Strong link
A relationship between two cells in a unit where a digit must occupy exactly one of them — the basic primitive that hidden singles, X-wings, and chain reasoning all rest on.
A strong link is one of the two relationships chain-based techniques are built from. Two cells in a unit — a row, a column, or a box — form a strong link on a digit when the digit's only candidate cells in that unit are exactly those two. One of them must hold the digit; the other must not.
The defining property is the exclusive-or. In a strong link on digit d, exactly one of the two cells is d, and the other isn't. If you can rule out d in one of them by any means, you immediately place it in the other.
Where it shows up
Hidden singles are the simplest strong-link argument: a digit has only two candidate cells in a unit, and any side-information — an elimination from a pointing pair, a placement in a neighbouring box — collapses the strong link into a placement. X-wings, swordfish, and the rest of the fish family are coordinated strong links across two or more units, where the constraint propagates between them.
Chain techniques like simple coloring, XY-chain, and AIC alternate strong and weak links along a sequence of cells, exploiting the strict exclusive-or to carry placement information from one end of the chain to the other.
Strong vs. weak
A strong link is the stricter cousin of the weak link. A weak link guarantees that two cells aren't both the same digit; a strong link guarantees they aren't both not the digit. Both relationships matter for chains. Strong links are the steps that force a placement; weak links are the steps that forbid one. Most chains alternate between them.
See also
- Weak link— A relationship between two cells where at most one can hold the digit. Looser than a strong link — both might be other digits — and the steady half of every chain technique.
- Bilocation— When a digit has exactly two candidate cells in a unit. The underlying configuration that strong links, X-wings, and chain techniques all reach for as their starting shape.
- Hidden single— A digit with only one possible cell within a unit (row, column, or 3×3 box) — even if that cell could legally hold other digits. The unit-first sibling of the naked single.
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- Simple coloring— A technique that two-colours the strong-link graph of a single digit, then eliminates candidates that see both colours — the entry point into chain reasoning.
- Alternating Inference Chain (AIC)— The general-purpose chain technique. Alternates strong and weak links along a sequence of candidates, eliminating a digit from any cell that sees both endpoints' candidates.
Read more
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