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

<a href="/en/glossary/weak-link/">Weak links</a> 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, <a href="/en/glossary/coloring/">Coloring</a> 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.