Proven Sudoku
X-Chain
Also called Single-digit chain, Simple Colors chain, Nice Loop on one digit.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A chain about one number only. You hop between squares where that number has just two homes. Follow the hops and the two ends cannot both be empty. Anything seeing both ends loses the number.
The exact rule, for stronger players
The rule, stated exactly: For digit d, an alternating chain of strong and weak links on d alone, beginning and ending with a strong link. Any cell seeing both endpoints cannot hold d.
What it removes: Remove d from every cell seeing both endpoints.
Why it works: Alternation guarantees that at least one endpoint is true: assume the first false, and the alternation propagates truth to the far end. A cell seeing both endpoints therefore sees a true d either way.
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
- Turbot FishPick one digit.
- Simple ColoringPick a digit.
Related chains
- XY-ChainA chain of squares that each hold exactly two numbers.
- 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.
How often does it come up?
Our rough estimate: common once a grid resists subsets. Length four is the Turbot Fish; longer chains are the general case.