Follow a single digit from cell to cell, alternating two kinds of link: a strong link (a row, column or box where the digit has only two places, so one of them holds it) and a weak link (two cells that see each other, so at most one holds it). Start and end on a strong link and one end of the chain must hold the digit. Any cell that sees both ends can't.
An X-Chain is the long version of the Skyscraper, the 2-String Kite and the Turbot Crane: those are X-Chains with four cells. Longer chains reach further across the grid.
It's one of the two chain techniques behind our Extreme puzzles.
An X-Chain
The pattern
Candidates removed
Solved as a result
Follow the 6 along R1C4 → R1C3 → R3C2 → R5C2 → R5C9 → R6C9. The links alternate: in a unit where the 6 has just two places, one of them holds it; between two cells that see each other, at most one does. So if R1C4 isn't the 6, the next cell is, the one after isn't, and so on, until R6C9 is. One of R1C4 and R6C9 is the 6, so it can be removed from every cell that sees both: R6C4. That leaves R6C4 with only one candidate: 7.
Only the 6s are shown, so the pattern stands out.
This position comes from a puzzle generated on this site, after every single has been filled in. Boxes are numbered 1–9 from the top left, row by row; R5C4 means row 5, column 4.
How to spot it
1Pick a digit and mark its strong links: units where it has exactly two places.
2Start at one end of a strong link. Hop to a cell that sees the other end (a weak link), then along that cell's strong link, and so on.
3Stop after a strong link. The first and last cells are the ends.
4Remove the digit from every cell that sees both ends.
Why it works
Along a strong link exactly one end holds the digit; along a weak link at most one does. So the cells alternate: if the first end doesn't hold the digit, the next does, the one after doesn't, and so on to the last end, which does.
Either way one of the two ends holds the digit, and a cell that sees both would clash with it.
Common mistakes
Two weak links in a row, or two strong links in a row. They must alternate.
Ending on a weak link. Both ends must be on strong links.
Treating a unit with three places as a strong link. It needs exactly two.
Questions
How long can an X-Chain be?
Any length, as long as the links alternate. Our hints use chains of up to ten cells, shortest first.
How is it related to the Skyscraper?
A Skyscraper, a 2-String Kite and a Turbot Crane are all four-cell X-Chains. The X-Chain is the general idea.
What is an X-Cycle?
An X-Chain whose ends link back to each other, forming a loop. Loops give even more eliminations but are rarer.
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