Remote Pairs

Level 9 · Purple 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

Starting position

Look for Remote Pairs.

1

Find a bivalue chain on 3 and 5

Find a chain of bivalue cells all containing the same pair { 3, 5 }.

2

Chain from r3c4 to r8c5

This chain has 5 cells from r3c4 to r8c5, where each cell sees the next.

3

Odd-distance cells take opposite values

Cells at odd distance in the chain have opposite values; one is 3 and the other is 5.

4

Cells that see both chain ends

Any highlighted cell that sees both ends of an odd-distance pair cannot keep 3 or 5.

5

Remove 3 and 5 from common peers

Remove 3 and 5 from cells seeing both ends of the chain: r7c6.

6

Result

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.