XY-Chain

Level 10 · Brown Belt

Strategy:

Multi-Digit Chains

Requires:

XY-Wing

Learn after:

AIC

Overview

XY-Chain links bivalue cells (cells with exactly 2 candidates) through shared candidates. Each consecutive pair of cells shares a candidate, creating alternating strong and weak inferences that force eliminations.

How It Works

  1. Find bivalue cells that share a candidate with neighboring bivalue cells.
  2. Build a chain where consecutive cells share one candidate, alternating which is the shared digit.
  3. The first and last cells must share a common candidate on their strong links.
  4. Eliminate that common candidate from cells seeing both endpoints.

Example

Look for XY-Chain.

1

XY-Chain

Found an XY-Chain of 6 bivalue cells from r5c3 to r8c1.

2

XY-Chain

Each cell has exactly 2 candidates. Consecutive cells share one candidate, creating alternating strong and weak links.

3

XY-Chain

Both endpoints r5c3 and r8c1 have candidate 2 on a strong link. One of them must be 2.

4

XY-Chain

Any highlighted cell that sees both endpoints cannot keep 2.

5

XY-Chain

Remove 2 from cells seeing both endpoints: r5c1.

6

Result after applying the technique.

Tips & Patterns

  • XY-Chains extend XY-Wing to longer chains.
  • Every cell in the chain must have exactly 2 candidates.
  • The key insight: the common candidate at the endpoints must be in at least one endpoint, so cells seeing both can't have it.