Florence chief prosecutor Giuseppe Creazzo told a news conference that investigators had detained Cheik Diaw based on witness testimony and DNA analysis, and also because he had Ms Olsen's mobile phone
He said they had consensual sex.
He said the autopsy determined that Ms Olsen had suffered two fractures to her skull that were so violent they alone would have killed her.
She was subsequently strangled.
Police detained Diaw after DNA analysis came back from a used condom and cigarette butt found in Ms Olsen's bathroom, as well as DNA samples taken from under her fingernails.
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