# Alternating Inference Chain (AIC)

An Alternating Inference Chain, better known by its acronym AIC, is a chain of candidates with alternating strong and weak inference.

The vertices in the chain are usually individual candidates, but it is also possible to use groups of candidates or complex patterns like Almost Locked Sets.

It is possible to write AICs with the Eureka notation system.

An example:

(1)r1c1=(1)r1c5-(1)r5c5=(1)r6c6-(1)r6c1=(1)r1c1

This chain can be broken down into the following implications:

- If r1c1<>1 then r1c5=1 (strong inference)
- If r1c5=1 then r5c5<>1 (weak inference)
- If r5c5<>1 then r6c6=1 (strong inference)
- If r6c6=1 then r6c1<>1 (weak inference)
- If r6c1<>1 then r1c1=1 (strong inference)

The chain proves that r1c1 must contain digit 1.

When the vertices of an AIC consist of only individual candidates, then it is either a X-Chain, a XY-Chain or some combination of X-Chains and XY-Chains.

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