A family of advanced techniques that trace logical links between candidates to derive contradictions and eliminate possibilities.

Chain refers to a family of techniques that trace logical sequences of "if A then B, if B then C..." between candidates. This includes Simple Coloring, XY-Chain, and AIC (Alternating Inference Chain). Sometimes required at Extreme difficulty.

Fundamental Concept

Assume a candidate is true (the digit goes there) and trace the consequences. If a contradiction arises, that candidate must be false (the digit does not go there). Conversely, if assuming false leads to a contradiction, the candidate must be true. This proof-by-contradiction reasoning chain is the essence of chain techniques.

Practicality

Chain techniques are extremely powerful but very difficult for humans to apply manually. Most players find X-Wing-level techniques sufficient, and puzzles requiring chains are limited to Extreme difficulty.