storm_norm22 wrote:i'd like to clarify something in my previous post about loops. I was saying how the nodes must start and end in the same house. the chain must also come back to the same number candidate. so for example if the chain starts on candidate (3)r3c8, then the chain then must declare a strong inference on another candidate 3 in row 3 OR column 8 OR in the same box.

that would then form a loop.

What you describe is about three quarters of the meaning of a loop in Eureka notation.

An AIC loop is formed when the last node in a chain is connected back to the first using a link that follows the alternating pattern.

Your definition requires that the chain starts and ends with strong links to instances of the same digit that see each other, but misses out the case when the two candidates are different but occupy the same cell.

To round things off; to prove an inference between the first and last nodes of an AIC chain, these nodes must be connected to the chain by the same type of link. The usual case is when the links are strong when the two nodes must contain at least one truth, but if the links are weak the chain proves that they can only contain one truth at most and at least one of them must be false.

The weak link form can be used when the nodes overlap so that if (a)r12c3 - ...... – (ab)r12c3 is proved, then r12c3 <> ab.

If final node is true the first must be true too which is invalid, so only the first node can possibly be true.