XY-Chain in Sudoku: How to Spot It
Learn the XY-Chain Sudoku technique: linked bivalue cells prove a candidate cannot stay in a cell that sees both chain ends.
Guided example
See the XY-Chain on this board
Read this as one teaching unit: first identify the active unit, then the marked pattern cells, then the candidates removed or maintained.
Quick answer
An XY-Chain in Sudoku is a chain of bivalue cells connected by shared candidates. If both ends of the chain imply the same candidate, any cell that sees both ends cannot contain that candidate.
How to spot it
Follow the board in order
- 1 Mark cells with exactly two candidates.
- 2 Build a chain where neighboring cells share one candidate and alternate possibilities.
- 3 Check whether both chain ends contain the same candidate.
- 4 Remove that candidate from any cell that sees both ends.
What is an XY-Chain?
An XY-Chain is a chain of bivalue cells. Each cell has exactly two candidates, and neighboring cells in the chain share a candidate.
The chain proves that one of the endpoint cells must contain a target candidate. Any cell that sees both endpoints cannot also contain that candidate.
When to look for it
Look for XY-Chains in hard puzzles after local techniques stop helping. They are most useful when many bivalue cells are visible.
Keep chains short at first. A short, explainable chain is better than a long chain you cannot verify.
Example walkthrough
This walkthrough uses a real expert app puzzle tagged XY-Chain. Follow the blue bivalue cells: 16 → 36 → 13 → 17. The green cell sees the chain endpoints that threaten candidate 1, so r4c8 cannot keep candidate 1.
Why the elimination works
The chain creates a forced either-or relationship between the endpoints. One end or the other must take the target candidate.
A cell that sees both endpoints would conflict with either outcome, so that target candidate is impossible in the affected cell.
XY-Chain vs. XY-Wing
An XY-Wing has three cells and is easier to visualize.
An XY-Chain uses the same bivalue logic but extends through more links.
Common mistake
Do not include a cell with three or more candidates in a basic XY-Chain. If a link is not bivalue, the alternating logic breaks.
FAQ
What is an XY-Chain in Sudoku?
An XY-Chain is a linked sequence of bivalue cells used to eliminate a candidate seen by both ends of the chain.
How is XY-Chain related to XY-Wing?
An XY-Wing is a short three-cell version of XY-chain logic.
Do all cells in an XY-Chain need two candidates?
For the standard XY-Chain, yes. Each link should be a bivalue cell.
Why are XY-Chains expert-level?
They require tracking a conditional chain across multiple cells, which is much easier to misread than local pairs or triples.
In this lesson
- Board example: see the pattern first.
- Walkthrough: connect each highlight to the rule.
- FAQ: check edge cases after the move is clear.
Practice this technique in Sudoku Coach
Read the pattern, then practice it step by step with guided hints that explain why the move works.
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