X-Chain
An alternating chain for one digit: strong and weak links ensure that at least one end is true, so a cell seeing both ends loses that digit.
What it is
An X-Chain follows one candidate digit through alternating links. A strong link means that a row, column or box has exactly two places for the digit, so one of them must be true. A weak link connects two cells that see each other, so they cannot both be true. When the chain begins and ends with a strong link, at least one endpoint must contain the digit. Any other candidate that sees both endpoints is therefore impossible.
How to spot it
Choose one digit and mark units where it has exactly two possible cells. Those are your strong links. Join them with weak links only where two candidates see each other, and alternate the link types. After an odd number of links, check whether an outside candidate sees both endpoints; only those common peers are valid eliminations.
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
- 4/2, 1/2, 1/3, 4/3
- Digits
- 5
- Eliminations
- 4/5, 4/8, 4/9
Press a marked square to point it out on the board above.
Why it matters
X-Chains are the clear bridge from simple colouring to longer inference chains. They use one digit only, so every link can be checked directly on the board, yet they find eliminations that short fish patterns miss.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
What is the difference between a strong and a weak link?
A strong link has exactly two possible positions for a digit in one unit, so one must be true. A weak link only says that two cells see each other and cannot both be true.
Why do the endpoints eliminate a candidate?
With strong links at both ends, the alternating chain guarantees that at least one endpoint contains the digit. A cell seeing both would clash with that endpoint either way, so it cannot keep the digit.
May I remove the digit from every cell near the chain?
No. A target must see both endpoints, not merely one link or one endpoint. Sudoku Luna marks only candidates that pass that complete visibility check.
Put it to use
Where you will meet it
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