Remote Pairs in Sudoku: how chaining bivalue cells eliminates candidates

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Published April 17, 2026 · 10 min read

You already know that a Naked Pair — two cells in the same house with identical bivalue candidates — lets you eliminate those candidates from the rest of the house. But what if the two bivalue cells are in different houses, connected only through a chain of other bivalue cells? That is where Remote Pairs comes in.

Remote Pairs finds a chain of cells that all contain exactly the same two candidates. Each consecutive pair in the chain shares a row, column, or box. Because the two digits must alternate along the chain, any cell that can “see” two chain cells of opposite parity (colour) cannot hold either digit — both are already accounted for.

In this guide we walk through the logic, solve a concrete example that produces 5 candidate eliminations and 3 naked singles, and show you how to spot Remote Pairs in your own puzzles.

✅ What is Remote Pairs?

Remote Pairs is an intermediate-to-advanced Sudoku technique that exploits a chain of bivalue cells — cells that each contain exactly the same two candidates. When these cells form a chain through shared houses (rows, columns, or boxes), the two digits must alternate along the chain, creating a “virtual Naked Pair” effect that extends across multiple houses.

🧠 How Remote Pairs works

Why the alternation works

Because C₁ holds either a or b, and C₁ sees C₂ (same house), C₂ must hold the opposite. C₃ sees C₂, so it flips back again, and so on. This creates two groups:

• Colour A (odd-numbered cells): C₁, C₃, C₅, … — all hold the same digit.
• Colour B (even-numbered cells): C₂, C₄, C₆, … — all hold the other digit.

🔎 Step-by-step example

Let’s apply Remote Pairs to a real puzzle position, producing 5 eliminations in 4 cells.

Step 1 — Spot the bivalue cells

Scan the grid for cells containing exactly {4, 9}. We find four of them that can be linked into a chain:

• R2C1 = {4, 9}
• R2C6 = {4, 9}
• R7C6 = {4, 9}
• R7C9 = {4, 9}

Step 2 — Build the chain

1. R2C1 → R2C6 — connected through Row 2.
2. R2C6 → R7C6 — connected through Column 6.
3. R7C6 → R7C9 — connected through Row 7.

Chain: R2C1 – R2C6 – R7C6 – R7C9 (4 cells, 3 links).

Step 3 — Colour the chain

• Colour A (blue): R2C1, R7C6
• Colour B (green): R2C6, R7C9

R2C1 and R7C6 must hold the same digit (either both 4 or both 9). R2C6 and R7C9 hold the other digit.

Step 4 — Find elimination targets

Look for non-chain cells that see one A cell and one B cell and contain 4 or 9:

Row 2 (sees R2C1 ‘A’ and R2C6 ‘B’)

• R2C3 = {1, 4, 9} → eliminate 4, 9 → naked single {1}.

Column 6 (sees R2C6 ‘B’ and R7C6 ‘A’)

• R5C6 = {2, 4, 9} → eliminate 4, 9 → naked single {2}.

Row 7 (sees R7C6 ‘A’ and R7C9 ‘B’)

• R7C7 = {1, 4} → eliminate 4 → naked single {1}.
• R7C8 = {2, 7, 9} → eliminate 9 → {2, 7}.

5 candidate eliminations, 3 naked singles from one Remote Pair chain!

Step 5 — Result

After removing 5 candidates, three cells resolve: R2C3 = 1, R5C6 = 2, and R7C7 = 1.

🔄 Remote Pairs vs. other techniques

Remote Pairs can be viewed as a special case of Simple Colouring where the chain uses two digits at once through bivalue cells rather than one digit through conjugate pairs. It is also closely related to XY-Wing — an XY-Wing is essentially a 3-cell chain where the endpoints don’t share both candidates.

🕵️ How to spot Remote Pairs

⚠️ Common mistakes to avoid

1. Cells don’t all share the same two candidates

Every cell in the chain must contain exactly {a, b} — no extra candidates. A cell with {a, b, c} breaks the chain.

2. Chain links don’t share a house

Each consecutive pair must share a row, column, or box. A chain cell that connects only diagonally is not a valid link.

3. Eliminating from the wrong cells

Only cells that see both an A-coloured cell and a B-coloured cell are elimination targets. A cell seeing two cells of the same colour learns nothing.

4. Chain too short

You need at least 4 cells. Two cells in the same house is just a regular Naked Pair. Three cells don’t produce cross-house eliminations in the basic Remote Pair pattern.

5. Not checking all affected houses

Eliminations can occur in every house along the chain. Check rows, columns, and boxes between opposite-coloured chain cells — don’t stop after the first elimination.

📅 When to look for Remote Pairs

1. Basic: Naked Singles, Hidden Singles.
2. Intermediate: Naked Pairs, Hidden Pairs, Pointing Pairs, Remote Pairs.
3. Advanced: X-Wing, Skyscraper, XY-Wing.
4. Expert: Simple Colouring, 3D Medusa, Sue de Coq.

Remote Pairs sits at the border of intermediate and advanced. When you see multiple bivalue cells with the same candidate pair, check for a chain before moving to more complex techniques.

🚀 Beyond Remote Pairs

If Remote Pairs clicks for you, try Simple Colouring next — it extends the same alternating-colour logic to conjugate pairs of a single digit, and 3D Medusa takes it further by colouring across multiple digits.

🎯 Practice Remote Pairs