Strong Link
strong link
An exclusive relationship where a digit is limited to exactly 2 cells in a unit, with one of them necessarily true.
A Strong Link refers to the state where, for a specific digit X, X's candidates within a unit (row, column, or block) are limited to exactly 2 cells. It has the strong exclusive relationship 'one is X if and only if the other isn't, and both cannot be non-X.' It is a fundamental concept of all chain-based techniques and synonymous with conjugate pair.
Definition of Strong Link
The strict definition of a strong link is 'at least one of two propositions must be true.' In Sudoku context, this becomes the proposition pair 'cell A is X, or cell B is X.' The possibility of both being non-X is excluded. This corresponds to disjunctive syllogism in logic - if A is not X, B is confirmed as X. The reverse holds too, allowing bidirectional inference, which is the defining feature of strong links.
Differences from Weak Links
Weak links have the weaker exclusive relationship 'at least one of two cells is not X.' Both being non-X is permitted. For example, if a row has X candidates in 3+ cells, any 2 of those cells form a weak link. Strong links are 'one must be X,' weak links are 'both cannot be X simultaneously.' Chain construction alternates between them to build long chains and find contradictions.
Use in Techniques
Strong links underpin many advanced techniques. X-Wing forms a rectangle from 2 strong links, Swordfish combines 3 strong links, Coloring chains strong links, and W-Wing links 2 bi-value cells via strong links. Having an eye to quickly identify strong links on the board is a prerequisite for mastering advanced solutions. The systematic habit of counting candidates per unit for each digit is effective.