Simple Chains
Also known as X-Chains.
Alternating strong and weak links in a single candidate. Following the chain yields eliminations wherever both endpoints see a common cell.
Candidate 8 links four cells via alternating strong and weak connections.
How to spot it
- 1Build an alternating strong/weak link chain for one candidate.
- 2Trace the implications from end to end.
- 3Any cell seen by both endpoints can't hold the candidate.
When to use
When fish and wings fall short — chains generalise them all.
Common mistake
Mixing up strong (only-two) and weak (shared-house) links, which invalidates the chain.
Worked Example
A chain follows one candidate through a sequence of alternating strong and weak links. A strong link (typically a conjugate pair) means if one end is false, the other must be true. A weak link (two candidates sharing a house) means if one end is true, the other must be false.
Start at one end and trace the implications link by link to the other end. Whatever the chain concludes about its two endpoints, any cell that sees both of them can have the candidate removed — the chain has proven that one endpoint or the other must hold it. Chains generalize fish and wings: an X-Wing, skyscraper, or XY-Wing can all be re-expressed as a short chain.