An exclusive relationship where at least one of 2 cells is not the specific digit, allowing both to be false.

A Weak Link refers to the exclusive relationship between 2 cells regarding digit X where 'both cannot simultaneously be X.' States where one or both are non-X are permitted. When X remains as a candidate in multiple cells within the same unit, any 2 cells among them form a weak link. It is an important concept used in combination with strong links in chain-based techniques.

Basics of Weak Links

The definition of weak link corresponds to logical 'incompatibility (half of exclusive disjunction).' It only guarantees that 'cell A is X' and 'cell B is X' don't hold simultaneously, allowing both to be false. For example, if a row has X candidates in 4 cells, any 2 of those cells form a weak link. This relationship arises naturally from the basic Sudoku rule 'one X per unit.'

Combining with Strong Links

Remembering <a href="/en/glossary/strong-link/">strong links</a> as 'one of two must be X' and weak links as 'both cannot be X' clarifies their relationship. Combining them alternately builds complex logical chains. From the chain 'A strong-link B, B weak-link C, C strong-link D,' one can deduce 'if A is X, D is X.' Top-tier techniques like AIC (Alternating Inference Chain) leverage these alternating strong/weak link chains.

Practical Recognition

In actual puzzles, weak links exist far more abundantly than strong links. It can be said that some weak link exists between most cell pairs on the board. The important thing is identifying 'weak links that can be promoted to strong links.' The moment X's candidates in a unit drop to 2, a new strong link is born there. This dynamic process where new strong links emerge with each technique application is the heart of advanced solving.