# Alternating Inference Chain

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Jump to navigationJump to searchAn **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 => r6c1<>1

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)

The chain proves that either **r1c1** or **r6c6** must contain digit **1**. Therefore **r6c1** cannot 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.