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Nick had no idea how twisted Amy really was, no idea at her level of wickedness. True, he had an affair. But that's not against the law. Murder is, and Amy was a cold-blooded, calculating, murderer. Nick should have had a glass of champagne when she disappeared and then moved to another country, and disappeared.

I don't know. I was confused too when he said that.

One of the lies is when he lies about his whereabouts on the morning of Amy’s disappearance. He says he was walking and drinking coffee when in fact he was cheating on Amy with his student/ex-student.

I can’t remember the others.

Edit -

But now that I think about it, weren't the lies slowly revealed after he admitted that he lied? It's been so long since I've read it.

one of them would be about reservation at the houston's.

He lied about not understanding what the clue meant that amy had left for him,i think so.