Remote Pairs in Sudoku: The Complete Guide

What is a Remote Pair?

A remote pair is an advanced Sudoku technique that introduces the concept of chaining—tracking relationships between distant cells. Unlike naked pairs which work within a single unit, remote pairs connect two cells with identical candidates through a chain of intermediate cells.

The key insight: If two cells with candidates {X, Y} are connected through a chain of cells that also contain only {X, Y}, the chain endpoints must contain opposite values. One has X, the other has Y (or vice versa).

Example:

Cell A has {3, 7}. Cell E has {3, 7}. They're connected by a chain: A→B→C→D→E, where B, C, and D also have {3, 7}. If the chain has an even number of links, both endpoints will have opposite values. Any cell seeing both A and E cannot contain 3 or 7.

Why Remote Pairs Matter

  • They introduce chaining logic—a fundamental concept for advanced solving.
  • They find eliminations across distant parts of the grid.
  • They work when local techniques (pairs, triples, wings) fail.
  • They're a gateway to understanding forcing chains and other Master-level techniques.
  • They demonstrate that Sudoku relationships extend beyond adjacent cells.

How to Spot a Remote Pair

  1. Identify bi-value cells.
    Look for all cells with exactly two candidates. Mark them clearly.
  2. Find matching pairs.
    Look for two cells with the same pair of candidates (e.g., both have {2, 5}).
  3. Check if they see each other.
    If they're in the same unit, they're just a naked pair, not a remote pair.
  4. Trace a chain between them.
    Find a path of cells connecting them where each cell contains only those two candidates.
  5. Verify chain length.
    Count the connections. For simple remote pairs, the chain should have an even number of cells total.
  6. Find elimination targets.
    Look for cells that see both chain endpoints.
  7. Eliminate.
    Remove both candidates from any cell that sees both endpoints.

Remote Pairs vs Naked Pairs

These techniques share similar logic but different scopes:

  • Naked Pair:
    • Two cells in the same unit (row, column, or box)
    • Both have the same two candidates
    • Eliminate from other cells in that unit
    • Local effect
  • Remote Pair:
    • Two cells connected by a chain, not in the same unit
    • Both have the same two candidates
    • Eliminate from cells seeing both chain endpoints
    • Long-distance effect

Think of remote pairs as "naked pairs at a distance."

Step-by-Step Example

Let's identify a remote pair chain:

Bi-value cells with {4, 8}:

  • Cell A: Row 1, Col 2 = {4, 8}
  • Cell B: Row 1, Col 7 = {4, 8} (sees A via Row 1)
  • Cell C: Row 3, Col 7 = {4, 8} (sees B via Column 7)
  • Cell D: Row 3, Col 4 = {4, 8} (sees C via Row 3)
  • Cell E: Row 6, Col 4 = {4, 8} (sees D via Column 4)

Chain tracing:

A → B → C → D → E

Logic:

  • If A = 4, then B = 8 (they see each other)
  • If B = 8, then C = 4 (they see each other)
  • If C = 4, then D = 8 (they see each other)
  • If D = 8, then E = 4 (they see each other)
  • So if A = 4, then E = 4 (both contain 4)
  • Alternatively, if A = 8, then E = 8
  • Conclusion: A and E always contain the same value!

Wait, that's wrong! Let me reconsider...

Corrected logic:

Actually, for a proper remote pair, we need an even-length chain where endpoints have opposite values. Let me redo this:

  • If A = 4, then B = 8
  • If B = 8, then C = 4
  • If C = 4, then D = 8

So A and D form a remote pair (chain length of 4 cells: A→B→C→D). If A = 4, then D = 8. If A = 8, then D = 4. They have opposite values.

Elimination: Any cell that sees both A (Row 1, Col 2) and D (Row 3, Col 4) cannot contain 4 or 8. For example, if a cell is in Row 1 and Column 4, or if there's a box relationship.

Understanding Chain Parity

The chain length determines the relationship:

  • Even number of cells (2, 4, 6...): Endpoints have opposite values → Can eliminate from cells seeing both
  • Odd number of cells (3, 5, 7...): Endpoints have the same value → Different elimination pattern

For classic remote pairs, focus on even-length chains where endpoints are opposites.

Visual Example

  • Setup: You have many cells with {2, 9} scattered across the grid.
  • Chain identification: You trace a path: Cell 1 → Cell 2 → Cell 3 → Cell 4, all with {2, 9}.
  • Each link: Adjacent cells in the chain see each other (same row, column, or box).
  • Endpoints: Cell 1 and Cell 4 don't see each other directly but are connected through the chain.
  • Parity check: 4 cells = even length → Cell 1 and Cell 4 have opposite values.
  • Elimination: Find a cell that sees both Cell 1 and Cell 4. Remove 2 and 9 from it.

Strategies for Spotting Remote Pairs Quickly

  1. Map all bi-value cells
    Create a visual map or list of all cells with exactly two candidates.
  2. Group by candidate pair
    Organize them: all {1,3} cells together, all {2,5} cells together, etc.
  3. Look for strong links
    Two cells with the same pair that see each other form a "strong link." Chain these together.
  4. Trace chains systematically
    Start from one cell and follow connections. Keep track of chain length.
  5. Focus on common pairs
    If many cells share {4,7}, there's a higher chance of finding chains.

Common Pitfalls

  • Wrong chain length: Make sure you're counting correctly. The number of cells, not the number of links.
  • Broken chains: Every adjacent pair in the chain must see each other (same row, column, or box).
  • Same vs opposite values: Even chains → opposite values. Odd chains → same values.
  • Missing the elimination cell: The target must see BOTH endpoints, not just one.
  • Confusing with naked pairs: If two cells with the same candidates see each other directly, use naked pair logic instead.

Practice: Find the Remote Pair

Given these cells all with {3, 6}:

  • Cell A: Row 2, Col 3
  • Cell B: Row 2, Col 8 (sees A via Row 2)
  • Cell C: Row 5, Col 8 (sees B via Column 8)
  • Cell D: Row 5, Col 1 (sees C via Row 5)

Question: Is there a remote pair? What can be eliminated?

Solution:

  • Chain: A → B → C → D (4 cells, even length)
  • Endpoints: A (Row 2, Col 3) and D (Row 5, Col 1)
  • They have opposite values (one is 3, the other is 6)
  • Elimination target: Find cells that see both A and D
  • For example, if there's a cell in Row 2 that's also in a box with Row 5, Col 1, or other complex visibility
  • Action: Eliminate 3 and 6 from any cell seeing both endpoints

Why Remote Pairs Set the Stage

Remote pairs are your introduction to chaining techniques:

  • They teach you to track relationships across multiple cells
  • They introduce the concept of "strong links" (cells that see each other)
  • They prepare you for forcing chains, alternating inference chains (AIC), and nice loops
  • They demonstrate that Sudoku solving can involve graph-like reasoning
  • They bridge the gap between local patterns and Master-level techniques

Quick Recap

Technique Scope Connection Elimination Difficulty
Naked Pair Local (one unit) Direct Same unit Intermediate
Remote Pair Global (chain) Via chain Sees both ends Advanced

Final Thought

Remote pairs open the door to chaining logic in Sudoku. Found two matching bi-value cells connected through a chain? You've discovered a remote pair—now find what sees both endpoints!

Frequently Asked Questions

What is a Remote Pair in Sudoku?

A remote pair is an advanced Sudoku technique where two cells with identical candidates {X,Y} are connected through a chain of intermediate cells that also contain only those same two candidates. If any cell can see both endpoints of the chain, you can eliminate X and Y from that cell, since the endpoints must contain opposite values.

How do I spot a Remote Pair?

To spot remote pairs: 1) Look for cells with exactly two candidates (bi-value cells), 2) Find two cells with the same pair of candidates that don't see each other directly, 3) Trace a chain of cells between them where each cell contains only those two candidates, 4) Count the chain length (should be even), 5) Eliminate from cells that see both chain endpoints.

What's the difference between Remote Pairs and Naked Pairs?

Naked pairs are two cells in the same unit (row, column, or box) with identical candidates, eliminating from that unit. Remote pairs are two cells with identical candidates connected through a chain, not necessarily in the same unit. Remote pairs eliminate from cells that see both chain endpoints. Naked pairs are local; remote pairs work at a distance.

Why are Remote Pairs important?

Remote pairs are important because they introduce chaining logic to Sudoku solving, they find eliminations across distant parts of the grid, they work when local techniques fail, and they're a gateway to understanding forcing chains and other advanced chaining techniques.

When should I look for Remote Pairs?

Look for remote pairs after exhausting local techniques like naked and hidden subsets. They're most useful in advanced puzzles with many bi-value cells. Start by identifying all cells with exactly two candidates, then look for chains connecting cells with identical pairs.

Ready to advance? Check out our complete strategy guide for more techniques.

Related Strategies

Once you've mastered remote pairs, these techniques build naturally:

  • Naked Pairs - The local version of this technique
  • XY-Wing - Another technique using cell relationships
  • X-Wing - Pattern recognition across rows/columns
  • Forcing Chains - Advanced chaining technique (coming soon)
  • Nice Loops - Closed chain patterns (coming soon)

Practice Remote Pairs

Next up: Try Jellyfish to continue with Expert techniques (coming soon).

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