X-Chains
Learn the X-Chain: a single-digit chain alternating strong and weak links that starts and ends on a strong link, eliminating the digit from cells seeing both ends.
An X-Chain follows one digit along an alternating path of strong and weak links. A strong link is a conjugate pair — a unit where the digit appears only twice; a weak link is just two cells of the digit sharing a unit. The chain must begin and end on a strong link.
Because the chain alternates, at least one of its two endpoints must hold the digit. So any cell that can see both endpoints cannot be the digit, and it is removed. Skyscrapers and two-string kites are the shortest X-Chains; longer ones reach eliminations nothing else can.
X-Chains are the single-digit heart of advanced chaining and a natural next step after coloring. The example highlights the chain endpoints and the candidate they jointly eliminate.
Practise the X-Chain
The best way to learn a technique is to use it. Play a puzzle at the level where it first appears, or drop a tricky board into the solver to watch it in action.
Frequently asked questions
What is an X-Chain in Sudoku?
A single-digit chain alternating strong and weak links, starting and ending on a strong link. One endpoint must be the digit, so cells seeing both endpoints lose it.
How is an X-Chain related to coloring?
Simple coloring is X-Chains restricted to strong links only. A full X-Chain may also use weak links, which lets it find eliminations that coloring cannot.
Is a Skyscraper an X-Chain?
Yes — a Skyscraper is a short X-Chain of two strong links and one weak link. The same logic, applied to longer chains, is the general X-Chain.
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