Proven Sudoku
XY-Chain
Also called Bivalue chain, XY chain, Chain of bivalue cells.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A chain of squares that each hold exactly two numbers. You enter on one number and leave on the other. At the ends the same number turns up, so squares that see both ends lose it.
The exact rule, for stronger players
The rule, stated exactly: A chain of bivalue cells where consecutive cells see each other and share a digit, arranged so that the shared digits alternate through the chain. If the first and last cells both contain digit d as their outer candidate, d is eliminated from every cell seeing both ends.
What it removes: Remove d from every cell seeing both endpoint cells.
Why it works: In a bivalue cell, the two candidates form a strong link: one of them is true. Chaining bivalue cells that see each other creates alternating inference. Either the first cell is d, or it is its other candidate, which forces the next cell along, and so on to the far end, which is then d. So one end is d, and anything seeing both ends cannot be.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Naked PairTwo squares in the same group both hold only the same two digits.
- X-ChainA chain about one number only.
Related chains
- AIC with AHS NodesThe same as above but using sets of numbers that are hiding rather than sets of squares.
- AIC with ALS NodesA chain that can step through a small set of squares holding one more number than it has room for.
- Alternating Inference ChainA chain that switches between two kinds of step.
- Bowman's BingoPick a digit, assume it, and write out everything that follows until you either finish or hit a contradiction.
- Cell Forcing ChainTake one square and try each number it could hold.
How often does it come up?
Our rough estimate: common on hard grids, and the most approachable general chain because every node is a bivalue cell and needs no grouping.