AIC
Reading only — there is no drill for this one.
The hint engine reaches chains last, after every simpler pattern has failed, and on the puzzles generated here a simpler advanced pattern is always available first. Rather than hand you a puzzle where the chain never fires, this page is the explanation only.
The closest thing you can drill is the XY-Wing, which is the smallest chain, followed by X-Wing and Swordfish.
A chain of alternating strong and weak links that rules out a candidate at its far end.
A strong link says: if this is false, that must be true. It exists when a digit has only two possible cells in a unit, or when a cell has only two candidates — one of the pair has to be the case.
A weak link says: these cannot both be true. It exists whenever two candidates share a unit, or when two different digits compete for the same cell.
Start at a candidate and alternate: strong, weak, strong, weak, ending on a strong link. Each step carries the consequence forward. What such a chain proves is that at least one of its two ends is true.
So if both ends are the same digit, any cell that sees both ends can drop that digit. If they are different digits in the same cell, the cell must be one of them, and every other candidate in it is dead.
An X-Wing is a short AIC whose links are strong links along two rows. An XY-Wing is a three-cell AIC built on bivalue cells. Once chains are on the table, the earlier patterns stop being separate rules and become special cases of one idea.
That also explains why chains are hard: instead of recognising a fixed shape, you are searching a graph of links, and the search space grows quickly.
Chains are only worth attempting after every simpler elimination is exhausted, because they cost the most attention per move. Mark the bivalue cells and the digits with exactly two positions per unit first — those are the only places strong links can start.
On this site, AIC is elimination-only: it removes candidates rather than placing a digit. On Extreme puzzles, one such removal is usually what restarts the whole grid.
This is also the one technique here without a drill. The solver only reaches chains after every simpler pattern has failed, and on generated puzzles an XY-Wing or an X-Wing is always available first — so a puzzle where the chain is genuinely required does not come up. The XY-Wing trainer is the closest practice: it is the same reasoning with three cells instead of a chain.