Difficulty
Expert
Sudoku technique guide
XY-Chain
Sometimes the obvious moves disappear, but the grid is still giving you a useful clue. XY-Chain is a calm way to follow it.
By the end, you will know what to notice, how the idea works and when it is worth using.
At a glance
Technique family
Chains
Purpose
Removes candidates
Typical puzzle stage
Late
Frequency
Uncommon
Prerequisites
XY-Wing and bivalue cells
Why this technique matters
XY-Chains generalise XY-Wing. They are useful when a short wing does not exist but a sequence of bivalue cells carries the same logic further.
The idea in plain English
Connect bivalue cells so adjacent cells share one candidate. The chain begins and ends with the same candidate. That candidate can be removed from any cell that sees both endpoints.
How to recognise it
Start with a single digit that has several tight candidate positions. The pattern is easier to see with clean pencil marks and a deliberate scan, not by guessing.
Pause when you see this shape. You do not have to force it; just check whether the pattern is complete.
How the logic unfolds
Think of this as a short conversation with the grid. Take one check at a time, and let each answer tell you what to inspect next.
Start by. Choose one digit and mark every relevant candidate position clearly.
Then. Identify the strong links first: a strong link means the digit has exactly two positions in one unit.
Next. Trace only the links required by the pattern and check that each connection is valid.
Finally. Apply the elimination only to cells that satisfy the pattern’s stated visibility rule.
When it usually appears
Use this after singles, locked candidates, subsets and simpler named patterns have stopped producing progress. Keep the chain short and verify it before acting.
Common traps
These are easy places to get turned around. They are useful checks, not signs that you are doing badly.
- Treating a link as strong when the digit has more than two positions in that unit. The forced conclusion then fails.
- Eliminating from a target that does not meet the visibility condition for both relevant endpoints.
Frequently asked questions
Do I need to memorise every chain shape?
No. Learn to verify the link logic first; named shapes become easier to recognise later.
Why are these techniques late-game tools?
They need a well-reduced candidate map. Earlier techniques usually produce a quicker, clearer move.
Quick takeaway
- A XY-Chain belongs to the chains family.
- Its purpose is to remove candidates.
- Look for a complete pattern, not one that only nearly fits.
- It is most useful late.
- Once you make the deduction, return to the simpler scans.