Remote Pairs

Level 7 · Green Belt

Strategy:

Remote Pairs

Requires:

Simple Coloring

Overview

Remote Pairs uses a chain of bi-value cells all containing the same two candidates. Cells at opposite ends of an even-length chain have opposite values, allowing eliminations.

How It Works

  1. Find a chain of bi-value cells all containing the same two candidates {X,Y}.
  2. Each cell in the chain must see the next cell.
  3. Cells at ends of an even-length chain have opposite values (one is X, other is Y).
  4. Eliminate both X and Y from cells that see both endpoints.

Example

Look for Remote Pairs.

1

Remote Pairs

Find a chain of bivalue cells all containing the same pair { 1, 6 }.

2

Remote Pairs

This chain has 4 cells from r4c4 to r8c5, where each cell sees the next.

3

Remote Pairs

Cells at ODD distance (0-1, 0-3, 1-2...) have OPPOSITE values - one is 1, the other is 6.

4

Remote Pairs

Any highlighted cell that sees both ends of an odd-distance pair cannot keep 1 or 6.

5

Remote Pairs

Remove 1 and 6 from cells seeing both ends of the chain: r9c5.

6

Result after applying the technique.

Tips & Patterns

  • The chain must have an even number of cells (4, 6, 8, etc.) for eliminations.
  • Cells alternate: if first is X, second is Y, third is X, etc.
  • Any cell seeing both endpoints can't be either candidate.