Box/Line Reduction in Sudoku: Claiming Technique Explained

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Published April 12, 2026 · 10 min read

You’ve learned Pointing Pairs — scanning a box and eliminating along a row or column. But there’s a mirror technique that works in the opposite direction, and it’s just as powerful. It’s called Box/Line Reduction, sometimes known as Claiming.

Instead of starting inside a box, you scan along a row or column. If a candidate in that line is confined to a single box, the line “claims” that candidate within the box — and it can be eliminated from every other cell in the box.

In this guide we explain exactly what Box/Line Reduction is, walk through the logic, and demonstrate the technique on a real puzzle with before-and-after diagrams.

✅ What Is Box/Line Reduction in Sudoku?

Box/Line Reduction (also called Claiming) occurs when a candidate number within a row or column is restricted to cells that all fall inside the same 3×3 box. Because the candidate must appear somewhere in that row or column, and the only options are within one box, the candidate can be eliminated from every other cell in that box outside the row or column.

This is the exact inverse of Pointing Pairs. While Pointing Pairs look inside a box and eliminate along a line, Box/Line Reduction looks along a line and eliminates inside a box.

🧠 How It Works (The Logic)

The reasoning is straightforward. Consider a real grid:

• In Row 2, candidate 2 appears in only two cells: R2C7 and R2C8.
• Both cells are in Box 3 (the top-right box).

Since candidate 2 must appear somewhere in Row 2, and the only positions with candidate 2 are within Box 3, the digit 2 in Box 3 is locked to Row 2. No other cell in Box 3 outside Row 2 can contain 2.

Therefore, candidate 2 can be eliminated from every other cell in Box 3 that is not in Row 2.

🔎 Step-by-Step Example

Let’s walk through a real Box/Line Reduction. We’re looking at Row 2, Box 3 (the top-right box), and candidate 2.

Step 1: Scan the row for restricted candidates

Check Row 2 for candidate 2. It appears in only two cells:

• R2C7 — candidates {2, 7}
• R2C8 — candidates {2, 3, 7}

Both cells fall within Box 3 (rows 1–3, columns 7–9). No other cell in Row 2 contains candidate 2.

Step 2: Confirm the Box/Line Reduction

Since all occurrences of candidate 2 in Row 2 are confined to Box 3, the row claims that digit within the box. Candidate 2 is locked to Row 2 inside Box 3.

Step 3: Eliminate inside the box

Remove candidate 2 from every cell in Box 3 that is not in Row 2:

• R1C8 — {2, 3, 7} → {3, 7}
• R1C9 — {2, 5, 7} → {5, 7}
• R3C7 — {1, 2, 5, 6, 7, 8} → {1, 5, 6, 7, 8}
• R3C8 — {1, 2, 3, 6, 7, 8} → {1, 3, 6, 7, 8}
• R3C9 — {1, 2, 5, 6, 7, 8} → {1, 5, 6, 7, 8}

That’s 5 eliminations from a single Box/Line Reduction — simplifying Box 3 and potentially exposing new pairs or singles.

Step 4: Continue solving

With fewer candidates in Box 3, other techniques become applicable. Notice that R1C8 now has only {3, 7} — a bi-value cell that may participate in further pair interactions or chains.

🕵️ How to Find Box/Line Reduction

🔄 Box/Line Reduction vs Pointing Pairs

Box/Line Reduction and Pointing Pairs are two sides of the same coin. They exploit the same box-line interaction from opposite directions.

Both techniques should be checked together. Many solvers group them under the umbrella term “box-line interactions” and scan for both in a single pass.

📌 Row vs Column Claiming

Box/Line Reduction works with both rows and columns. The logic is identical — only the orientation changes.

• Row Claiming: The candidate in a row is confined to one box. Eliminate from the rest of the box outside that row. This is the type we saw in our example (Row 2, Box 3).
• Column Claiming: The candidate in a column is confined to one box. Eliminate from the rest of the box outside that column.

⚠️ Common Mistakes to Avoid

1. Eliminating outside the box

Box/Line Reduction eliminates candidates inside the box (but outside the claiming row or column). Don’t accidentally remove candidates from cells outside the box — that would be a Pointing Pair elimination instead.

2. Missing cells in other boxes

Before declaring a Box/Line Reduction, confirm that the candidate does not appear in any cell in that row or column outside the target box. If it does, the candidate is not confined to one box and the technique doesn’t apply.

3. Confusing with Pointing Pairs

With Box/Line Reduction you start from the line and eliminate inside the box. With Pointing Pairs you start from the box and eliminate along the line. Make sure you’re eliminating in the right zone.

4. Forgetting to check both rows and columns

Always check both orientations. A candidate might be restricted to one box in a row, or in a column, or both. Checking only one direction means missing half the opportunities.

📅 When to Look for Box/Line Reduction

1. Basic techniques: Naked singles, hidden singles, full house.
2. Intermediate techniques: Pointing Pairs, Box/Line Reduction, Naked Pairs, Hidden Pairs, Naked Triples.
3. Advanced techniques: X-Wing, Swordfish, XY-Wing.
4. Expert techniques: XYZ-Wing, W-Wing, Chains, ALS.

Box/Line Reduction sits alongside Pointing Pairs in the intermediate tier. They should be checked together after exhausting basic singles, often appearing in medium-difficulty puzzles and above.

🚀 Beyond Box/Line Reduction

Master Box/Line Reduction and Pointing Pairs together — they form the foundation of box-line interaction logic that underpins many advanced strategies.

🎯 Practise Box/Line Reduction

• Fill in all pencil marks: Box/Line Reduction requires complete candidate information.
• Scan row by row, column by column: For each candidate, check whether it’s restricted to one box.
• Check both directions: Test rows and columns.
• Verify with the solver: Use our Sudoku solver to confirm your findings.