X-Chain

Level 9 · Purple Belt

Strategy:

Single-Digit Chains

Requires:

Simple Coloring

Overview

X-Chain is a single-digit chain technique that connects cells through alternating strong and weak links. When both endpoints are on strong links, the digit can be eliminated from cells that see both endpoints.

How It Works

  1. Choose a digit and find strong links (conjugate pairs in a house).
  2. Build a chain alternating between strong links and weak links (cells sharing a house).
  3. The chain must start and end with strong links.
  4. Eliminate the digit from cells that see both chain endpoints.

Example

Look for X-Chain.

1

X-Chain

Look at digit 1. There is an X-Chain of 4 cells connecting r6c5 to r9c5.

2

X-Chain

The chain alternates between strong links (conjugate pairs) and weak links (shared house).

3

X-Chain

The chain starts and ends on strong links, so either r6c5 or r9c5 must be 1.

4

X-Chain

Any highlighted cell that sees both endpoints cannot keep 1.

5

X-Chain

Remove 1 from cells that see both endpoints: r4c5.

6

Result after applying the technique.

Tips & Patterns

  • X-Chains generalize Skyscrapers and Two-String Kites to longer chains.
  • Odd-length chains (3, 5, 7 cells) are the ones that produce eliminations.
  • Either endpoint must contain the digit, so any cell seeing both can't have it.