Alternating Inference Chains (AIC)
Extreme
Used by Smart Hint
The most general chaining technique: follow a chain of candidates that alternates "at least one of these is true" with "at most one of these is true", hopping between digits as it goes. Whichever way it resolves, one of the two chain ends must be true.
- First colour in the chain
- Second colour in the chain
- Where the conclusion lands
- Candidate ruled out
How it works
- Read the highlighted cells as a chain. It alternates two kinds of link: a strong one ("at least one of these two is true") and a weak one ("at most one of these two is true"), and it both starts and ends on a strong link.
- A1 holds only {3, 5}, so if it isn't 5 it must be 3 — a strong link inside one cell. A1's 3 and E1's 3 sit in the same row, so at most one of them is a 3 — a weak link. With its 3 gone, E1 must be 7. E1's 7 and E5's 7 share column E — weak again — so E5 must then be 5.
- Follow it end to end: if A1 isn't 5, E5 is. One of the two chain ends is a 5, so any cell that sees both ends can't be 5 — A5 sees A1 down column A and E5 across row 5, so its 5 goes.
- Strong links also come from a unit where a digit has only two homes left, not just from two-candidate cells — that reach is what lets AIC cover X-Chains, XY-Chains, and most wing techniques as special cases of one pattern.