Alternating Chain (AIC)

An AIC (Alternating Inference Chain) links candidates, not cells. A strong link joins a digit's only two places in a unit, as in an X-Chain, or a cell's only two candidates, as in an XY-Chain: if one is false, the other is true. A weak link joins two candidates that cannot both be true: the same digit in cells that see each other, or two digits of one cell.

The chain takes strong and weak links in turn, starting and ending with a strong one, and may change digit along the way. If its first candidate is false, the second is true, the third false, and so on to the last, which is true. So the first candidate or the last is true.

Remove what that rules out: with the same digit at both ends, it goes from every cell that sees both; with two digits in cells that see each other, each loses the other's digit; with both ends in one cell, every other candidate goes from it. An X-Chain is an AIC on one digit; an XY-Chain, one whose strong links are all two-candidate cells.

What to look for

Start from a strong link, then go from candidate to candidate: through a unit where a digit has two places, or through a cell with two candidates.