XY-Chain
A longer chain of bi-value cells. Linked pairs force a shared endpoint digit, which can be eliminated from cells seeing both ends.
What it is
An XY-Chain extends the XY-Wing into a sequence of bi-value cells. Consecutive cells see each other and share one candidate, so a choice at one end forces the next link. The same candidate appears at both ends. If it is false at one end, the alternating chain forces it true at the other; therefore any cell that sees both endpoints cannot contain that candidate.
How to spot it
Start with a bi-value cell and follow matching candidates through other bi-value cells that see the preceding cell. Keep the links alternating and look for a chain whose endpoints share a candidate. That endpoint candidate can be eliminated only from cells seeing both ends.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 4/5, 4/9, 7/9, 7/4
- Digits
- 2, 4, 5, 6
- Eliminations
- 4/4, 5/4, 9/5
Press a marked square to point it out on the board above.
Why it matters
XY-Chains turn small bi-value relationships into longer, controlled deductions. They are especially useful when no compact wing is available, while still relying on candidate pairs that can be checked one link at a time.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
Must consecutive cells in the chain see each other?
Yes. Each consecutive pair must share a row, column or box as well as a candidate; otherwise the candidate cannot force the next link in the chain.
Which candidate can be eliminated?
The candidate present at both endpoints. It can be removed only from a cell that sees both endpoint cells, because the chain guarantees that at least one endpoint must contain it.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
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