XY-Chains
Learn the XY-Chain: a chain of bi-value cells linked by shared digits whose two ends carry a common digit Z, eliminating Z from any cell seeing both ends.
An XY-Chain is a chain of bi-value cells, each linked to the next by a shared digit. Walk the chain and each cell "flips" its value to the other candidate, passing the link along: {Z,a} to {a,b} to {b,c} and so on, until the final cell reads {…,Z} again. Both ends carry the same digit Z.
Whatever the first cell turns out to be, the chain forces one of the two endpoints to equal Z — so any cell that can see both ends cannot be Z, and you remove it. The XY-Wing is simply the shortest XY-Chain, three cells long.
XY-Chains are among the most versatile manual techniques, reaching deep eliminations on the hardest boards without guessing. The example highlights the chain ends and the Z they remove.
Practise the XY-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 XY-Chain in Sudoku?
A chain of bi-value cells linked by shared candidates, with both endpoints holding a common digit Z. One endpoint must be Z, so any cell seeing both ends loses Z.
How long can an XY-Chain be?
Any length. Three cells is an XY-Wing; longer chains of four, five or more bi-value cells reach eliminations that shorter wings cannot.
Is an XY-Chain the same as an X-Chain?
No. An X-Chain follows a single digit through strong and weak links; an XY-Chain hops between digits through bi-value cells. Both prove one of two endpoints holds a digit.
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