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X-Chain

Master· L9
Elimination

An X-Chain is a chain that stays on one digit, alternating strong and weak links — a special AIC.

You already know the shortest forms: Skyscraper, Two-String Kite, and Crane (strong–weak–strong).

Before this: Skyscraper, Two-String Kite, and Crane are already short X-Chains.

Why it works

Strong links: exactly one end is true. Weak links: not both true. Alternating them from one end to the other means the two endpoints cannot both be false.

If the chain is strong at both ends, any cell that sees both endpoints sees a true candidate either way — so it cannot be that digit.

How to spot it

Start from bi-locals (rare strong links), connect with weak links (see-each-other), keep strong–weak alternation.

Demonstration

452153653471453538926359214557234582

Follow strong and weak links for a single digit into a useful chain. Prefer starting at bi-locals.

452153653471453538926359214557234582

The green cells are an X-Chain on 6 — same AIC idea as a long Skyscraper family chain.

452153653471453538926359214557234582

The alternating links force a truth at the ends: both ends cannot be false. Shared neighbors get stung either way.

452153653471453538926359214557234582

Eliminate 6 from cells that see both ends (red).

Example 1

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Build an alternating chain on one digit (strong–weak–strong…).

7212138749213852852379781892437954596

This X-Chain on 3 gives an elimination.

7212138749213852852379781892437954596

Remove 3 from cells that see both ends (red). At least one end must be true.

Example 2

36522153584721334549563728745358634357345

Build an alternating chain on one digit (strong–weak–strong…).

36522153584721334549563728745358634357345

This X-Chain on 1 gives an elimination.

36522153584721334549563728745358634357345

Remove 1 from cells that see both ends (red). At least one end must be true.

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