Box-Line Reduction

Box-Line Reduction is the line-to-box direction of Locked Candidates. It is also widely called Claiming or Claiming Candidates.

Start with one row or column and one digit.

If every remaining position for that digit in the line lies inside the same 3×3 box, the line has proved that the box receives its copy of the digit from that intersection.

The same candidate can therefore be removed from the rest of the box.

Box-Line Reduction at a glance

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

remove X from the rest of that box outside the row.

The same rule works with a column.

Direction: line → box.

Why Claiming works

Suppose row 7 still needs digit 3.

The only legal positions for 3 in row 7 are r7c1 and r7c3, and both cells lie inside the same box.

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

Therefore that box is guaranteed to receive its 3 from row 7.

A second 3 elsewhere in the box would violate the box constraint, so candidate 3 can be removed from every other unsolved cell in the box outside row 7.

The line has claimed the box's copy of the digit.

Step-by-step row example

Verify a row-based Claiming move in this order:

1. choose one digit;
2. identify every legal position for that digit in the source row;
3. confirm that all source positions lie in one box;
4. keep the source candidates;
5. remove the digit only from the rest of that box;
6. re-scan the box and affected cells.

Claiming works from columns too

The vertical form is identical.

If every candidate 8 in column 5 lies inside the center box, column 5 must place its 8 somewhere inside that box.

Candidate 8 can therefore be removed from other cells in the box outside column 5.

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

The two names describe the same deduction from different viewpoints.

Claiming

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

Box-Line Reduction

Information from the line reduces the candidate positions available in the box.

This Guide uses Box-Line Reduction as the page title and Claiming as the shorter alternate name.

A common solver taxonomy also calls this Locked Candidates Type 2.

The source positions can occupy two or three cells

Claiming does not require exactly two source candidates.

A row-box or column-box intersection contains up to three cells. If all possible Xs in the source line lie inside that intersection, the line claims the box regardless of whether two or three source cells remain.

Again, the condition is confinement, not candidate count.

The source line must be complete

Before eliminating anything, verify that no legal X remains elsewhere in the source row or column.

If one candidate survives in a different box, the source line has not claimed a single box and the deduction fails.

This makes complete candidate information especially valuable when solving intermediate puzzles.

If you use selective pencil marks, confirm the omitted positions from the actual grid rather than treating the displayed notes as automatically complete.

Where can Claiming eliminate?

The target area is the source box outside the source line.

For row-based Claiming:

• keep all source Xs on the row;
• stay inside the claimed box;
• remove X only from other rows of that box.

For column-based Claiming, rotate the same logic.

Do not remove X from arbitrary cells elsewhere in the source row or from unrelated peers.

How to find Box-Line Reduction efficiently

Claiming is a digit-first search.

1. Choose one digit

Candidate highlighting can make the positional pattern much easier to read.

2. Inspect constrained rows

Look for a row where all remaining positions for the digit fall inside one box.

3. Inspect constrained columns

Repeat vertically.

4. Check the rest of the claimed box

The move is productive if the same candidate exists elsewhere in that box.

5. Re-scan the box

One Claiming elimination can create:

• a Naked Single;
• a Hidden Single;
• a Naked Pair;
• another Locked Candidates pattern.

Claiming vs Pointing

The source-house test is the cleanest distinction.

Pointing

You prove the restriction by inspecting the box.

box → line

Claiming

You prove the restriction by inspecting the row or column.

line → box

The highlighted cells can look almost identical. The direction of the proof is what determines the name.

Claiming vs Hidden Single

Suppose row 4 still needs digit 9.

Hidden Single

9 has exactly one legal position in the row.

→ Place 9.

Claiming

9 has multiple legal positions in the row, but all are inside one box.

→ Remove 9 from the rest of that box.

The exact cell is not solved, but the digit's box location within that row is constrained.

Claiming vs a box-based Hidden Single

It is also possible for Claiming to reduce a box until the digit has only one position left.

The Claiming step and the later Hidden Single are separate deductions:

Claiming
↓
remove candidate X from the box
↓
only one X remains in the box
↓
Hidden Single

This distinction helps you understand why candidate elimination counts as genuine progress.

Claiming can expose a subset

A single candidate removal can change the structure of several cells.

For example:

Claiming removes candidate 6
↓
two cells become {2,8} / {2,8}
↓
Naked Pair
↓
2 and 8 are removed elsewhere
↓
new placement

Common mistakes

Eliminating from the source line

That reverses the technique.

Claiming eliminates from the box outside the source row or column.

Forgetting a candidate elsewhere in the line

If X can still appear in another box on the same row or column, no single box has been claimed.

Assuming exactly two source positions are required

Two or three positions inside the intersection can support the same logic.

Deleting the source candidates

Those possibilities remain unresolved and must stay.

Using incomplete notes as proof

A missing legal candidate can create a false Claiming pattern.

Expecting an immediate placement

The direct move is normally candidate elimination.

Recognition drill

For each candidate digit, ask:

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

Then repeat for columns.

Compare that with the Pointing question:

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

The mirrored wording makes the two directions much easier to remember.

FAQ

Is Box-Line Reduction the same as Claiming?

Yes. They are common names for the same line-to-box Locked Candidates direction.

Is Claiming the same as Locked Candidates Type 2?

Yes in the common Type 1/Type 2 naming convention used by solvers such as HoDoKu.

Does Claiming work with three candidate positions?

Yes, provided every source position lies inside the same box.

Does Box-Line Reduction work with columns?

Yes. The column version is logically identical to the row version.

Is Claiming harder than Pointing?

The proof is equally simple. Some players notice Pointing faster because boxes form compact visual regions, while Claiming requires scanning a full row or column.

Can Claiming immediately solve a cell?

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

What to learn next

Once Pointing and Claiming both feel natural, move into Naked Pairs and Hidden Pairs.

Those techniques no longer reserve one digit to an intersection. They reserve multiple digits for a fixed number of cells inside one house.