X-Chain

Level 9 · Purple Belt

Strategy:

Single-Digit Chains

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

Starting position

Look for X-Chain.

1

X-Chain of 4 cells on digit 2

Look at digit 2. There is an X-Chain of 4 cells connecting r1c5 to r2c7.

2

Strong and weak links alternate

The chain alternates between strong links, where one endpoint must be true, and weak links, where both cannot be true.

3

One endpoint must be 2

The chain starts and ends on strong links, so either r1c5 or r2c7 must be 2.

4

Cells seeing both endpoints lose 2

Any highlighted cell that sees both endpoints cannot keep 2, because one endpoint must contain it.

5

Remove 2 from r2c6

Remove 2 from cells that see both endpoints: r2c6.

6

Result

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.