example:

Claiming removes candidate 6
↓
two cells in the box become {2,8} / {2,8}
↓
Naked Pair
↓
2 and 8 removed elsewhere
↓
Hidden Single

This is a strong Learn example because it shows why “just removing one note” can be meaningful.

Common mistakes

Eliminating from the source row/column

That reverses the direction.

Claiming eliminates from the box outside the line.

Assuming exactly two source positions are required

The row/box or column/box intersection contains up to three cells. Two or three source positions can support the same logic.

Forgetting another candidate elsewhere in the source line

If X can still appear in another box on the same row/column, the line has not claimed one box.

Treating the pattern as useful when nothing can be removed

The restriction may be true but unproductive at that moment.

Using incomplete candidates

Claiming depends on knowing all remaining positions for the digit in the source line.

Recognition drill

Use the sentence:

“Does this row's X live entirely inside one box?”

Then repeat for columns.

This is the Claiming equivalent of Pointing's:

“Does this box's X live entirely on one line?”

FAQ

Is Box-Line Reduction the same as Claiming?

Yes. They are standard names for the same Locked Candidates direction.

Does Claiming work with three candidate positions?

Yes, if all source positions lie inside the same box.

Is Claiming harder than Pointing?

The proof is equally simple. Some players notice Pointing faster because boxes are visually compact.

Can Claiming immediately solve a cell?

Its direct action is an elimination, though that elimination can create a forced placement.

What to learn next

Once both intersection directions feel natural, move into Naked Pairs and Hidden Pairs.

Those techniques reserve multiple digits for multiple cells rather than one digit for an overlap.

techniques · intermediateLocked CandidatesLearn Locked Candidates in Sudoku, including Pointing and Claiming, and use box-line intersections to make logical candidate eliminations.techniques · intermediatePointing PairsLearn Pointing Pairs and Pointing Candidates: when a digit is locked to one line inside a box and can be removed elsewhere on that line.techniques · intermediateNaked PairLearn how Naked Pairs reserve two digits for two cells and eliminate those candidates from other cells in the same row, column or box.techniques · intermediateHidden PairLearn how Hidden Pairs work when two digits are restricted to the same two cells, and remove the extra candidates hiding the pair.